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Are Risk Premium Anomalies Caused by Ambiguity? Author(s):
Robert A. Olsen and George H. Troughton Source: Financial Analysts
Journal, Vol. 56, No. 2 (Mar. - Apr., 2000), pp. 24-31Published by:
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Are Risk Premium Anomalies Caused by Ambiguity?
Robert A. Olsen and George H. Troughton
Numerous studies have provided evidence of two equity return
anomalies in recent years. The "risk-premium puizzle" is the
anomaly that equity returns have been excessive relative to risk.
The "small-firm effect" is the anomaly that risk premiums on
small-cap stocks have been excessive relative to premiums on
large-cap stocks. We present unique evidence that both of these
anomalies may be caused by the presence of ambiguity. More
generally, we propose that the current conceptions of risk are too
limited to explain equity returns and, therefore, that the
distinction between risk and uncertainty developed by Frank Knight
approximately 80 years ago be revisited. As numerous other studies
hzave found, risk in the traditional sense is primarily a function
of the possibility of incurring a loss. Uncertainty (ambiguity) is
directly related to lack of information and lack of confidence in
estimatingfuture distributions of possible returns and the
possibility of incurring a loss.
.............~~~~~~~~~~~~~~~~~~~~~... ......
_T wo equity return anomalies have received extensive attention
in the last few years. For the first, called the "risk premium
puzzle" by Siegel and Thaler (1997), the finding is
that equity returns have been excessive relative to equity risk
in the last half century. For the second, called the "small-firm
effect," the finding is that risk-adjusted returns on small-cap
stocks have been overly large relative to those of large firms
(Banz 1981). Previous studies have suggested many possible causes
for these anomalies, such as myopic loss aversion, consumption
patterns, extreme loss aversion, differences in asset liquidity,
and risk misspecification.1
In contrast to this shotgun and, in some cases, ad hoc approach,
we suggest that these two anom- alies have a common,
straightforward explanation. This explanation requires amending the
descrip- tively incorrect conception of risk implicit in the
subjective expected utility model underpinning modern finance.
Specifically, we argue that what appear to be excessive risk
premiums are, in fact, ambiguity premiums.
Almost 80 years ago, Knight (1921) drew a sharp distinction
between risk and uncertainty. He hypothesized that the bearing of
uncertainty (now called "ambiguity") is the primary reason for an
entrepreneur's profit. In modem finance, however, risk, which is a
function of an assumed known distribution of future outcomes, has
taken center stage. Recent research has shown that linking risk to
variability of returns is descriptively incomplete. For example, it
is known that investors are loss averse and more concerned with
avoiding returns below some personal target than with variability
in return.2 Thus, the time appears ripe to reexamine the impact of
uncertainty on security market returns. A return to the past may be
necessary to make the future comprehensible.
Uncertainty/Ambiguity: A Brief History According to Knight, with
risk, the distribution of possible outcomes of an economic variable
is known; with uncertainty, the location and shape of the
distribution is open to question. Knight believed that uncertainty
was the normal state of affairs in business, and it was the primary
reason for the entrepreneur's profits.
Keynes (1936) elaborated on the distinction between risk and
uncertainty by suggesting that uncertainty is a function of the
degree of confidence
Robert A. Olsen is professor offinanceat California State
University at Chico and research associate at Decision Research.
George H. Troughton, CFA, is professor of finance at California
State University at Chico.
24 22000, Association for Investment Management and Research
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Are Risk Premium Anomalies Caused by Ambiguity?
or "weight" attached to a probability judgment. In addition, he
argued that uncertainty can be reduced to risk, as has occurred in
modern finance, only if the outcome-generating system operates in a
deterministic fashion as in a pure game of chance, such as
roulette.
Knight's approach to the distinction between risk and
uncertainty was refined by Savage (1954) and Ellsberg (1961).
Ellsberg appears to be respon- sible for coining the term
"ambiguous probabili- ties." Keynes' behavioral approach to risk
and uncertainty, which took into account the many faces of
"unknowing," has also been the object of further investigation. For
example, Shackle (1952) developed a theory of uncertainty in which
proba- bilities were replaced by "anticipations of potential
surprise." In 1957, Carter presented a model in which ranks and
ranges replaced probability point estimates; this approach
anticipated recent attempts to apply "fuzzy set theory" to the
concept of uncertainty (Lopes 1997). Tversky and Koehler (1994)
developed "support theory," in which peo- ple are shown to
associate probabilities with descriptions of events rather than the
events them- selves. Similarly, Pennington and Hastie (1993) showed
that people use stories to construct a "chain of reason" for a
forecasted event. Thus, Pennington and Hastie argued that
probabilities are a positive function of the consistency,
completeness, and coherence of a story rather than the probability
of the event itself.
Recent nontraditional subjective expected util- ity (SEU)
theories have incorporated uncertainty/ ambiguity in utility models
through nonadditive probabilities or the direct placement of
ambiguity in personal utility functions (Camerer and Weber 1992).
However, consistent with the traditional SEU model, these newer
models do not view ambi- guity from a motivational or cognitive
point of view; they view it as merely a reaction to the man- ner in
which decision makers experience quantity (diminishing marginal
utility).
In contrast to these economically based, psy- chophysical
approaches, psychologists have tested theories that focus on
behavioral reasons for feel- ings of ambiguity and ambiguity
aversion. These theories identify factors, such as feelings of
compe- tence, control, and personal responsibility, and the use of
heuristics, such as anchorinf and adjust- ment, as determinants of
ambiguity.
In summary, support of the traditional SEU model has become
unjustifiable. The model cava- lierly dismisses ambiguity through
the normative ploy of arguing that ambiguity is meaningless because
all probabilities must be subjectively known, if only to oneself,
or through the reduction-
ist strategy of second-order probabilities (i.e., prob-
abilities of probabilities). To the contrary, the following
statements summarize the known impact of ambiguity on decision
making: * Ambiguity influences selection. * In general, decision
makers are ambiguity
averse. * Ambiguity causes more weight to be placed on
negative information. * Buyers pay lower prices for, and
insurers
require higher premiums on, objects or hazards subject to
greater difficulty in estimation of value or probability of
outcome.
* Risk aversion and ambiguity aversion do not appear to be
highly correlated.4
Data and Method Our data are from questionnaires distributed to
professional money managers at two educa- tion-oriented
professional meetings (N = 209) and a mail survey (N = 105).
Approximately 68 percent of the respondents were holders of the
Chartered Financial AnalystTM (CFA?) designation, and their average
length of work experience was 15 years, with 90 percent having 6 or
more years of experi- ence. Some 84 percent of the respondents
listed their primary duties as institutional analyst, strate- gist,
or portfolio manager; 16 percent listed their occupations as
investment counselor. In general, the respondents were well-trained
and experienced money managers.
All questionnaires were pretested and struc- tured to avoid
response bias. Respondents were allowed to remain anonymous.
The mail survey sample was obtained from a randomly selected
group of CFA charterholders. The mail survey response rate was 26
percent, which is typical for this type of survey. A call to 10
percent of the questionnaire recipients (N = 40) did not suggest
any significant sources of nonresponse bias.
Responses were not significantly different between the mail and
the meeting respondents, so we pooled the data on tests related to
the hypothe- ses.
Professional Perceptions of Risk and Ambiguity Extensive
cross-disciplinary and cross-cultural studies by Slovic (1987) and
others (for example, Goszczynska and Tadeusz 1991) that used the
psy- chometric paradigm suggest that professional as well as novice
decision makers focus on two "uncertainty related" but multifaceted
dimen-
March/April 2000 25
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Financial Analysts Journal
Table 1. Importance of Risk-Related Attributes (N= 169)
Attribute Mean Rating 1. The chance of incurring a large loss
2.0 2. Uncertainty about the true distribution of possible future
returns 2.2 3. The chance of earning less than the target 2.8 4.
Variability in the asset's return as measured numerically by
standard deviation, beta, etc. 3.5 5. The chance of obtaining very
large gains relative to what was expected 4.7
Note: A rating of 1 = extremely important; a rating of 5 = not
important. Differences between means signifi- cant at the 1 percent
level for Attributes 3, 4, and 5.
sions-downside risk (or risk of loss) and ambigu- ity (or
unknowing/lack of knowledge). Downside risk usually refers to the
risk of not meeting a target or aspiration level. Olsen's 1997
studies of invest- ment professionals and experienced investors
showed that downside risk is positively related to required
returns. A large-scale study of investors commissioned by the U.S.
SEC also found that downside risk is the most important
risk-related attribute to mutual fund investors (Investment Company
Institute 1996). Table 1 presents our find- ings on professional
investors' feelings about downside risk and, for the first time,
information about the importance of ambiguity/uncertainty in
professional judgments about riskiness.
The data in Table 1 came from the responses to a question that
asked respondents to rate, on a Likert-type scale from 1 (extremely
important) to 5 (not at all important), the investment importance
of a preselected set of risk-related attributes. The attributes
were selected from risk descriptors prominent in the investment
literature.
In congruence with previous studies, we found that these
professional investors rated downside risk, as represented by the
chance of incurring a large loss or failure to meet a target, as a
dominant dimension of risk. Consistent with the developing
ambiguity literature, we also found, however, that these
professional investors rated uncertainty
about the true distribution of possible future returns as a
close second in importance. Variability of return, as measured by
standard deviation or beta, received ratings of only slightly to
moderately important. The chance of earning a large gain was
considered to be unimportant. The low weight given to variability
of return and upside potential as risk factors is consistent with
the results of pre- vious studies by Olsen.
Table 2 presents the results of our attempt to identify the
separate effects of risk and ambiguity by asking respondents to
rank, on a seven-point Likert scale, 20 actual stocks as to level
of perceived risk. Some participants ranked the stocks without
knowing the company names; a second group ranked them with the
company names provided. Participants were to use the values we
provided of the stocks' standard deviations of returns, betas,
Value Line safety ranks,5 and an Index of Analyst Disagreement
(IAD), which we computed. With the exception of the IAD data, we
took the stock values provided by Value Line. The IAD was com-
puted by ranking stocks on a scale of 1 to 5 by their coefficient
of variation of forecasted earnings based on data from I/B/E/S
International. The number 1 indicated the least disagreement among
the ana- lysts; 5 indicated the most disagreement. Respon- dents
were told that the IAD should be seen as a
Table 2. Relationship between Risk Attributes and Perceived
Risk: Partial Correlation Coefficients
No Company Names With Company Names Risk Attribute (N = 210) (N
= 230) Safety rating 0.32 0.36 Index of Analyst Disagreement 0.29
0.31 Beta 0.24 0.27 Standard deviation 0.05 0.23
R2 (all attributes) 0.54 0.70 Note: All coefficents significant
at the 1 percent level except the 0.05 coefficient for stan- dard
deviation in the first column.
26 ?2000, Association for Investment Management and Research
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Are Risk Premium Anomalies Caused by Ambiguity?
Exhibit 1. Attitudes toward Information for Decision Making (N=
209)
Question 1 I would treat two securities with equivalent
quantitative risk measures as equally risky.
Agree: 33% Disagree: 67%
Question 2 The ability to construct a coherent and complete
"story" with the facts of a situation is one of the most important
factors when making projections or recommendations.
Agree: 88% Disagree: 12%
proxy for the degree to which analysts disagree among themselves
about the future behavior of the stock. Because of this
disagreement among infor- mation sources, the IAD is a measure of
ambiguity or uncertainty.
The magnitude of the partial correlation coef- ficients in
Column 1 in Table 2, which provides responses when the company
names were not given, shows that downside risk, as measured by the
safety rank, was the most important dimension of perceived risk.6
The IAD was a close second in importance. Standard deviation was
seen as insig- nificant. As will be discussed, the insignificance
of standard deviation is probably a result of respon- dents'
difficulty in evaluating this measure of risk when a frame of
reference, such as a company name or industry, was not present.
Column 2 of Table 2 presents partial correlation coefficients
for risk attributes for the same compa- nies as Column 1, but in
this case, respondents were told the names of the companies. Note
that the relative rankings of the attribute coefficients stayed
about the same but all of them increased in absolute value, as did
the R2 for the equation as a whole. With the exception of the
ambiguity variable that we added to our study, the results are
similar to those reported by Farrelly and Reichenstein (1984).
Using named real companies and professional port- folio managers,
they found downside risk, as mea- sured by the Value Line safety
rank, to be the dominant measure of perceived risk. The authors
included I/B/E/S earnings predictability indexes in their model. If
one makes the not unrealistic assumption that measures of earnings
predictabil- ity can be seen as ambiguity measures, Farrelly and
Reichenstein's results confirm those of Table 2. That is, Farrelly
and Reichenstein found earnings pre- dictability indexes to be
second, and sometimes first, in importance as an attribute of
perceived risk.
The most notable change from Column 1 to Column 2 in Table 2 is
the large increase in the partial correlation coefficient for
standard devia- tion. A likely reason for the increased
correlations when the names were given is that identification of
the company helped the respondents "frame" the
information and interpret the meaning of the quan- titative risk
and ambiguity measures.
Two pieces of evidence support this hypothe- sis. First, the
partial correlation coefficients for beta, the safety index, and
the IAD increased much less when company names were revealed than
did the coefficient for standard deviation, as would be expected
because the former measures are already relative measures of risk
and, therefore, already framed to some degree. The second piece of
evi- dence is provided in Exhibit 1, which reports the responses to
two questions relevant to the hypoth- esis. Exhibit 1 shows that 67
percent of the respon- dents would not treat stocks with equivalent
quantitative risk measures as equally risky. In addi- tion, 88
percent of the respondents said that it is important to be able to
construct a complete story to make projections and recommendations.
These responses indicate that analysts define risk and ambiguity
much more broadly than the numbers alone do.
These findings are consistent with a recent SEC study of mutual
fund investors (Investment Com- pany Institute), which found that
only 26 percent of recent mutual fund purchasers used any quanti-
tative risk measures at all and that approximately 52 percent of
long-term investors preferred narra- tive-based information to
quantitative measures of risk.
In a third exercise, respondents were asked to rate asset
classes by level of perceived risk (see Appendix A for the exact
wording of the questions and the asset classes). The risk and
ambiguity attributes they were to use can be summarized as follows:
"large loss" and "below target return" as measures of risk;
"ability to predict risk" and "familiarity with the investment" as
measures of ambiguity. These measures of ambiguity were intended to
reflect the completeness of information about each asset class.
Table 3 presents the results.
All of the partial correlation coefficients in Table 3 are
significant, as is the relatively large R2. Consistent with the
results in Table 1 and empirical evidence from a prior study of
professional inves- tors (Olsen 1997a, 1997b), we found risk to be
most
March/April 2000 27
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Financial Analysts Journal
Table 3. Relationship between Risk Attributes and Perceived Risk
of Asset Types (N = 610)
Attribute Partial Correlation Very large loss 0.58 Ability to
estimate risk 0.46 Familiarity 0.23 Below-target returns 0.20
R2 (all attributes) 0.73 Note: All coefficients significant at
the 1 percent level.
strongly related to the possibility of realizing a large loss.
Consistent with Knight's conception of uncertainty, ambiguity was
highly associated with the inability to estimate risk (that is,
identify with confidence the distributions of possible future
returns).
Ambiguity and the Small-Firm Effect The small-firm effect is the
finding that observed risk-adjusted returns on small-cap stocks
have been overly large relative to those of larger and more
well-known companies. Current financial models judge risk-adjusted
returns by reference to a mea- sure of risk based on an assumed
known prospec- tive distribution of returns. However, as Chan and
Chen (1991) noted, small firms are characterized by more marginal
efficiency and weaker competitive positions than large firms, which
makes a quanti- tative estimate of their future distribution of
returns very difficult. Also, the confidence with which one can
estimate those returns is much lower. Empirical studies by Foster,
Olsen, and Shevlin (1984), Bernard and Thomas (1990), and Bernard
(1993) presented evidence that abnormal returns after earnings
announcements are signifi-
cantly greater for small firms than for large firms. Therefore,
a reasonable supposition is that ambigu- ity about future return
distributions, and thus ambiguity premiums, might account, in part,
for the anomalously large observed risk premiums on small-firm
stock. Exhibit 2 presents evidence sup- porting this
hypothesis.
Responses to the first and second questions reproduced in
Exhibit 2 indicate that professional investors find estimating
stock return distributions for small firms more difficult than for
large firms and generally feel less confident about their predic-
tions when investing in small-cap stocks. Responses to the third
and fourth questions shown suggest that, in general, when
predictability declines and ambiguity rises, reliance on formal
quantitative metrics declines. In particular, 64 per- cent said
that judgment, as opposed to quantitative analysis, becomes more
important as complexity increases, and 89 percent of respondents
agreed that quantitative analysis is of little use in evaluat- ing
volatile companies. Thus, in the case of small, little-known
companies, traditional quantitative measures of risk, such as
standard deviation and beta, may be incomplete predictors of
risk-adjusted returns and may need to be augmented by mea- sures of
ambiguity.
Conclusions and Implications Our findings suggest that, like
other professional decision makers, professional investors are
ambigu- ity averse. Thus, observed market returns should reflect
ambiguity premiums as well as risk premi- ums. Current equilibrium
models, such as the cap- ital asset pricing model, tend to
underestimate required returns because they do not contain any
Exhibit 2. Ambiguity, Confidence, and Company Size (N= 209)
Question 1 Estimates of future stock return distributions are
more unreliable for small than large firms. Agree: 84% Disagree:
16%
Question 2 Greater ambiguity (uncertainty about probability
estimates) tends to make me less confident when investing in small
versus large firm stocks.
Agree: 78% Disagree: 28%
Question 3 As a forecasting/recommendation task becomes more
complex and difficult, I tend to rely more on judgment and less on
formal, quantitative analysis.
Agree: 64% Disagree: 36%
Question 4 Quantitative valuation models are less useful in
analyzing securities of new or more volatile companies. Agree: 89%
Disagree:11%
28 ?2000, Association for Investment Management and Research
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Are Risk Premium Anomalies Caused by Ambiguity?
provision for ambiguity. Moreover, understatement of returns may
be especially pronounced for assets whose return potentials are
most ambiguous and difficult to quantify. We have offered some
tentative survey evidence for this hypothesis as it relates to
small-cap stocks.
The presence and pricing of ambiguity may account, in part, for
two other risk-related phenom- ena. First, most initial public
offerings (IPOs) are sold at relatively large discounts. Studies by
Beatty and Ruthen (1986), Muscarella and Vetsuypens (1989), and
Clarkson and Merkley (1994) showed that ex ante uncertainty is
positively related to the size of IPO discounts. Thus, the large
discounts may be partly caused by the high degree of ambi- guity
surrounding the future performance of new stocks. Second, Poterba
and Summers (1995) and Miller (1978) noted that required returns on
large, nonroutine, capital-budgeting expenditures tend to be set
high relative to costs of capital based on existing financial
models. They suggested that the excess required return may be a
result of the fact that managers tend not to evaluate projects in a
portfolio context. Another possibility, however, is that the excess
required return is a result of the
ambiguity associated with forecasting the future of large,
nonroutine capital projects.
Appendix A. Asset-Class Questions Survey respondents were asked
to rate 10 asset classes on a seven-point scale along the following
dimensions: * Overall, how risky is each of the following
investments? * How likely is it that this asset could generate
a
very large loss? * How likely is it that each of the
following
investments will earn a return below what you expect (your
target)?
* How familiar are you with the risks and returns of each of the
following investments?
* To what extent do you feel it is possible to accurately
estimate the future risk (distribution of returns) for each of the
following invest- ments?
The 10 asset classes were insured savings accounts, long-term
U.S. T-bonds, long-term high-grade cor- porate bonds, junk bonds,
blue chip stocks, OTC stocks, shares in real estate investment
trusts, stock options, residential real estate, and gold
bullion.
Notes 1. For examples, see Fama and French (1993, 1996);
Gneezy
(1997); Berk (1997); Bemartzi and Thaler (1995); Jensen and
Johnson (1997, 1998); Schwert (1983); Lakonishok and Sha- piro
(1986); Barber and Lyon (1998).
2. See Shapira (1995); Tversky and Kahneman (1992); Harlow and
Rao (1989); Olsen (1997a, 1997b); Laughhunn and Payne (1980); Lopes
(1997).
3. Einhom and Hogarth (1985, 1986); Heath and Tversky (1991);
Jungerman (1997); Huber (1995); Sarin and Weber (1992); Tversky
(1997).
4. See Weber and Millimon (1997); Smidts (1997); Dyer and Sarin
(1982); Wakker and Fennema (1996); Ghosh and Ray (1997); Sarin and
Weber (1992); Muthukrishnan (1995); Kunreuther, Meszaros, Hogarth,
and Spranca (1995).
5. Value Line (1999) describes its safety rank as "a measure-
ment of potential risk associated with individual common stocks.
The safety rank is computed by averaging two other Value Line
indexes-the Price Stability Index and the Financial Strength
Rating."
6. Multicollinearity is not likely to be a major source of
diffi- culty when interpreting the correlation coefficients in
Table 2 because the actual correlations between the risk variables
were very low and stepwise regression did not reveal sig- nificant
instability in the variable coefficients. In addition, a test with
an artificially constructed set of securities, where (by design)
values of risk variables were made orthogonal, gave virtually
identical results to those shown in Table 2.
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Article Contentsp. 24p. 25p. 26p. 27p. 28p. 29p. 30p. 31
Issue Table of ContentsFinancial Analysts Journal, Vol. 56, No.
2 (Mar. - Apr., 2000), pp. 1-120Front Matter [pp. 1-15]Author
Digests [pp. 6+8-10+12-14]Behavioral FinanceInvestor Sentiment and
Stock Returns [pp. 16-23]
Market AnomoliesAre Risk Premium Anomalies Caused by Ambiguity?
[pp. 24-31]
Market StructureAn Empirical Study of Bond Market Transactions
[pp. 32-46]
Risk ManagementValue at Risk [pp. 47-67]
ValuationFranchise Labor [pp. 68-76]Finding Firm Value without a
Pro Forma Analysis [pp. 77-84]Symmetrical Information and Credit
Rationing: Graphical Demonstrations [pp. 85-95]Stocks versus Bonds:
Explaining the Equity Risk Premium [pp. 96-113]
Book ReviewsReview: untitled [p. 114]Review: untitled [pp.
115-116]Review: untitled [pp. 116-117]
Back Matter [pp. 118-120]