Franchise Value, Competition and Insurer Risk-takingaria.org/meetings/2006papers/RenSchmit.pdf · Franchise Value, Competition and Insurer Risk-taking ... (MM) paradigm, under certain
Post on 13-Apr-2018
215 Views
Preview:
Transcript
Franchise Value Competition and Insurer Risk-taking
Yayuan RenUniversity of Wisconsin-Madison
Joan T Schmit
University of Wisconsin-Madison
July 2006
ABSTRACT
Franchise value and competition provide contrary risk-taking incentives to firms
Franchise value provides a risk-constraining incentive to firms while competition
generally induces firms to take more risk Existing empirical evidence on these
relationships however have been mixed motivating us to reexamine these issues
This study adds to the literature by considering the influence of franchise value
and competition on risk-taking simultaneously rather than separately importantly
including an interaction term between the two factors to account for their joint effect
We further add to the literature by incorporating the effect of the underwriting cycle
on these relationships
Our main findings are that the effect of franchise value and competition on
insurer risk-taking is jointly determined and conditional on the underwriting cycle
The specific relationships between the influences of franchise value competition and
the underwriting cycle vary across different business lines and ownership structures
1
1 Introduction
Insurer solvency is an issue of great importance to insurance regulators
consumers as well as the owners and managers of the firms themselves As a result a
large body of research has been conducted to understand factors that influence insurer
solvency In particular recent research has focused on factors that influence insurer
risk-taking behavior Increased incentives to take risks are expected to increase the
potential for insolvency
Two important results are well established in the existing literature regarding
risk-taking incentives First as reported by Marcus (1984) Keeley (1990) and
Demsetz et al (1996) (among others) franchise value1 provides a risk-constraining
incentive to firms Second as reported by Rhoades and Rutz (1982) Keeley (1990)
and Harrington and Danzon (1994) (among many others) competition induces firms
to take more risk The empirical evidence regarding the effect of franchise value and
competition however is mixed
11 Franchise value and firm risk-taking
The economic worth of a firm includes the value of both tangible and intangible
assets Franchise value represents a firms intangible assets that is the value of the
firm above and beyond the value of its tangible assets In insurance intangible assets
typically generate from an insurers goodwill growth opportunities market power
existing distribution networks and renewal rights on existing business arrangements
with reinsurers as well as specialized knowledge about the risks generating from their
current book of business
Franchise value increases the costs of financial distress (bankruptcy) because
shareholders will loose the franchise value in case of bankruptcy Franchise value
therefore provides risk-constraining incentives to firms to protect their franchise value
Marcus (1984) and Li et al (1995) develop option-pricing models that demonstrate 1 The definition and discussion of franchisecharter value is detailed in section 11
2
how franchise value can induce risk-averting which is known as Franchise Value
Theory (FVT) This theory predicts negative relationship between franchise value and
firm risk-taking Keeley (1990) and Demsetz et al (1996) provide empirical evidence
in favor of FVT Most notably Keeley (1990) documents declines in bank franchise
value during the 1950s 1960s and 1970s when the banking industry was
experiencing deregulation and increased competition from non-bank financial
institutions He argues that this drop in franchise value led to increased risk-taking in
the 1980s An insurance study made by Staking and Babbel (1995) reports evidence
in support of FVT Their results suggest that insurers will expend scarce resources
(leverage and interest rate risk) to control risk in order to protect franchise value They
did not however examine the relationship between franchise value and insurer
overall risk-taking
A stream of empirical literature however shows that the risk-averting
incentives attributed to franchise value may be constrained or even inverse under
certain situations Boyd and De Nicolo (2004) report a positive relationship between
bank size (generally positively correlated with franchise value) and the probability of
a banking crisis which is contrary to FVT Hughes et al (1996) Demsetz and Strahan
(1997) and Saunders and Wilson (2001) report that a banks franchise-enhancing
expansions increase systematic risk exposures which eventually may expose
high-franchise-value banks to potentially large losses during economic contractions
These studies suggest a sensitivity of the relationship between franchise value and
bank risk-taking to the business cycle
12 Competition and firm risk-taking
Competition has an important external effect on firm risk-taking decisions
Increased competition is generally hypothesized to induce more risk-taking Existing
empirical evidence on the relationship between competition and risk-taking however
is far from being conclusive While some literature2 supports a positive relationship
2 Eg Rhoades and Rutz1982 Keeley 1990 Harrington and Danzon 1994 Browne and Hoyt
3
between competition and insolvency some other research reports either a negative or
an inconclusive correlation between competition and bank failure For example
Jayaratne and Strahan (1998) find that deregulation was followed by sharp reductions
in loan losses contrasting Keeleys earlier results De Nicoloacute etal(2005) take a
different approach to empirically represent banking system fragility They construct a
probability of failure measure for the five largest banks in a country viewed as an
indicator of banking fragility Their measure of competition is a five-bank
concentration ratio They find that the probability of failure measure is positively and
significantly associated with bank concentration meaning that ceteris paribus a more
concentrated banking industry is more prone to banking fragility Another work is by
Beck et al (2003) who find that banking crises are less likely in more concentrated
banking system however in a banking market with less restrictions on bank entry
indicating more competition the probability of bank crisis also decreases This result
leads the authors to question if concentration ratios (which have long been a standard
measure of market structure in finance and banking literature) can be used as simple
proxy measures for competition
The mixed evidence on relations of franchise value and competition with firm
risk suggests that some important factors or pontential are missed in the prior
analysis Some literature has found that business cycle have important effect on firm
risk-taking strategies (eg Rampini 2004) therefore this study incorporates this
factor into the analysis and examine if the underwriting cycle affects the relationships
between franchise value competition and firm risk
13 Research purpose
The roles of franchise value and competition on firmsrsquo risk-taking behavior are
important issues in insurance because of their implications for regulatory policies
Franchise value and competition provide contrary risk-taking incentives to firms
Theoretical studies argue that high franchise value constrains firm risk-taking while
1995 Browne Carson and Hoyt 1999
4
competition induces risk-taking
The motivation for this paper is two-fold First even though the theoretical
predictions are clear empirical evidence on the influence of franchise value and
competition is mixed motivating us to reexamine these relationships Second recent
research has identified other important factors related to firm risk-taking such as
business cycle (eg Rampini 2004)
Much of the research to date has considered these factors singly rather than as a
whole This study therefore adds to the literature by considering the influence of
franchise value and competition on risk simultaneously rather than separately
importantly including an interaction term between the two factors to account for their
joint effect By doing this we can test whether or not the mixed results occur because
franchise value and competition jointly influence risk-taking Furthermore we add to
the literature by considering the effect of the underwriting cycle on these
relationships
In summary the purpose of the research reported here is to examine the effect
of franchise value and competition on insurer risk-taking strategies simultaneously in
context of the underwriting cycle Due to the complicated interactive relationships
between franchise value competition and underwriting cycle the net effect of each
factor is ambiguous which may explain why the prior evidence on each effect is
mixed A true picture of the factors driving risk-taking decisions at insurers may not
emerge unless franchise value competition and underwriting cycle are all examined at
the same time
The rest of this study is organized as follows Section 2 provides a theoretical
analysis on the factors affecting insurer risk-taking and develops research hypotheses
Section 3 explains empirical methodology Section 4 describes data and variables to
be used Section 5 presents the estimation results Section 6 summarizes our
conclusions and suggests future research
5
2 Factors Affecting Insurer Risk-taking
The section reviews relevant literature and discuss factors affect insurer
risk-taking Research hypotheses are developed following the analysis
21 Firm Risk
Firm risk generates from numerous sources and its management is critical to a
firmrsquos success Considering only financial risk3 variability is caused by investment
risk interest rate risk credit risk exchange rate risk etc all of which have been
studied extensively Each of these sources of variability affects a firmrsquos assets
liabilities or both For instance both investment risk and credit risk influence
variability in asset values while exchange rate risk and interest rate risk may influence
both asset and liability values For purposes of this study our interest is not so much
with the sources of risk but rather with their influence on the sufficiency of assets to
pay liabilities which we define as a firmrsquos level of solvency
Much of the existing literature considers firm risk-taking strategies in terms of
asset risk and leverage neglecting liability risk For banks the subject of much of the
literature the relatively smooth nature of bank liabilities allows for such omission
But for insurers whose liabilities can fluctuate dramatically liability risk is a critical
component of solvency risk Therefore in the study reported here we consider firm
solvency risk which incorporates asset risk leverage and liability risk
22 Franchise Value and Asset-substitution Moral Hazard
According to Modigliani-Miller (MM) paradigm under certain friction-free
assumptions (including perfect information no taxes or transaction cost and efficient
market) neither capital structure choices nor corporate risk management affects the
value of the firm Shareholders will be indifferent to the level of risk-taking because
the security-specific or nonsystematic risk already has been diversified by the
individual shareholders through portfolio formation Itrsquos obvious that assumption of 3 Firms face non-financial risk as well but these are not considered here
6
perfect market is unrealistic but MM theorems provide a clear benchmark to help us
understand firm financing and risk management decisions through exploring the
consequences of relaxing the MM assumptions
One of the important market imperfections is information asymmetry leading to
a variety of agency problems A well-established result about the agency conflict
between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo
or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather
than the total of equity and debt value of the firm have an incentive to increase the
risk of investment assets at the expense of the debtholders interests Limited liability
can be considered an option held by shareholders to put losses onto the debtholders
whenever the firm is liquidated Since option value increases with asset risk and
leverage shareholders have incentives to take excessive risks to exploit this option
value This theory implies two results First for any given level of capital firms will
always seek to increase shareholder value by maximizing risk and looting the firms
assets (Jensen and Meckling 1976) Second high leveraged firms have more
incentive to increase risk-taking (Green and Talmor 1985)
The asset-substitution moral hazard is exacerbated by the existence of state
guarantee funds and deposit insurance which charge a flat premium on insurer and
bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put
option with exercise price equal to the promised value of its debt Increasing the
volatility of surplus will increase the value of the put option Thereby an equity value
maximizing bank shareholder has an incentive to take excessive risks to exploit this
option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins
(1988) made a similar analysis on the impact of guarantee funds which provide an
incentive for insurers to increase volatility
Although asset substitution theory is an appealing explanation for excessive
risk-taking it fails to explain the moderate risk-taking by many firms A sizable
literature 4 presents different motivations for firmrsquos risk management taxes
bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc
7
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
ABSTRACT
Franchise value and competition provide contrary risk-taking incentives to firms
Franchise value provides a risk-constraining incentive to firms while competition
generally induces firms to take more risk Existing empirical evidence on these
relationships however have been mixed motivating us to reexamine these issues
This study adds to the literature by considering the influence of franchise value
and competition on risk-taking simultaneously rather than separately importantly
including an interaction term between the two factors to account for their joint effect
We further add to the literature by incorporating the effect of the underwriting cycle
on these relationships
Our main findings are that the effect of franchise value and competition on
insurer risk-taking is jointly determined and conditional on the underwriting cycle
The specific relationships between the influences of franchise value competition and
the underwriting cycle vary across different business lines and ownership structures
1
1 Introduction
Insurer solvency is an issue of great importance to insurance regulators
consumers as well as the owners and managers of the firms themselves As a result a
large body of research has been conducted to understand factors that influence insurer
solvency In particular recent research has focused on factors that influence insurer
risk-taking behavior Increased incentives to take risks are expected to increase the
potential for insolvency
Two important results are well established in the existing literature regarding
risk-taking incentives First as reported by Marcus (1984) Keeley (1990) and
Demsetz et al (1996) (among others) franchise value1 provides a risk-constraining
incentive to firms Second as reported by Rhoades and Rutz (1982) Keeley (1990)
and Harrington and Danzon (1994) (among many others) competition induces firms
to take more risk The empirical evidence regarding the effect of franchise value and
competition however is mixed
11 Franchise value and firm risk-taking
The economic worth of a firm includes the value of both tangible and intangible
assets Franchise value represents a firms intangible assets that is the value of the
firm above and beyond the value of its tangible assets In insurance intangible assets
typically generate from an insurers goodwill growth opportunities market power
existing distribution networks and renewal rights on existing business arrangements
with reinsurers as well as specialized knowledge about the risks generating from their
current book of business
Franchise value increases the costs of financial distress (bankruptcy) because
shareholders will loose the franchise value in case of bankruptcy Franchise value
therefore provides risk-constraining incentives to firms to protect their franchise value
Marcus (1984) and Li et al (1995) develop option-pricing models that demonstrate 1 The definition and discussion of franchisecharter value is detailed in section 11
2
how franchise value can induce risk-averting which is known as Franchise Value
Theory (FVT) This theory predicts negative relationship between franchise value and
firm risk-taking Keeley (1990) and Demsetz et al (1996) provide empirical evidence
in favor of FVT Most notably Keeley (1990) documents declines in bank franchise
value during the 1950s 1960s and 1970s when the banking industry was
experiencing deregulation and increased competition from non-bank financial
institutions He argues that this drop in franchise value led to increased risk-taking in
the 1980s An insurance study made by Staking and Babbel (1995) reports evidence
in support of FVT Their results suggest that insurers will expend scarce resources
(leverage and interest rate risk) to control risk in order to protect franchise value They
did not however examine the relationship between franchise value and insurer
overall risk-taking
A stream of empirical literature however shows that the risk-averting
incentives attributed to franchise value may be constrained or even inverse under
certain situations Boyd and De Nicolo (2004) report a positive relationship between
bank size (generally positively correlated with franchise value) and the probability of
a banking crisis which is contrary to FVT Hughes et al (1996) Demsetz and Strahan
(1997) and Saunders and Wilson (2001) report that a banks franchise-enhancing
expansions increase systematic risk exposures which eventually may expose
high-franchise-value banks to potentially large losses during economic contractions
These studies suggest a sensitivity of the relationship between franchise value and
bank risk-taking to the business cycle
12 Competition and firm risk-taking
Competition has an important external effect on firm risk-taking decisions
Increased competition is generally hypothesized to induce more risk-taking Existing
empirical evidence on the relationship between competition and risk-taking however
is far from being conclusive While some literature2 supports a positive relationship
2 Eg Rhoades and Rutz1982 Keeley 1990 Harrington and Danzon 1994 Browne and Hoyt
3
between competition and insolvency some other research reports either a negative or
an inconclusive correlation between competition and bank failure For example
Jayaratne and Strahan (1998) find that deregulation was followed by sharp reductions
in loan losses contrasting Keeleys earlier results De Nicoloacute etal(2005) take a
different approach to empirically represent banking system fragility They construct a
probability of failure measure for the five largest banks in a country viewed as an
indicator of banking fragility Their measure of competition is a five-bank
concentration ratio They find that the probability of failure measure is positively and
significantly associated with bank concentration meaning that ceteris paribus a more
concentrated banking industry is more prone to banking fragility Another work is by
Beck et al (2003) who find that banking crises are less likely in more concentrated
banking system however in a banking market with less restrictions on bank entry
indicating more competition the probability of bank crisis also decreases This result
leads the authors to question if concentration ratios (which have long been a standard
measure of market structure in finance and banking literature) can be used as simple
proxy measures for competition
The mixed evidence on relations of franchise value and competition with firm
risk suggests that some important factors or pontential are missed in the prior
analysis Some literature has found that business cycle have important effect on firm
risk-taking strategies (eg Rampini 2004) therefore this study incorporates this
factor into the analysis and examine if the underwriting cycle affects the relationships
between franchise value competition and firm risk
13 Research purpose
The roles of franchise value and competition on firmsrsquo risk-taking behavior are
important issues in insurance because of their implications for regulatory policies
Franchise value and competition provide contrary risk-taking incentives to firms
Theoretical studies argue that high franchise value constrains firm risk-taking while
1995 Browne Carson and Hoyt 1999
4
competition induces risk-taking
The motivation for this paper is two-fold First even though the theoretical
predictions are clear empirical evidence on the influence of franchise value and
competition is mixed motivating us to reexamine these relationships Second recent
research has identified other important factors related to firm risk-taking such as
business cycle (eg Rampini 2004)
Much of the research to date has considered these factors singly rather than as a
whole This study therefore adds to the literature by considering the influence of
franchise value and competition on risk simultaneously rather than separately
importantly including an interaction term between the two factors to account for their
joint effect By doing this we can test whether or not the mixed results occur because
franchise value and competition jointly influence risk-taking Furthermore we add to
the literature by considering the effect of the underwriting cycle on these
relationships
In summary the purpose of the research reported here is to examine the effect
of franchise value and competition on insurer risk-taking strategies simultaneously in
context of the underwriting cycle Due to the complicated interactive relationships
between franchise value competition and underwriting cycle the net effect of each
factor is ambiguous which may explain why the prior evidence on each effect is
mixed A true picture of the factors driving risk-taking decisions at insurers may not
emerge unless franchise value competition and underwriting cycle are all examined at
the same time
The rest of this study is organized as follows Section 2 provides a theoretical
analysis on the factors affecting insurer risk-taking and develops research hypotheses
Section 3 explains empirical methodology Section 4 describes data and variables to
be used Section 5 presents the estimation results Section 6 summarizes our
conclusions and suggests future research
5
2 Factors Affecting Insurer Risk-taking
The section reviews relevant literature and discuss factors affect insurer
risk-taking Research hypotheses are developed following the analysis
21 Firm Risk
Firm risk generates from numerous sources and its management is critical to a
firmrsquos success Considering only financial risk3 variability is caused by investment
risk interest rate risk credit risk exchange rate risk etc all of which have been
studied extensively Each of these sources of variability affects a firmrsquos assets
liabilities or both For instance both investment risk and credit risk influence
variability in asset values while exchange rate risk and interest rate risk may influence
both asset and liability values For purposes of this study our interest is not so much
with the sources of risk but rather with their influence on the sufficiency of assets to
pay liabilities which we define as a firmrsquos level of solvency
Much of the existing literature considers firm risk-taking strategies in terms of
asset risk and leverage neglecting liability risk For banks the subject of much of the
literature the relatively smooth nature of bank liabilities allows for such omission
But for insurers whose liabilities can fluctuate dramatically liability risk is a critical
component of solvency risk Therefore in the study reported here we consider firm
solvency risk which incorporates asset risk leverage and liability risk
22 Franchise Value and Asset-substitution Moral Hazard
According to Modigliani-Miller (MM) paradigm under certain friction-free
assumptions (including perfect information no taxes or transaction cost and efficient
market) neither capital structure choices nor corporate risk management affects the
value of the firm Shareholders will be indifferent to the level of risk-taking because
the security-specific or nonsystematic risk already has been diversified by the
individual shareholders through portfolio formation Itrsquos obvious that assumption of 3 Firms face non-financial risk as well but these are not considered here
6
perfect market is unrealistic but MM theorems provide a clear benchmark to help us
understand firm financing and risk management decisions through exploring the
consequences of relaxing the MM assumptions
One of the important market imperfections is information asymmetry leading to
a variety of agency problems A well-established result about the agency conflict
between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo
or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather
than the total of equity and debt value of the firm have an incentive to increase the
risk of investment assets at the expense of the debtholders interests Limited liability
can be considered an option held by shareholders to put losses onto the debtholders
whenever the firm is liquidated Since option value increases with asset risk and
leverage shareholders have incentives to take excessive risks to exploit this option
value This theory implies two results First for any given level of capital firms will
always seek to increase shareholder value by maximizing risk and looting the firms
assets (Jensen and Meckling 1976) Second high leveraged firms have more
incentive to increase risk-taking (Green and Talmor 1985)
The asset-substitution moral hazard is exacerbated by the existence of state
guarantee funds and deposit insurance which charge a flat premium on insurer and
bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put
option with exercise price equal to the promised value of its debt Increasing the
volatility of surplus will increase the value of the put option Thereby an equity value
maximizing bank shareholder has an incentive to take excessive risks to exploit this
option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins
(1988) made a similar analysis on the impact of guarantee funds which provide an
incentive for insurers to increase volatility
Although asset substitution theory is an appealing explanation for excessive
risk-taking it fails to explain the moderate risk-taking by many firms A sizable
literature 4 presents different motivations for firmrsquos risk management taxes
bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc
7
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
1 Introduction
Insurer solvency is an issue of great importance to insurance regulators
consumers as well as the owners and managers of the firms themselves As a result a
large body of research has been conducted to understand factors that influence insurer
solvency In particular recent research has focused on factors that influence insurer
risk-taking behavior Increased incentives to take risks are expected to increase the
potential for insolvency
Two important results are well established in the existing literature regarding
risk-taking incentives First as reported by Marcus (1984) Keeley (1990) and
Demsetz et al (1996) (among others) franchise value1 provides a risk-constraining
incentive to firms Second as reported by Rhoades and Rutz (1982) Keeley (1990)
and Harrington and Danzon (1994) (among many others) competition induces firms
to take more risk The empirical evidence regarding the effect of franchise value and
competition however is mixed
11 Franchise value and firm risk-taking
The economic worth of a firm includes the value of both tangible and intangible
assets Franchise value represents a firms intangible assets that is the value of the
firm above and beyond the value of its tangible assets In insurance intangible assets
typically generate from an insurers goodwill growth opportunities market power
existing distribution networks and renewal rights on existing business arrangements
with reinsurers as well as specialized knowledge about the risks generating from their
current book of business
Franchise value increases the costs of financial distress (bankruptcy) because
shareholders will loose the franchise value in case of bankruptcy Franchise value
therefore provides risk-constraining incentives to firms to protect their franchise value
Marcus (1984) and Li et al (1995) develop option-pricing models that demonstrate 1 The definition and discussion of franchisecharter value is detailed in section 11
2
how franchise value can induce risk-averting which is known as Franchise Value
Theory (FVT) This theory predicts negative relationship between franchise value and
firm risk-taking Keeley (1990) and Demsetz et al (1996) provide empirical evidence
in favor of FVT Most notably Keeley (1990) documents declines in bank franchise
value during the 1950s 1960s and 1970s when the banking industry was
experiencing deregulation and increased competition from non-bank financial
institutions He argues that this drop in franchise value led to increased risk-taking in
the 1980s An insurance study made by Staking and Babbel (1995) reports evidence
in support of FVT Their results suggest that insurers will expend scarce resources
(leverage and interest rate risk) to control risk in order to protect franchise value They
did not however examine the relationship between franchise value and insurer
overall risk-taking
A stream of empirical literature however shows that the risk-averting
incentives attributed to franchise value may be constrained or even inverse under
certain situations Boyd and De Nicolo (2004) report a positive relationship between
bank size (generally positively correlated with franchise value) and the probability of
a banking crisis which is contrary to FVT Hughes et al (1996) Demsetz and Strahan
(1997) and Saunders and Wilson (2001) report that a banks franchise-enhancing
expansions increase systematic risk exposures which eventually may expose
high-franchise-value banks to potentially large losses during economic contractions
These studies suggest a sensitivity of the relationship between franchise value and
bank risk-taking to the business cycle
12 Competition and firm risk-taking
Competition has an important external effect on firm risk-taking decisions
Increased competition is generally hypothesized to induce more risk-taking Existing
empirical evidence on the relationship between competition and risk-taking however
is far from being conclusive While some literature2 supports a positive relationship
2 Eg Rhoades and Rutz1982 Keeley 1990 Harrington and Danzon 1994 Browne and Hoyt
3
between competition and insolvency some other research reports either a negative or
an inconclusive correlation between competition and bank failure For example
Jayaratne and Strahan (1998) find that deregulation was followed by sharp reductions
in loan losses contrasting Keeleys earlier results De Nicoloacute etal(2005) take a
different approach to empirically represent banking system fragility They construct a
probability of failure measure for the five largest banks in a country viewed as an
indicator of banking fragility Their measure of competition is a five-bank
concentration ratio They find that the probability of failure measure is positively and
significantly associated with bank concentration meaning that ceteris paribus a more
concentrated banking industry is more prone to banking fragility Another work is by
Beck et al (2003) who find that banking crises are less likely in more concentrated
banking system however in a banking market with less restrictions on bank entry
indicating more competition the probability of bank crisis also decreases This result
leads the authors to question if concentration ratios (which have long been a standard
measure of market structure in finance and banking literature) can be used as simple
proxy measures for competition
The mixed evidence on relations of franchise value and competition with firm
risk suggests that some important factors or pontential are missed in the prior
analysis Some literature has found that business cycle have important effect on firm
risk-taking strategies (eg Rampini 2004) therefore this study incorporates this
factor into the analysis and examine if the underwriting cycle affects the relationships
between franchise value competition and firm risk
13 Research purpose
The roles of franchise value and competition on firmsrsquo risk-taking behavior are
important issues in insurance because of their implications for regulatory policies
Franchise value and competition provide contrary risk-taking incentives to firms
Theoretical studies argue that high franchise value constrains firm risk-taking while
1995 Browne Carson and Hoyt 1999
4
competition induces risk-taking
The motivation for this paper is two-fold First even though the theoretical
predictions are clear empirical evidence on the influence of franchise value and
competition is mixed motivating us to reexamine these relationships Second recent
research has identified other important factors related to firm risk-taking such as
business cycle (eg Rampini 2004)
Much of the research to date has considered these factors singly rather than as a
whole This study therefore adds to the literature by considering the influence of
franchise value and competition on risk simultaneously rather than separately
importantly including an interaction term between the two factors to account for their
joint effect By doing this we can test whether or not the mixed results occur because
franchise value and competition jointly influence risk-taking Furthermore we add to
the literature by considering the effect of the underwriting cycle on these
relationships
In summary the purpose of the research reported here is to examine the effect
of franchise value and competition on insurer risk-taking strategies simultaneously in
context of the underwriting cycle Due to the complicated interactive relationships
between franchise value competition and underwriting cycle the net effect of each
factor is ambiguous which may explain why the prior evidence on each effect is
mixed A true picture of the factors driving risk-taking decisions at insurers may not
emerge unless franchise value competition and underwriting cycle are all examined at
the same time
The rest of this study is organized as follows Section 2 provides a theoretical
analysis on the factors affecting insurer risk-taking and develops research hypotheses
Section 3 explains empirical methodology Section 4 describes data and variables to
be used Section 5 presents the estimation results Section 6 summarizes our
conclusions and suggests future research
5
2 Factors Affecting Insurer Risk-taking
The section reviews relevant literature and discuss factors affect insurer
risk-taking Research hypotheses are developed following the analysis
21 Firm Risk
Firm risk generates from numerous sources and its management is critical to a
firmrsquos success Considering only financial risk3 variability is caused by investment
risk interest rate risk credit risk exchange rate risk etc all of which have been
studied extensively Each of these sources of variability affects a firmrsquos assets
liabilities or both For instance both investment risk and credit risk influence
variability in asset values while exchange rate risk and interest rate risk may influence
both asset and liability values For purposes of this study our interest is not so much
with the sources of risk but rather with their influence on the sufficiency of assets to
pay liabilities which we define as a firmrsquos level of solvency
Much of the existing literature considers firm risk-taking strategies in terms of
asset risk and leverage neglecting liability risk For banks the subject of much of the
literature the relatively smooth nature of bank liabilities allows for such omission
But for insurers whose liabilities can fluctuate dramatically liability risk is a critical
component of solvency risk Therefore in the study reported here we consider firm
solvency risk which incorporates asset risk leverage and liability risk
22 Franchise Value and Asset-substitution Moral Hazard
According to Modigliani-Miller (MM) paradigm under certain friction-free
assumptions (including perfect information no taxes or transaction cost and efficient
market) neither capital structure choices nor corporate risk management affects the
value of the firm Shareholders will be indifferent to the level of risk-taking because
the security-specific or nonsystematic risk already has been diversified by the
individual shareholders through portfolio formation Itrsquos obvious that assumption of 3 Firms face non-financial risk as well but these are not considered here
6
perfect market is unrealistic but MM theorems provide a clear benchmark to help us
understand firm financing and risk management decisions through exploring the
consequences of relaxing the MM assumptions
One of the important market imperfections is information asymmetry leading to
a variety of agency problems A well-established result about the agency conflict
between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo
or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather
than the total of equity and debt value of the firm have an incentive to increase the
risk of investment assets at the expense of the debtholders interests Limited liability
can be considered an option held by shareholders to put losses onto the debtholders
whenever the firm is liquidated Since option value increases with asset risk and
leverage shareholders have incentives to take excessive risks to exploit this option
value This theory implies two results First for any given level of capital firms will
always seek to increase shareholder value by maximizing risk and looting the firms
assets (Jensen and Meckling 1976) Second high leveraged firms have more
incentive to increase risk-taking (Green and Talmor 1985)
The asset-substitution moral hazard is exacerbated by the existence of state
guarantee funds and deposit insurance which charge a flat premium on insurer and
bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put
option with exercise price equal to the promised value of its debt Increasing the
volatility of surplus will increase the value of the put option Thereby an equity value
maximizing bank shareholder has an incentive to take excessive risks to exploit this
option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins
(1988) made a similar analysis on the impact of guarantee funds which provide an
incentive for insurers to increase volatility
Although asset substitution theory is an appealing explanation for excessive
risk-taking it fails to explain the moderate risk-taking by many firms A sizable
literature 4 presents different motivations for firmrsquos risk management taxes
bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc
7
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
how franchise value can induce risk-averting which is known as Franchise Value
Theory (FVT) This theory predicts negative relationship between franchise value and
firm risk-taking Keeley (1990) and Demsetz et al (1996) provide empirical evidence
in favor of FVT Most notably Keeley (1990) documents declines in bank franchise
value during the 1950s 1960s and 1970s when the banking industry was
experiencing deregulation and increased competition from non-bank financial
institutions He argues that this drop in franchise value led to increased risk-taking in
the 1980s An insurance study made by Staking and Babbel (1995) reports evidence
in support of FVT Their results suggest that insurers will expend scarce resources
(leverage and interest rate risk) to control risk in order to protect franchise value They
did not however examine the relationship between franchise value and insurer
overall risk-taking
A stream of empirical literature however shows that the risk-averting
incentives attributed to franchise value may be constrained or even inverse under
certain situations Boyd and De Nicolo (2004) report a positive relationship between
bank size (generally positively correlated with franchise value) and the probability of
a banking crisis which is contrary to FVT Hughes et al (1996) Demsetz and Strahan
(1997) and Saunders and Wilson (2001) report that a banks franchise-enhancing
expansions increase systematic risk exposures which eventually may expose
high-franchise-value banks to potentially large losses during economic contractions
These studies suggest a sensitivity of the relationship between franchise value and
bank risk-taking to the business cycle
12 Competition and firm risk-taking
Competition has an important external effect on firm risk-taking decisions
Increased competition is generally hypothesized to induce more risk-taking Existing
empirical evidence on the relationship between competition and risk-taking however
is far from being conclusive While some literature2 supports a positive relationship
2 Eg Rhoades and Rutz1982 Keeley 1990 Harrington and Danzon 1994 Browne and Hoyt
3
between competition and insolvency some other research reports either a negative or
an inconclusive correlation between competition and bank failure For example
Jayaratne and Strahan (1998) find that deregulation was followed by sharp reductions
in loan losses contrasting Keeleys earlier results De Nicoloacute etal(2005) take a
different approach to empirically represent banking system fragility They construct a
probability of failure measure for the five largest banks in a country viewed as an
indicator of banking fragility Their measure of competition is a five-bank
concentration ratio They find that the probability of failure measure is positively and
significantly associated with bank concentration meaning that ceteris paribus a more
concentrated banking industry is more prone to banking fragility Another work is by
Beck et al (2003) who find that banking crises are less likely in more concentrated
banking system however in a banking market with less restrictions on bank entry
indicating more competition the probability of bank crisis also decreases This result
leads the authors to question if concentration ratios (which have long been a standard
measure of market structure in finance and banking literature) can be used as simple
proxy measures for competition
The mixed evidence on relations of franchise value and competition with firm
risk suggests that some important factors or pontential are missed in the prior
analysis Some literature has found that business cycle have important effect on firm
risk-taking strategies (eg Rampini 2004) therefore this study incorporates this
factor into the analysis and examine if the underwriting cycle affects the relationships
between franchise value competition and firm risk
13 Research purpose
The roles of franchise value and competition on firmsrsquo risk-taking behavior are
important issues in insurance because of their implications for regulatory policies
Franchise value and competition provide contrary risk-taking incentives to firms
Theoretical studies argue that high franchise value constrains firm risk-taking while
1995 Browne Carson and Hoyt 1999
4
competition induces risk-taking
The motivation for this paper is two-fold First even though the theoretical
predictions are clear empirical evidence on the influence of franchise value and
competition is mixed motivating us to reexamine these relationships Second recent
research has identified other important factors related to firm risk-taking such as
business cycle (eg Rampini 2004)
Much of the research to date has considered these factors singly rather than as a
whole This study therefore adds to the literature by considering the influence of
franchise value and competition on risk simultaneously rather than separately
importantly including an interaction term between the two factors to account for their
joint effect By doing this we can test whether or not the mixed results occur because
franchise value and competition jointly influence risk-taking Furthermore we add to
the literature by considering the effect of the underwriting cycle on these
relationships
In summary the purpose of the research reported here is to examine the effect
of franchise value and competition on insurer risk-taking strategies simultaneously in
context of the underwriting cycle Due to the complicated interactive relationships
between franchise value competition and underwriting cycle the net effect of each
factor is ambiguous which may explain why the prior evidence on each effect is
mixed A true picture of the factors driving risk-taking decisions at insurers may not
emerge unless franchise value competition and underwriting cycle are all examined at
the same time
The rest of this study is organized as follows Section 2 provides a theoretical
analysis on the factors affecting insurer risk-taking and develops research hypotheses
Section 3 explains empirical methodology Section 4 describes data and variables to
be used Section 5 presents the estimation results Section 6 summarizes our
conclusions and suggests future research
5
2 Factors Affecting Insurer Risk-taking
The section reviews relevant literature and discuss factors affect insurer
risk-taking Research hypotheses are developed following the analysis
21 Firm Risk
Firm risk generates from numerous sources and its management is critical to a
firmrsquos success Considering only financial risk3 variability is caused by investment
risk interest rate risk credit risk exchange rate risk etc all of which have been
studied extensively Each of these sources of variability affects a firmrsquos assets
liabilities or both For instance both investment risk and credit risk influence
variability in asset values while exchange rate risk and interest rate risk may influence
both asset and liability values For purposes of this study our interest is not so much
with the sources of risk but rather with their influence on the sufficiency of assets to
pay liabilities which we define as a firmrsquos level of solvency
Much of the existing literature considers firm risk-taking strategies in terms of
asset risk and leverage neglecting liability risk For banks the subject of much of the
literature the relatively smooth nature of bank liabilities allows for such omission
But for insurers whose liabilities can fluctuate dramatically liability risk is a critical
component of solvency risk Therefore in the study reported here we consider firm
solvency risk which incorporates asset risk leverage and liability risk
22 Franchise Value and Asset-substitution Moral Hazard
According to Modigliani-Miller (MM) paradigm under certain friction-free
assumptions (including perfect information no taxes or transaction cost and efficient
market) neither capital structure choices nor corporate risk management affects the
value of the firm Shareholders will be indifferent to the level of risk-taking because
the security-specific or nonsystematic risk already has been diversified by the
individual shareholders through portfolio formation Itrsquos obvious that assumption of 3 Firms face non-financial risk as well but these are not considered here
6
perfect market is unrealistic but MM theorems provide a clear benchmark to help us
understand firm financing and risk management decisions through exploring the
consequences of relaxing the MM assumptions
One of the important market imperfections is information asymmetry leading to
a variety of agency problems A well-established result about the agency conflict
between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo
or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather
than the total of equity and debt value of the firm have an incentive to increase the
risk of investment assets at the expense of the debtholders interests Limited liability
can be considered an option held by shareholders to put losses onto the debtholders
whenever the firm is liquidated Since option value increases with asset risk and
leverage shareholders have incentives to take excessive risks to exploit this option
value This theory implies two results First for any given level of capital firms will
always seek to increase shareholder value by maximizing risk and looting the firms
assets (Jensen and Meckling 1976) Second high leveraged firms have more
incentive to increase risk-taking (Green and Talmor 1985)
The asset-substitution moral hazard is exacerbated by the existence of state
guarantee funds and deposit insurance which charge a flat premium on insurer and
bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put
option with exercise price equal to the promised value of its debt Increasing the
volatility of surplus will increase the value of the put option Thereby an equity value
maximizing bank shareholder has an incentive to take excessive risks to exploit this
option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins
(1988) made a similar analysis on the impact of guarantee funds which provide an
incentive for insurers to increase volatility
Although asset substitution theory is an appealing explanation for excessive
risk-taking it fails to explain the moderate risk-taking by many firms A sizable
literature 4 presents different motivations for firmrsquos risk management taxes
bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc
7
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
between competition and insolvency some other research reports either a negative or
an inconclusive correlation between competition and bank failure For example
Jayaratne and Strahan (1998) find that deregulation was followed by sharp reductions
in loan losses contrasting Keeleys earlier results De Nicoloacute etal(2005) take a
different approach to empirically represent banking system fragility They construct a
probability of failure measure for the five largest banks in a country viewed as an
indicator of banking fragility Their measure of competition is a five-bank
concentration ratio They find that the probability of failure measure is positively and
significantly associated with bank concentration meaning that ceteris paribus a more
concentrated banking industry is more prone to banking fragility Another work is by
Beck et al (2003) who find that banking crises are less likely in more concentrated
banking system however in a banking market with less restrictions on bank entry
indicating more competition the probability of bank crisis also decreases This result
leads the authors to question if concentration ratios (which have long been a standard
measure of market structure in finance and banking literature) can be used as simple
proxy measures for competition
The mixed evidence on relations of franchise value and competition with firm
risk suggests that some important factors or pontential are missed in the prior
analysis Some literature has found that business cycle have important effect on firm
risk-taking strategies (eg Rampini 2004) therefore this study incorporates this
factor into the analysis and examine if the underwriting cycle affects the relationships
between franchise value competition and firm risk
13 Research purpose
The roles of franchise value and competition on firmsrsquo risk-taking behavior are
important issues in insurance because of their implications for regulatory policies
Franchise value and competition provide contrary risk-taking incentives to firms
Theoretical studies argue that high franchise value constrains firm risk-taking while
1995 Browne Carson and Hoyt 1999
4
competition induces risk-taking
The motivation for this paper is two-fold First even though the theoretical
predictions are clear empirical evidence on the influence of franchise value and
competition is mixed motivating us to reexamine these relationships Second recent
research has identified other important factors related to firm risk-taking such as
business cycle (eg Rampini 2004)
Much of the research to date has considered these factors singly rather than as a
whole This study therefore adds to the literature by considering the influence of
franchise value and competition on risk simultaneously rather than separately
importantly including an interaction term between the two factors to account for their
joint effect By doing this we can test whether or not the mixed results occur because
franchise value and competition jointly influence risk-taking Furthermore we add to
the literature by considering the effect of the underwriting cycle on these
relationships
In summary the purpose of the research reported here is to examine the effect
of franchise value and competition on insurer risk-taking strategies simultaneously in
context of the underwriting cycle Due to the complicated interactive relationships
between franchise value competition and underwriting cycle the net effect of each
factor is ambiguous which may explain why the prior evidence on each effect is
mixed A true picture of the factors driving risk-taking decisions at insurers may not
emerge unless franchise value competition and underwriting cycle are all examined at
the same time
The rest of this study is organized as follows Section 2 provides a theoretical
analysis on the factors affecting insurer risk-taking and develops research hypotheses
Section 3 explains empirical methodology Section 4 describes data and variables to
be used Section 5 presents the estimation results Section 6 summarizes our
conclusions and suggests future research
5
2 Factors Affecting Insurer Risk-taking
The section reviews relevant literature and discuss factors affect insurer
risk-taking Research hypotheses are developed following the analysis
21 Firm Risk
Firm risk generates from numerous sources and its management is critical to a
firmrsquos success Considering only financial risk3 variability is caused by investment
risk interest rate risk credit risk exchange rate risk etc all of which have been
studied extensively Each of these sources of variability affects a firmrsquos assets
liabilities or both For instance both investment risk and credit risk influence
variability in asset values while exchange rate risk and interest rate risk may influence
both asset and liability values For purposes of this study our interest is not so much
with the sources of risk but rather with their influence on the sufficiency of assets to
pay liabilities which we define as a firmrsquos level of solvency
Much of the existing literature considers firm risk-taking strategies in terms of
asset risk and leverage neglecting liability risk For banks the subject of much of the
literature the relatively smooth nature of bank liabilities allows for such omission
But for insurers whose liabilities can fluctuate dramatically liability risk is a critical
component of solvency risk Therefore in the study reported here we consider firm
solvency risk which incorporates asset risk leverage and liability risk
22 Franchise Value and Asset-substitution Moral Hazard
According to Modigliani-Miller (MM) paradigm under certain friction-free
assumptions (including perfect information no taxes or transaction cost and efficient
market) neither capital structure choices nor corporate risk management affects the
value of the firm Shareholders will be indifferent to the level of risk-taking because
the security-specific or nonsystematic risk already has been diversified by the
individual shareholders through portfolio formation Itrsquos obvious that assumption of 3 Firms face non-financial risk as well but these are not considered here
6
perfect market is unrealistic but MM theorems provide a clear benchmark to help us
understand firm financing and risk management decisions through exploring the
consequences of relaxing the MM assumptions
One of the important market imperfections is information asymmetry leading to
a variety of agency problems A well-established result about the agency conflict
between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo
or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather
than the total of equity and debt value of the firm have an incentive to increase the
risk of investment assets at the expense of the debtholders interests Limited liability
can be considered an option held by shareholders to put losses onto the debtholders
whenever the firm is liquidated Since option value increases with asset risk and
leverage shareholders have incentives to take excessive risks to exploit this option
value This theory implies two results First for any given level of capital firms will
always seek to increase shareholder value by maximizing risk and looting the firms
assets (Jensen and Meckling 1976) Second high leveraged firms have more
incentive to increase risk-taking (Green and Talmor 1985)
The asset-substitution moral hazard is exacerbated by the existence of state
guarantee funds and deposit insurance which charge a flat premium on insurer and
bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put
option with exercise price equal to the promised value of its debt Increasing the
volatility of surplus will increase the value of the put option Thereby an equity value
maximizing bank shareholder has an incentive to take excessive risks to exploit this
option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins
(1988) made a similar analysis on the impact of guarantee funds which provide an
incentive for insurers to increase volatility
Although asset substitution theory is an appealing explanation for excessive
risk-taking it fails to explain the moderate risk-taking by many firms A sizable
literature 4 presents different motivations for firmrsquos risk management taxes
bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc
7
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
competition induces risk-taking
The motivation for this paper is two-fold First even though the theoretical
predictions are clear empirical evidence on the influence of franchise value and
competition is mixed motivating us to reexamine these relationships Second recent
research has identified other important factors related to firm risk-taking such as
business cycle (eg Rampini 2004)
Much of the research to date has considered these factors singly rather than as a
whole This study therefore adds to the literature by considering the influence of
franchise value and competition on risk simultaneously rather than separately
importantly including an interaction term between the two factors to account for their
joint effect By doing this we can test whether or not the mixed results occur because
franchise value and competition jointly influence risk-taking Furthermore we add to
the literature by considering the effect of the underwriting cycle on these
relationships
In summary the purpose of the research reported here is to examine the effect
of franchise value and competition on insurer risk-taking strategies simultaneously in
context of the underwriting cycle Due to the complicated interactive relationships
between franchise value competition and underwriting cycle the net effect of each
factor is ambiguous which may explain why the prior evidence on each effect is
mixed A true picture of the factors driving risk-taking decisions at insurers may not
emerge unless franchise value competition and underwriting cycle are all examined at
the same time
The rest of this study is organized as follows Section 2 provides a theoretical
analysis on the factors affecting insurer risk-taking and develops research hypotheses
Section 3 explains empirical methodology Section 4 describes data and variables to
be used Section 5 presents the estimation results Section 6 summarizes our
conclusions and suggests future research
5
2 Factors Affecting Insurer Risk-taking
The section reviews relevant literature and discuss factors affect insurer
risk-taking Research hypotheses are developed following the analysis
21 Firm Risk
Firm risk generates from numerous sources and its management is critical to a
firmrsquos success Considering only financial risk3 variability is caused by investment
risk interest rate risk credit risk exchange rate risk etc all of which have been
studied extensively Each of these sources of variability affects a firmrsquos assets
liabilities or both For instance both investment risk and credit risk influence
variability in asset values while exchange rate risk and interest rate risk may influence
both asset and liability values For purposes of this study our interest is not so much
with the sources of risk but rather with their influence on the sufficiency of assets to
pay liabilities which we define as a firmrsquos level of solvency
Much of the existing literature considers firm risk-taking strategies in terms of
asset risk and leverage neglecting liability risk For banks the subject of much of the
literature the relatively smooth nature of bank liabilities allows for such omission
But for insurers whose liabilities can fluctuate dramatically liability risk is a critical
component of solvency risk Therefore in the study reported here we consider firm
solvency risk which incorporates asset risk leverage and liability risk
22 Franchise Value and Asset-substitution Moral Hazard
According to Modigliani-Miller (MM) paradigm under certain friction-free
assumptions (including perfect information no taxes or transaction cost and efficient
market) neither capital structure choices nor corporate risk management affects the
value of the firm Shareholders will be indifferent to the level of risk-taking because
the security-specific or nonsystematic risk already has been diversified by the
individual shareholders through portfolio formation Itrsquos obvious that assumption of 3 Firms face non-financial risk as well but these are not considered here
6
perfect market is unrealistic but MM theorems provide a clear benchmark to help us
understand firm financing and risk management decisions through exploring the
consequences of relaxing the MM assumptions
One of the important market imperfections is information asymmetry leading to
a variety of agency problems A well-established result about the agency conflict
between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo
or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather
than the total of equity and debt value of the firm have an incentive to increase the
risk of investment assets at the expense of the debtholders interests Limited liability
can be considered an option held by shareholders to put losses onto the debtholders
whenever the firm is liquidated Since option value increases with asset risk and
leverage shareholders have incentives to take excessive risks to exploit this option
value This theory implies two results First for any given level of capital firms will
always seek to increase shareholder value by maximizing risk and looting the firms
assets (Jensen and Meckling 1976) Second high leveraged firms have more
incentive to increase risk-taking (Green and Talmor 1985)
The asset-substitution moral hazard is exacerbated by the existence of state
guarantee funds and deposit insurance which charge a flat premium on insurer and
bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put
option with exercise price equal to the promised value of its debt Increasing the
volatility of surplus will increase the value of the put option Thereby an equity value
maximizing bank shareholder has an incentive to take excessive risks to exploit this
option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins
(1988) made a similar analysis on the impact of guarantee funds which provide an
incentive for insurers to increase volatility
Although asset substitution theory is an appealing explanation for excessive
risk-taking it fails to explain the moderate risk-taking by many firms A sizable
literature 4 presents different motivations for firmrsquos risk management taxes
bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc
7
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
2 Factors Affecting Insurer Risk-taking
The section reviews relevant literature and discuss factors affect insurer
risk-taking Research hypotheses are developed following the analysis
21 Firm Risk
Firm risk generates from numerous sources and its management is critical to a
firmrsquos success Considering only financial risk3 variability is caused by investment
risk interest rate risk credit risk exchange rate risk etc all of which have been
studied extensively Each of these sources of variability affects a firmrsquos assets
liabilities or both For instance both investment risk and credit risk influence
variability in asset values while exchange rate risk and interest rate risk may influence
both asset and liability values For purposes of this study our interest is not so much
with the sources of risk but rather with their influence on the sufficiency of assets to
pay liabilities which we define as a firmrsquos level of solvency
Much of the existing literature considers firm risk-taking strategies in terms of
asset risk and leverage neglecting liability risk For banks the subject of much of the
literature the relatively smooth nature of bank liabilities allows for such omission
But for insurers whose liabilities can fluctuate dramatically liability risk is a critical
component of solvency risk Therefore in the study reported here we consider firm
solvency risk which incorporates asset risk leverage and liability risk
22 Franchise Value and Asset-substitution Moral Hazard
According to Modigliani-Miller (MM) paradigm under certain friction-free
assumptions (including perfect information no taxes or transaction cost and efficient
market) neither capital structure choices nor corporate risk management affects the
value of the firm Shareholders will be indifferent to the level of risk-taking because
the security-specific or nonsystematic risk already has been diversified by the
individual shareholders through portfolio formation Itrsquos obvious that assumption of 3 Firms face non-financial risk as well but these are not considered here
6
perfect market is unrealistic but MM theorems provide a clear benchmark to help us
understand firm financing and risk management decisions through exploring the
consequences of relaxing the MM assumptions
One of the important market imperfections is information asymmetry leading to
a variety of agency problems A well-established result about the agency conflict
between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo
or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather
than the total of equity and debt value of the firm have an incentive to increase the
risk of investment assets at the expense of the debtholders interests Limited liability
can be considered an option held by shareholders to put losses onto the debtholders
whenever the firm is liquidated Since option value increases with asset risk and
leverage shareholders have incentives to take excessive risks to exploit this option
value This theory implies two results First for any given level of capital firms will
always seek to increase shareholder value by maximizing risk and looting the firms
assets (Jensen and Meckling 1976) Second high leveraged firms have more
incentive to increase risk-taking (Green and Talmor 1985)
The asset-substitution moral hazard is exacerbated by the existence of state
guarantee funds and deposit insurance which charge a flat premium on insurer and
bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put
option with exercise price equal to the promised value of its debt Increasing the
volatility of surplus will increase the value of the put option Thereby an equity value
maximizing bank shareholder has an incentive to take excessive risks to exploit this
option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins
(1988) made a similar analysis on the impact of guarantee funds which provide an
incentive for insurers to increase volatility
Although asset substitution theory is an appealing explanation for excessive
risk-taking it fails to explain the moderate risk-taking by many firms A sizable
literature 4 presents different motivations for firmrsquos risk management taxes
bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc
7
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
perfect market is unrealistic but MM theorems provide a clear benchmark to help us
understand firm financing and risk management decisions through exploring the
consequences of relaxing the MM assumptions
One of the important market imperfections is information asymmetry leading to
a variety of agency problems A well-established result about the agency conflict
between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo
or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather
than the total of equity and debt value of the firm have an incentive to increase the
risk of investment assets at the expense of the debtholders interests Limited liability
can be considered an option held by shareholders to put losses onto the debtholders
whenever the firm is liquidated Since option value increases with asset risk and
leverage shareholders have incentives to take excessive risks to exploit this option
value This theory implies two results First for any given level of capital firms will
always seek to increase shareholder value by maximizing risk and looting the firms
assets (Jensen and Meckling 1976) Second high leveraged firms have more
incentive to increase risk-taking (Green and Talmor 1985)
The asset-substitution moral hazard is exacerbated by the existence of state
guarantee funds and deposit insurance which charge a flat premium on insurer and
bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put
option with exercise price equal to the promised value of its debt Increasing the
volatility of surplus will increase the value of the put option Thereby an equity value
maximizing bank shareholder has an incentive to take excessive risks to exploit this
option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins
(1988) made a similar analysis on the impact of guarantee funds which provide an
incentive for insurers to increase volatility
Although asset substitution theory is an appealing explanation for excessive
risk-taking it fails to explain the moderate risk-taking by many firms A sizable
literature 4 presents different motivations for firmrsquos risk management taxes
bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc
7
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
and real service efficiency One of the important reasons for risk management is that
financial distress or bankruptcy is costly for firms especial when the intangible assets
(franchise value) are considered As explained in section 121 franchise value can be
understood as intangible assets for insurance companies and cannot be fully liquidated
Provided franchise value is sufficiently large then shareholders will have an incentive
to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)
develops option-pricing models that demonstrate how franchise value can
counterbalance asset substitution moral hazard and constrain risk-taking
Optimal insurer risk-taking decisions involve trade-offs between risk-constraining
strategies which reduce the likelihood of losing the franchise and risk-maximizing
strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively
when franchise value is sufficiently large the moral hazard problem of risk shifting
may be alleviated and when franchise value is small the incentive to shift risk to
debtholders may dominate This trade-off however may be affected by some other
factors The impact of competition on insurer risk-taking will be discussed in the
following part
23 Competition and Insurer Risk-taking
A traditional perception is that there is a trade-off between efficiency and financial
stability in competitive market Applying standard industrial economics to the
insurance industry in a perfectly competitive market insurers are profit-maximizing
price-takers such that costs and prices are minimized Therefore insurers are more
efficient in a competitive market than in a non-competition market On the other hand
a variety of models show firmsrsquo risk-taking increases in competition5 indicating a
negative relationship between competition and financial stability
Following these arguments insurance companies react to increased competition in
two ways to keep profitability one is to improve efficiency so as to maintain or
5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial
stability and competition
8
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
increase market share6 and the other way is to increase risk for higher return The
first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos
success in long run As competition becomes very intensive however the room for
efficiency improvement reduces and thus dropped profitability is likely resulted
Therefore the efficiency improving strategy alone may not effectively keep market
share and profitability The second choice is a strategy of higher risk for higher return
In a competitive insurance market the risk-increasing strategy usually involves in
low-price market expansion strategy The insurers expect to increase or maintain their
existing market share through low-price marketing assuming their risk cannot be
fully priced due to information asymmetry between customers and insurers
Low-price marketing strategy is usually followed by negative loss development7 and
risky investment resulting in greater insolvency risk This risk-increasing strategy
might be attractive to insurance companies because the claim is not paid when
insurance policies are sold which gives insurers time to make income before
liabilities are due The uncertainty nature in the timing and the amount of insurance
claim especially for long-tail lines magnifies the incentive to take risky strategy
As competition increases itrsquos likely that insurers take both efficiency improving
strategy and risk-increasing strategy The question is which strategy dominates If
efficiency improving strategy dominates increased competition will not result in more
risk-taking On the other hand if the risk-increasing strategy dominates competition
will cause financial instability In the following we will discuss how the balancing
between the efficiency strategy and the risk-increasing strategy may depend on an
insurance companyrsquos franchise value and underwriting cycle
As we discussed before high-franchise-value firms have stronger incentive to
protect franchise value by avoiding liquidation Therefore high-franchise-value firms
should also be motivated to prevent their franchise from reduction in competition
6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle
determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus
leading to negative loss development
9
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Franchise value representing future profitability is largely generated from a firmrsquos
market power (De Jonghe and Vander Vennet 2005) As increased competition tends
to erode market power (Keeley 1990) high-franchise-value firms will react so as to
avoid loosing market power and resultant franchise value Improving efficiency is a
good choice for high-franchise-value insurers since it enhances profitability without
increasing risk and high-franchise-value insurers are usually large firms and have
advantages in economy scale8 and efficiency improvement It is however likely that
efficiency improving strategy alone cannot successfully make high-franchise-value
insurers maintain their market share and then the risk-increasing strategy may be
under consideration9 This case is likely resulted especially when severe competition
exists between large players In summary competition will encourage
high-franchise-value insurers to improve efficiency which counters risk-taking but
may also induce them to take risky strategy as efforts to maintain market power
The case is different for low-franchise-value insurance companies in an
increasingly competitive market A traditional view is that for low-franchise-value
firms the asset-substitution moral hazard dominates and as a result they have less
incentive to improve efficiency and are likely to take gambling strategy The gambling
strategy may become less attractive to low-franchise-value insurers under two
conditions First a successful low-price market expansion strategy requires high level
of capacity but low-franchise-value insurers may not have enough capacity to survive
the low-price marketing strategy especially when the competition is very intensive In
this case the gambling strategy would not be a rewarding and financially feasible
choice for low-franchise-value firms Second low-franchise-value insurers are
exposed to more monitoring by regulators and may not be able to take the gambling
strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation
They argue that higher capital requirements decrease charter value which indicates that a negative relationship
between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may
derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling
or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always
10
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
excessive risk as competition increases
Above discussion shows that the effect of franchise value on insurer risk-taking is
conditional on the degree of competition and vice versa We can have the following
hypothesis
Hypothesis 1 The effects of franchise value and competition on insurer risk-taking
strategies are jointly determined
This hypothesis implies that a prior expectation about the effects of franchise
value and competition on insurer risk-taking cannot be tested without also accounting
for their joint effect That is the degree of competition is not necessarily positively
related with risk-taking and neither is franchise value negatively related with
risk-taking rather the influence of franchise value (competition) is conditional on the
degree of competition (franchise value)
24 Underwriting Cycle and Insurer Risk-taking
Business cycle has encompassing influence on industry insiders Business cycle
influences franchise value market structures managerial incentives and nearly every
aspects of the industry Firms may become more (or less) risky in some stages of
business cycle than in other stages Many studies have investigated the effect of
business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which
indicates the important influence of business cycle on firm risk-taking
Underwriting cycle is an insurance industry specific business cycle that consists
of alternative periods in which insurance price is low (soft market) and periods in
which insurance price is high (hard market) There are few studies examining the
relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and
Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer
insolvency The main contribution of these studies is to demonstrate that not only firm
internal factors but also external factors play an important role in insurer solvency
While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)
11
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
external factors on insurer risk-taking this study assumes that outside-industry factors
usually affect insurer risk-taking in an indirect way through changing insurance
industry environment which can be represented by the underwriting cycle
The underwriting cycle is a comprehensive indicator of insurance industry
conditions that have significant influence on insurer risk-taking strategies It consists
of alternating periods of soft markets with plentiful coverage supply and flat or falling
premium rate and hard markets with restricted coverage supply and sharp premium
rate increases
Numerous theories have been developed to explain the underwriting cycle but
none has been conclusively confirmed The goal of the following review of these
theories12 is not to provide a definitive explanation of the causes of underwriting
cycle but rather to evaluate potential influence of the underwriting cycle on insurer
risk-taking behavior
Explanations of the underwriting cycle often begin with what is referred to as
the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses
the uncertainty about the frequency and severity of those expenses the timing of
future claim payments (ie the length of the tail) interest rate and the cost of holding
capital These factors taken together constitute the cost of providing insurance
Because these fundamentals fail to explain many aspects of the underwriting cycle
however researchers have looked to additional factors to understand the cycle
The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo
theory which posits that (a) industry supply depends on the amount of available
insurer capital and (b) hard markets are triggered by periodic exogenous large
negative shocks to insurer capital because raising capital from external markets is
more costly compared with internal capital In these models13 a shock to insurer
capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories
regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon
(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several
dimensions
12
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
contraction of capacity reflected in leftward shifting of the short-run supply curve and
increasing premium rate
The capacity constraint theory contributes substantially to the explanations for
hard markets Yet it is far from a complete explanation Capacity constraint models
fail to explain why the unpredictable capacity shocks can cause a cycle and do not
persuasively explain what causes soft markets
Harrington and Danzon (1994 2005) develop and test alternative hypotheses of
excessive competition during the soft market They hypothesize that if some insurers
undercharge due to either inexperience or moral hazard of excessive risk-taking then
other insurers will cut prices to preserve market share and avoid loss of quasi-rents
from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The
winners in the competition for market share are the low-pricing insurers who in the
end may well find the premiums are insufficient to pay the claims which is known as
ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid
premium growth is often followed by negative loss reserve development Soft-market
periods of underpricing cannot continue indefinitely Whether the excessive price
cutting in the soft market ultimately contributes to overpricing in the followed hard
market remains an untested hypothesis
All the contributing factors discussed above are directly or indirectly related to
insurer risk-taking behavior The influence of the underwriting cycle on insurers
risk-taking behavior can be analyzed from two angles first the underwriting cycle
represents changes in the competitive conditions to which insurers are exposed and
second the underwriting cycle is likely to affect low- and high-franchise value firms
differently These effects are discussed instantly as follows
Similar to the four typical phases of an economic cycle the underwriting cycle
undergoes four stages soft market peak hard market and trough Market conditions
and the nature of competition change along the underwriting cycle At the start of the
soft market competition increases moderately price drops and then demand for
insurance increases As a result the market expands and insurers undergo positive
premium growth As the soft market deepens premium growth declines since
13
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
insurance demand is nearly saturated At this stage insurers compete intensely for
revenue and market share through price-cutting According to Harrington and
Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo
who undertake the underpricing due to either inexperience or excessive risk-taking
and then cause a herd behavior of price-cutting around the industry As a result
significant overhang risk accumulates due to a lack of underwriting discipline These
conditions generally lead to unfavorable development of loss reserves
As the market softens to the point that profits diminish or vanish completely the
capital needed to underwrite new business is depleted A ldquohardrdquo turn in an
underwriting cycle comes when insurers collectively respond to the fact that
prevailing premiums cannot cover future claim payments As a result the supply of
coverage is restricted and price increases sharply At the beginning of the hard market
competition within the insurance industry is lessened and insurers tend to behave
conservatively At the same time the high profit of hard market attracts new players
enter the insurance industry lead to a new round of competition and underwriting
cycle
Generally speaking the intense competition in the soft market induces insurers to
take more risk and in the hard market insurers tend to reduce risk-taking The next
question is if this result is generally true for all insurers For instant we are
particularly interested in whether or not this result is compatible with the franchise
value theory which predicts that high-franchise-value firms take less risk compared
with low-franchise-value firms and whether high-franchise-value firms take less risk
moderate risk or excessive risk in soft market In another words we are interested in
whether or not the risk-constraining effect of franchise value varies with underwriting
cycle
Franchise value has two sometimes incompatible effects on firm risk-taking
decisions On one hand insurers with high franchise value have incentives to avoid
losing their franchise value through bankruptcy by taking less risk On the other hand
high franchise value indicates large quasi-rents from renewal business for insurance
companies which motivate them to compete for market share so as to preserve the
14
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
existing franchise value In this case high-franchise-value firms may take more risk
Whether either of these two effects dominates in a particular stage of underwriting
cycle remains unknown A few factors discussed below may magnify
high-franchise-value insurersrsquo incentive to take more risk to preserve market share in
soft market
First customers tend to shop for lower price and choose low-pricing
underwriters over high-pricing underwriters In a soft market especially the deepened
soft market the demand for insurance is nearly saturated The insurers offering a
lower price could steal market share from high-pricing insurers Watching premiums
flow to other high-franchise-value insurers would revise their prices so that they are
more in line with those being offered elsewhere in the market so that they can keep
the existing business and the quasi-rent from renewal business Second the
expectation of the regular alternating of soft market and hard market creates moral
hazard of increasing risk-taking in the soft market When insurance companies
compete for market share through low-pricing marketing at expense of their
profitability in soft market they expect to be able to recoup their loss from the
following hard market where price rises This moral hazard may become more severe
for high-franchise-value firms compared to low-franchise-value firms because the
former group has stronger incentive to prevent market share (and resultant franchise
value) from reduction These factors may attribute to a weaker risk-constraining effect
of franchise value in a soft market than in a hard market
The above analysis shows that the underwriting cycle implies a varying nature of
competition and influence on the effect of franchise value on insurer risk-taking
incentives A hypothesis regarding the interactive relationships between franchise
value competition and underwriting cycle can be stated as follows
Hypothesis 2 The effects of franchise value and competition on insurer risk-taking
strategies are influenced by the underwriting cycle
15
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
3 Methodology
31 Multilevel Analysis
Multilevel analysis is a conditional modeling framework taking account of the
nested relationships (interactions) across different levels Multilevel models are
specified through conditional relationships where the effects described at one level
are conditional on the variables of the level above it Multilevel analysis has been
used increasingly in the fields of education demography and sociology to
simultaneously examine the effects of group- or macro-level and individual-level
variables on individual-level outcomes Multilevel method has many advantages over
single-level approaches in that it contains rich information and is less biased and more
robust A detailed discussion of advantages and limitations of the multilevel methods
can be found in Diez-Roux (2000)
The idea that individual firms may be influenced by both the market and
industry context makes the multilevel approach appealing to our analysis To
investigate the effect of market competition and the underwriting cycle on individual
firm risk-taking we specify two-level longitudinal models where individual firms are
level-1 units of observations and industry variables are level-2 variables
32 Regression Models
Hypotheses 1 described above suggests an interactive effect of franchise value
and competition on firm risk-taking Considering franchise value as firm-level effect
and competition as industry-level effect the nested relationship of franchise value in
the context of industry can be specified by the following two-level model The level-1
model can be written as
Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit
( 1 )
Where there are i = 1 hellip n firms and t = 1hellipTi years
Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and
16
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Bigg 2003) indicate a non-linear relationship between risk and franchise value
Therefore the measure of risk is logged to capture the potential nonlinearities14 We
use one-period lagged franchise value to investigate its effect on ex post firm risk
In equation (1) the intercept a0i is random among individual firms and a3 is
constant over all observations a1t and a2t are time-specific intercept and slope which
will be modeled by level-two variables One feature of multilevel model is that the
parameters in level-1 model themselves are also models
Our interest is to examine how the time-varying parameter a1t and a 2t vary over
market competition Then the level-2 model to specify a1t and a 2t can be written as
a1t = a11 (competition)t + e1t (11)
a2t = a20 + a21 (competition)t + e2 t (12)
Equation (11) represents the main effect of competition on dependent variable
and equation (12) represents the interaction effect of competition and franchise value
Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the
combined equation
Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise
value)it-1 + a3 (control variables)it-1 + variance (13)
= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise
value)it-1 + a3 (control variables)it + variance (14)
Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random
variables
From equation (13) itrsquos easy to see that the effect of franchise value on firm risk
which is represented by [ a20 + a21 (competition)t ] is conditional on competition A
positive coefficient a21 indicates that as competition increases the effect of franchise
value on risk tends to be positive Similarly by rearranging equation (13) to equation
(14) we see that the effect of competition on risk is also conditional on franchise
value
14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our
samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a
logarithm relationship between franchise value and the dependent variable is employed
17
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Equations (13) and (14) can be expressed in the following equation (15) which
is the model we need to fit A significant interaction term a21 (Competition)t (franchise
value)it-1 would indicate a support to Hypothesis 1
Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t
(franchise value)it-1 + a3 (control variables)it + variance (15)
Hypothesis 2 posits that the influence of competition and franchise value on firm
risk is conditional on the underwriting cycle To examine these conditional
relationships we incorporate the underwriting cycle effect into the model
In order to make interpretations easier we substitute equation (11) into to
equation (1) and rewrite the level-1 model as follows
Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control
variables)it +ζit (2)
Now the variables of franchise value and competition all appear in the level-one
model Please note that b0i is a random effect for each firm b2t and b3t are
time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as
functions of underwriting cycle The level-2 model can be written as
b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)
b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)
Note that b1t depends on both competition and the underwriting cycle and b2t
depends on the underwriting cycle Substituting the level-2 models (21) and (22) into
level-1 model (2) we have
Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1
+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21
(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance
(23)
where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]
To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20
b21 and the parameters for control variables The measurement of all variables is
described later in section 35
18
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
4 Data and Variables
41 The CRSP sample and the NAIC sample
The empirical work is based on two panel datasets one obtained from The Center
for Research in Security Prices (CRSP) database and the other from National
Association of Insurance Commissioners (NAIC) database over the period of
1994-2003 CRSP database includes around 100 publicly-traded PampC insurance
companies and NAIC database provide historical financial information for about
3000 PampC (mutual and stock) insurers
The CRSP and NAIC databases employ different accounting practice rules and
provide different financial information The CRSP (merged with COMPUSTAT)
database using the Generally Accepted Accounting Principles (GAAP) provides
general information of balance sheet income statement cash flows as well as stock
price return and volume data for publicly-traded stock companies The NAIC
database using Statutory Accounting Principles (SAP) 15 contains detailed
information of annual financial statements including balance sheet income cash
flows detailed underwriting and investment exhibit and loss reserve development etc
for all types of insurance companies but does not collect stock price return and
volume data because most of the insurers are not publicly traded
We test the hypotheses on two samples for several reasons One is that if we
relied solely on the CRSP data base we would be limited in the number of insurers
observed Furthermore CRSP allows us to observe only publicly traded stock insurers
Using the NAIC data base allows us to rectify these two limitations however the
NAIC data base does not permit measurement of Tobins q which is the commonly
employed measure of franchise value Tobins q is based on stock values Undertaking
the analysis on both data sets allows us to succeed in achieving objectives across our
spectrum of purposes Neither data set is perfect yet with the combination we will
15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements
19
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
obtain the best information currently feasible
42 By-line Analysis
An important aspect of this study is to examine the influence of industry factors
(competition and underwriting cycle) on firm risk The insurance industry however is
segmented by different lines each with its own market and characteristics For
example the firms specializing in auto insurance may face different market conditions
compared to the firms specializing in commercial liability lines To control for the
differences across lines a by-line analysis is needed Particularly for this study we
examine four major lines separately personal auto liability insurance homeowner
insurance general liability insurance and commercial multiple peril insurance The
first two are personal lines and the other are commercial lines which in sum account
for more than 50 of total premium written by the property and casualty industry In
addition to their importance another reason to select these four lines is the different
risk nature of these lines
Since by-line data is only available in NAIC database the by-line analysis is only
conducted for the NAIC sample As for the CRSP sample the industry variables are
calculated based on the overall property and casualty industry This will not be an
issue for the CRSP sample because most of the publicly-traded insurance companies
included in our sample are group companies focusing on multiple lines
As many firms are engaged in more than one business line in order to reduce
overlaps across the samples the sample for each line is collected to include firms with
more than 30 premium written in a particular line
43 Measuring Firm Risk
Four measures of the level of firm risk-taking are employed in this study (i) the
volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)
a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of
insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage
20
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
an indicator of a firmrsquos financial strength We describe them in turn as follows
Standard deviation of stock returns
The first measure of risk we consider is standard deviation in stock return which
is the most commonly used market-based measure of risk16 Specifically we look at
the annualized standard deviation of a firmrsquos daily stock returns Given the
assumption of efficient market this would give a good measure of firm risk because
all the information about profitability and risk should be reflected in the stock price
This measure is unavailable for the most of the insurance companies however
because most insurers are not publicly traded stock companies
Value-at-Risk
Volatility is the most popular measure of risk The main problem with volatility
however is that it does not account for the direction of a stock returns movement a
stock can be volatile because it suddenly jumps higher17 But both investors and firms
care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy
and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally
concerned with avoiding a possible disaster and that the principle of safety plays a
crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili
Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used
Value-at-Risk (VaR) as a measure of downside risk and examined the relationship
between downside risk and stock return
VaR measures the maximum likely loss over a given time period at a given
confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos
downside risk The estimation is based on the lower tail of the actual empirical
distribution We use the empirical distribution of daily returns during the past 12
months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR
and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the
left tail of a firmrsquos stock return distribution It should be noted that the original VaR
16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels
Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004
21
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
measures are multiplied by -1 before running our regressions The original maximum
likely loss values are negative stock returns since they are obtained from the left tail
of the distribution The downside risk measure 1 VaR and 5 VaR used in our
regression is defined as -1 times the maximum likely loss Therefore downside risk is
positively related with the value of VaR
The information needed (such as stock price) to calculate variance of stock return
and VaR is only available for publicly-traded stock companies which is provided by
the CRSP database Most of insurance companies however are non-publicly-traded
Therefore we need another measure of risk-taking for the non-publicly-traded
insurance companies contained by NAIC database
Risk-Based Capital Ratios
Risk-Based capital (RBC) is a method developed by the NAIC used to set capital
requirements for an insurance company considering the degree of risk taken by the
insurer The components of the RBC formula for PampC insurance companies include
asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains
comprehensive information about an insurance companyrsquos financial strength it is used
as an important regulatory solvency prediction method by regulators in
property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual
capital the lower possibility of insolvency The RBC system requires regulators to
take specified actions if an insurerrsquos actual capital falls below certain thresholds A
few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips
1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting
insurer insolvency and show that when used in isolation RBC is not very successful in
predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an
informative comprehensive measure of firm risk available for all insurance companies
18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis
and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency
Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the
predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the
ratios themselves
22
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level
of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC
ratio as a measure of risk for the insurance companies contained by NAIC database
Higher rank of RBC ratio represents for higher risk
Leverage
Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and
surplus are strong indicators of insurer financial strength and insolvency risk We
employ leverage as one of measures of firm risk Particularly for this study using
leverage as a measure of firm risk has an advantage in that it provides the same risk
measure for the CRSP and NAIC samples We use the ratio of (total assets-total
surplus) total surplus as a measure of leverage To account for the different
accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory
capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs
by adding the product of expense ratio (the ratio of underwriting expenses to net
premiums written) and the unearned premium reserve to statutory surplus Also the
reserve for unauthorized reinsurance and the excess of statutory over statement
reserves are added to surplus These are standard GAAP adjustments
44 Measuring Franchise Value
Our purpose in measuring franchise value is to consider the true value of what is
lost if a firm becomes insolvent Tangible assets are only a portion of what is lost
franchise value represents the remainder of firm value above and beyond the value of
tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)
goodwill growth opportunities market power existing distribution networks and
renewal rights on existing business arrangements with reinsurers as well as
specialized knowledge about the risks generating from their existing book of business
These are not monetary assets yet nonetheless have great value to the firm as a going
concern
Tobinrsquos q
23
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the
market value of a firm to the replacement cost of its assets The higher a firmrsquos
franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for
franchise value and presents evidence of a negative relationship between franchise
value and risk Smirlock (1984) argues that because q relates the market value of
firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents
Any pricing power irrespective of its source would be reflected in the market value
of a companyrsquos equity and thus assets but not in the cost of acquired assets
Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing
comparability across different firm sizes
Determining the market value of a firm and the replacement cost of its assets is a
difficult task We need estimators to approximate the true value of q The most
commonly used estimator which is also employed in this study is defined as
following
q = (Market value of equity + book value of liabilities) book value of tangible
assets
The market value is set to equal the market value of equity plus the book value of
insurersrsquo liabilities This is reasonable since the value of a going concern is reflected
in the market value of the equity as the equity holders would be the beneficiaries not
the debt holders Previous studies have lacked a market value estimator of the
replacement cost of assets They generally use the book value of tangible assets For
the sample of publicly traded insurers (the CRSP sample) we will conduct the
analyses using this standard measure of franchise value
Ratings
Although Tobinrsquos q is a well-established measure of franchise value the majority
of insurers are not publicly traded and therefore the sample available when Tobinrsquos q
is used is very limited To develop a proxy for franchise value for both publicly and
non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating
as a proxy of its franchise value
To find an appropriate proxy for franchise value of a non-publicly traded stock
24
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
company is difficult Financial ratings of a firm can be used as an instrument variable
for franchise value Yu et al (2003) employ AM Best ratings as a measure of
intangible assets and find a negative relationship between an insurerrsquos intangible asset
and asset risk In this research we also use transformed A M Bests financial rating to
measure a firmrsquos franchise value Instead of using the level of rating directly we
transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level
according to the distribution of ratings in a year For example if 90 of all insurersrsquo
ratings are lower than A++ then the revalued number for A++ is 090 Therefore the
value of rating rank ranges from 0 to 1 Using percentile rank as a measure of
franchise has two advantages compared to absolute (number) level of ratings (1)
percentile rank better reflects the relative standing of a firmrsquos franchise value within
the industry than the number level (2) A firmrsquos rating may not change for a long time
but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers
changes over years
45 Measuring Competition
We employ two measures for degree of competition each of which captures a
certain characteristic of market competition
Herfindahl Index
A commonly used measure of competition in the insurance literature is
HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)
which measures the degree of market concentration As market concentration
increases economic theory suggests that competition decreases This line of
discussion derives from the economics of increased market power with a larger share
of the market concentrated in one or a few firms As a result HHI inversely related
with the degree of competition In this study HHI is equal to the sum square of each
firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed
so that it positively correlated with the degree of competition
19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range
25
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Efficiency
While the Herfindahl index is often used and represents easily obtained measures
of competition an alternative representation may be found in measures of efficiency
Increased competition should force firms to operate more efficiently so that high
efficiency would indicate the existence of competition and vice versa Furthermore
increasing concentration actually could represent higher levels of competition if the
concentration occurs because more efficient insurers are purchasing less efficient
insurers and benefiting from the opportunity to earn profits through improved
efficiency (Fenn et al 2006)
Among various types of efficiency X-efficiency is generally expected to relate
closely to competition Leibenstein (1966) introduced the theory of X-inefficiency
generated from non-competition As a concept it may be summarized as follows for
a variety of reasons people and organizations normally work neither as hard nor as
effectively as they could In situations where competitive pressure is light many
people will trade the disutility of greater effort or search for the utility of feeling less
pressure and of better interpersonal relations (See Leibenstein 1966) Economic
theory suggests that increased competition forces insurance companies to drive down
their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of
a firm is defined as the difference in costs between that firm and the best practice
firms of similar size and input prices Errors lags between the adoption of the
production plan and its implementation human inertia distorted communications and
uncertainty cause deviations between firms and the efficient frontier formed by the
best-practice life insurers with the lowest costs controlled for output volumes and
input price levels (Leibenstein 1966)
Various approaches (Non-parametric approaches or parametric approaches) are
available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All
methods involve determining an efficient frontier on the basis of observed minimal
values rather than presupposing certain technologically determined minima Each
26
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
method using different assumptions and has advantages and limitations20
We use the data envelopment analysis (DEA) a non-parametric approach to
estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used
extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few
insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use
DEA to estimate efficiency and productivity of insurance companies The descriptions
of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)
The details of DEA cost efficiency estimation is explained in Appendix I After
calculating X-efficiency score for each firm industry X-efficiency is computed by the
average of all firmsrsquo X-efficiency score weighted by market share
45 Measuring the Underwriting Cycle
The underwriting cycle is generally demonstrated by the fluctuation of the
industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums
earned Each line of insurance may well be subject to its own cycle21 The combined
ratio for each of the selected line is calculated separately
46 Control Variables
We also include a number of control variables that may be systematically related
to insurer risk-taking behavior These control variables are mainly firm characteristics
The industry factors like the shocks due to interest rate and stock market are
considered to be absorbed by the industry combined ratio which is used as a proxy of
industry performance
Firm Size
Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein
(1995) and Cummins Grace and Phillips (1998) find that small firms are more
vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)
27
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
logarithm of total assets
Ownership structure
A firms risk-taking behavior is highly influenced by its ownership structure First
due to the limited access to capital in the presence of financial stress mutual insurers
usually operate more conservatively than stock companies Regan and Tzeng (1999)
report that stock insurers are involved in more risk than mutual insurers Second
Ownership structure implies different managerial incentives As the literature on
agency theory demonstrates managers and owners of firms do not automatically have
consistent objectives leading to potential moral hazard problems Managers who are
not closely monitored andor whose objectives are not closely aligned with those of
the owners may take actions inconsistent with shareholder objectives With regard to
risk-taking behavior managers may take a more conservative strategy or a over
aggressive strategy than shareholders desire Prior research shows that ownership
structure serves as an internal mechanism to control managerial incentives The stock
form of ownership provides a superior mechanism (such as equity-based
compensation or stockholders monitoring incentives) for owners to monitor and
control managers Mutual ownership form eliminates the conflict between
policyholders and owners by merging the policyholder and ownership functions but is
less effective in monitoring and controlling managers (Mayers and Smith 1981) due
to the lack of interest conflict aligning mechanism between managers and owners
Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and
mutual insurers to changes in the underwriting environment from 1984 to 1991 and
find that stock companies are much quicker to exit unprofitable markets and expand
business in profitable markets This result implies that stock insurers are more flexible
in adjusting their strategies than mutual insurers To account for the effect of
ownership structure on insurer risk we use a dummy equal to 1 for mutual companies
and zero for stock companies
Group Affiliation
As noted in prior studies (eg Baranoff and Sager 2003) membership in a group
of affiliated companies can be an important factor for corporate operations Insurance
28
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
companies that belong to a group can benefit more from internal capital support and
risk diversification among the affiliated members of the group An affiliated firm is
expected to tend to take more risk than an unaffiliated firm A dummy variable equal
to 1 for companies in a group and equal to zero for unaffiliated companies is included
to control for difference due to corporate affiliation membership
Business Diversification
An insurance firm can reduce risk through internal diversification among different
product lines Therefore a more business diversified firm faces less risk than a less
diversified firm To control for the effect of business diversification we employ a
firmrsquos product line Herfindahl index based on the proportion of net premium written
by product lines The product line Herfindahl index is inversely related to business
diversification
Interest Rate
Interest rate is an important affecting factor for insurance industry Interest rate is
used to discount expected future claim and claim cost and directly affect the
investment profit Therefore interest rate affects not only the value of insurersrsquo
liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer
assets needed to pay a future claim We use the return of one-year return of US
treasury as a measure of interest rate
Stock Index
Stock index is directly related to insurersrsquo investment income and consequent
operation profitability We use SampP 500 index as a reprehensive of stock index
Descriptions of the variables used in the regression model are summarized in
Table 41
29
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Variable Description Variable Description
Dependent Variable
Risk Return_Std Annualized standard deviation of daily stock returns
Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]
1 VaR -1 (1 percentile of the daily stock return of a year)
Rank_RBC Rank of RBC ratio
5 VaR -1 (5 percentile of the daily stock return of a year)
Leverage Log[10+(total assetsndashsurplus)surplus]
Independent Variable
Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets
Rank_rate Percentile rank of rating levels A++ to F
Competition COMP -1HerfindahlndashHirschman Index +N
Efficiency Industry weighted average score of cost efficiency
Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned
Control variables Size Log (market value of equity ) Size Log (total assets)
Mutual =1 if mutual =0 if stock
Group Group=1 if affiliated =0 if unaffiliated
Bus_Div Herfindahl index of a firms product line concetration
Interest Return of 1-year US treasury
Stock index SampP 500 stock index
The NAIC SampleThe CRSP Sample
Table 41 Descriptions of Variables
30
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
47 Summary Statistics
In this section summary statistics for the CRSP sample and the NAIC sample are
presented respectively
The CRSP Sample
The CRSP sample is obtained from CRSP database The final sample size is 987
observations and sample period is 1994-2003 All the firms in this sample are
publicly-traded stock companies and most of which are group companies They are
influenced by both the insurance industry conditions and the stock market changes
Table 42 gives the summary statistics of the industry-level variables over year used
for the CRSP sample Table 43 provides the summary statistics of the firm-level
variables in the CRSP sample
Table 42 Industry variables by year (the CRSP sample)
Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Herfindahl index () 232 234 240 245 239 241 227 237 238 247
Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001
Stock index 461 547 675 876 1088 1331 1420 1186 989 968
Interest rate () 232 840 551 624 614 431 699 744 341 147
Table 43 Summary statistics of firm-level variables (the
CRSP sample N=987)
Variable Mean Std Dev Minimum Maximum
Return_Std 003 002 001 025
1VaR 007 005 000 073
5VaR 004 003 000 030
Leverage 240 164 -344 910
Q 109 023 049 506
Size 598 211 -142 1143
31
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Table 44 gives the correlations between each pair of firm-level variables It shows
that three stock risk measures Return_Std 1VaR and 5VaR are highly positively
correlated Leverage is inversely correlated with all these three measures indicating
that higher levered firms tend to have lower stock risk In addition stock risk
(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage
increases in firm size The correlations between Q and all risk measures are
significantly negative indicating a relationship of higher franchise value with lower
level of risk without control of other factors
Table 44 Correlation of major variables (the CRSP sample)
Return_Std 1VaR 5VaR Leverage Q Size
Return_Std 1 092 095 -011 -010 -061
lt0001 lt0001 00023 00021 lt0001
1VaR 1 092 -011 -007 -061
lt0001 00021 00275 lt0001
5VaR 1 -010 -009 -063
00067 00048 lt0001
Leverage 1 -011 028
00013 lt0001
Q 1 015
lt0001
Size 1
Of particular interest is to examine if the relationship between franchise value and
firm risk-taking is influenced by competition and the underwriting cycle both of
which changes over time Table 45 provides the correlations of Q and various risk
measures over years which shows a significant variation The variations are reflected
in three aspects (1) the level of correlations fluctuates over time The correlations are
positive in some years and are negative in other years (2) the significance of the
correlations also changes over year (3) the correlation of leverage and Q is inverse to
32
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
other correlations of risk and Q This is consistent with the negative relationship
between leverage and stock risk shown in Table 44
Table 45 Correlations between risk and Q over years (the CRSP sample)
Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR
Corr p-value Corr p-value Corr p-value Corr p-value
1994 001 08900 002 08763 004 06617 -022 00249
1995 012 01969 017 00732 026 00054 -039 00002
1996 014 01481 013 01955 019 00479 -024 00211
1997 -012 02220 -012 01893 -012 02241 -011 03280
1998 -008 04414 -015 01439 -001 03588 -011 03086
1999 -016 01133 -016 01192 -014 01791 002 08860
2000 -016 01526 -018 01058 -016 01407 022 00691
2001 -021 00644 -024 00391 -023 00439 028 00227
2002 -022 00577 -023 00569 -020 00844 018 01507
2003 -038 00011 -028 00187 -033 00056 001 09527
Figure 41 and Figure 42 displays the changing pattern of the correlations
between Leverage and Q as well as Return_Std and Q The significant values are
labeled differently from the insignificant values We see that the correlations are
particularly significant at two stages 1995-1996 and 2000-2002 Now we put the
graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here
together to see what is special with these two periods Interestingly we find that
1995-1996 and 2000-2002 are around the turning points industry underwriting cycle
and represent for a soft market and a hard market respectively We find that the
correlations between leverage and Q are significantly negative during 1995-1996 and
positive during period 2000-2001 while the correlations between stock risk and Q are
the opposite
33
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Figure 41 Correlation between Q and Leverge by year
-060
-040
-020
000
020
040
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 42 Correlation between Q and Return_Std by year
-060
-040
-020
000
020
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Corr
-o- significant at 15 level -- insignificant
Figure 43 HHI () for PampC industry
210
220
230
240
250
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
34
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Figure 44 Combined ratio () for PampC industry
95
100
105
110
115
120
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
In summary the descriptive statistics of the CRSP sample shows that (1) The
relationship between franchise value and risk varies with industry conditions
although it is generally negative during 10-year sample period (2) Two sub periods
1995-1996 and 2000-2002 need special attention because these periods are through
the turning points of the underwriting cycle and the franchise-value vs risk
relationship is substantially different between these two stages indicating an influence
of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively
related
The NAIC Sample
The NAIC sample contains in total 14429 firms for period 1995-200322 In this
sample only stock and mutual companies are included for the purpose of comparing
between them The firms with other types of ownership structure are dropped
Table 46 gives the summary statistics of the industry-level variables over year
used for the NAIC sample As we explained before since different lines may be
subject to their own market competition and the underwriting cycle we conduct a
by-line research for the NAIC sample and fortunately the information contained by
NAIC database allows this work To visualize the changing trend of the underwriting
cycle and competition measures Figure 45 -47 presents the graphs of combined ratio
Herfindahl index of market concentration and the industry weighted average
X-efficiency over years
22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003
35
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Table 46 Industry variables by year (the NAIC sample)
Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003
Combined ratio ()
Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324
Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910
Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937
General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017
Herfindahl Index ()
Auto personal liability 699 698 673 640 641 627 642 657 661
Homeowner 855 846 830 833 855 844 856 877 867
Commercial multiple peril 145 180 168 214 221 200 199 215 219
General liability 429 480 535 465 357 434 515 653 671
Cost efficiency (weighted mean)
Auto personal liability 045 046 041 046 047 048 047 051 057
Homeowner 043 038 050 044 043 045 044 043 050
Commercial multiple peril 044 045 044 059 051 048 051 049 049
General liability 026 031 031 032 035 023 027 029 025
Figure 45 shows that auto personal liability homeowner and commercial multiple
perils have similar underwriting pattern with tough at year 1997 and peak point at
2001 General liability line undergoes a longer and deeper concave through 1996 to
2000 and then rise to the peak point 2002 This is consistent to the statement that
long-tail lines are subject to a longer cycle than short-tail lines due to the greater
uncertainty involved in the claim estimation and payment (Danzon et al 2004)
In Figure 46 we see that homeowner insurance market is the most concentrated
market among the four lines and commercial multiple peril market is the least
concentrated Itrsquos noticed that the market concentration of general liability line
undergoes quite a lot fluctuation over time compared to other lines
36
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Figure 47 displays the cost efficiency of the four lines General liability stands out
as the least efficient line Commercial multiple peril line demonstrates highest
efficiency combined with its low concentration indicating the most competitive line
among the four The auto personal liability and homeowner insurance market are
shown to be more efficient than general liability market although less concentrated
than general liability Figure 46 and Figure 47 show that a less concentrated market
is not necessarily a more efficient or competitive market For this reason we used
both concentration and efficiency to measure degree of competition
Figure 45 Combined ratio by lines
50
70
90
110
130
150
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liability
Homeowner
Commercial multiple peril
General liability
Figure 46 HHI () by lines
0
2
4
6
8
10
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
37
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Figure 47 Cost efficiency by lines
00
02
04
06
08
1995 1996 1997 1998 1999 2000 2001 2002 2003
Auto personal liabilityHomeowner Commercial multiple perilGeneral liability
Table 47 provides the summary statistics of the firm-level variables in the NAIC
sample
Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)
Variable Mean Std Dev Minimum Maximum
RBC 301 059 074 893
Rank_RBC 056 056 000 1
Leverage 246 013 -245 626
Rate 1231 185 100 1500
Rank_rate 040 027 000 094
Size 448 176 -494 1129
Bus_Div 123 3960 007 10000
Mutual 021 041 0 1
Group 076 043 0 1
Table 48 gives the correlations between each pair of firm-level variables The
alternative risk measures Rank_RBC and Leverage are positively correlated The
measure of franchise value and Rank_rate are negatively correlated with risk
measures In addition both firm rating and risk increase in firm size
38
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Table 48 Correlation of variables (the NAIC sample)
Rank_RBC Leverage Rank_rate Size
Rank_RBC 1 016 -012 031
lt0001 lt0001 lt0001
Leverage 1 -004 009
lt0001 lt0001
Rank_rate 1 042
lt0001
Size 1
Table 49 provides the correlations of ratings and risk measures over years With
sufficiently large sample size most of the correlations are shown significant
Although all the correlations are negative the value of correlations changes over time
Particularly we see that the negative relationship between leverage and ratings
become less significant and even insignificant in year 2000 and 2001 which is similar
to the descriptive statistics of the CRSP sample
Table 49 Correlations between risk and franchise value over years (the NAIC sample)
YEAR Leverage Rank_rate Rank_RBC Rank_rate
Corr p-value Corr p-value
1995 -008 00024 -027 00000
1996 -012 00000 -023 00000
1997 -010 00001 -023 00000
1998 -004 00662 -018 00000
1999 -006 00289 -016 00000
2000 -005 00347 -011 00007
2001 -004 01377 -011 00007
2002 -007 00032 -019 00000
2003 -003 01679 -019 00002
39
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
In summary the descriptive statistics of NAIC sample shows that (1) General
liability insurance market shows different competition and underwriting cycle pattern
than the other three lines (2) The relationship between franchise value measures and
risk measures is generally negative but both the degree of correlation and significance
vary over time Particularly the relationship turns to less significant around year 2000
In the next section the regression results for the model with more control
variables will be presented to analysis how franchise value competition and the
underwriting cycle affect firm risk-taking simultaneously
5 Regression Results
This section presents the regression results for the CRSP sample and the NAIC
sample respectively Section 51 reports the results of the CRSP sample Section 52
presents the results of NAIC sample A summary and discussion of the results for both
the CRSP and the NAIC samples is provided in Section 53
51 Regression Results for the CRSP Sample
Table 511 presents the regression results of Model 1 with four alternative
dependent variables for the CRSP sample To interpret the results we fit the
parameters into the Model 1 For example when the dependent variable is Leverage
Model 1 is fitted as follows
Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control
variables)it + eit (51)
We see that the slope of Q is composite of a negative intercept -284 and a
positive effect of competition 136 COMPt Note that the value of COMP ranges from
247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It
can be interpreted that for publicly-traded stock insurers franchise value and leverage
are generally negatively correlated but this relationship is weaken as competition
increases
Rearranging (41) gives the expression to easily see the effect of competition
40
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control
variables)it + eit (52)
We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive
and increases in Q indicating a stronger positive relationship between competition
and leverage for a firm high-franchise-value firm These results are significant after
control of firm size stock index and interest rate
When the dependent variable becomes Return_Std 1VaR or 5VaR we also
find a positive interaction term of QCOMP but with low significance
Hypothesis 2 is tested by Model 2 the results of which are displayed in Table
512 In Model 2 the effect of franchise value and competition is made to condition
on underwriting cycle Before go into interpreting Model 2 note that in Table 512
the effect of Q COMP and QCOMP become insignificant after controlling with
underwriting cycle indicating an ambiguous interaction effect between underwriting
cycle franchise value and competition In both Table 511 and Table 512 we see
that firm risk is significantly influenced by stock index and interest rate
41
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486
Table 512 Regression Results of Model 2 (The CRSP Sample N=984)Dependent variable
= LeverageDependent variable
=Return_StdDependent variable
= 1Var Dependent variable
= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446
42
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
In summary the empirical results of the CRSP sample provide strong support to
Hypothesis 1 which positing that firm risk is jointly determined by franchise value
and competition but show little evidence for Hypothesis 2 Particularly for the
publicly-traded stock insurers firms with higher franchise value tend to have higher
leverage and stock risk especially when competition increases In addition we find
the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but
leverage increases in firm size
52 Regression Results for the NAIC Sample
As explained previously in Section 42 for the NAIC sample we conduct a
by-line analysis to account for the substantial difference between various lines
Particularly we examine four lines auto personal liability insurance homeowner
insurance commercial multiple perils insurance and general liability insurance
Section 521 to Section 524 presents regression results for each of the four lines in
order A comparison of the results across lines is provided in Section 525
521 Auto Personal Liability Insurance
The regression results of Model 1 for auto personal liability insurance is
presented in Table 5211 and Table 5212 Competition is measured by
concentration in Table 5211 and by efficiency in Table 5212
43
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5212 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)
Table 5213 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Table 5214 Regression Results of Model 2 (NAIC Sample Auto personal liability N=3089)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
44
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
When dependent variable is Leverage Table 5211 shows similar results as in
the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is
generally negative and increases in COMP It indicates that the negative effect of
Rank_rate on Leverage decreases as market become less concentrated The slope for
COMP (032 +016 Rank_rate) is positive and increases in Rank_rate
Shown by Table 5212 when dependent variable is the rank of RBC ratio the
results are similar but with lower significance Table 5212 reports the results for
Model 1 when the competition is measured by Efficiency the industry weighted
average of X-efficiency Higher efficiency indicates higher degree of competition
Since the value of Efficiency for auto liability insurance is less than 05 the
overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is
negative especial when industry efficiency increases As for the influence of
efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that
firm with lower ratings tends to increase its leverage as the industry efficiency
improves These relationships are about the same when the dependent variable is
Rank_RBC
Note that the results regarding the effect of franchise value and competition on
firm risk are different between Table 5211 where competition is measured by
concentration and Table 5212 where competition is measured by efficiency This
leads to a question that which one concentration or efficiency is a better proxy of the
degree of competition But in either case the interaction term of franchise value and
competition is significant indicating a support to Hypothesis 1
The results of Model 2 for auto personal liability insurance are shown in Table
5213 and Table 5214 When the dependent variable is Leverage and competition is
measured by concentration as in Table 5213 Model 2 is fitted as follows
Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit
b2t = -096 + 018 COMPt + 015 UWCt +ζ2t
b3t = 046 + -005 UWCt + ζ 3t (52)
We see that the slope of Rank_rate increases in UWC indicating that when the
industry is less profitable (higher industry combined ratio) the relationship of
45
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
franchise value and leverage tends to be positive The negative interaction term (-005
UWCCOMP) indicates an increasing negative effect of competition on leverage as
industry becomes less profitable
When dependent variable is Rank_RBC the major explanatory variables become
insignificant suggesting an ambiguous influence of underwriting cycle on the
relationships between franchise value competition and risk
In Table 5214 the measure of competition is Efficiency instead of COMP
Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and
Rank_rate Efficiency reserves compared to those in Table 5213 The interaction
terms with UWC are significantly negative when the dependent variable is leverage
but are less significant when dependent variable becomes Rank_RBC which is as
same as in Table 5213
As for the effect of control variables firm risk increases in firm size Insurers
with more diversified business have a significant lower leverage Firms belong to a
group tend to have higher leverage but lower insolvency risk measured by RBC ratio
Mutual companies are shown to have lower leverage Firm risk is found sensitive to
the interest rate but not to stock index
In summary for the sample of auto personal liability insurance the interaction
effect between competition and franchise value is significant which is consistent to
the Hypothesis 1 The different measures of competition concentration and efficiency
lead to opposite sign of the interaction term of competition and franchise value The
risk-constraining effect of franchise value decreases in competition as if the degree of
competition is measured by concentration but increases in competition if degree of
competition is measured by efficiency The effect of franchise value and competition
on firm leverage is significantly influenced by industry combined ratio providing a
support to Hypothesis 2 When the market is less profitable (combined ratio is higher)
the risk-constraining effect of franchise value and the risk-increasing effect of
competition tends to be dampened However this result is not significant when the
risk is measured by the rank of RBC ratio
46
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
522 Homeowner Insurance
Homeowner insurance is a personal line with combined property and liability risk
Compared to auto personal liability homeowner insurance is a shorter tailed line with
less uncertainty of loss expenses Many mutual insurance companies focus on
homeowner insurance Particularly in our sample of homeowner insurance 62 of
the firms are mutual companies As we discussed before different ownership structure
has different implications for corporate management and risk decisions The test
results of the homeowner insurance sample largely exhibit risk-taking behavior of
mutual insurers
Table 5221-Table 5224 presents the test results for the sample of homeowner
insurance
Compared with the sample of auto personal liability the results of the homeowner
insurance sample has two major differences (1) we see a negative interaction term of
franchise value and competition which indicates that risk-constraining effect of
franchise value is magnified as competition increases (2) The signs of the major
variables are consistent between the two competition measures COMP and Efficiency
This suggests that industry efficiency improves as the market becomes less
concentrated and therefore either efficiency or concentration is a good measure of
competition for homeowner insurance market
With respect to the effect of underwriting cycle the interaction terms related with
UWC are found significant in both Table 5223 and Table 5224 The negative
interaction term of Rank_rate UWC and the positive interaction term CompUWC
indicates that when industry is less profitable the risk constraining effect of franchise
value and the risk-increasing effect of competition tend to be strengthened
47
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Table 5222 Regression Results of Model 1(NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266
Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Table 5224 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322
48
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
523 General Liability Insurance
General liability insurance (including product liability) is commercial liability
insurance long-tail insurance with great uncertainty and complexity Most companies
with high volume of business in general liability are organized in form of stock
ownership rather than mutual ownership Particularly in our sample 93 of these
firms are stock companies Hence the results regarding this sample provide
information about the risk-taking behavior of stock companies most of which are
non-publicly traded stock firms The test results for general liability insurance are
presented in Table 5231 ndash Table 5234
The results with respect to the interaction effect between franchise value and
competition shown by Table 5231 and Table 5232 are similar as in the sample of
auto personal liability insurance A positive Rank_rateCOMP and a negative
Rank_rateEfficiency are found
The effect of underwriting cycle is given by Table 5233 and Table 5234 In
both tables we see a negative interaction term of Rank_rate UWC which means the
slope of Rank_rate decreases in UWC and a positive interaction term CompUWC
indicates the slope of Comp decreases in UWC These results indicate that other
things being equal when industry is less profitable the risk constraining effect of
franchise value and the risk-increasing effect of competition tend to be strengthened
This is the same as what we observe in the sample of homeowner insurance but with
greater significance It indicates that for insurers focusing on general liability
49
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000
Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186
Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Table 5232 Regression Results of Model 1(NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Table 5234 Regression Results of Model 2 (NAIC Sample General Liability N=1531)
Dependent variable = Rank_RBC
50
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
insurance the effect of franchise value and competition on risk-taking is more
influenced by the industry profitability
524 Commercial Multiple Perils Insurance
Commercial multiple perils insurance is a commercial insurance with combined
property and liability risk Itrsquos a shorter tailed insurance compared to general liability
insurance The test results for the sample of commercial multiple perils insurance are
provided in Table 5241 ndash Table 5244
Table 5241 and Table 5242 present the test results for Model 1 Similar to the
sample of homeowner insurance a negative interaction term of franchise value and
competition is found
With regard to the effect of underwriting cycle the interaction term of
(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of
underwriting cycle on the relationship of franchise value and firm risk In Table
5244 the interaction term (EFFICENCYUWC) is found significantly negative
indicating a decreasing risk-increasing effect of competition as industry efficiency
increases
51
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950
Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5243 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)
Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Table 5242 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)
Dependent variable = Leverage
Dependent variable = Rank_RBC
Dependent variable = Leverage
Dependent variable = Rank_RBC
52
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
525 Summary of the By-line Analysis
As we are primarily interested in the interaction effect between franchise value
competition and underwriting cycle on insurer risk-taking the following Table 5251
gives a summary of the signs of the interaction terms for each of the selected lines
Since we have two measures of risk and two measures of competition the results are
reported for each combination of them
Table 5251 Sign of interaction terms by lines
Sample Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
Rank_rate
COMP
Rank_rate
UWC
COMP
UWC
(Leverage COMP) (Rank_RBC COMP)
Auto personal liability + + - - NS NS
Homeowner - - + - - +
General Liability + - + + - +
Commerical Multiple
Peril - NS + - NS NS
(Leverage Efficiency) (Rank_RBC Efficiency)
Auto personal liability - - - - NS NS
Homeowner - - + - - +
General Liability - - + - - +
Commerical Multiple
Peril - NS - - + -
NS = insignificant
When competition is measured by concentration the samples of auto personal
liability and general liability shows a positive interaction term of franchise value and
competition suggesting a decreasing risk-constraining effect of franchise value as
competition increases For the samples of homeowner and commercial multiple perils
the interaction term of franchise value and competition is negative indicating
increasing risk-constraining effect of franchise value as market become more
53
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
competitive When the competition is measured by efficiency all lines show a
negative interaction term of franchise value and competition
With regard to the underwriting cycle homeowner insurance and general
liability insurance are shown to be more significantly influenced by underwriting
cycle than the other two lines Risk-constraining effect of franchise value and
risk-increasing effect of competition tend to be strengthened in less profitable market
In summary the by-line test results for the NAIC sample show that the effect of
franchise value on firm risk is significantly conditional on the degree of competition
and vice versa providing strong support to Hypothesis One The specific relationship
regarding the interaction effect between franchise value and competition varies across
lines and different measures of competition We also find support for Hypothesis two
especially for the samples of homeowner insurance and general liability insurance
53 Discussion of Results
In previous sections the two research hypotheses are empirically tested
respectively for the CRSP Sample and each of the selected lines for the NAIC sample
This section provides a comparison between different samples and a discussion of the
relationship between ownership structure and insurer risk-taking
531 The CRSP Sample vs the NAIC Sample
The CRSP sample contains publicly-traded stock insurance companies most of
which are group companies The NAIC sample contains mutual and stock companies
at individual firm level The regression results for the CRSP sample are similar to the
results for the samples of general liability and auto personal liability which are largely
composed of non-publicly-traded stock companies in that a positive interaction term
of franchise value and competition is found when the risk is measured by leverage and
competition is measured by concentration This indicates a reduced risk-constraining
effect of franchise value as competition increases The results also suggest that the
effect of franchise value and competition on firm risk is less influenced by the
54
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
underwriting cycle for publicly-traded stock insurers than for non-publicly-traded
stock insurers
532 Stock Company vs Mutual Company
Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship
between the ownership structure and choice of business lines stock insurers tend to
involved in more complex lines and mutual insurer usually focus on less complex
lines This is due to that mutual companies have less control on managerial behavior
than stock companies Table 5321 shows percentages of the number of and premium
written by mutual firms in our sample for each line and confirms this claim The
sample of homeowner insurance mainly consists of small-size mutual companies
while the firms in the sample of general liability insurance are nearly all stock
companies
Table 5321 Mutual firms in the NAIC sample
Sample of number of premium written
Auto personal liability 17 43
Homeowner 62 11
General Liability 7 07
Commercial Multiple Peril 30 26
The comparison between the sample of homeowner insurance and the sample of
general liability insurance sheds light on the difference between mutual and stock
companies in terms of risk-taking behavior with a control of the endogenous variance
across business lines First in Table 5251 we see a negative interaction term of
franchise value and competition for homeowner insurance when competition is
measured by concentration but a positive interaction for general liability insurance It
indicates that mutual insurers have stronger incentive to protect their franchise value
by reducing risk than stock insurers when market becomes more competitive Second
comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with
55
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Table 5233 and Table 5234 (the sample of general liability insurance) we see that
although the signs of the interaction terms related with UWC are same but the sample
of general liability insurance show larger magnitude of the slope and higher
significance with the interaction terms of underwriting cycle This suggests that stock
insurers reacts more to the industry profitability than mutual insurers This is to some
extent consistent with the evidence reported by (Born et al 1995) who find that stock
insurers respond to the industry changes more efficiently than mutual insurers
6 Conclusions
This section consists of two parts Section 61 provides a summary of the main
findings of this research Section 62 contains a discussion of potential limitations
underlying this study and suggestions for future research
61 Summary of the Study
The purpose of this study is to examine the influence of franchise value and
competition on insurer risk-taking behavior Franchise value and competition provide
two important and contrary incentives of corporate risk-taking Franchise value is
believed to have a risk-constraining effect on firm risk because of the inability to
capture it in the case of bankruptcy On the other hand competition generally induces
firms to take more risk in order to maintain and even improve their position whether
high franchise value or not Prior empirical studies however show ambiguous
evidence regarding the effects of franchise value and competition on risk which
motivates the current study
The main contributions of this research can be summarized as follows First this
study examines the effect of franchise value and competition on risk-taking behavior
simultaneously Although franchise value provides an incentive for firms to reduce
risk firms with high franchise value are also motivated to protect franchise value
from reduction in competition and may consequently increase risk as an effort to
maintain their existing market position Therefore the risk-constraining effect of
56
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
franchise value should be examined in the context of market competition Second this
paper incorporates the influence of the underwriting cycle to examine if the effect of
franchise value and competition on firm risk-taking is influenced by this macro effect
Third we conduct a by-line analysis which not only allows a comparison across lines
but also better controls the endogenous variation in insurer risk-taking across lines
Lastly we employ both concentration and efficiency as a measure of competition
Different measures of competition provide more information about the role of
competition in insurer risk-taking
Two hypotheses are empirically tested The first hypothesis is that franchise value
and competition jointly affect insurer risk-taking The second hypothesis is that the
effect of franchise value and competition on insurer risk-taking is influenced by the
underwriting cycle
The empirical analysis provides strong support to the first hypothesis Our results
show that the risk-constraining effect of franchise value is conditional on the degree
of competition and vice versa When competition becomes intense firms with high
franchise value appear to increase risk in order to maintain their existing market
position We find evidence of this tendency for stock insurers but not for mutual
insurers When market becomes more competitive the risk-constraining effect of
franchise value tends to be strengthened for mutual insurers It indicates that as
competition increases mutual insurers have stronger incentive to protect their
franchise value by reducing risk than stock insurers
We also find support for the second hypothesis and for differences across lines
For homeowner insurance and general liability insurance the evidence shows that
when the market become less profitable both the risk-constraining effect of franchise
value and risk-increasing effect of competition tend to be stronger For auto personal
liability insurance and commercial multiple perils insurance the influence of the
underwriting cycle is ambiguous
57
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
62 Limitations and Further Research
There are several potential limitations in the study These limitations should be
kept in mind when interpreting our results they also lead to potential for future
research
First the measurement of franchise value still has room to improve especially for
non-publicly traded insurance companies It is particularly important for the insurance
industry to find a better measure of franchise value because the majority of insurance
companies are non-publicly traded firms Existing literature has made little effort in
this area
Second due to data limitation our 9-year study period contains only one soft and
one hard market period If this particular cycle was unusual the results will be
unrepresentative We generalize therefore with caution
Third our two measures of competition concentration and efficiency lead to
different results regarding the sign of interaction effect between franchise value and
competition Recent work (Fenn et al 2006) may offer some indication for the
reasons for the opposite results of these two measures yet further study is needed
58
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Appendix I Compute Cost efficiency Using DEA Method
This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis
(DEA) approach DEA is a linear programming method for assessing the efficiency
and productivity We use input-oriented distance function to estimate a firmrsquos cost
efficiency The input-oriented model of DEA to for cost efficiency can be defined as
follows
sum=
K
kkikix
xwMini 1
St sumge i kiiki xx λ kforall
sumge i niini yy λ nforall
0geiλ iforall
Where X denotes the input vector W denotes the input price vector and Y
denotes the output factor K is the number of inputs N is the number of output and i is
the number of firms The X-efficiency score is given by the ratio of frontier cost to
actual cost where X is the solution of the above minimizing
problem A score of 1 indicates that the firm is fully cost efficient
iT
iiT
i XWXW =φ
Defining inputs and outputs and their prices is an important step in efficiency
analysis There has been an extensive and unresolved debate in the literature about the
appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see
Cummins and Weiss 2000) The product provided by insurers to their policyholders
can best be viewed as the expected present value of the future claims that might be
paid on those policies Follow the method of Fenn et al (2006) we use net loss
incurred as a proxy for an insurance companyrsquos output
Two types of inputs are employed in our study capital and labor The input
quantity of capital is defined as the shareholderrsquos capital and reserves plus total
borrowing from outsiders reported in the balance sheet The input price for capital is
59
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
measured by the one-year interest rate of US treasury The input of labor
(wagesquantity of labor) is measured by the total expenses on the administration
agent and brokers claim service and employee wages and benefit SAS procedures
are employed to implement the model
60
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Reference
Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54
Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and
Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400
BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance
Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574
Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and
Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation
Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and
Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and
Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of
Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327
Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659
Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special
About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market
Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673
Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability
Insurance Industry Overview Journal of Financial Services Research 2112 5-14
61
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092
Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the
USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia
Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal
of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the
Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)
Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency
Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center
De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency
Costs An Analysis of Franchise Values in European Banking working paper available at SSRN
De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp
H Goldstein (Eds) Multilevel modelling of health statistics187-204
Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank
Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual
Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support
Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006
Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN
Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the
Social Sciences Cambridge University Press
62
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561
Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of
Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle
Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and
dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273
John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance
and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American
Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel
models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry
Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp
Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative
Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal
of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business
CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health
Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its
Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195
63
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355
Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure
Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718
Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and
Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN
64
- ABSTRACT
- 1 Introduction
- 11 Franchise value and firm risk-taking
- 12 Competition and firm risk-taking
- 13 Research purpose
- 2 Factors Affecting Insurer Risk-taking
- 21 Firm Risk
- 22 Franchise Value and Asset-substitution Moral Hazard
- 23 Competition and Insurer Risk-taking
- 24 Underwriting Cycle and Insurer Risk-taking
- 3 Methodology
- 31 Multilevel Analysis
- 32 Regression Models
- 4 Data and Variables
- 41 The CRSP sample and the NAIC sample
- 42 By-line Analysis
- 43 Measuring Firm Risk
- 44 Measuring Franchise Value
- 45 Measuring Competition
- 45 Measuring the Underwriting Cycle
- 46 Control Variables
- 47 Summary Statistics
- The CRSP Sample
- The NAIC Sample
- 5 Regression Results
- 51 Regression Results for the CRSP Sample
- 52 Regression Results for the NAIC Sample
- 521 Auto Personal Liability Insurance
- 522 Homeowner Insurance
- 523 General Liability Insurance
- 524 Commercial Multiple Perils Insurance
- 525 Summary of the By-line Analysis
- 53 Discussion of Results
- 531 The CRSP Sample vs the NAIC Sample
- 532 Stock Company vs Mutual Company
- 6 Conclusions
- 61 Summary of the Study
- 62 Limitations and Further Research
- Appendix I Compute Cost efficiency Using DEA Method
- Reference
- table511-12pdf
- crspmodel
- table522pdf
- home
top related