A framework for assessing credit risk in depository institutions toward regulatory reform

anking am. Finance

! 5 [ 1991) 78.5-8

Robert S. Chirinko
Harris Graduafr School of Public PoCc_vSrudies. The i’niverria~ q/ Chicago
Chicago, IL 60637-278s. USA

Gene D. Guill*
Bankers Trust Company, New York. NY f&11 7, i’S.4
Final version received January

1991

This paper develops and illustrates a new method for evaluating the credit risk borne by
depository institutions that may prove to be an important element in a regulatory mxhanism
sensitive to risk. In our framework, depository institutions are forced to bear the costs of their
risk-exposure 2nd hence to internalize this cost when extending loans. Using various loan
portfolios and alternative macroeconomic scenarios, we present numerical calculations demonstrating the ability of our framework to capture variattons in risk-exposure and highlighting the
significance of portfolio concentrations
These calculations are based on an important new
source of information that permits an econometric analysis of loan losses by industry.

1. Introduction
The amount of risk faced by depository institutions
concern for policymakers because of the perceived link
and the performance of the economy. There is broad
agreement that a substantial number of failures would

(Dls) is of substantial
bet-seen their stability

(though not universal)
destatxiize the system

*The authors would like to acknowledge the helpful comments from Richard Aspinwall,
George French, Gerard Gennotte, Charles Goodhart, Joseph Hotz, Mervyn King, Robert
Taggart, an anonymous
referee, and seminar participants
at the Federal Reserve Bank of
Chicago, the London School of Economics, the University of Chicago, and the West Coast
Academic-Federal
Reserve Economic Research Seminar. Excellent research assistance has been
provided by Paul Hebert. The Shared National Credits data have been kindly distributed by the
Office of the Comptroller of the Currency. Partial financial support from ?hi: Federal Home
Loan Bank Board under Grant No. C88066 is gratefully acknowledged. All errors, omissions,
and conclusions remain the sole responsibility of the authors, and do not necessarily reflect the
views of the organizations with which they are associated nor the Federal Home Loan Bank
Board.
03784266/91/$03SO

0

1991---Elsevier Science Publishers

B.V. (North-


786

R.S. Chirinko and G.D. Guill, Assessing

creditrisk

in depository instirurions

of monetar;r payments and monetary control and impair the flow of funds to
borrowers lacking access to capita1 markets. 1 Assessing the vulnerability of
K)Is has taken on prominent importance following their recent troubles and
the dramatic increase in realized U.S. government insurance liabilities. While
it has been recognized for some time that the flat-rate structure of the
deposit insurance system substantially lowers the price of incremental risk,
tnis explicit incentive for risk-taking had been balanced historically by
implicit prices imposed by regulators in the form of operating restrictions.2
owever, the exceptional changes occurring in the financial services industry
have lowered, if not effectively eliminated, these implicit regulatory prices.
Thus, rather than attenuating financial instability as initially intended, the
deposit insurance system may have been the primary culprit in disrupting the
U.S. financial system in recent years.
In light of these problems, risk-based deposit insurance and capital
standards have emerged as important policy options under discussion. This
study will develop and illustrate a new method for evaluating the risks borne
by DIs that may prove important in structuring a regulatory mechanism
sens;tive to risk* \vv b begin OUi analysis i-ILsection 2 by reviewing previously
proposed methods for assessing DI risk-exposure. These proposals have some
important limitations avoided with the approach illustrated in this paper.
The proposed framework relates the credit risk associated with a loan
portfolio to variables, such as exchange rates, the prices of primary commodities, Federal Reserve decisions, and federal tax and spending policies. These
exogenous risk variables will be linked to loan losses by estimated, nonlinear econometric .quations relating aggregate variables to the performance
of industries from which loan portfolios are constructed. The risk borne by a
DI will be determined by the proportions of its loan portfolio held in these
various industries and by the characteristics of the loan loss distribution

reflecting industry means, variances, and covariances. In cof- ;tructing loan
portfolios, DIs will face a schedule of risk-based premiums, and thus are
forced to internalize the costs of their risk-exposure when extending loans.
Section 3 develops our framework for assessing risks borne by DIs and for
setting risk-based regulations. A key element is the link between industry
loan losses and macroeconomic and industry variables, and this link is
forged with an important new source of information from the Shared
National Credits database. To the best of our knowledge, these data have
‘Se Eisenbeis (1987), Kane (19871, and Gerticr (1988) for recent discussions and citations.
Apart from macroeconomic go& there is additiona! concern for protecting small depositors
who are unlikely to possess sufiicient information to evaluate DIs with a reasonable degree of
accuracy. This information asymmetry cou!d itself be responsible for bank runs and, hence, also
contribute to macroeconOmic instability.
‘T’he dual price interpretation
of deposit insurance has been deveioped by Buser, Chen and
Kane ( 1981) and F!annery ( 1982).


estimated loan loss

omit scenarios, we present i
the ability of our ~ro~o~d

2.

met

The variety of pr osed methods for assessi~l
forecasting, and form te their projections with in
financial markets or regulators. This section reviews extan

general problem of assessing DI risk. but does not discuss t
important issues concerning adjustments in deposit insuf
or capital standards or other aspects of regulatory reforrm3
One set of proposals would turn to financial markets for assistance in
assessing risk and, a~ with much of economic analysis, the central idea is to
rely on private, self-interested agents to perform the complex risk calculations. An innovative proposal introdueed by Merton (1977) views deposit
insurance as a put option, and uses modem option valuation techniques to
Other market valuation methods
determine the value of the guarantee.’
involve assigning risk-premiums
based on the spread of uninsured deposits
over the safe rate of interest [Peltzman (19X!)] or allowing private parties to
co-insure deposits in conjunction with the government [Baer (1985, Boyd

and Rolnick (1988)].
While these methods
portfolio

diversification,

are sensitive to ex-ante
a fundamental

difficulty

risk and, in principle,
with all of these market-

based proposals is that they assume sufficient information is publicly
available to financial market participants to allow them to form reasonable

judgments. Yet, this possibility is precluded by the special role in the
financial intermediation process held by Dls - using private, client-specific
information, they create illiquid assets in the loan market for which no close

‘See, among many studies, Benstcn and Kaufman (1988), Brookings Task Force (1989), Kane
(1986), Shadow Financial Regulatory Committee (1989), and White (1989) for comprehensive
reform proposals: Avery and Belton ( 1987). Chan. Greenbaum and Thakor ( 1988). and Flannery
(1989) for a comparison of insurance premiums and capital standards; and Pennacchi (1987a)
and Pyle ( 1986) for a consideration of closure procedures.
‘Marcus and Shaked (1984). Pennacchi (1987b). and Ronn and Verma (1986) have also
applied this technique to valuing deposit insurance. The results were shown to be sensitive to
assumptions about the distribution of asset returns, the term of the deposit guarantee, and the
regulator’s closure rule, respectively.


78R

R.S. Chirinko ond G.B. Guill. Assessing rreBir risk in depository institutions

substitutes exist.’ The potential success of market-based proposals is largely
inconsistent with the raison d’etre for overnment regulation of DLL~
is concern is supported by the empirical results of Avery, B&o
(1988), who found no relation between the risk-premium on
related long-term debt and measures of bank ~~~OIIIUIILX, risk, and bond
ratings by private agencies. Analyzing bank holding companies, Randall
(1989) concluded that the stock market and bond rating
unable to anticipate problems before substantial damage had
even after identification, neither the market nor agencies were able to
uate the seriousness of credit problems. In regard to the options
approach, there is the further difficulty that 95% of banks are not traded

actively enough to be evaluated by this technique. Coupled with current
questions about the efficiency of financial markets and their substantial
volatility, financial markets are unlikely to prove useful in assessing DI
risks.’
The aiternative set of proposals provides a more direct role for regulators.
Relying less on unbridled market forces, these alternatives have received the
most serious consideration. The Federal Reserve System, ahg with 11 other
central banks, has implemented a plan that assesses credit risk by activities
in which a DI is engaged. Capital standards are determined by allocations
among broad asset groups, with commercial and industrial loans taken as a
homogenous aggregate requiring the greatest amount of capital [Federal
Reserve System (1QSS)]. However, it is doubtful that the proportion of assets
in these broad categories will serve as a reliable indicator of future prohlems.
Furthermore, the important role of diversification among loans in the
portfolio is not considered systematically. ‘The experience of institutions with
a heavy exposure to the oil industry - as well as the calculations to be
presented in this study - indicates that igrloring the covariance relations
between loans in the portfolio can lead to a substantial misstatement of
risk-exposure. ’ The Federal Reserve plan is likely to have little effect in
curtailing risk-exposure by adventurous institutions.
Another non-market proposal would determine risk-based deposit insure premiums with an objective risk index and subjective evaluations
rschhorn ( 1986)J The index is a predictive device for determining
‘See Diamorldand Dybvig (1956) and Goodhart (1987) for further discussion, and Fama
(1985) and James (1987) for supporting evidence.
*Apart from this information problem, the market will fail to value any aggregate externalities
arising from bank failures.
‘On the volatility issue, see Shiller (1990). Using ootion valuation techniques, Marcus and
Shaked (1984. section 3.D) found that their ris” e&mates were sensitive to the standard
deviation of the asset rate of return, which is derived from the standard deviation of the equity
rate of return.

*In his study of bank holding companies that experienced difficulties, Randall (1989)
concluded that the concentration
of loans with common risk characteristics ‘appearsto have
played a significant role in nearly all of the cases studied’ (p. 15).


whether or not
variables describi

faces two dificuft pro
standards are costs t

make it difficult for reg
en face
requirements,

costs -

due to increased insurance premiums, capital
market rates - may we11 find it optimal to undertake
policies.

As with the

distribution
proposals

of loans,
are rot

adven
ral Reserve plan, no acestint
is taken of the
the deleterious effects of excessive portfolio

fully adequate

for setting

risk-b,>sed

premiums

or

standards.

3. An alternative framework
The framework developed in this section utilizes portfolid characteristics
and other confidential information to force greater sensitivity to ex-ante
risk-exposure.10 Our analysis of DI risk quantifies the tsral credit risk arising
from outstanding
loans. From a rtgulatory
perspective, total risk is the
appropriate
concern because it creates demands for regulatory
reserves.
While there are other risks faced by DIs, credit risk has been and is likely to
continue to be the primary cause oi failures.”
Credit risk is measured by the distribution of loan losses associated with

the Dl’s loan portfolio. This distribution is calculated as a weighted average
of industry loan loss distributions, where the weights equal the proportion of
9A recent example of substantiai classification bias is the accounting practice of restructuring,
which ‘lets banks transform non-accruing loans into accruing loans by granting more favorabie
terms to the borrower, er,en though those terms may involve below-market interest rates that
actually lose money for the bank’ [Suskind (199011. Banks benefit from this reriassification
because the amount of non-accruing loans in the portfolio, inter alia. determines loss reserves.
‘The additional information required for our approach is modest, and could be collected
within the existing regulatory apparatus.
“Credit risk was the primary cause for three-quarters of bank failures [FDIC (1983, p. IM)].
There are additional sources of risk alfecting Ms. Risks arising from unscrupulous management
practices are likely to be checked only with supervision, and fall outside of the present study.
While playing a major role in past problems, interest rate and exchange rate risks are of less
current concern because of the emergence of hedging instruments and the relaxation of thrift
regulations on deposits. Nonetheless, with a detailed description of a Dl s income statement and
balance sheet, the framework developed in this paper can assess these additional risks and their
relation to credit risk.


790

R.S. Chirinko and G.D. Guill, Assessing credit risk in deposirory

institutions

the loan portfolio extended to firms in each industry. Industry loan losses are
determined by industry and economywide variables that affect profitability. A
distribution of loan losses is constructed with different assumptions a
possible states of the world, indexed by s = 1,2,. . . ,S.” These considerations
lead to the following set of equations for the I industries,

where li,, is loan losses in industry i tor state s per dollar of outstanding

loans, ,d[.] is an econometrically eq+imated function (discussed in section 41,
yi,s is a vector of variables affecting loan losses, and Ei is an industry-specific
shock.
A DI is characterized by the proportion of its loans (~0~)extended to firms
in different industries. Fundamental to the evaluation of the DI is that the
risks associated with the assets constituting its portfolio may be correlated.
In terms of (I), this implies that the determinants of loan losses in industry i
@ias) may be correlated with the loan loss determinants for industry i’. In our
framework, this correlation will be induced by fluctuations in macroeconomic
variables, such as interest rates and the components of Gh;P, to which the
industries are more or less responsive. Critical to making our method
operational is linking the industry-specific variables to macroeconomic
outcomes, and this is achieved by means of an input/output model for the
U.S. economy that relates final expenditures to industry production, as well
as capturing production flows among industries.
The final step in our analysis is to identify the sources of risk in the
macroeconomy impacting industries through the input/output model. We
,issume that the macroeconomy can be adequately represented by a iargez-tale, nonlinear econometric model and that risk arises from the diyersity of
possible outcomes of a subset of exogenous variables. Exogenoub variabies
are divided between those that remain fixed (Z) and those that vdry between
states, such as primary commodity prices (including energy), exchange rates
and monetary and fiscal policies. For each latter variable, wz specify a set of
possible outcomes (Sj,.) and the probability that each wil! occur (pi,“), where
j refers to an exogenous risk variable and TVa possible outcome. The
permutations of the _Yj,u’
s {with the associated pi,u’S) are formed, and the
probability of any given combination is represented by the probability

weights, x,, that sum to unity. The relations between industry variables, the
macroeconomic and input/output models f Y[.]) and the exogenous variables
are .epresented by the foiiowing equation,

‘*It may be easiest to think of the model as atemporal
from as yet to be specified probability distribution,
framework to multiple periods.

and the states determined

but it is straightforward

by draws

to extend the


The Y~,~‘senter

e
ee

vector of loan
industries.

the macroeconometric
an
industry-specific
variables
compute

a vector of e

ed loan

losses

We have chosen this approach for generating inforuxxtion
about industry
loan losses because it provides a tractabIe means for using the scarce
available information and is forward-looking.‘4
As discussed in section 2, all
methods for assessing risk involve forecasting, and our method allows us to
enter information about the risks expected to be faced in the future. While
the usefulness of our framework is enhanced the more accurately the set of
possible outcomes can be described, it is no more restrictive than existing or
proposed methods, and much more flexi41e in incorporating
information
about risk variables and the probability of their occurrence. Furthermore, it
does not restrict the number of possible outcomes (nor their interactions with
the fixed exogenous variables) that may be considered.* 5 Being forwardlooking and not trapped by historical happenstance,
the framework presented here provides a flexible method for quantifying DI r”sk-exposure.
Deposit insurance premiums or capital standards would be determined by
the interaction
between the loan portfolio chosen by a DI and three
!‘SC the Appendix in Chirinko and Guill (1990) for a mar: mathematical statement of the
method for calculating rhe loan loss distribution. Note that the covariance calculations will
incorporate the covariance of the ENSfrom the sample period.
“With similar quantitative relations for other countries (e.g., Project LINK), this approach
can be extended to international loans, thus providing a meaxre of the effects of loan
concentrations emphasized by Bennett (1984).

“The covariance matrix of loan losses fC[!]) generated by our framework will be similar, in
principle, to the covarianc- matrix of loan losses computed from historical data (CH(!]) if we
expect the future to bc affected by the same shocks as in the past. Insofar as they difier, CC11
will be a better estimate. In practice, estimating C,[fl will be very difficult because of a lack of
data. Apart from these problems, using the covariance matrix of the macroeconomic
risk
variables to approximate CC/] would ignore the substantial information in the mpWoutput
model and nonlinear relations in the macroeconomic model. Neither of these covariance
matrices could provide information on p, and hence could not deliver a complete a%SSment of
DI ri:k-exposure.


792

RX Chirinko and G.D. Guill. Assessing credit risk in depository institutions

constraints selected by regulators. The first set of constraints reflects
ceived risks affecting the overall economy and industries and, as discussed
eve, is represented by M[1] and C’[l].‘” Second, bas
on the relation
between loan losses and DI failures, regulators would cho
the critical loan
loss rate, f*; loan losses in excess of this rate undermine DI viability for a
grespecified minimt;m level of capital. In our framework, risk-exposure is
measured by the area under the portfolio’s loan loss distribution to
of l*, and this critical region is labeled q. The lower I*, ceterid par
rester q and hence the more conservative the stance taken by regulatorsi’
Note that q captures changes in both the location and dispersion of the loan
loss distribution. Assuming that the DI‘s loan losses are distributed normal,
the mean and standard deviation of the loan portfolio completely characterize the distribution.

The third constraint is the statutory premium schedule, p[q]. Apart from
.q, this would depend on a number of additional factors (e.g., the strength of
the balance sheet, management practices) affecting DI performance and the
!ike!ihood of insuraace claims. l8 Since risk-taking is likely to become acute
when DIs near financial distress, ,$q] should be nonlinear in its arguments.
The proper determination of p[q] would also depend on a welfare analysis
that is beyond the scope of the present paper and complicated by the
difficulty in defining the relevant objective function. The subsidy for risktaking enjoyed currently by DIs is largely, if not entire& shifted to
borrowers and, if eliminated, would force other sectors in the economy to
bear more risk [Goodman and Santomero (1986)]. If there are efficiencies in
bearing risk by a partnership between Dls and government insurers or
macroeconomic externalities arising from bank failures, maintaining an
actuarially fair system is unlikely tc be optimal.
Payments to the insurance fund (or additions to the capital base) would be
determined by p[q], and thus would depend on ex-ante risk and (positively)
on both the mean and the standard deviation of the loan loss distribution.
The latter parameter incorporates the effect of loan portfolio Diversification
that we believe is critical to any risk-sensitive regulatory system. With M[Q,
CC/], I*, and p[q] announced in advance, DIs would determine their
insurance payments by altering the composition of their loan portfolios.
Thus, our framework quantifies the cost of risk-exposure, and forces DIs to
internalize this cost when extending loans.
Given the many factors outside of our model that affect DI performance,
‘6That is to say, regulators choose {pj..‘s, X, rS. Y’pC.1.A[-]} and generate {M[I], C[fl}.
“lt would be incorrect to increase I* becaue of a perceived increase in risk in the
macroeconomy, which will be reflected in the choice of the Xj.b’s and pj._‘s, hence in the spread
of the computed loan loss distribution.
“SPremiums would depend negatively on the level of DI capital ia excess of the minimum
tevr.! K- d in setting I*. Equivalently, I* could be adjusted for the level of capital held by a DI.

The prop xd framework requires atr on loan Iosses by
turn, must be related to variables i

t

institutions, and be at least $20 million. These annual data are constructed at
a two-digit SIC code classification. and mostly pertain to Commercial and
Industrial (C & I) Loans. The C & I Evans in the sampIe constitute approximately one-third of the vake of outstanding
C&I Loans by the
supervised by these three regulatory agencies.
Given

our

interest

in identifying

problem

institutions,

the

loan

loss

variable is defined as the percentage of loans in one of the following four

criticized categories: Special Mention, Sub-Standard, Doubtful. and Loss. In
1988, loans in these four categories amounted to 7.34?, of the value of loans
in the SNC database; the Doubtfuf and Loss categories amounted to 1.07”;
of the total.
In estimating a loan loss equation, we are guided by two considerations.
Statistically, in order to obtain a reasonable amount of variation in the
regression, we pool the sample across industries, though the intercepts (Zi)
vary across industries. In keeping with the estimation method of other
equations in the macroeconometric
model, the loan loss equation is estiTheoretically,
we postulate that loan
mated by ordinary least squares.”
losses are related systematically to the recent growth of cash flows for that
industry. We do not have sufkient data permitting explicit cal~~lat~o~ of
cash flow, but have available two major components: sales revenues (Ri,,)
and the costs of intermediate inputs and labor services (C+), where ‘i’ refers
to industries and ‘t’ to time periods. The growth rates of these series are
entered as 4-year moving averages. In addition, to capture t
“This estimation technique does not preclude the possibility that the estimated li__‘smay be
less than zero, but inspection oh the simulations reveals iittle problem from omttting this
constraint.


R.S. Chirinkn and G.D. Guill. Assessingcredit risk in depository

institutions

Table 1
Pooled I

squares, estimates of the loan loss equation (3).”

(I)
-.
Fkxed
eflects

__^..___..
Revenue, /I

(21
--

FIxed
effects

(3)
No fixed
e@ects

(4)
Fixed
effts

- 0.549
(0.120)

-0.237
(0.104)

-0.319
(0.096)

Cost. y

0.431
tO.131)

0.302
(0.117)

-0.157
(0.097)

0.029
(0. Ial )

Federal funds. (5

0.319
(0.093)
_
_

0.160
(0.087)
_

0.282
(0.089)

_

0.614
(0.175)

GNP. B
8’

0.276
108

Observations

0.088
168

0.182
138

(51
No fix
effects

-

-

- 0.268
(0.178)
0.151

108

0.362
(0.180)
-0.105
ZO.8.180)
O.Q9?
108

“Estimation is with annual data from 1985-1988. All coeficients have begn stanJar&&.
Standard errors are in parentheses. For all entries but column (2). the industries included in the
estimation had positive loan losses; column (2) includes the zero-loss industries. An overall
constant term has been inc!uded in m!umns (3! and (S), and is statistically insignificartt

effects brought about by variations in the cost of funds, the federal funds rate
(F,) enters contemporaneously. These considerations give rise to the following equation,

+

iiF, + Ci.tq

i = 1.27, or 42; t = 1985, l%S,

where Ei,l is an error term,
Table 1 contains the pooled least squares estimates of (3), and all of the
reported coeffkients have been standardized. The preferred fixed-effect estimates are presented in column (I), and all three coefficients are statistically
significant and of the correct sign. 2o Over the sample period, the variation in
revenue has had the largest effect on 1i.r. These estimates are based on a
sample in which industries with no loan losses for at least one year in the
sample are excluded; column (2) expands the sample to include these

additional (zero-loss) industries. The coefftcient estimates are broadly similar,

“Very
similar results are obtained when the q’s are treated as random effects and a
variance-components
mode! estimated. We have chosen to use the fixed effects estimates (as well
as abstaining from using instrumental variables) because they are more in keeping with the
estimation techniques used in the rna~r~~on~~et~~
model.


loans, and allowing these categories to have different sensitivities to variations in the rea-zssors might prove important. Ail of these issues can be
addressed wth a richer dataset. and the calculations presented in this paper
should be viewed as illustrating the potential of our framework for assessing
DI risk.

5. Specific ¶~antitati~e asomptions

framework proposed in this paper links the mean 1~) and standard
deviation (6) of loan portfolio losses to aggregate and indUSFry variables. To
establish this link, we must make specific quantitative assumptions about
values of these risk variables, the weights (or probabilities) associated with
each of these values5 and the economic models relating these variables to
loan portfolios.
We begin by specifying the number of exogenous risk varia
The

“The resuk in columns (I) and (2) OFtable 1 suggest that using the latter estrmates would
not radically change the simulation results reported below. The estimated in column ( I) haw
use,

in OUF ~~~~~~a~
pd_pent, the iqe
concentration
of zeros dktorts the
ken
used
loss coefficients in OUT relatively small sample. The zero-loss industries are
estinkated 1
in the simulations by estimating z, as the difference in the means of the variables in (3)
a~~ro~~ately by /?, 7. and 6.


796

R.S. Chirinko end G.D. Guill, Assessing credit risk in depository ictitutions

values. For reasons of computational expense, four sets of risk variables
(J =4) are examine:J and, for each set, a Basecase and an Alternative set of
values are considered. The Basecase assumptions, as well as values for the
fixed exogenous variables, are taken from the ongoing forecasting project at
DRI/McGraw-Hill. Alternative values have been chosen to capture important developments affecting DIs, and are described relative to the Basecase
forecast. First, the trade-weighted dollar exchange rate appreciates by 2.3%
per year. Second, the federal deficit is lowered by reducing defense and
nondefense spending and increasing personal and corporate taxes. Third, a
contract;onary monetary policy raises the federal funds rate an average of
167 basis points over the 3-year simulation period; relative to the Benchmark, this represents a 19.7% increase in this interest rate. Fourth, the prices
of primary commodities are assumed to rise by 4.5% per year. Ail changes
are annual averages relative to the Benchmark over the 3-year simulation
period.
The permutations of Basecase and Alternative values for four sets of

exogenous risk variables lead to 16 possible states, a Benchmark (defined as
the Basecase value for each of the four risk variables) and 15 Alternatives.
From an aggregate perspective these Alternatives are contractionary relative
to the Benchmark. To provide a more balanced view of possible macroeconomic outcomes and to minimize computational expenses, we assume that
the loan loss outcomes are symmetric about the Becprovides us with 15 additional observations with which ts i. -proximate loan
loss distributions. The values of these sets of the exoger>tiJs variables are
represented by X, xs, dimensioned 4 by 3 1.
The states must be weighted by probabilities and, for each risk variable
(~EJ), we assume probabilities of occurrence (Pi,,) for the Basecase (U= 1)
and two Alternatives (u=2,3) that sum to unity. (For computational
convenience, we assume that the pj,u’Sare independent across the j’s, though
it is straightforward to relax this assumption.) These probabilities of occurrence are multiplied together to form the probability for a given state.
Calculating the permutations of the pj,u’S across 1, we obtain the probabiiities for the 3 1 possible states (x,, s = 1,. . . ,31; EWE
II, x 1). For example, for
Scenario 1 listed in column (1) of table 2, we assume that the Basecase
probabilities for all four j’s equal 0.80. Thus, Pi, 1=0.80 for j = 1,2,3,4, and
the probability of the Scenario 1 Benchmark is 8.41 ( =0.804).
To gain a better understanding of the responsiveness of our measure of
risk-exposure to variations in the probabilities, additional plausible scenarios
are examined, and are represented by the remaining entries in table 2.
Scenarios 2-5 are similar in that they maintain the 0.8O/O.IO/O.10weights for
all but one of the sets of exogenous variables. In the exceptional caweight on the Basecase value is halved, and the weights on the alternatives
raised accordingly. Scenario 6 is, in a sense, a collection of the prior four


R.S. Chirinko and G.D. Guill, Assessing credit risk in depository

institutions

797

Table 2
Probabilities

~___---

of occurrence for sets of exogenous variables (p’s).”
Scefi.,

1.

Exchange

__ .__

1

2

3

4

5

6

0.80

0.40
0.30
0.30

0.80
0.10

0.80

0.80

0.10
0.10

0.10
0.10

0.10
0.10

0.40
0.30
0.30

rate

Base (u= 1)
Alt 1 (u=2)
Ah 2 (u=3)

II.

.~
,o

0.10

Fiscal policy

Base (u= 1)
Alt 1 (u=2)
Alt 2 (u=3)

0.80

0.80

0.10
0.10

O.lG
0.10

III. Monetary policy
Base (u= 1)
Alt 1 (u=2)
Alt 2 (u=3)

0.80
0.10

0.10

IV. Primary commodity
Base (u= 1)
Alt 1 (u=2)
Alt 2 (u=3)

0.40
0.30
0.30

0.80

0.80

0.10
0.10

0.10
0.10

0.80

0.40

0.80

0.10
0 !O

0.30
0.30

0.10
0.10

0.40
0.30
0.30

0.40
0.30
0.30

0.40
0.30
0.30

0.40
0.30
0.30

prices
0.80

d.‘s.L

0.80

0.80

0.10
0.10

0.13
0.10

0.10
0.10

0.10
0.10

‘See section 5 for a discussion of these entries. For a given scenario
(i.e., a column), the probability of a state, IL,, is computed as the product
of one entry from each of the four panels. There are 31 states. and they
sum to unity.

scenarios, and places higher probability on the alternative assumptions for
the four exogenous risk variables. All six scenarios generate unique II, XI
vectors.
With values of the risk variables in the Basecase and Alternatives
established, we then rely on the DRi Model of the U.S. Economy to relate
XX and 2 to the endogenous variables, such as irlterest rates, prices, and
fiLalsdemands.22 This model is highly disaggregated, and has been used and
developed in ongoing forecasting exercises. At the core of the DRI Model is
a long-term growth model in which productive capacity is determined by the
growth in technical progress, the labor force, and the capital stock. Shortterm dynamics are determined
largely by the data, and are always fully

%ee Eckstein (1983) for further details. Much criticism has been raised against the use of
macroeconometric
models in quantitative
analysis [Lucas and Sargent (1978)]. While the
coefficient instability at the core of the Lucas Critique must be granted, the important question
for the current study is whether this instability
is sufficiently severe to invalidate the
perturbat’ons under consideration. The analysis in Chirinko (1988) indicates that, even in the
face of major changes in tax policy. equations for business fixed investment remainec! relatively
stable in the 1980s. Such stability is not inconsistent with forward-looking behavior ,an the part
of public and private economic agents [cf. Sims (1982) and Sargent (198i)].


798

R.S. Chirinko and G.D. Guill. Assessing credit risk in depository institutions

consistent with the circular flow of income and spending and other intrinsic
macroeconomic
identities.
In turn, estimates of industry revenues and costs are obtained from the
DRI Interindustry Model. The structure of this model is based on a Leontief
input/output
system, and is modified to permit (direct) input coefficients to
adjust to technology and product use and to include estimates of industry
Model for this
wages and prices. 23 An important feature of the Interindustry
study is its expiicit recognition of the interdependencies
among industries.
This feature enables the model to capture both the direct and indirect claims

on production
associated
with the delivery of a given vector of final
demands. Since approximately
50% of all production
in the United States
supports other industry production
(i.e., indirect claims), it is critical to
account for both direct and indirect claims in assessing industry performance.
For the purposes of this study, the Interindustry
Model (as well as the SNC
data) has been aggregated to the 46 industries listed in table 3. The revenue
and cost variables for these industries, as well as the federnl funds rate from
the macroeconometric
model, enter the loan loss equation developed in
section 4. The simulations of the macroeconometric
and input/output
models
are for 1989-‘1991, and the exogenous risk variables affect the simulations
throughout these three years. The results reported in the next section are for
1991, but loan losses will be affected by the risk variables in all years becaue
of the lags involved in (3). Lastly, a DI is characterized by thz distribution of
its loan portfolio across 46 industries (0, X,), and five different portfolios
(listed in table 3) will be analyzed.
6. Illustrative calculations
This section presents our results from simulating the macroeconomic,
input/output,
and loan loss models according to the method and quantitative
assumptions described in sections 3-5 and tables l-3. Risk depends on the
mean (p) and the standard deviation (a) of the loan loss distribution and on

a critical loan loss rate (I*), and is measured by the critical region (q). The
calculations in table 4 (except as noted in panel B) use a value of I* = 24.00%,
which implies a loan charge-off rate of 3.507&24
6.1.

Risk-exposure

qf depository

institutions

DIs are characterized by the distribution of their loan portfolios and, by
considering different w-vectors, we can assess variations in risk-exposure
23See Guill and Kraft (1985) for a detailed description.
24The ratio of loans in the Doubtful and Loss categories to all criticized loans (the latter
equal to 6,., multiplied by the amount of outstanding loans) is 0.146, which, when multiplied by
24.00)<, yields 3.50%.


R.S.

Chirinko

and G.D. Guill, Assessing credit risk in depository institutions

799

Table 3
Distribution

of loan portfolios

(“J.

Portfolio
Industry

description

1. Ag Production,

2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
:P
21.

22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
:::
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.

Crops
Ag Production, Livestock
Ag Services, Forest. & Fish
Metal Mining
Coal Mining

Oil and Gas Extraction
Nonmet. Minerals, Ex. Fuels
Contract Construction
Food & Kindred Products
Tobacco Manufacturer!5
Textile Mill Products
Apparel & Other Textile Prod.
Lumber & Wood Products
Furniture & Fixtures
Paper & Allied Products
Printing & Publishing
Chemicals & Allied Products
Petroleum & Coal Products
Rubber & Misc. Plastics Prod.
Leather & Leather Products
Stone, Clay and Glass Prod.
Primary Metal Industries
Fabricated Metal Products
Machinery, Except Electrical
Electric & Electronic Equip.
Transportation
Equipment
Instruments & Related Prod.
Misc. Manufacturing Indust.
Railroad Transportation
Local & Interurb Pass. Tran.
Trucking & Warehousing
Water Transportation
Transportaiton
by Air

?ipe Lines, Ex. Natural Gas
Transportation
Services
Communications
Elec., Gas & Sanitary Serv.
Wholesale Trade
Retail Trade
Banking & Insurance
Real Estate & Rental
Personal Services. Ex. Auto
Business Services
Auto Repair
Medical Services
Other Services

Total

A

B

C

0.08
0.06
0.04
0.67
0.30
7.44
0.07

1.75
2.49
2.35
0.54
0.87
0.62
0.16
1.74
2.08
4.20
2.58
1.46
0.17
1.60
2.28
1.47
2.60
1.92
3.88
0.50
0.48
0.83
0.22
0.28
0.40
1.82
0.10
0.29
4.28
9.21

1.98
5.86
15.12
6.68
0.04
2.11
0.67
2.14
3.60

2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17

2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17

100.00

100.00

100.00

D

E

0.05

0.08

0.11

0.02
0.01
0.09
0.68
5.55
0.07
1.55
1.55
2.19
0.78
1.03
0.85
0.30
3.19
4.32
8.30
3.70

1.13
0.2 1
1.36
1.29
1.98
2.40
1.86
2.88
0.77
0.46
1.07
0.24
0.22
0.28
I .36
0.07
0.11
8.92
7.05
1.41
6.92
12.81
3.37
0.03
2.85
0.95
2.12
1.55

0.03

0.02
0.57
0.91
19.72
0.05
0.37
2.12
1.44
0.11
0.06
0.52
0.15
0.63
1.27
2.49
6.70
1.45
0.22
1.79
2.41
1.52
1.97
2.09
3.51
9.27
0.47
0.72
0.14
0.41
0.31

I .97
0.13
0.27
3.65
13.01
2.14
4.71
10.41
4.11
L’00
1.71
0.6’1
1.68
1.06

0.05
0.00
0.78
0.42
11.82
0.00
3.90
3.15
1.25
0.3 1
0.00
0.00
0.00
0.62
1.65

4.77
4.84
1.27
0.00
2.02
2.95
1.93
2.99
?.47
4.50
0.52
0.34
0.97
0.00
0.54
0.00
2.71
0.00
0.00
4.49
11.12
1.03
5.07
10.21
6.1@
0.66
1.76
0.00
0.63
2.01

lcQ.00

100.00


800

R.S. Chirinko and G.D. Guill, Assessing credit risk :n deposiidpy mstitutions
Table 4
(Characteristics of loan loss distributions,

alternative

p’ rtfolios (w’s).’

___-.
Portfolios

A. Conlplete estimates
c1
d
rt
% change (v)~

(E)
(5)

9.08
6.18

0.80
- 65.67

12.02
6.99
4.36
87.12

11.80
6.77
3.59
54.08

11.07
5.39
0.82
182.76

9.08
4.24
0.01
- 96.55

12.02
5.61
1.62
458.62

11.80
5.11

0.84
189.66

2.33
0.00

4.36
87.12

0.40
- 82.83

6.94
197.85

4.85
108.15

- 38.70

- 36.36

-45.75

- 24.60

- 32.49

(B)
(2)

10.79
6.63
2.33
0.00

11.07
7.35
3.92
68.24

B. Coumimces constrained to zero
P
10.79
0
4.78
tl
0.2o
% change 01)~
0.00
V’
% change 01)~
C. Biosd

-~
0)
(4)

(A)
(1)

(C)
(3)

“The portfolios are described in section 6 and table 3. The mean, standard
deviation, and critical region for the loan loss distribution are denoted by p, rr,
and 9, respectively. The simulations begin in 1989, and the reported results are
for 1991. t Mess otherwise noted, I* = 24.00
bPercen~ age change calculated with respect to the q in column (1).
‘Calculat~xi with I* = 20.30.
dBias cahxlated as (ou-a,,)/~,.
where A and B refer to the panel irom which
the standard devi:u!nn is taken.

across institutions. The results discussed in this sub-section are based on the
first macroeconomic scenario that assigns a weight of 0.80 on Basecase
values and 0.10 on Alternatives for the four exogenous risk variables (see
table 2). Portfolio A is determined by the proportion of loans held by banks
in the SNC database, and represents the ‘average’ DI. For this o-vector, the
critical region in excess of I* is 2.33 [panel A, column (l)], and this value of
4 serves as a reference point for subsequent calculations. Portfolio B assigns
an equal weight to loans from each of the 46 industries; hence Oi=2.17°/o for
i = 1,2,. . .,,1. This uniformity leads to a modest rise in p but a much larger
change in o’. Overall, there is a marked increase in loan portfolio risk, as q
increases by 68.24% relative to Portfolio A.
The remaining three portfolios are chosen to describe different DIs.
Portfolio C is constructed to reduce risk by having major concentrations in
the communications and non-durable manufacturing industries {including
paper, printing and publishing, and chemicals). With this distribution of
loans, q falls from 2.33 to 0.80, a drop in risk-exposure of 65.67%. In

recognition of recent problems faced by a number of DIs, Portfolio D is
heavily weighted toward energy and energy-related lines of business. Our


RX Chirinko

and G.D. Guill, Assessing credit risk in depositrry

institutions

801

simulations indicate that the risk-exposure for this institution increases by a
substantial 87.12% relative to the ‘average’ institution. Lastly, we represent a
DI with concentrations in energy, construction, and durable manufacturing
industries by Portfolio E, and ye increases to 3.59. In sum, these results
demonstrate that our framework for assessing credit risk is feasible and
capable of capturing wide variations in risk-exposure.
6.2. The importance of covariation
A notable advantage of this method for calculating risk-exposure is that
we are able to measure the covariation between loans in the portfolio. To
assess the quantitative importance of covariation, the second row in panel B
contains variances for which the covariance terms have been constrained to
zero. The bias in using these estimates - rather than the correct estimates in
panel A - is displayed in panel C. Regardless of the portfolio, the bias is
large and always negative, reflecting, as expected, that the industries move
together over the cycle. The bias ranges from -24.60% for the energyintensive portfolio to -45.75% for Portfolio C, which has the least exposure
to risk. Ignoring covariation would substantially understate risk premiums.
For example, the risk-exposure of the energy-intensive Portfolio D would be
only 37% of the correct figure, based on the estnmate of q in panel A. For the

‘average’ institution, the comparable estimate is 12%.
Not only would the risk premiums levied using the constrained variance
be too low, they would also be quite volatile, as indicated in the fourth row
of panel B. This volatility is only partly due to the non-linearities at the tail
of the normal distribution. To adjust for these non-linearities, the last two
rows of panel B are based on a I* of 20.30, which generates an 9 of 2.33 for
Portfolio A (as in panel A). Nonetheless, the volatility in 9 persists.
The calculations in panel B are representative of those that might be
undertaken by a regulator unable to assess covariation or believing that it is
of second-order importance. The comparisons drawn in table 4 indicate that
such an approach can be highly misleading and can lead to substantial
errors in estimating credit risk.
4.3. The impact of alternative macroeconomic scenarios

The previous results
on risk-exposure under
mic outcomes. Table 5
in the IC,‘sfor the six

have examined the effects of various loan portfolios
a fixed set of probabilities (71,‘s)for t: macroeconoexplores the sensitivity of risk-exposu: 2 to variations
scenarios in table 2 for Portfolios A ;-nd D.25 For

“Note that, across the six scenarios, the values of the risk variables (XJxs) remain fixed and
that the symmetry assumption used in calculating the loan loss distribution constrains p to be
constant.


R.S. Chirinko and G.D. Guill, Assessing credit risk in depository institutions

802

Table 5
Characteristics

of loan loss distributions,
Scenario
1

2

alternative
---.
3

scenarios (x’s) and portfolios (w’s).

4

5

6

.4. Portfolio A
p
d
1
%

change01)~

Bias’

10.79
6.63
2.33
0.00
- 38.70

10.79
6.59
2.28
-2.15
- 37.58

10.79
6.61
2.28
-2.15
- 37.71

10.79
9.3 1
7.78
233.91
- 90.78

10.79
6.60
2.28

-2.15
- 36.08

10.79
8.92
6.94
197.85
- 80.20

12.02
6.99
4.36
0.00
- 24.60

12.02
7.03
4.46
2.29
-25.31

12.02
7.10
4.55
4.36
- 26.33

12.02
9.46
10.20

133.94
- 66.84

12.02
6.44
3.14
- 27.98
- 13.18

12.02
8.88
8.85
102.98
-54.17

B. Portfolio D
F
c7
1

% change (v)~
Bias’

“The portfolios are described in section 6 and table 3. The mean, standard deviation,
and critical region for the loan loss distribution are denoted by p, u, and q, respectively.
The simulations begin in 1989, and the reported results are for 1991. Unless otherwise
noted, !* = 24.00.
bPercentage change calculated with respect to the q in column (1).
‘Bias calculated as discussed in note d of table 4.

Portfolio A and with Scenario 1 serving as the reference point, risk-exposure
varies widely across the scenarios, falling slightly for Scenarios 2, 3, and 5
ilut rising dramatically for Scenarios 4 and 6. These latter two give greater
weight to high interest rate outcomes, and highlight the considerable impact
of tight credit conditions on loan losses.
A different pattern emerges for Portfolio D, concent,rated in energyintensive industries. In contrast to Portfolio A, risk-exposure rises modestly
in Scenarios 2 and 3. Scenarios 4 and 6 continue to slaow the greatest
percentage increase in q, but the changes are much lower thian in panel A. A
more extreme response is evident in Scenario 5, which accents the rise in
primary commodity prices. For this scenario, the changes in v are - 2.15%
for Portfolio A but
27.98% for Portfolios D.

The significant number of failed and failing depository institutions (Dls) in
the United States and the subsequent claims on insurance funds have
highlighted the need for reform in the deposit insurance system. Failures are
likely to continue as DIs operate in an increasingly competitive environment
with p-verse incentives for risk-taking. Proposed methods for risk-based
deposit insurance do not account for the effects of ex-ante risk and portfolio
diversification or rely too heavily on financial markets. In this study, we have


R.S. Chirinko and G.D. Guill, Assessing credit risk in depository

institutions

803

developed a framework for setting insurance premiums or capital standards
that avoids these deficiencies by relating the credit risk associated with a IX’S

loan portfolio to aggregate and industry variables. These relations were
determined by econometric equations and an input/output model for the
U.S. economy. Of independent interest were the industry loan loss data
collected under the Shared National Credits program and analyzed econometrically in this study.
We then presented illustrative calculations for alternative loan portfolios
and macroeconomic scenarios, and these results indicated that our framework can capture variations in the risk-exposure of Dls. Although our
proposed framework does not account for all factors that must be considered
in determining risk-sensitive insurance premiums, it takes some key first steps
toward developing a tractable means for assessing ex-ante risk and portfolio
concentrations. The framework illustrated in this study may thus prove to be
an important element in a comprehensive and incentive-compatible regulatory approach.
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