Loan Losses Provision

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Preliminary Draft. For Comments Only

BANK LOAN-LOSS PROVISIONING,

Methodology and Application

J. Dermine and C. Neto de Carvalho*

April 9 2004

* INSEAD (Fontainebleau) and Universidade Catolica Portuguesa (Lisbon),

respectively. The authors are grateful to Professor Santos Silva for his insights inthe econometrics of fractional responses, to M. Suominen for comments on a first

draft, to J. Cropper for editorial assistance, and to Banco Comercial Portugus(BCP) for access to internal credit data.


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BANK LOAN-LOSS PROVISIONING,

Methodology and Application

Abstract

A fair level of provisions on bad and doubtful loans is an essential input in mark-to-

market accounting, and in the calculation of bank capital and solvency. Fewacademic studies have analyzed the adequacy of loan-loss provisioning because, dueto the private nature of bank loan transactions, few micro data are readily available.Access to data on recovery over time on bad and doubtful bank loans allowsdeveloping and applying two methodologies to calculate a fair level of loan-loss

provisions. Empirical estimates are then compared to a regulatory provisioningschedule imposed by a central bank.


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Introduction

Fair provisioning on bad and doubtful loans is of great importance for bankregulators. If there has recently been intense discussion on the merits of Basel 2, the

revised capital accord that would much better capture the actual risks taken by banks

(Basel Committee, 2003), it is quite evident that this accord will not have much

relevance if the measurement of bank capital is not satisfactory. A key input in the

measurement of bank capital is the amount of loan-loss provisions1 on bad and

doubtful loans. Well-known cases of significant under-provisioning include the

French Credit Lyonnais in 1993, Thailand in 1997, Japan in late 1990s (Genay,

1998), and, more recently, China.

As bank loans are, by their economic nature, private, there is not much market-based

information to estimate their current value, so that loan-loss provisions must be

estimated. In several countries, central banks have provided a provisioning schedule

for non-performing loans that takes into account the number of days since the default

date and the quality of collateral support. A segment of the academic literature has

studied whether or not loan-loss provisioning is used to manage or smooth reported

earnings and capital, its impact on investors returns, and its contagious effects on

other banks. To the best of the authors knowledge, not much has been written on

normative methodologies that could be used to estimate a fair level of loan-loss

provisioning at a given point in time, and its dynamic evolution over time. The

purpose of this paper is to provide a methodology to calculate dynamic loan-loss

provisions. Having access to a unique set of micro data on losses on loans to small

and medium size firms over the period 1995-2000, the methodology can be illustrated

with real bank data. In terms of contribution to the academic literature, this is the first

paper to apply mortality analysis and multivariate statistics to calculate dynamic loan-

loss provisioning, and to compare a micro databased empirical estimate of

provisioning schedule to a regulatory schedule enforced by a central bank.

1 Note that European terminology is being used. Loan-loss provisions represent the expected losses

on a portfolio of impaired loans. They constitute a contra-account, which is deducted from the value ofgross loans in a balance sheet. Provisions are referred to as loan-loss allowance or loan-lossreserves in US bank accounts.


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The paper is structured as follows. The literature on bank loan-loss provisioning is

reviewed in Section 1 of the paper. In Section 2, the database on individual loan-

losses is presented. The mortality-based approach to analyzing fair provisioning on

bad and doubtful loans is discussed in Section 3. Empirical univariate estimates of

provisioning over time are presented in Section 4, and these estimates are compared to

those imposed by a central bank. Finally, a multivariate statistics approach to loan-

loss provisioning is developed in Section 5. Section 6 concludes the paper.

Section 1. Review of the Literature

The accounting and finance literatures have analyzed three main provisioning issues

related to private information held by banks on loans, one of the fundamental

characteristic which explains the economic role of banks (Diamond, 1984): the extent

of earnings and capital smoothing, the impact of reported provisions on a banks stock

returns, and the systemic impact on the banking industry of disclosure on loan

provisions by one bank.2

A series of papers have analyzed the extent of earnings and capital smoothing through

a pro-cyclical loan-loss provisioning, with high provisions in good times and lower

provisions in bad times. For instance, Laeven and Majnoni (2003) and Hasan and

Wall (2004) report empirical evidence throughout the world consistent with the

earnings smoothing hypothesis.3 It is argued that the Basel Accord cannot achieve a

level playing field if it does not address adequately the loan-loss provisioning

practices around the world. Consistent with the above analysis, Gunther and Moore

(2003) find that supervisory examinations in the US precipitated a significant numbers

of adverse revisions of financial statements during their sample period. Similar

studies, documenting managerial discretion in loan-loss provisioning, include Wahlen

(1994), Wetmore and Brick (1994), Beattie et al. (1995), Soares de Pinho (1996), Kim

and Kross (1998), and Ahmed, Takeda and Thomas (1999). It must be noted that none

of the above studies propose a methodology to calculate fair provisions on bad and

doubtful loans, but rather report evidence that the actual level of aggregate

2 See the survey on loan-loss accounting by Wall and Koch (2000).3 A theoretical argument for earnings smoothing can be found in Degeorge et al. (1999).


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provisioning is correlated with accounting income data.4

A second stream of the literature has analyzed the impact of reported provisions on

bank stock returns. Whalen (1994) finds that unexpected provisions have a positive

impact on stock returns. This, at first counter-intuitive, result is interpreted as a signal

that future earnings will be good, allowing the build-up of provisions by bank

managers. Musumeci and Sinkey (1990) report similar results in the context of

provisioning and the international debt crisis.

A third stream of the loan-loss reserve literature has analyzed the signalling impact of

loan-loss reserves announcements on the stock returns of the announcing bank and

that of other institutions (for instance, Grammatikos and Saunders, 1990, and Docking

et al., 1997). Again, this stream of research is related to aggregate loan-loss reserves

reported in financial statements. The purpose of the current study is quite different

from that of the above literature. It proposes a micro-based methodology to calculate

fair provisions on bad and doubtful loans.

Two approaches have been suggested to measure credit risk and provisions on a loan

portfolio (Crouhy et al., 2000): a mark-to-market mode and a default mode. In a

mark-to-market mode, the value of loans (both performing and non-performing) is

estimated, either with actual market prices (available for large loans in the USA, Allen

et al., 2003), or with an estimate of their fair value, which will integrate the

probability of default over time, of losses-given-default, and a risk-adjusted discount

rate. In the default-mode approach, provisions are estimated only for non-performing

loans. With the exception of cases with readily available market prices, one notices

that, in both the mark-to-market mode and the default-mode, one must estimate the

expected losses-given-default. This is the objective of the paper. It is an important

issue as, according to the above literature, bank managers use discretion in loan-loss

provisioning. Bergeret al. (1989 and 1991), in their critical review of market value

accounting, suggest that value adjustment for credit risk should be based on a loan-

loss reserve on nonperforming loans. According to regulators (Basel Committee,

1998, or Wall and Koch, 2000), these reserves should be prudent and conservative,

falling within an acceptable range of expected losses. The paper aims to provide a

methodology to calculate over time loan-loss provisions on bad and doubtful loans.

4 Related papers on bank earnings management include Barth et al. (1990) who document income

smoothing through the realization of capital gains and losses, Scholes et al. (1990) who analyze therealization of capital gains and losses in the context of tax planning, and Galai et al. (2003) whoanalyze, in a theoretical model, the timing of realized capital gains on real assets (such as buildings).


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Section 2. Bank Loan-losses, Database and Measurement Issues

The largest private bank in Portugal, Banco Comercial Portugus, provided the

database used in this study. It consists of financial credit given to 4,000 small and

medium size companies5 over the period June 1995 to December 2000. All these

companies have a turnover of more than 2.5 million. Table 1 (Panels A and B)

provides information on the number of defaults per year, and on the amount of debt

outstanding at the time of default. One observes that the series of 371 default cases is

distributed evenly over the six-year period, and that the distribution of debt

outstanding at the time of default is highly skewed towards the low end. Half of the

debt is less than 50,000.6 The available information in the database includes the

industry classification, the interest rate charged on the loan, the history of the loan

after a default has been identified, the type of collateral or guarantees, and the internal

rating attributed by the bank.7

In Table 1 (panel C), the various forms of guarantees, or collateral, are reported along

the classification used by the Bank for International Settlements (Basel Committee,

2003). These include:

Personal guarantee

Real estate collateral

Physical collateral (inventories)

Financial collateral (bank deposits, bonds or shares)

In 35.6% of the cases, there is no guarantee or collateral. Personal guarantees, which

are used in 58.2% of the cases, refers to written promises made by the guarantor

(often the owner or the firms director) that allows the bank to collect the debt against

5 The data gathered for this study did not include any reference to the identity of the clients or any otherinformation which, according to Portuguese banking law, cannot be disclosed. The data set concernsSME loans, mostly from the region of Lisbon.6 This sample includes loans of much smaller size than those used in the reported US bank studies. Theface value of loans was higher than US$ 100 million in Altman and Suggitt (2000), and the averagecommercial and industrial loan was US$ 6,3 million in Asarnow and Edwards (1995).7

The database used in this study did not exist in the appropriate format. The bank provided help toidentify all these variables, and to recover the data located in various databases. The history of eachloan, after a default had occurred, has been carefully analyzed.


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the personal assets pledged by the guarantor. Collateral is used in 15.1 % of the

cases.8

Any empirical study of credit risk and loan provisioning raises two measurement

issues. Which criterion should be used to define the time of the default event? Which

method should be used to measure the recovery rate on a defaulted transaction?

The criterion used for the classification of a loan in the default category is critical

for a study on provisions, as a different classification would lead to different results.

Three default definitions are used in the literature:

i) A loan is classified as doubtful as soon as full payment appears to be

questionable on the basis of the available information.9

ii) A loan is classified as in distress as soon as a payment (interest and/or

principal) has been missed.

iii) A loan is classified as default when a formal restructuring process or

bankruptcy procedure is started.

In this study, because of data availability, we adopt the second definition, that is, a

loan is classified as in default as soon as a payment is missed.10 For information, the

reporting to the Central Bank of Portugal takes place after thirty days, if the loan

remains unpaid or unrestructured.

The second methodological issue relates to the measurement of recovery on defaulted

loans, as provisions will attempt to measure the amount that will not be recovered.

There are two methodologies:

8 Jimenez and Saurina (2002) also observe, in the case of Spain, that a very large proportion of bankloans are not collaterized.9 Hurt and Felsovalyi (1998).10 For the sake of comparison, the definition of default adopted by the Basel Committee is as follows(Basel Committee, 2001, p 52): A default is considered to have occurred with regard to a a particularobligor when one or more of the following events has taken place:a) It is determined that the obligor is unlikely to pay its debt obligations (principal, interest, or fees) infull;

b) A credit loss event associated with any obligation of the obligor, such as a charge-off, specificprovision, or distressed restructuring involving the forgiveness or postponement of principal, interest or

fees;c) The obligor is past due more than 90 days on any credit obligation; ord) The obligor has filed for bankruptcy or similar protection from creditors.


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i) The price of the loan at the default date, defined most frequently as the trading price

one month after the default. This approach has been used in studies on recoveries on

corporate bond defaults.

ii) The discounted value of future cash flows recovered over time after the default

date.

As no market price data are readily available for defaulted bank loans in Portugal, the

second methodology -the present value of actual recovered cash flows- is the only

feasible alternative. In any case, this approach is preferable as it allows the study of

the actual recovery of cash flows over time, whereas the price of a loan after the

default date is only representative of the value of expected cash flows. Moreover, the

actual recovery approach avoids eventual problems of price biases created by a

lack of liquidity on the defaulted loan market. This approach was adopted, in studies

on recovery on bad and doubtful loans, by Asarnow and Edwards (1995), Carty and

Lieberman (1996), and Hurt and Felsovalyi (1998).

In order to measure the cash flows recovered after a default event, we tracked, each

month, the post-default credit balances. Capital recovery is a reduction in the total

balance. The total cash flow recovered is this capital recovery plus the interest on the

outstanding balance.

To estimate the present value of the cash flows recovered, one must choose a discount

rate. We follow Asarnow and Edwards (1995), Carey (1998), Hurt and Felsovalyi

(1998), and the Basel Committee (1999) who suggest using a contractual pre-default

interest rate on the loan to calculate the present value. This approach has the

advantage that, if a loan is fully repaid, the present value of actual cash flows

recovered will be equal to the outstanding balance at the default date. While the above

authors did not have access to the interest rate charged on individual loans and had to

rely on an approximation of credit-risk adjusted yield curve, data on interest rates

charged on the loans are available in this study.

If, at first, the tracking of cash flows after a default event would appear a relatively

simple (but time consuming) exercise, special cases did require some judgmental

adjustment. Two such cases are discussed hereafter.


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i) First, there are fifty-two cases of multiple defaults. This refers to situations

in which a company enters a default category, returns to performing

status at a later date after paying the loan fully, and then falls back into the

default category. A first option could have been to consider each default as

a separate event, but this might have biased the econometric analysis with

several defaults linked to the same borrower. In the econometric results

that will be reported, we have kept the first default cases.

ii) Second, in the case of formal loan restructuring, with the loan returning to

a performing status, we did not consider these cases as a 100%

recovery. Indeed, in many cases, these loans subsequently fell back into

the default category. The cash flows received on restructured loans were

carefully identified.11

Two approaches will be used to analyze loan-loss provisioning, a univariate mortality-

based approach, and a multivariate statistical analysis of the determinants of recovery.

Section 3. Loan-Loss Provisioning, a Mortality-based Approach

To calculate provisions, we shall, in a first step, analyze recovery on bad and doubtful

loans. Having access to the history of cash flows on these loans after default, we can

study the time distribution of recovery. With reference to studies by Altman (1989)

and Altman and Suggit (2000), we apply the mortality approach. It must be noted that

the mortality approach was applied to measure the percentage of bonds or loans that

defaulted n years after origination. The application of mortality to loan recovery rates

and provisions is, to the best of our knowledge, novel. It examines the percentage of a

bad and doubtful loan, which is recovered t months after the default date. This

methodology is appropriate because the population sample is changing over time. For

some default loans, those of June 1995, we have a long recovery history (66 months),

while for the recent 2000 loans in default, we have an incomplete history of

11 Note that this approach is more conservative than the one adopted by Hurt and Felsovalyi (1998)who considered a 100% recovery when the debt was reclassified to a performing status.


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recovery. The actuarial-based mortality approach, based on the Kaplan-Meier

estimator (Greene, 1993), adjusts for changes over time in the size of the original

sample.12

To define the concepts used to measure loan recovery rate and provisions, it is, for

expository reasons, useful to refer to a simple example. Consider a loan of 100 that

enters the default category in December 2000. We track the subsequent payments on

this loan, assuming, for expository convenience, that all payments take place at the

end of the year, with a final payment in December 2003. The interest rate is 10%.

Dec. 2000 Dec. 2001 Dec. 2002 Dec. 2003

Loan outstanding 100 110 66 44(before cash payment)

Cash payment 0 50 26 14

Loan balance 100 60 40 30(after cash payment)

Let us define theMarginal Recovery Rate at December 2001, MRR1, as the proportion

of the outstanding loan in December 2001 that is being paid, one period (in the

example, one year) after default:

MRR1 = Cash flow paid 1 / Loan balance 1

= 50/110 = (50 / 1.10) / 100 = 5/11

The marginal recovery rate can also be interpreted as the percentage repayment on the

loan outstanding, in present value terms.

Let us define thePercentage Unpaid Loan Balance after payment in December 2001,

PULB1, as the proportion of the December 2001 loan balance that remains to be paid

one period after default :

PULB1 = 1 MRR1 = 1 5/11 = 6 /11

12

The different approaches (cohort analysis used by Moodys, static pool employed by Standard andPoor, and mortality rate) to measure credit risk are discussed and contrasted in Caouette, Altman, and

Narayan (1998).


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Similarly, one can define theMarginal Recovery Rate at December 2002 =

MRR2 = Cash flow paid 2 / Loan 2

= 26/66

ThePercentage Unpaid Loan Balance after payment in December 2002, two periods

after default is equal to :

PULB 2 = 1 MRR2 = 1 26/66 = 40/66

And the Cumulative Recovery Rate in December 2002 for a loan defaulting in

December 2000, CRR0,2 , is defined as:

CRR0,2 = 1 (PULB1 x PULB2)

= 1 (6/11 x 40/66) = 1 240/726 = (1 40/121) = 81/121

= (81/1.12) /100 = 66.9%

Similarly, one can calculate aMarginal Recovery Rate, MRR3, aPercentage Unpaid

Loan Balance, PULB3, and a Cumulative Recovery Rate, CRR0,3, at December 2003

=

MRR3 = Cash flow paid 3 / Loan 3

= 14/44

PULB3 = 1 MRR3 = 1 14/44 = 30/44

CRR0,3 = (1 (PULB1 x PULB2 x PULB3)

= 1 (6/11 x 40/66 x 30/44) = 1 7,200 / 31,944 = 1 30/133.1

= 103.1/133.1 = (103.1/1.13) / 100 = 77.5%

Similar to Carey (1998), Asarnow and Edwards (1995), Carty and Lieberman (1996),

Hurt and Felsovalyi (1998), and La Porta et al. (2003), the Cumulative Recovery Rate

at time T on a loan balance outstanding at time 0, CRR0,T , represents the proportion

of the initial defaulted loan that has been repaid (in present value terms), T periods

after default. Note that these authors report only the total cumulative recovery rate

over a long (unidentified) period, whereas we, adopting the Altman mortality-based


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approach, report the extent of cumulative recovery over time. This information will

allow calculating dynamic provisions on the remaining loan balance, several months

after the default date.

The Loan-Loss Provision, LLP0, on a loan balance outstanding at the default date,

December 2000, is equal to:

LLP0 = 1 - CRR0,3 = 1 - 0.775 = 22.5%

Moving forward, one can define a Cumulative Recovery Rate,CRR1,3 , on a loan

balance outstanding at December 2001, and a dynamicLoan-Loss Provision, LLP1 ,on

a loan balance outstanding at December 2001. These are defined as :

CRR1,3 = (1 PULB2x PULB3) = 1 - 40/66 x 30/44 = 58.7%

LLP1 = 1 CRR1,3 = 41.3%

The Cumulative Recovery Rate, CRR2,3, and the dynamic Loan-Loss Provision,

LLP2, on a loan balance outstanding at December 2002 are defined as :

CRR2,3 = (1 PULB3) = 1 - 30/44 = 31.8%

LLP2 = 1 CRR2,3 = 68.2%

To generalize for an individual loan i in default, we define four concepts, t denoting

the number of periods after the initial default date 0:

MRRi,t = Marginal Recovery Rate in period t

= Cash flowi paid at the end of period t / Loani outstanding t

PULBi,t = Percentage Unpaid Loan Balance at the end of period t = 1 MLRRi,t

The Cumulative Recovery Rate evaluated from the default date 0 until infinity,

CRRi,0, , and the Loan Loss Provision, LLPi,0, are equal to:


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CRRi,0, = Cumulative Recovery Rate periods after the default = 1 ,1

i t

t

PULB

=

LLPi,0 = Loan-loss provisions = 1 CRRi, 0,

Note that for the sake of presentation, the loan-loss provision was calculated on a loan

balance outstanding at the default date, 0. In a more general dynamic provisions

setting, the provision can be calculated on a loan balance outstanding at any date n

after the default date. For instance, one can compute the cumulative recovery on loan

balances outstanding 4 or 13 months after the default date.

Having computed the cumulative recovery rate on individual loans, one can compute

an unweighted average cumulative recovery rate for the sample of loans. This is the

approach adopted in the losses-given-default literature. Alternatively, one can

compute a sample weighted average recovery rate that will take into account the size

of each loan. This is defined as follows:

SMRRt = Sample (weighted) Marginal Recovery Rate at time t

= ,1 1

m m

i t i t

i i

Cash flow received Loan outstanding = =

, , where i stands for each

of the m loan balances outstanding in the sample, t periods after default.

SPULBt = Sample (weighted) Percentage Unpaid Loan Balance at period t

= 1 SMLRRt

SCRR = Sample (weighted) Cumulative Recovery Rate, an infinite number of

periods after the default

=1

1 tt

SPULB

=

A comparison of the Sample (weighted) Cumulative Recovery Rate with the average

of recovery rates on individual loans will be indicative of a size effect.


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Section Four. Loan-Loss Provisioning, Empirical Evidence with aMortality-based Approach

The application of the mortality-based approach to calculate dynamic provisions is

followed by a comparison with the mandatory dynamic provisioning imposed by the

Central Bank of Portugal.

Dynamic Loan-Loss Provisioning, Empirical EvidenceThe sample marginal and cumulative recovery rates for the sample T periods after the

default date, SMRRT and SCRRT, respectively, are reproduced in Figures One and

Two. One observes, in Figure One, that most of the marginal recovery rates in excess

of 5 % occur in the first five months after the default. In Figure Two, one observes

that the cumulative recovery rate is almost completed after 48 months, and that the

weighted cumulative recovery rates are lower than the unweighted cumulative

recovery rates. For instance, the unweighted cumulative recovery rate after 48 months

is 70%, while the weighted recovery rate is 56.3 %. This is indicative of a size effect,

further analyzed and found statistically significant in Neto de Carvalho and Dermine

(2003). Cumulative recovery on large loans appears to be significantly lower.

It is also of interest to analyze the distribution of cumulative recovery rates across the

sample of loans. The distribution of cumulative recovery rates after 48 months is

reproduced in Figure Three. This figure shows a bi-modal distribution with many

observations with low recovery, and many with complete recovery. These results are

quite similar to those reported by Asarnow and Edwards (1995) for the US, and Hurt

and Felsovalyi (1998) for Latin America. Loan portfolio models which incorporate a

probability distribution for recovery rates should take into account this bi-modal

distribution.13

13Current commercial credit portfolio models do not incorporate the bi-modaldistribution. For instance, CreditRisk+, developed by Crdit Suisse FinancialProducts, assumes a fixed expected recovery rate within each band, whileCreditMetrics uses a beta distribution (Crouhy et al., 2000).


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Cumulative recovery on outstanding balances on bad and doubtful loans are reported

in Table 2. These dynamic cumulative recoveries are calculated on loan balances

outstanding n months after the default date, with n varying from 0, the time of

financial distress, to 37 months after the default date. Estimates of dynamic

recoveries will allow the calculation of dynamic provisioning on expected loan-losses.

One first observes, for the total sample, that the reported difference between

unweighted and weighted recoveries is significant at time zero, the time of default,

(72.6% vs. 63.8%, respectively), but less significant at later dates (for instance, 33%

vs 35.8%, 19 months after the default date). This is expected as, in Figure Two, the

difference between the weighted and the unweighted cumulative recovery rates does

not increase through time. Over time, the weighted (and unweighted) cumulative

recovery rates on the unpaid loan balance are decreasing monotonously over time,

55.7% (57.8%) in period 4, to 23.3% (17.1%) in period 37. More complete

information is obtained, in Table 2, by dividing the sample into three groups,

according to the absence of personal guarantee/collateral, the existence of personal

guarantee, or the existence of collateral support. As expected, the cumulative

recovery rates (unweighted, so as not to be affected by the size effect) is the highest

for the case of loans with collateral for every period, for instance 85.3% at time 0, the

default date. A counterintuitive and significant observation is that the (unweighted)

cumulative recovery rates on loans without any type of real or personal guarantee

dominates, in every period, the cumulative recovery rate on loans with personal

guarantees. For instance, at time 0, (unweighted) recoveries on loans without any type

of guarantee/collateral is 80.6%, vs.63.9% for recoveries on loans with personal

guarantee (or 47.0% vs. 20.8%, 19 months after the default date). A director of the

bank explained that this result is likely to be due to two factors. First, guarantee or

collateral support is not usually requested from reliable clients, so that the existence

of a guarantee is an indicator of greater risk. Second, some borrowers are able to

shift ownership of personal assets to other persons, so that, when the bank tries to

execute the debt, there is not much left. This empirical result, if confirmed in other

studies, implies that regulatory provisions should not penalize loans without personal

guarantee, as the absence of a guarantee might be justified by higher expected

recoveries.


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In Figures 4a and b, we show the dynamic cumulative recoveries on unpaid balance at

time 4 and 25. As expected, the weighed and unweighted curves are very similar,

confirming that the size effect is mostly at work in the early recoveries. The frequency

of cumulative recoveries on unpaid balance at times 4 and 25 are reported in

Figures 5a and b. These show again a bipolar distribution of cumulative recoveries on

outstanding balance at time 4, but that there are few cases of full recovery on

balances outstanding at time 25.

Loan-Loss Provisioning: Central Bank Mandatory Provisions vs. Mortality-based

Provisions

In Table 3, we report the provisions rules of the Bank of Portugal for bad and doubtful

loans for applications other than consumer credit or residence credit. The 1%

provisions rule for time 0 to 3 months after default reflects the central banks

policy of imposing a conservative general provisions of 1% on all outstanding bank

loans in Portugal. A first observation is that specific provisioning on bad and doubtful

loans starts 3 months after the default date, that is, two months after the loan is

reported to the Bank of Portugal. A second observation is that provisioning is

increasing through time with 100% provision required at month 13 for loans with no

personal guarantee/collateral, at month 19 for loans with personal guarantee, and at

month 31 for loans with collateral. A third observation is an implicit assumption,

according to which recoveries on loans without guarantee/collateral are the lowest at

all points in time. It is quite interesting to compare the regulatory provisioning

schedule of a central bank, from the one that could be inferred from the empirical

estimates of cumulative recoveries.

In Figures 6a,b,c, we report the provisioning schedule of the central bank several

months after the default date and the provisioning schedule implied by the estimates

reported in Table 2, for loans with no guarantee/collateral, loans with personal

guarantee, and loans with collateral support. A first observation is that the regulatory

practice of enforcing specific provisions three months after the default event does not

seem justified by the data. Provisioning should start at the time of the default event.

A second observation is that the provisioning on loans without guarantee/collateral is

excessively conservative. It calls for 100% provisioning 13 months after the default

date, when our data shows an expected (weighted) recovery of 66.7%. A third


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observation is that the provisioning on loans with personal guarantee is too

optimistic. It calls for provisioning of 50%, 13 months after the default date, when

the data shows an expected recovery of only 20.5%. It is only in the case of loans

with collateral support that the divergence between the estimated and the regulatory

schedule is minimal.

Section Five. Loan-Loss Provisioning, a Multivariate Analysis

In the previous section, univariate mortality-based estimates of cumulative recoveries

and provisions were provided. In this section, we attempt to estimate empirically the

determinants of the cumulative recovery rates and dynamic provisions. A discussion

of the choice of explanatory variables and the econometric specification is followed

by the empirical results.

Explanatory variables and econometric specification

Explanatory variables include the size of the loan, the type of guarantee/collateral

support, past cumulative collection, and the default year.14 The size of the loan is

included because some empirical studies and the sample univariate weighted and

unweighted average cumulative recovery data have pointed out the effect of the loan

size. Past cumulative collection is included on the assumption that a good level of

collection could indicate a genuine effort by the borrower to repay the loan fully. A

year dummy is included so as to have a better understanding of the volatility of the

recovery rate over time. In the case of Banco Comercial Portugus, it was indicated

by the bank that a reorganization of the workout unit could have an impact on

recoveries. Finally, it is of interest to know the impact of guarantee/collateral, as, if

statistically significant, this variable could be taken into account in calculating loan-

loss provisions on bad and doubtful loans.

14 As we had access to information on the banks internal rating on a subset of loans,we also attempted to test the impact of ratings with this subset of data. As the rating

explanatory variable was found not to be statistically significant, the results are notreported. Similarly, the fifteen industrial sectors variables were not significant.


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The size of loan excepted, the explanatory variables will be represented by dummy

variables. The dependent variable, the cumulative loan recovery rate, is a continuous

variable over the interval [0-1]. Due to the boundaries of the dependent variable, one

cannot use the ordinary least square (OLS) regression,

1 2 2( | ) . ... .k kE y x x x x = + + + = (1)

as it cannot guarantee that the predicted values from the model will lie in the bounded

interval (Greene, 1993). A common econometric technique is to use a transformation

G(y) that maps the [0-1] interval onto the whole real line [- , + ] (McCullagh and

Nelder, 1989). For instance, one can model the log-odds ratio transformation as a

linear function of explanatory variables. In other words, instead of having y as the

dependent variable, the model uses the following transformation of y:

log1

yy

y

and the regression becomes:

log1

yE x

yx

=

where x is a k*1 vector of explanatory variables, and is a k*1 vector of slope

coefficients. The drawback of the log-odds ratio transformation is that it is not defined

for the dependent variable, y, taking values of 0 or 1, so that an approximation must

be used. Since our data set includes a sizeable series of cases with extreme loan

recoveries of 0% or 100%, the log-odds transformation is not an attractive solution.

Instead, we follow Papke and Wooldridge (1996) who studied econometric methods

for fractional response variables in the context of employee participation rates in 401

(k) pension plans. A model is specifically developed to consider the fact that the

dependent variable, y, is bounded between 0 and 1, with positive probabilities at the

extremes.

Assuming a sequence of observations (xi, yi ; i=1,2,N), where 0y1 andNis the

sample size:


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18

1 2 2( | ) ( . ... . ) ( )i i k k iE y x G x x G x = + + + = (2)

where G(.) is a known function satisfying 0


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19

of provisioning. Second, the coefficient of collateral is positive at all time intervals,

although statistically significant at two horizons only, 4 and 7 months. Finally, and

most interestingly, is the sign of the past recovery variable. It is positive and

statistically significant at all horizons indicating that past recovery is a good indicator

of future recovery.

To assess further the magnitude of the impact of past recovery on fair loan-loss

provision, we use the estimated regression to simulate the level of fair provisions for

different levels of past recovery. These are reported in Table 5. If, for instance, one

considers the balance outstanding seven months after the default date on a loan with

no guarantee/collateral, one observes that the level of provisions should be 53.2%

when past recovery has been zero, but that this provisions falls to 16.5% in the case of

a past recovery of 50%. Although one would need additional empirical research to

confirm these results, it appears that, for this sample of loans, past recovery has a

significant impact on loan-loss recoveries and on the level of fair loan-loss provisions.

Section Six. Conclusions

A fair level of provisions on bad and doubtful debt is an essential part of capital

regulation and bank solvency. Micro data on recovery overtime on bad and doubtful

loans allows us to provide two methodologies to compute dynamic provisions. First a

univariate mortality-based approach allows us to compute provisions for three classes

of loans: no guarantee/collateral, personal guarantee only, and collateral with or

without guarantee. A multivariate approach facilitates analyzing more precisely the

determinants of loan recoveries and provisions over time. Three significant results are

as follows. First, bad and doubtful loans with no guarantee/collateral exhibit better

recoveries than loans with personal guarantee. This could be due to the fact that the

decision to lend without guarantee took into account the higher expected recovery

rates. Second, the past recovery history has a highly significant positive impact on

future recovery. Third, a comparison with the Bank of Portugal mandatory

provisioning rules indicates some conservatism in calling for 100% provision 31

months after the default date, when, in fact, significant amounts are still recovered

after that date. But, more stringent provisions could be enforced in the shorter run,


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20

before the 90-day- provisioning trigger date. Additional empirical studies are

needed to validate the empirical findings of the paper, but the two methodologies

presented in this paper provides a basis to compute fair loan-loss provisions on bad

and doubtful bank loans.


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21

Table One: Descriptive Statistics for the Sample of Doubtful Loans16

Panel A: Number of Defaults per yearNumber of cases

1995 651996 891997 591998 57

1999 472000 54

Total 371

Panel B: Debt Outstanding at the Time of Default (Euros)

Number ofobservations

Percentage

0


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22

Table 2: Mortality-based estimate of cumulative recoveries on loan balances outstanding n months af

Total sample No Collateral /

No Guarantee

Personal Guarantee only

Number of

months after

default (n)

Unweighted Weighted Unweighted Weighted Unweighted Weighted

0 72.6% 63.8 % 80.6% 80.0% 63.9% 45.9%

4 57.8% 55.7% 69.6% 75.3% 46.8% 33.4%

7 50.2% 47.7% 63.3% 70.8% 38.5% 27.0%

13 41.03% 42.1% 56.6% 66.7% 27.6% 20.5%

19 33.0% 35.8% 47.0% 59.4% 20.8% 13.6%

25 27.1% 32.2% 41.3% 56.7% 16.3% 11.6%

37 17.1% 23.3% 28.3% 43.2% 8.6% 6.9%

Note: These are cumulative recovery rates up to month 68, calculated on the loan balance outstanding n mont


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23

Table 3: Bank of Portugal Provisions Rules for Applications other than

Consumer Credit or Residence Credit

Risk Class Time period If the credit has no

guarantee/collateral

If the credit has

a personal

guarantee

If the credit

has a real

guarantee

Class I From 0 to 3 months 1% 1% 1%

Class II From more than 3

months to 6 months

25% 10% 10%

Class III From more than 6

months to 9 months

50% 25% 25%

Class IV From more than 9

months to 12 months

75% 25% 25%

Class V From more than 12

months to 15 months

100% 50% 50%

Class VI From more than 15

months to 18 months

100% 75% 50%

Class VII From more than 18

months to 24 months

100% 100% 75%

Class VIII From more than 24

months to 30 months

100% 100% 75%

Class IX From more than 30

months to 36 months

100% 100% 100%

Class X From more than 36

months to 48 months

100% 100% 100%

Class XI From more than 48

months to 60 months

100% 100% 100%

Class XII More than 60 months 100% 100% 100%

Source: Aviso de Banco de Portugal n 8/2003, Dirio da Repblica- I Srie-B, N 33,

8 February 2003.


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24

Table 4: Statistical estimate of cumulative recoveries on loan balances outstanding n months after defa

(The estimate of the parameter is followed by the p-value)

Number of Months after Default (n)

4 7 13 19

Constant 0.39

(0.115)

0.55

(0.049*)

0.28

(0.302)

0.04

(0.858)

Past Recovery 5.23

(0.000*)

2.88

(0.001*)

2.34

(0.00*)

1.88

(0.000*)

Loan Size 0.02

(0.911)

0.02

(0.962)

- 0.285

(0.604)

- 0.58

(0.176)

Year Dummy 0.10

(0.666)

-0.28

(0.226)

-0.22

(0.324)

-0.19

(0.416)

Personal Guarantee -0.47

(0.048*)

-0.67

(0.005*)

-0.81

(0.001*)

-0.73

(0.002*)

Collateral 1.19

(0.002*)

0.92

(0.038*)

0.805

(0.078)

0.61

(0.186)

R2 0.286 0.26 0.339 0.359

CHSQ 35.04

(0.000

*

)

28.74

(0.000

*

)

38.0

(0.000

*

)

32.9

(0.000

*

)Reset - 1.88

(0.05*)

-1.30

(0.191*)

-0.83

(0.404)

0.14

(0.883*)

Number of 125 112 96 85


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25

observations

*: Significant at the 5% level.

Note: The table presents the result of the log-log regression. The dependent variable is the cumulative recoveoutstanding at 4, 7, 13, 19 , 25, and 37 months after the default date. The explanatory variables include a coninitial loan already recovered, the loan size, a dummy for personal guarantee, and collateral. Because of datarecovery is calculated up to 48 months after the default date. This is unlikely to create a bias as Figure Two inachieved 48 months after the default date.


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26

Table 5: Multivariate-estimate of provisions vs. Central bank (CB) mandatory provisioning (in percent

Period No Guarantee Personal Guarantee

Level of past recovery Level of past recovery

CB 0% 20% 50% CB 0% 20% 50% CB

4 25 44.8 18.8 4.2 10 61.6 28.5 6.7 10

7 50 53.2 34.8 16.5 25 77.5 56.8 29.8 25

13 100 62.4 45.7 26.1 50 89.0 74.8 49.5 50

19 100 71.1 57.3 38.3 100 92.5 83.0 63.5 100

25 100 81.2 71.2 55.0 100 96.1 91.0 78.7 100

37 100 95.2 89.8 77.4 100 99.9 99.4 96.5 100

Note: The level of provisioning (provision = 1 cumulative future recovery) is estimated with the regr


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27

Figure One: Sample Unweighted Marginal Recovery Rate at time t+n

(SMRRt+n)

0%

5%

10%

15%

20%

25%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65

Time (number of months after default)

Note: This figure presents the marginal recovery n- months after default. The

mortality-based approach is used to calculate the marginal recoveries.

Figure Two: Sample Unweighted and Weighted Cumulative Recovery Rate

at time t+n (SCRRt+n) on Balances outstanding at time 0

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65

Time (number of months after default)

Weighted Unweighted

Notes: The figure presents the cumulative weighted and unweighted recovery

rates n- months after default. They have been calculated with the mortality-based

approach.


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28

Figure Three: Distribution of individual loan cumulative recovery rates on

balances outstanding at time 0.

0%

10%

20%

30%

40%

50%

60%

0%-5%

5%-10%

10%-15%

15%-20%

20%-25%

25%-30%

30%-35%

35%-40%

40%-45%

45%-50%

50%-55%

55%-60%

60%-65%

65%-70%

70%-75%

75%-80%

80%-85%

85%-90%

90%-95%

95%-100%

Recovery rates

Loans

frequency

0%

10%

20%

30%

40%

50%

60%

0%-5%

5%-10%

10%-15%

15%-20%

20%-25%

25%-30%

30%-35%

35%-40%

40%-45%

45%-50%

50%-55%

55%-60%

60%-65%

65%-70%

70%-75%

75%-80%

80%-85%

85%-90%

90%-95%

95%-100%

Recovery rates

Loans

frequency

Note : The figure presents the frequency of cumulative recovery on individual loans,

48 months after default.17

17

Due to data limitation (five years), the cumulative recovery is calculated up to 48 months afterdefault. This does not seem too restrictive as Figure Two indicates that most of the recovery is achieved48 months after default.


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29

Figure Foura Cumulative recoveries as a % of loan outstanding in month 4

Time 4

0%

10%

20%

30%

40%

50%

60%

70%

4 10 16 22 28 34 40 46 52 58 64

Number of months after default

Total Recovery

Weighted

Total Recovery

Unweighted

Figure Fourb Cumulative recoveries as a % of loans outstanding in month 25

Time 25

0%

10%

20%

30%

40%

50%

60%

70%

25 28 31 34 37 40 43 46 49 52 55 58 61 64 67

Number of months after default

Total Recovery

Weighted

Total Recovery

Unweighted


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30

Figure Fivea Frequency of cumulative recoveries on loans outstanding 4 months

after the default date.

0%

5%

10%

15%

20%

25%

30%

35%

40%

0

%-5%

5%

-10%

10%

-15%

15%

-20%

20%

-25%

25%

-30%

30%

-35%

35%

-40%

40%

-45%

45%

-50%

50%

-55%

55%

-60%

60%

-65%

65%

-70%

70%

-75%

75%

-80%

80%

-85%

85%

-90%

90%

-95%

95%-100%

Recovery rates

Loans

frequency

Figure Fiveb Frequency of cumulative recoveries on loans outstanding 25

months after the default date.

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

0%-5%

5%-1

0%

10%-1

5%

15%-2

0%

20%-2

5%

25%-3

0%

30%-3

5%

35%-4

0%

40%-4

5%

45%-5

0%

50%-5

5%

55%-6

0%

60%-6

5%

65%-7

0%

70%-7

5%

75%-8

0%

80%-8

5%

85%-9

0%

90%-9

5%

95%-10

0%

Recovery rates

Loans

frequency

Note : The figure presents the frequency of cumulative recovery on individual loans,

48 months after default.


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31

Figure Sixa: Comparison of empirical (weighted) estimates of loan-loss

provisions to those imposed by the central bank, for the loans without collateral

or personal guarantee.

No collateral/ no guarantees

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

Bank of Portugal Provisioning rules Estimated Provisioning

Figure Sixb : Comparison of empirical estimates to those imposed by the central

bank for the loans with personal guarantee

Personal guarantee only

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48



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32

Figure Sixc: Comparison of empirical estimates to those imposed by the central

bank for the loans with collateral (with or without personal guarantee)

Collateral with or without guarantee

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48



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33

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Loan Losses Provision

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