The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
konomic
Review
Federal Reserve Bank
of San Francisco
Fall 1991
Number 4
Mark E. Levonian
Have Large Banks Become Riskier?
Recent Evidence from Option Markets
Jonathan A. Neuberger
Risk and Return in Banking:
Evidence from Bank Stock Returns
Chan G. Huh
Recession Probability Indexes: A Survey
Sun Bae Kim
The Use of Equity Positions by Banks:
The Japanese Evidence
Table o f Contents
Have Large Banks Become Riskier?
Recent Evidence from Option Markets
,3
Mark E„ Levoniae
Risk and Return In Banking:
Evidence from Bank Stock Returns
18
Joeatlhae A. Neeberger
Recession Protoatolity Indexes: A Survey
31
Chan Go Hell
Ttoe Use of Equity Positions toy Banks:
Ttoe Japanese Evidence
41
See Bae K im
Federal Reserve Bank of San Francisco
1
Opinions expressed in the Economic Review do not neces
sarily reflect the views of the management of the Federal
Reserve Bank of San Francisco, or of the Board of Governors
of the Federal Reserve System.
The Federal Reserve Bank of San Francisco’s Economic Review
is published quarterly by the Bank’s Research Department under the
supervision of Jack H. Beebe, Senior Vice President and Director of
Research. The publication is edited by Judith Goff. Design, production,
and distribution are handled by the Public Information Department,
with the assistance of Karen Flamme and William Rosenthal.
For free copies of this and other Federal Reserve publicatons, write or
phone the Public Information Department, Federal Reserve Bank of San
Francisco, P.O. Box 7702, San Francisco, California 94120. Phone
(415) 974-2163.
2
E conom ic R eview / Fall 1991
Have Large Banks Become Riskier?
Recent Evidence from Option Markets
Mark E. Levonian
Senior Economist, Banking and Regional Studies, Federal
Reserve Bank of San Francisco. I am grateful to Brian
Cromwell, Randall Pozdena, and the editorial committee
of Frederick Furlong, Brian Motley, and Jonathan Neuberger, for numerous helpful comments and suggestions.
This paper examines trends in risk at the largest U.S.
commercial banks during the late 1980s. Prices of
exchange-traded options on bank equity are used to derive
several measures ofbanking risk. The results show that the
riskiness ofbank assets and activities did increase at large
banks during the period. However, market capital-asset
ratios generally rose, leaving the burden on the deposit
insurance fund little changed. Hence, while the results
support the notion that banks now engage in a riskier
business than previously, the general increase in capital
has been sufficient to hold overall banking risk relatively
constant.
Federal Reserve Bank of San Francisco
A series of events during the 1980s generated renewed
concern about the condition of large commercial banking
firms in the United States. Losses on loans to .lessdeveloped countries, energy-related loans, and problems
related to real estate markets in various regions reduced the
financial strength of many banks. At roughly the same
time, large banks expanded their activities in a variety
of nontraditional areas-including securities underwriting, trading of interest-rate and foreign-exchange-rate
instruments, and financing of highly leveraged transactions-many of which appeared to hold potential for, and
in some cases actually caused, significant losses. The
combination of reductions in financial strength and expansion into new activities raised the fear that large U.S. banks
became significantly riskier during the 1980s.
The riskiness of banks might be ofless general interest if
not for its impact on federal deposit insurance. The liability
borne by the insurance fund roughly depends on expected
losses due to bank failures. If banks became riskier during
the 1980s, losses may have become more likely, and the
liability of the insurance fund may have grown substantially. Large banks are of particular concern, not only
because individually they are large components of the
banking system, but also because they, more so than
smaller banks, have been involved in the nontraditional
activities mentioned above. If risk has increased at large
banks, then some form of regulatory response-for example, increased bank capital standards, or restrictions on
bank activities-may be desirable. Alternatively, the adverse conditions of the 1980s may not have affected risk
materially, in which case calls for an active regulatory
response to reduce risk are misdirected.
The well-publicized decline in the bank deposit insurance fund, from 1.19 percent of insured deposits at the
beginning of 1985 to 0.70 percent at the end of 1989, may
seem to constitute clear evidence of an increase in risk.
However, Shaffer (1991) has demonstrated a fairly high
probability of problems of this magnitude, without any
change in the distribution of losses. That is, it is quite likely
that the FDIC could experience such losses purely through
a series of bad years, random "bad luck," without any
3
change in banking risk. Thus, trends in banking risk cannot
be examined simply by observing changes in the reserves
of the insurance fund over time.
This paper focuses on the evolution of risk at nine of the
largest U. S. bank holding companies. Changes in several
measures of banking risk are examined. The primary contribution of the paper is the use of a new type of data: The
prices of exchange-listed options on bank stocks. The size
of the deposit insurance liability at any point in time
depends critically on the prospects of insured banks.
Option prices provide a unique· source of information on
market beliefs regarding both future risk and current
financial condition, information that can be used to construct estimates of the risk to the insurance fund.! In
addition, this paper provides empirical implementation of
a relatively new model of insured banks, which is used to
link the option price data with stock price and financial
data to derive measures of banking risk.
The use of options data restricts the analysis to the
second half of the 1980s, when options on most bank stocks
began trading. Although some of the events that reduced
the financial strength of banks-for example, losses on
energy loans and loans to less-developed countriesoccurred during the early 1980s, others, such as increased
involvement in securities underwriting and trading of relatively exotic financial instruments, also had effects in the
second half of the decade. A study by Furlong (1988) provides a useful complement to the present paper: Furlong
applied similar methods to analyze changes in the first half
ofthe 1980s.
The first section of this paper defines three measures of
banking risk: The volatility ofreturns on bank asset portfolios, the size of bank capital cushions as reflected in capital
ratios, and the overall liability imposed by banks on the
deposit insurance fund. Section II presents a contingentclaim model of an insured bank and formalizes the three
measures of banking risk. Section III describes a method
for computing the market value and volatility of bank
assets for use in the contingent-claim model; the section
also discusses in detail the reasonable range of values for
some key unobservable parameters of the model. Section
IV explains the methodology and data used to infer estimates of risk from the market prices of bank stock options
and presents the resulting estimates. Section V contains
the major results of the paper regarding changes in risk at
large banks in the late 1980s. The last section of the paper
provides some concluding remarks.
I. Risk in Banking
From an ultimate policy perspective, probably the most
important banking-related risk is the risk of losses to the
deposit insurance fund. The expected value of these losses
at any particular bank depends (1) on the probability that
the bank's assets will fall short of its liabilities, thereby
exhausting the bank's own capital, and (2) on the size ofthe
shortfall if losses should occur. Of course, payouts from the
insurance fund also depend on the degree of coverage offered by the insurer. But under any given coverage policy,
the probability that a bank will fail and the size of the
necessary insurance payment in the event of failure combine to determine the present value of the liability of the
fund.
Both factors in tum reflect two broad types of banking
risk. The first is financial risk, which depends on bank
capital: The probability that a bank will fail varies inversely with the bank's capitalization for a given combination of bank assets and activities. Capital is defined in this
paper as the difference between assets and liabilities, exclusive of deposit insurance. (Equity and capital are not
identical in this context; the value of equity includes the
value of the protection afforded by federal deposit insurance, which limits the liability of stockholders and protects
4
depositors from losses due to unanticipated declines in the
value of assets.) Capitalization is expressed most conveniently in terms of the capital ratio (the ratio of capital to
total assets), with a higher capital ratio implying lower
financial risk, all else equal.
The second broad type of risk is operating risk, which
depends on the riskiness of the bank's asset portfolio. This
risk is measured most directly by the variability of the rate
of return on bank assets, referred to as the "volatility" of
the bank's asset portfolio. Volatility is quantified by the
statistical standard deviation of percentage changes in the
value of bank assets. A bank with higher asset volatility is
more likely to fail (and, if it fails, is more likely to impose a
larger burden on the insurance fund) for any given capital
ratio.
Calculating capital ratios and asset volatilities in order
to measure risk is not a simple task. The relevant capital
ratios must be computed from the market values of assets
and liabilities, but market values often are not observable.
Similarly, the relevant volatilities are the volatilities of the
actual economic returns on the market value of assets;
these returns may be very different from the observable
accounting returns on the book value assets. Hence, to
Economic Review / Fall 1991
measure either financial risk or operating risk, or to
combine the two into an estimate of the insurance fund
liability, market values somehow must be calculated.
Although the market value of bank assets is not observable, the market value of bank equity is observable, since
large banks have shares traded on stock exchanges. If the
stock market is efficient, then the market value of equity
reflects the market value of assets (although it also may
depend on other factors, including the value of deposit
insurance); hence, a model that correctly specifies the
relationship between equity and asset values can be used to
infer the latter from the former. In addition, the volatility of
equity reflects the unobservable volatility of the underlying
assets, again suggesting the possibility of inferring one
from the other. The next section describes a model that, in
addition to filtering out the effects of deposit insurance on
equity values, relates the market value and volatility of
bank equity to the market value and volatility of bank
assets to permit inferences from observed market data.
n. Model of an Insured Bank
Merton (1974) applied contingent-claim techniques to
the general problem of valuing the debt and equity of
levered firms; in Merton (1977), the same techniques were
applied specifically to insured banks. Following Merton's
initial theoretical work, Marcus and Shaked (1984) implemented a similar model to derive empirical estimates of
bank capital, asset volatility, and the size of the deposit
insurance liability. In these models, banks have market
value of assets At (excluding the value of deposit insurance), and total liabilities maturing with face value B T at
date T, at which time the bank is examined by regulators
and is closed if assets do not equal or exceed liabilities.
These assumptions imply a value of equity E at date T of:
(1)
ET =
AT- BT if AT?;;B T
I
o
if AT<B T
At any time prior to T, the total market value of a bank's
equity is equal to the discounted value of this payoff
structure. Equity in the model is a contingent claim (a
positive payoff to equity is contingent upon the bank being
solvent at T), and its value at any earlier point in time can
be calculated using the same valuation techniques used in
pricing other contingent claims, such as options.
Levonian (1991) revised this contingent-claim model of
insured banks to incorporate both a flexible regulatory
closure threshold and positive bank charter value. 2 The
inclusion of charter value recognizes the fact that, in
practice, banks operate under special charters granted by
either state or federal authorities; because the supply of
bank charters is limited, the positive value conferred by a
charter is not competed away. Charter value is modeled as
being a fraction <1> of liabilities, and as being received by
bank equity holders at date T only if the bank is not closed
by regulators. 3
In Merton (1977), banks are closed if they are insolvent
Federal Reserve Bank of San Francisco
at date T. However, in reality regulators have some discretion regarding closure, and the regulatory closure threshold
need not be the point of actual insolvency. Banks may be
closed while net worth is positive, or may be allowed to
continue operating with negative net worth. If the regulatory rule is that a bank is closed if its capital ratio is less
than c, then the value of equity at the monitoring date T is
(2)
where c is not necessarily equal to zero, and the capital
ratio k is defined as
AT-B T
.
AT
(A minor difference between this model and (I) is that the
closure rule is stated in terms of the capital ratio rather than
in terms of the relationship between assets and liabilities.
Note that if c=O, then k>c implies A>B.) Banks that
remain open at date T experience a lump-sum increase in
value from the rents conferred by a banking charter, where
<1>B T is the value of those rents. 4
Realistically, ET can never be negative, since the owners
of a bank can always exercise their right of limited liability
to walk away from a losing proposition. Thus it must be
true that banks are closed at capital ratios above the level at
which the charter value would be completely offset by
negative net worth; that is, at the point k = c, it must also be
true that A - B - <1>B?;;O. Rewriting this restriction based
on the definition of the capital ratio, the closure threshold
must satisfy c?;; - <1>1 (1- <1». If the closure threshold were
set lower, regulators would be forced to inject funds-an
outright gift, not just a loan-to induce some low-capital
banks (those with c<k< - <1>/(1- <1») not to close voluntarily. The injection would have to be large enough to bring
assets, and hence the capital ratio, back up to the minimum
(3)
kT
==
5
level of - <1>/ (1- <1». While the FDIC does sometimes
provide so-called open bank assistance, the actual extent of
any wealth transfer is not obvious, since the emergency
funding generally must be repaid by the surviving institution, In such cases, any net injection of capital comes in the
form of FDIC acceptance of a below-market rate on the
funds. As an alternative and less complex treatment of this
possibility, any assistance anticipated by the market is
assumed to be capitalized into <1>, and c is always no less
than - <1>/ (1- <1».
As in most applications of contingent-claim methods,
assets are assumed to follow a stochastic process given by
(4)
where !-LA is the expected instantaneous periodic rate of
return on assets, t is a time index, dz is the differential of a
Wiener process, and a A is the instantaneous standard
deviation of the rate of return on assets, or asset volatility.
Let the date t = 0 represent the present, and let unsubscripted variables denote present values. Using standard
methods for valuing contingent claims (see Smith 1976),
the present value of equity with date T payoff as given in
(2) is
(5)
E=AN(x)-BN(x-aAVT) + <l>BN(x-aAVT),
(7)
where
((1 -
(6)
x -
In,
C)A)
B
VT =
a~T
+-2-
aAVT
and N(e)is the cumulative standard normal distribution
function. Equity is essentially a call option on assets, plus
an additional lump sum equal to the expected present value
of the charter. 5 The first two terms in (5) represent the
familiar option value; the third term is the charter value <l>B
weighted by a factor that is closely related to the probability that the bank will remain open. 6
Measures of Banking Risk
Given this theoretical framework, the central issue of
this paper can be posed more explicitly. In particular,
financial risk has increased at large banks if the market
6
value capital ratio k defined in (3) has decreased; operating
risk has increased at large banks if the volatility of assets
a A has increased.
The deposit insurance liability, which combines the
effects of both types of risk, also can be calculated explicitly once values for A and a A have been obtained. The
deposit insurance contract is another contingent claim and
can be evaluated using the same methods. All of the banks
in the sample are sufficiently large that the market has good
reason to expect that all creditors will be protected from
losses in the event of a failure; hence, the contingent
deposit insurance liability should be modeled under the
assurnption that the claim covered by the insurer is B, even
though not all liabilities are formally insured. The typical
method of resolution when such a large bank fails is to
locate a purchaser for the failed institution; the acquirer
receives the assets and the charter of the failed bank and
assumes all of the liabilities. If the liabilities assumed by
the acquirer exceed the value of the assets and charter, the
deposit insurer makes up the difference. Thus, the insurance fund pays the acquirer B - (<I>B + A) = (1 - <I»B - A if
that difference is positive, and otherwise pays nothing.
Formally, the insurer's payout is
(1-<I»BT-AT if BT>AT+<I>B T
I
o
if BT"'SA T + <l>B T
Again using standard contingent-claim valuation techniques, the value of the contingent payout in (7) is
(8)
V = (1- <I> )BN(y + a A VT) - Ae -yTN(y),
where
(1 - <I> )B\
(9)
y
==
In ( A
e
-"IT) -
a~T
-2-
aAVT
The dividend rate, "Y, appears in (8) and (9) because dividend payments directly reduce the assets available to the
deposit insurer in the event of failure. (Note that "Y is the
rate of dividend payments relative to assets, not equity.)
The overall risk to the deposit insurance fund posed by
large banks has increased if V has increased.
Economic Review / Fall 1991
III. A Method for Computing Asset Values and Asset Volatility
Assuming that the value of bank equity is determined as
in (5) it is possible to \\lork backward from the stock market
prices of large publicly traded banks to infer the market
value of assets and asset volatility. Various realistic values
can be assumed for bank liabilities B, the regulatory
monitoring interval T, the capital ratio closure threshold e,
and the charter value ratio <1>. The two remaining unknowns
in (5) are the value of assets (JA and the volatility of assets
(JA'
Obviously, a single equation cannot be solved for two
unknowns; a second independent equation is needed.
Merton (1974) suggests applying Ito's Lemma to the
expression for the value of equity, to yield a second
equation relating the volatility of equity and the volatility
of assets. Merton derives the relationship 7
(10)
(JE
=
(JA
aE A
aA
E
An intuitive grasp of (10) follows from considering the case
in which bank stockholders do not have limited liability for
the debts of the bank. In that case, the contingent aspect
that makes equity behave like a call option on assets
disappears, and the value of equity changes one-for-one
with the value of assets. 8 Then aElaA = 1, and (10) reduces
to (JE = (JA (AI E), with the straightforward interpretation
that the volatility of equity is simply the "levered-up"
volatility of the underlying assets. However, with limited
corporate liability, equity becomes somewhat less sensitive
to changes in asset values, as gains and losses are shared
partially with debtholders. Then aEliJA<I, and (JE falls
relative to (JAIn the present case, differentiation of (5) yields
(11)
aE
aA
=
N(x)
+
OBN'(x-(JA VT)
,
c;;-
,
A(JA vT
where N' (.) is the standard normal density function and
0= 1/(1- c) - (1- <1». Using (11), the expression in (10)
can be rewritten as
(12)
(JE=
AN(X)(JA VT +OBN'(x-(JA VT)
EVT
Equation (12) depends on all of the same variables as
equation (5). If (JE is observable, then under identical
assumptions regarding the parameters of the model, this
equation also has A and (JA as the only unknowns, and (5)
and (12) can be solved simultaneously for values of the two
unknown variables. 9
As noted above, solving these two equations to obtain
Federal Reserve Bank of San Francisco
market assets and volatility requires making assumptions
aboutthe other parameters: bank liabilities B, the regulatory monitoring interval T, the capital ratio closure thresholde, and the charter value ratio <1>. The market value of
bank liabilities is assumed to be approximately equal to
book value, since the bulk of bank liabilities are short term.
The monitoring interval is assumed to be one year; this
corresponds roughly to bank examination frequency. Assumptions regarding the charter value and closure threshold assumptions require more detailed explanation.
The Charter Value Ratio
Previous approaches to estimating bank charter value
are inappropriate for this analysis. For example, Keeley
(1990) divides the sum of book value liabilities and market
value equity by book value of assets, and uses this ratio as a
proxy for Tobin's q to examine changes in charter value;
Kwan (1991) applies a similar approach based on q. Such
estimates based on the market value of bank equity cannot
capture the concept of charter value as defined in this
paper, because they do not separate the effect of deposit
insurance from other components of measured charter
value. Some other method must be used to define a
reasonable value for <1>.
In practice, the value of a bank charter is likely to
manifest itself in nonmarket interest rate spreads: either a
rate of return on bank loans in excess of the required rate
for that level of risk, or a below-market rate of interest on
deposits, or some combination of the two. Hence, information on deposit and loan spreads can be used to develop an
estimate of <1>.
On the deposit side, if the bank charter gives the bank
the ability to set rd<rf and still attract federally insured
deposits, the basic contingent claim model of bank equity
must be modified; without the lump-sum charter value,
equation (5) becomes
(5')
E = AN(x') - Be(rd - rf)N(x' -
(J),
where T = 1 without loss of generality and
(6')
x' = In(AI B) + (rf - r d + (J2/2) .
(J
This can be viewed as an alternative formulation of the
basic model presented in (5), in which the charter value
is received as a flow over time in the form of a rate
spread rather than as a lump sum <1>B at the end of
the period. Comparing the two forms of the model, if
the relatively small effect of (r d - rf ) on x' is ignored,
7
then (1 - <p) = e(rd - rf). In this case, the charter value ratio
can be approximated by the deposit interest rate spread,
<p=rf - r d , since for realistic spreads it will be true that
e(rd- rf)=I- (rf - r d)'
If instead the charter allows the bank to earn an abovemarket rate of return on assets, a variant of the contingent
claim model is appropriate. McDonald and Siegel (1984)
consider the case of a contingent claim on an asset earning
a rate of return different from the appropriate risk-adjusted
rate. If A is the loan spread-the rate of return on loans
held by the bank minus the required rate of return for assets
of comparable risk-then the value of bank equity can be
expressed as
(5")
E
= Aet..N(x") -
BN(x" - cr),
where again T = 1 and
(6")
x"
=
In(AIB) + (A + cr 212)
cr
.
This version of the model, with A multiplied by a factor
et.. which is positively related to charter value, suggests that
the charter value should be modeled as being proportional to assets rather than liabilities in this case. However, recognizing that A = BI (1- k), that for most banks
N(x")=N(x" - cr), and that et..=1 + A for realistic values
of Ll, and ignoring the trivial effect of A on
a value of Ll
greater than zero increases the value of bank equity by an
amount equal to
x':
(13)
LiB
b.AN(x") = 1 _ k N(x" - cr).
Thus, in the context of the model presented above in (5),
the effect on bank equity is roughly equivalent to setting
loan spread was proxied by the difference between the
weighted average interest rate on short-term commercial
and industrial bank loans (from the Federal Reserve's
survey of terms of bank lending) and the rate on one-month
cOlnmercial paper. (One-month commercial paper was
used b~cause it was closest to the average maturity of bank
loans reported in the terms-of-Iending survey.) Combining
the average values of the interest rate spreads (based on
quarterly data for the sample period) with values of k
between 0 and 10 percent produced estimates of the value
of <p in the relatively narrow range of 0.016 to 0.018. Since
substantial approximation error is likely, these estimates
should be taken only as indicative of the neighborhood of
the charter value ratio; values for <I> of 0.01 and 0.02 are
used in Section V to bracket a reasonable range.
In the model, the charter value ratio is assumed to be
constant over time. In reality, interest rate spreads fluctuate, and a systematic trend might cause calculations based
on the assumption of constant <p to be biased. To test for the
existence of a trend, the sum of the interest rate spreads
was regressed on a time variable, with a correction for first
order autocorrelation. The trend coefficient was positive
but insignificant (at the 5 percent level) during the sample
period. Thus, the assumption that <I> is constant over time
probably is innocuous.
The charter value ratio also is assumed to be identical for
all banks in the sample. It is possible that differences
in managerial ability, location, and other factors might
cause different banks to reap different benefits from their
charters. However, the nine banks in this sample are sufficiently similar in size and character that interbank differences in <p are unlikely to be major, despite some
variation in business strategy among the sample firms.
(1- <p) = - Ll/(1- k).
If a chartered bank has positive spreads on both the
deposit and the loan side of the business, the joint effect
can be approximated as
(14)
where
(15)
The approximation in (15) was combined with data on
interest rates to provide a sense of reasonable values for <p.
The deposit rate spread was proxied by the difference
between the rate on six-month certificates of deposit (the
national average from Bank Rate Monitor) and the secondary market yield on six-month U.S. Treasury bills. The
8
The Closure Threshold
It is unlikely that regulators would seize any of the large
banks in the sample at positive market value capital ratios.
Hence, the assumed value of c almost certainly should be
zero or less. However, as noted in Section II, a credible
closure point cannot be so low that the charter value is
completely exhausted before the bank is closed; that is the
threshold must satisfy c;:?; - <1>/(1- <1». Since the charter
value ratio is assumed to be in the range of 0.01 to 0.02, the
closure threshold cannot be less than about 0.01 if <I> is on
the low side at 0.01, or 0.02 if <I> is 0.02.
As with the charter value ratio, there is some possibility
that c varies either over time, or across banks in the sample,
or both. Substantial interbank variation within this sample
seems unlikely, for the same reasons given above in the
discussion of <1>. As for variation over time, if closure
Economic Review I Fall 1991
policy changed during the period, there should be some
evidence of a change in the loss experience of the deposit
insurance fund. To examine this possibility, FDIC losses
resulting from bank closures (deposit payoffs, deposit
transfers, and purchase and assistance transactions) were
computed from the FDIC's Annual Report and divided by
the deposits of closed banks to construct a loss ratio. This
ratio was roughly the same at the end of the sample period
as at the beginning, and a regression of the ratio on a time
variable revealed no significant trend during the 1980s.
Thus, the assumption of constant c probably is a reasonable approximation. lO
IV. Equity Volatility From 'fraded Option Prices
The two-equation approach to deriving estimates of A
and <TA for a sample of banks has been used previously by
Marcus and Shaked (1984), Ronn and Verma (1986),
Furlong (1988), and Kendall and Levonian (1991), among
others. All of these earlier studies used the standard
deviation of historically observed stock returns for equity
volatility <TE' But conceptually, the relevant volatility is the
expected volatility over the period from t = 0 to t = T. Use
of historical volatility assumes that expectations at each
point in time are formed adaptively, and therefore reflect
realizations over some recent interval. If traders form their
expectations of <TE using information in addition to historical returns, then the historical standard deviation may be
a poor proxy for the expected volatility required in the
contingent-claim framework.
A more· direct measure of expected volatility is both
desirable and available. Options on bank stocks trade on
several U. S. options exchanges; the prices of stock options
are known to depend in part on the expected volatility of
the underlying stocks. Using an option pricing model,
values of expected <TE can be inferred from traded option
prices. ll Because exchange-traded stock options in the
United States have American terms (meaning that the holder may choose to exercise prior to expiration), expected
volatilities are inferred from an American option pricing
model developed by Barone-Adesi and Whaley (1987)
given by
(16)
C=Se
8'W(z)-Xe-rrN(z-<TE~
+ P(S,X,T,<TE,r,'&),
where C is the value of a T-period American call option
with exercise price X on a stock with price S and continuous dividend rate '& (dividends relative to equity), r is the
risk~free interest rate, and z is defined as
(17)
z ==
In(~)
+ T(r-'&)+
X
T<T~
2
<TEVT
The first two terms in (16) give the value of a European
option, which cannot be exercised prior to the expiration
date. The function peS, X, T, <TE . r, '&) is an approximation
Federal Reserve Bank of San Francisco
of the early exercise premium (the difference in value
between an American option and a European option due to
the possibility of early exercise), the exact form of which is
derived by Barone-Adesi and Whaley. They demonstrate
that their approximation works well for the range of
expirations used in this paper.
All of the variables in (16) are observable in the financial
press or elsewhere, with the exception of <TE' Although (16)
cannot be inverted for (J"E> standard numerical techniques
can be used to find the unique value of <TE satisfying (16),
which is referred to as the "implied volatility" of the stock.
This implied volatility can then be used in (12) to solve for
<TA andA.
Levonian (1988) showed that implied volatilities of bank
stocks differ substantially from volatilities calculated using historical stock returns. Both Black and Scholes (1972)
and Latane and Rendleman (1976) used tests based on
observed option prices to show that historical volatility is
inferior to implied volatility as a predictor of future volatility; Schmalensee and Trippi (1978) obtained similar
results. Hence, volatilities implied by option prices should
provide better information about the riskiness of bank
stocks, and consequently about the various types of banking risk, than would volatility estimates based on historical
stock returns.
However, the use of implied volatility is not without
cost. Since far fewer banks have traded options than have
traded stock, the sample size is reduced substantially. As
always in empirical research, small sample size may bias
the results. Thus, it is possible that the results may fail to
represent adequately the riskiness of the banking industry
as a whole, even though the volatility estimates for each
individual bank are likely to be superior.
Options Sample
The sample for this paper consists of listed call options
from the various options exchanges in the United States,
sampled at the ends of the second and fourth quarters of the
five years 1985 through 1989, for nine large banking firms:
BankAmerica, Bankers Trust, Chase Manhattan, Chemical, Citicorp, First Chicago, J.P.Morgan, Manufacturers
9
Hanover, and Security Pacific. This group comprised nine
of the top ten U. S. banks at the beginning of 1985, ranked
by assets. (The tenth, First Interstate, also has exchangelisted options, but trading was too infrequent to allow
construction of a reliable time series.) These are options on
the common stocks of bank holding companies, not banks;
however, to the extent that the predominant assets of
holding companies are banking-related, the implied volatilities provide information on bank asset risk. The term
"bank" is used to refer to these firms throughout the paper.
The interest rates used in the option pricing model were
the yields-to-maturity on the U.S. Treasury bills maturing
closest to the expiration date of each option. The dividend
rates were computed by assuming that expected dividends
during the life of each option were identical to dividends
actually paid·and then calculating equivalent continuous
rates. 12 Last -trade~of-the-week call option prices and stock
prices for the nine banks were collected from published
listings in The Wall Street Journal.
Day and Lewis (1988) describe two sources of potential
bias in the use of published prices. One is the problem of
nonsynchronous trading, that the last option trade for any
given bank may not have occurred at the last observed stock
price; the option valuation model in (16) requires the use of
a contemporaneous stock price. The other is that stocks and
options trade with a spread between the bid price and the
ask price, and reported trades may occur at either the bid or
the ask or at prices in between, making it impossible to
observe a precise estimate of value. Day and Lewis argue
that estimates of implied volatility should incorporate
information from the prices of several different options on
the same stock in order to minimize the potential bias.
Studies of option volatility have used a variety of methods
for combining different options on a single underlying
security (for example, compare Day and Lewis to Latane
and Rendleman or Schmalensee and Trippi.
To deal with these problems, for each bank only the two
options with exercise prices closest to the current stock
price are used. That is, for all of the options with exercise
prices above the current stock price, the option with the
lowest exercise price is selected; in addition, for all of the
options with exercise prices below the stock price, only the
one with the highest exercise price is selected, for each
bank. Day and Lewis show that trading volume is concentrated in these "near-the-money" options; for the index
options they examine, about 70 to 90 percent of the volume
is in options with exercise prices just above and just below
the current stock price. Even a cursory review of published
options sales data confirms that this relationship is true in
general. As Day and Lewis point out, any lack of synchronization between the closing stock price and the closing
10
option price will be minimized for these options. They also
note that the percentage bid-ask spread is less for these
options, reducing the second source of· bias as well.
(Feinstein 1988 provides a discussion of other desirable
properties of near-the-money options for the purpose of
inferring volatilities from prices.)
It is possible that at any point in time market traders
anticipate that volatility will change in some predictable
way over time. In that case, the options from which the
stock volatility is inferred should have expirations identical
to the regulatory monitoring interval for banks, assumed to
be one year in this paper. However, until very recently
exchange~traded stock options were restricted to expira~
tions ofless than a year; moreover, the most active trading
generally occurs in options with short expirations. Thus,
short-term options are likely to yield superior estimates of
expectedcrE' and these estimates can be used in the bank
equity model provided that volatility is not expected to
change drastically between the expiration date of the
option and the end of the regulatory monitoring period.
However, using the shortest expirations may introduce
other problems; Day and Lewis document a statistically
significant increase in implied volatility for options as the
expiration date approaches, especially in the last few
trading days. They attribute this effect to technical factors
related to the unwinding of hedged positions. To achieve a
balance between both types of distortions, the options
sample for this study consists of the shortest-term options
for each bank, but with a minimum time to expiration of
one month. This sample selection process is similar in
spirit to that used by Schmalensee and Trippi (1978).
An additional complicating factor is that unusual events
or changes in option market liquidity might cause option
prices from a single week to be unrepresentative of the true
riskiness of banks. To minimize this problem, prices were
sampled for three consecutive weeks surrounding each
semiannual sample point: The week of the financial reporting date, one week before that date, and one week after. For
each bank in each of the weeks, prices of the two call
options with exercise prices nearest to the underlying stock
price and with shortest time to expiration (but exceeding
one month) were collected. Implied stock volatility was
calculated for each option, and all six options averaged for
each bank at each semiannual date. The procedure produced 90 estimates of volatility (ten semiannual observations for nine banks).!3
Stock Volatility Estimates
A weighted average of the nine banks was computed for
each time period to summarize the resulting implied stock
Economic Review / Fall 1991
volatilities and to present the pattern of changes during the
late 1980s. The weights for the observations were the
market value of each bank's equity (stock price multiplied
by number of shares) divided by the total market value of
equity of all nine banks for that date. The resulting weighted average can be viewed as an index of implied bank stock
volatility, with heavier emphasis given to banks that are
larger components of total bank stock market value. (Alternatively, if returns on bank stocks were perfectly correlated, this average would equal the volatility of a stock
portfolio consisting of equal percentages of each bank's
equity, for example 5 percent of Bank A, 5 percent of Bank
B, etc.) The results are presented in Chart 1, with volatility
stated in annual terms (that is, the figures can be interpreted as standard deviations of annual percentage changes
in the prices of the stocks). A similarly constructedindex of
historical volatility is presented for comparison. Historical
volatility was computed as the annualized standard deviation of stock returns for the 60 trading days (roughly three
months) preceding the end of the quarter.
One notable feature of Chart 1 is the upward spike in
both implied and historical volatility in the fourth quarter
of 1987. Implied volatility rose from 22 percent to 36
percent, and historical from 26 percent to 40 percent. This
spike corresponds to the period immediately following the
stock market crash of October 1987. Over the following
year, volatility returned to levels similar to those preceding
the crash. This pattern was not unique to bank stocks:
Schwert (1990) documents similar effects for implied and
historical volatility for the overall stock market as measured by the S&P500 stock index.
While the patterns of historical and implied volatility
around the time of the crash are similar, there are noticeable differences in the rest of the sample period. Historical
is almost always higher than implied for this sample, and
three of the nine quarter-to-quarter changes are opposite in
sign. The fourth quarter of 1989, in which the divergence is
especially pronounced, provides an excellent example of
the primary drawback of historical volatility. The high
standard deviation of realized returns for the fourth quarter
of 1989 is due to stock price movements on two dates,
Chart 1
Stock Return Volatility
Portfolio of 9 BHes
Annualized
Standard Deviation
.45
.40
GO-Day
Historical
~
.35
.30
.25
.20
.1 5 +---.-----.-,----,---,--,.---.----,-----,
85:11 85:IV 86:11 86:IV 87:11 87:IV 88:11 88:IV 89:11 89:IV
Friday October 13 and Monday October 16. On Friday, the
failure of VAL Corp. to obtain financing for a leveraged
buyout precipitated a large decline in the overall stock
market. Stocks of large banks were hit especially hard,
apparently because the news was taken as a signal of a
fundamental change in a major line of business. (Citicorp
had the largest percentage single-day drop at 16 percent,
and J.P. Morgan had the smallest at 5.5 percent.) On
Monday, stock prices increased, recovering a portion of the
value lost on the preceding Friday. A 60-day historical
volatility calculation treats returns from these days equally
with the other 58 days in the period. In reality, it is likely
that traders viewed these two days as extreme events, and
that by the end of December traders gave them little weight
in formulating expectations of bank stock volatilities. The
lower implied volatilities from option markets for 89:IV
are direct reflections of expectations at that date, automatically discounting any information that is irrelevant to
future returns.
V. Changes in Banking Risk, 1985-1989
The stock volatility results hold some intrinsic interest,
and are roughly comparable to the bank stock volatility
results presented by Jonathan Neuberger in another article
in this Review. (Neuberger examines changes in bank stock
risk during the 1980s in greater detail, and investigates the
relationship between bank stock returns and returns in the
bond market and the overall stock market.) However, the
Federal Reserve Bank of San Francisco
main purpose of the preceding stock volatility computations is to provide the raw material for other calculations
related to banking risk. In this section, estimates of the
three measures of banking risk are presented for the second
half of the 1980s. Asset volatilities are obtained from the
simultaneous solution of equations (5) and (12), using the
implied (J'E for each bank in each period as the input to (12).
11
The solutions for market asset values from (5) and (12) are
used to compute market value capital ratios from equation
(3). Finally, the liability of the insurance fund is calculated
from (8), also using the two-equation solution values of <TA
andA.
As discussed in Section III, the market value of bank
liabilities is assumed to be equal to book value, and the
monitoring interval is set equal to one year. The actual
dividends paid by each bank during each year are used to
compute the dividend rate 'Y in (8), under an assumption
that dividends were paid as expected. The earlier discussion of realistic ranges for the charter value ratio and the
closure threshold concluded that <1>=0.01 and <1>=0.02
would provide a reasonable bracket for charter value, and
that c should be less than or equal to zero, but no larger in
absolute value than <1>. Thus, four cases are considered for
combinations of these two parameters:
Cl: c = 0.00, <I> = 0.01
Charters have low value, and
banks are closed when they are
insolvent in market value, that
is, when A<B.
C2: c = 0.01, <I> = 0.01 Charters have low value, and
banks are closed when charter
value is exhausted.
C3: c = 0.01, <I> = 0.02 Charters have high value, and
banks are closed before charter
value is exhausted.
C4: c = 0.02, <I> = 0.02 Charters have high value, and
banks are closed when charter
value is exhausted.
Comparing the results from the four cases provides insight
into the sensitivity to changes in the assumptions. Three
pairwise comparisons are most interesting:
Cl vs. C2: impact of a lower closure threshold when
charter value is low.
C3 vs. C4: impact of a lower closure threshold when
charter value is high.
C2 vs. C3: impact of higher charter value with a fixed
closure threshold.
Operating Risk
Weighted averages are constructed to summarize the
individual bank results for each time period, with each
bank weighted by liabilities relative to total liabilities of
the nine banks for that date. The individual banks could
instead have been weighted by equity (as with the stock
volatilities above) or by assets. Other weightings produced
very similar results.
Chart 2 shows the evolution of bank operating risk as
reflected in annualized figures for asset volatility. Only
12
Chart 2
Asset Volatility
Assumptions: Case C4
Annualized
Standard Deviation
.012
.011
.010
.009
.008
.007
.006
.005
.004 +----.----r--r--,,....--.,..---r----r--r--,
85:11 85:IV 86:11 86:IV 87:11 87:IV 88:11 88:IV 89:11 89:IV
case C4 is presented, because alternative assumptions
about c and <I> had very little effect on the estimates of <TA .
The general upward trend shows that operating risk did
indeed increase at large banks during the late 1980s: The
level of asset volatility in 89:IV was about 80 percent
higher than in 85:II. At least in part, this increase may have
been due to the expanded range of activities conducted by
banks. The rate of increase in operating risk is consistent
with that found by Furlong (1988) for the early 1980s,
implying that bank assets became progressively more
volatile across the entire decade. Interestingly, the increase
in average asset volatility in the fourth quarter of 1987 was
not dramatically different from adjacent periods. Hence,
the significant jump in stock volatility in that period was
not due to any great increase in the riskiness of bank assets
as perceived by the market.
The pattern of asset volatility during the period is most
heavily influenced by the larger banks in the sample, such
as Citicorp, because of the use of a weighted average. The
patterns for individual banks differ somewhat, although for
each of the nine banks asset volatility was higher at the end
of the sample period than at the beginning.
Financial Risk
Chart 3 shows weighted-average market capital ratio
results for two illustrative cases, C2 and C3. Capital ratios
were higher at the end of the sample period than at the
beginning, implying that financial risk decreased at large
Economic Review / Fall 1991
Chart 3
Market Capital-Asset Ratio!)
Percent
.047
.042
.037
.032
.027
returns reflected in call option prices stemmed from
traders' recognition that any given percentage change in
the return on bank assets would translate into a much larger
percentage change in return on the stock, when viewed
relative to the lower base value of equity. (In terms of
equation (10), the ratio AlE increased; for a given (T A> this
leverage increase caused (TE to rise.) An interesting implication of the results presented here is that, at least for
banks, the increase in volatility was of roughly the magnitude that should be expected after a decline in market
equity-to-asset ratios of the extent experienced in the
October crash .
.022
.017
The Deposit Insurance Liability
.012
.007 +----,---,..----,-.....------,-------,-----,-.....-...,
Chart 4 shows the path of the estimated deposit insurance liability over the sample period. Because the overwhelming impact of the stock market crash makes it hard to
see the pattern of changes in the deposit insurance liability
for other periods, Panel B displays the same results as Panel
A, but with the 87:IV data omitted.
Panel A displays the total value of the liability at each
date, summed across banks, for each of the four parameter
cases. The stock market crash had a temporary but dramatic impact on the computed liability of the insurance fund.
In case Cl, for example, the liability rises from $2.4
million in 87:IIto $45.3 million in 87:IV, then falls back to
near the year-earlier level by 88:II. The reason is clear fTom
Chart 3: The fall in market capital ratios associated with
the decline in bank stock prices caused a large increase in
financial risk at these banks, and the ensuing recovery in
market value reversed the change. Each bank in the sample
exhibits roughly the same pattern.
In all four cases in Panel B, the liability is only slightly
higher at the end of the sample period than at the beginning. This conclusion would hold even if the correct values
of c and <p changed during the period. For example, if
regulators began allowing more poorly capitalized banks
to remain open as time passed, so that C3 was most
realistic at first and C4 was most realistic at the end, the
89:IV liability in case C4 is still little greater than the 85:II
liability in case C3.
However, it is also true that the deposit insurance liability increased substantially during the middle part of the
sample period, and that the increase predated the stock
market crash. The change in risk was driven by the general
increase in financial risk that began in 86:II, during a
period of rising operating risk. The increase in market
capital ratios toward the end of the sample period (assisted
by the relatively large drop in asset volatility in 88:II)
85:11 85:IV 86:11 86:IV 87:11 87:IV 88:11 88:IV 89:11 89:IV
banks. (The pattern also is representative of the banks
individually, except that several banks show slight declines
in capital ratios in the fourth quarter of 1989.) However,
market capital ratios suffered a tremendous hit in the stock
market crash, from which they only gradually recovered
over the next one-and-a-half to two years.
In the tw() cases omitted from Chart 3, Cl was essentially
the same as C2, and C4 was little different from C3, demon~
strating that variations in the assumed closure threshold
have a trivial impact on the resulting capital ratio estimates. The only major distinction among the four alternative sets of assumptions was that variations in the assumed
charter value produced capital ratios that differed by
roughly the magnitude of the difference in the charter value
ratio. The reason is straightforward. Recall that the capital
ratio k is based on assets exclusive of the charter value;
since a higher charter value should make bank stock more
valuable all else equal, a given market value of equity can
only be consistent with a lower market value of ass~ts,and
hence a lower market value of bank capital. Except forthis
charter value difference, the pattern over time is very
similar in all four cases.
The decline in the market capitalization of banks resulting from the October 1987 crash evident in Chart 3 explains
the pattern of implied stock volatility observed in Chart 1.
Although Chart 2 showed that the riskiness of bank assets
did. not increase, the market value of equity fell as st()ck
prices collapsed, and large banks suddenly becatIl~ nmch
mOre highly levered. The higher volatility of bank stock
Federal Reserve Bank of San Francisco
13
C hart 4
D e p o sit In su ra n ce L ia b ility
Panel A: With 1987:!V
brought the deposit insurance liability down to near its
earlier level.14
Comparison of the various cases reveals that assump
tions about the closure threshold and the charter value ratio
have some impact on the computed deposit insurance
liability at each point in time, although not a major impact.
Comparing Cl to C2 and C3 to C4 shows that an earlier
closure assumption reduces the total liability. The magni
tude of the effect is roughly the same under either charter
value assumption. (Note that this result does not demon
strate that instituting a policy of earlier closure would
reduce risk to the deposit insurance fund. These derived
results are conditional on the observed prices of bank
stocks; an explicit policy change probably would generate
a behavioral response by banks, and would alter the market
value of bank equity, thus complicating any evaluation of a
change in regulatory policy. This point is similar to the
“ Lucas critique” in macroeconomics.)
Comparing C2 to C3, different assumptions about the
value of bank charters have a somewhat larger impact on
the computed liability, for a given closure threshold as
sumption: The higher value of < implies a smaller deposit
j>
insurance liability. This effect stems from the assumption
that the deposit insurer uses the charters of failed banks to
offset at least partially any required transfer from the
insurance fund. It is interesting also to compare C2 to C4
in this regard. In both cases, the closure threshold is set so
that the bank is closed as late as possible, when the charter
value is completely exhausted by losses on bank assets.
14
$ Millions
Panel B: Without 1987:1V
Even with this extreme closure assumption, higher charter
value reduces risk to the insurance fund.
The inverse relationship between assumed charter value
and the deposit insurance liability might seem to be at odds
with the conclusion from Chart 3, which showed that
higher assumed charter value increases financial risk. The
apparent conflict can be resolved by recognizing that while
higher charter values reduce measured capital ratios, the
additional value is captured by the insurer in the event of a
bank seizure, leaving little net effect on the insurance
liability from changes in this parameter.
The moderate sensitivity of the deposit insurance results
to alternative assumptions about the unobservable param
eters makes it inappropriate to attach great weight to the
specific dollar amounts of the liability; it is the general sec
ular trends that are the important features for the aims of
this paper. The overall pattern is clear, using any of the four
parameter combinations: Despite a large increase in risk to
the deposit insurance fund during the middle of the sample
period, risk from these nine large banks was back down to a
relatively low level by the end of the decade.
It is interesting to return to the comparison of historical
stock volatility and implied stock volatility, and examine
whether the difference between the two would affect the
conclusions in this section. Chart 5 compares estimates of
the total deposit insurance liability based on implied and
historical crE, using C4 assumptions. The difference in the
fourth quarter of 1989 is huge. Using historical volatility,
the risk to the deposit insurance fund appears to be much
E conom ic R eview / Fall 1991
Chart 5
Effects of Implied and
Historical Volatility on
Deposit Insurance Liability
Assumptions: Case C4
$ Millions
40
Based on
Historical Volatility
35
30
25
~
Based on
Implied Volatility
~
20
15
10
5
o
-F==~~--,--,-_..----...,...-~~=i
85:11 85:IV 86:11 86:IV 87:11 87:IV 88:11 88:IV 89:11 89:IV
higher at the end of the sample period than at the beginning. However, as noted in Section IV, the difference
between historical and implied volatility in 89:IV is due
almost entirely to stock price movements on two consecutive trading days, probably related to the collapse of the
UAL leveraged buyout. In this case, implied and historical
volatility lead to significantly different conclusions, and
the results based on historical clearly are questionable.
Summary
The results in this section indicate that there was no
significant overall increase in the riskiness of large banks
during the late 1980s. The riskiness of bank assets and
activities did increase at large banks over the five-year
period studied, but concurrent with this increase in operating risk, financial risk fell as market capital ratios rose. The
increase in market capital ratios was sufficient to prevent a
large secular rise in the burden on the insurer. By the end of
the sample period, these large banks posed little more risk
to the deposit insurance fund than at the beginning of the
period.
It is not surprising that capital increased as asset volatility rose, since the regulatory guidelines in effect during
this period explicitly required banks engaged in riskier
activities to maintain higher capital ratios (Board of Governors 1985). The positive relationship is evident in Table 1,
which shows a high positive correlation between asset
volatility and capital across the sample within each period.
(If the results for individual banks were assumed to be
drawn from normal distributions for each variable, the 5
percent critical level for a null hypothesis of p = 0 would be
0.666; the correlation coefficients would be judged to be
significantly greater than zero, except in 1985). The rise in
market value capital ratios does not reflect simply a passive
increase as bank stock prices increased along with the
overall stock market. The book value of bank equity also
rose, both absolutely and relative to the market value of
bank assets, with much of the rise due to earnings retention
and new equity issuance. Thus, the reduction in financial
risk probably was an active response to a perceived need
for greater capital.
VI. Conclusions
This paper considers the evolution of bank risk during
the late 1980s, with.a focus on nine large U.S. banking
firms. The unusual element of this study is the use of
exchange-traded options on bank holding company stocks
to infer the volatility of bank assets and activities. The
Federal Reserve Bank of San Francisco
results show that operating risk increased by about 80
percent during the period. However, with the exception of
the period around the 1987 stock market crash, financial
risk generally declined. When the two separate changes are
combined to examine overall risk to the deposit insurance
15
fund, it appears that the burden imposed by large banks on
the deposit insurer was little different at the end of the
sample period than at the beginning.
Hence, while the data do support the notion that banks
now engage in generally riskier activities than they did
previously, market capital ratios have on average kept pace
with the evolving mix of banking services and products,
thus preventing deterioration in the degree of protection
provided by bank capital. Large banks did not become
substantially riskier in what is probably the most important
public policy sense, the risk imposed on the deposit
insurance fund. Additional regulatory actions to force
reductions in bank risk-taking appear neither necessary nor
warranted, at least on the strength of changes in risk at
large banks during the late 1980s.
ENDNOTES
1. The only known previous use of these data (Levonian
1988) examined a shorter time period and used a simple
but not strictly appropriate option pricing model.
2. The model presented by Levonian is a generalization of
Merton's and two others, Marcus (1984) and Ronn and
Verma (1986). The differences among the various models
are summarized in Levonian (1991).
3. The main motivation for assuming that charter value is
proportional to liabilities is modeling convenience; however, the assumption also is appropriate to the extent that
franchise value is related to the size of a bank's "core"
deposit base.
4. In a multi period setting, <1>8 would reflect the discounted value of the future stream of rents as well.
5. This formulation differs slightly from Levonian (1991). In
the present version, any regulatory costs are capitalized
into the value of bank assets. Note that the dividend rate
does not appear in (5) or (6). Equity is essentially a
"dividend-protected" call option, in which the option holder receives the benefits of the dividend cash flow that
otherwise would reduce the value of assets and hence
equity.
6. The factor N(x - (J'A vf) is actually the probability that
the bank would remain open in a world of risk-neutral
investors, that is, a world in which the assets of the bank
earn the risk-free rate of return.
7. According to It6's Lemma, if A(t) is determined by the
stochastic process in equation (4), and equity is a function
of A(t) and t, then the differential of E(A(t), t) is given by
dE
=
aE
aE
a2 E
aA dA+ar dt+ aN (dA)2,
which is essentially a Taylor series expansion of E, with all
higher-order terms vanishing as dt approaches zero (that
is, in continuous time). Substituting for dA from (4), regrouping terms, and recognizing that (dt)2=0, dtdz=O,
and (dz)2 = dt yields
dE =
16
dt+
The term in parentheses is the expected drift of the
process. Defining ftE as the expected drift term divided by
E (to create a percentage rate of change), the differential
dE can be written as
dE = ftEEdt + (J'EEdz,
where (J'E is given by (10). For a relatively simple discussion
of It6's Lemma and the associated stochastic calculus,
see Haley and Schall (1979), Chapter 10. For a more
rigorous but still accessible treatment, see Merton (1982).
8. This also is approximately true if the bank is very wellcapitalized, so that the probability of closure is insignificant. As a bank moves closer to the point of closure, the
contingent element becomes more important.
9. Again, if the contingent element of equity is trivial, then
N(x)=1 and N'(X-(J'AYT)=O, so that ITE=(J'A(AIE).
10. Linear regression analysis cannot rule out the possibility that c and vary in some nonlinear but known '«9,y
during the sample period. Neither direct nor anecdotql
evidence suggests that changes in either parameter are a
major problem for the period studied, although King and
O'Brien (1991) argue that regulators might systematically
vary the threshold (and the monitoring interval) with the
condition of each bank. Since this possibility cannot be
ruled out, some degree of caution is appropriate in interpreting the results. Most previous studies using similar
contingent-claim models have implicitly held both the
closure threshold and the charter value ratio constant over
time and across banks, often without the critical examination given to these assumptions in this paper; Furlong
(1988) is an exception.
11. Schellhorn and Spellman (1991) calculate implicit volatilities from the prices of subordinated debt issued by
bank holding companies, using the fact that risky debt
can be valued as riskless debt minus a put option on the
assets of the issuer. The spirit of the Schellhorn-Spellman
approach is very similar to the present analysis. One
drawback to their use of subordinated debt is that the
sample size is smaller, because so few banks have regularly traded subordinated debt outstanding.
12. Day and Lewis (1988) make identical assumptions
regarding interest rates and dividends.
13. Other methods for computing implied volatility typically involve weighted averages of obseNed option volatilities; see Bodurtha and Courtadon (1987, pages 28-30)
Economic Review I Fall 1991
for a discussion. All of the methods give heavier weight to
near-the-money options, and therefore in practice are
likely to yield results close to those obtained through the
simpler approach used here (arithmetically averaging
only the nearest-the-money options).
14. The relatively small estimated insurance liability in
Cha.rt 5 is a result of the assumption that the FDIC sells the
charters of failed banks to defray the cost of covering
deposits; only the liability net of the charter value, as
developed in equation (8), is presented.
REFERENCES
Barone-Adesi, G, and R. Whaley. 1987. "Efficient Analytic
Approximation of American Option Values." Journal
of Finance 42(3) pp. 301-320.
Black, F., and M. Scholes. 1972. "The Valuation of Options
Contracts and Test of Market Efficiency." Journal of
Finance 27(2) pp. 399-417.
Board of Governors of the Federal Reserve System. 1985.
"Revisions to Guidelines for Capital Adequacy." Federal Reserve Bulletin 71 (6) pp. 440-441.
Bodurtha, J., Jr., and G. Courtadon. 1987. The Pricing of
Foreign Currency Options. Salomon Brothers Center
for the Study of Financial Institutions Monograph.
Day, T., and C. Lewis. 1988. "The Behavior of the Volatility
Implicit in the Prices of Stock Index Options." Journal
of Financial Economics 22(1) pp. 103-122.
Feinstein, S. 1988. "A Source of Implied Volatility Estimates." Working Paper 88-9. Federal Reserve Bank of
Atlanta. (December).
Furlong, F. 1988. "Changes in Bank Risk-Taking." Federal
Reserve Bank of San Francisco Economic Review
(Spring) pp. 45-56.
Haley c., and L. Schall. 1979. The Theory of Financial
Decisions. New York: McGraw-HilI.
Keeley, M. 1990. "Deposit Insurance, Risk, and Market
Power in Banking." American Economic Review 80(5)
pp.1183-1200.
Kendatl, S., and M. Levonian.1991. "ASimpleApproachto
Better Deposit Insurance Pricing." Journal of Banking
and Finance 15, pp. 999-1018.
King, K., and J. O'Brien. 1991. "Market-Based Deposit Insurance Premiums: An Evaluation." Federal Reserve
Board of Governors (April) (unpublished).
Kwan, S. 1991. "Risk and Charter Value in Banking." Paper
presented at the 27th Annual Conference on Bank
Structure and Competition, May 1-3, Federal Reserve
Bank of Chicago, Chicago, IL.
Latane H., and R. Rendleman. 1976. "Standard Deviations
of Stock Price Ratios Implied in Options Prices." Journal of Finance 31 (2) pp. 369-381.
Levonian, M. 1988. "The Value of F.D.I.C. Insurance Using
Prices of Listed Options." Paper presented at the
meeting of the Financial Management Association,
October 12-15, New Orlea.ns, LA.
_ _ _ _ . 1991. "What Happens if Banks Are Closed
'Early'?" In Rebuilding Banking: Proceedings of the
27th Annual Conference on Bank Structure and Competition, May 6-8. Federal Reserve Bank of Chicago,
Chicago, IL.
a
Federal Reserve Bank of San Francisco
Marcus, A. 1984. "Deregulation and Bank Financial Policy.
" Journal of Banking and Finance 8 (December) pp.
557-565.
_ _ _ _ , and I. Shaked. 1984. "The Valuation of FDIC
Deposit Insurance Using Option-pricing Estimates."
Journal of Money, Credit, and Banking 16(4) pp. 446460.
McDonald, R., and D. Siegel. 1984. "Option Pricing When
the Underlying Asset Earns a Below-Equilibrium Rate
of Return: A Note." Journal of Finance 39(1) (March)
pp. 261-265.
Merton, R. 1974. "On the Pricing of Corporate Debt: The
Risk Structure of Interest Rates." Journal of Finance
29(3) pp. 449-470.
_ _ _ _ . 1977. "An Analytic Derivation of the Cost of
Deposit Insurance and Loan Guarantees." Journal of
Banking and Finance 1(3) pp. 3-11.
_ _ _ _ . 1982. "On the Mathematics and Economics
Assumptions of Continuous-Time Models." In Financial Economics: Essays in Honor of Paul Cootner, ed.
W. Sharpe and C. Cootner, pp. 19-51. Englewood
Cliffs: Prentice-Hall.
Neuberger, J. 1991. "Risk and Return in Banking: Evidence from Bank Stock Returns." Federal Reserve
Bank of San Francisco Economic Review Fall pp.
18-30.
Ronn, E., and A. Verma. 1986. "Pricing RiSk-Adjusted
Deposit Insurance: An Option-Based Model." Journal
of Finance 41(4) pp.871-896.
Schellhorn, C., and L. Spellman. 1991. "Subordinated
Debt Market Information and the Pricing of Deposit
Insurance." In RebUilding Banking: Proceedings of
the 27th Annual Conference on Bank Structure and
Competition, May 6-8, Federal Reserve Bank of Chicago, Chicago, IL.
Schmalensee, R., and R. Trippi. 1978. "Common Stock Volatility Expectations Implied by Option Premia." Journal of Finance 32(1) pp.129-147.
Schwert, G.w. 1990. "Stock Volatility and the Crash of '87."
Review of Financial Studies 3(1) pp.77-102.
Shaffer, S. 1991. "Aggregate Deposit Insurance Funding
and Taxpayer Bailouts." Journal of Banking and Finance 15, pp. 1019-1040.
Smith, C. 1976. "Option Pricing: A Review." Journal of
Financial Economics 3(1) pp. 3-51.
17
Risk and Return in Banking:
Evidence from Bank Stock Returns
Jonathan A. Neuberger
Economist, Federal Reserve Bank of San Francisco. The
author thanks Brantley Dettmer for research assistance.
The members of the editorial committee, Brian Motley,
Mark Levonian, and Gary Zimmerman, provided many
helpful comments.
In this paper, I investigate the behavior ofbank holding
company stock returns from 1979 to 1990 in order to
determine if bank risk has increased in recent years.
Simple statistics on total volatility ofreturns indicate that
the variance ofbank stock returns rose in the latter part of
the 1980s relative to earlier periods and to other stock and
bond investments. In the context of equilibrium asset
pricing models, I find that bank stock return covariance
with respect to overall stock market returns increased
during the 1980s while the sensitivity of bank stocks to
returns on long-term debt securities declined. I also divide
the sample by bank size andfind that stocks oflarger banks
exhibited more stock market risk than smaller banks in the
latter part of the 1980s, while no banks exhibited any
statistically significant interest rate risk in the late 1980s.
18
There is currently a widespread perception that the U.S.
banking system has become riskier in the past several
years. The large number of bank failures, negative media
coverage of the industry, and the rhetoric of legislative
efforts in Washington to restructure the banking system all
have contributed to this perception. Moreover, the legacy
of the savings and loan crisis serves as a constant reminder
of the excessive risks that some U. S. financial institutions
undertook in the 1980s.
Industry observers have identified a number of factors
that are potential causes of this apparent increase in bank
risk. The usual list of suspects includes deregulation of
financial markets, increased competition in banking, and
financial innovation. The cause of any increased risk in
banking probably will be a subject of debate for some time.
Nevertheless, it is instructive to investigate the recent
behavior of bank risk to determine if the public perception
of greater risk is justified and whether any changes in risk
have occurred in a systematic way. In this paper, I conduct
such an investigation.
As a measure of bank risk, I consider the volatility of
bank stock returns. Ideally, a direct measure of bank asset
Iisk might be preferred, but it is difficult to observe the
risks associated with specific bank assets. The behavior of
bank stocks provides a reasonable, and readily available,
alternative. In the absence of regulation or deposit insurance, there is a direct relationship between asset risk and
stock risk. This relationship is complicated by the presence
of financial regulation and the deposit insurance system,
but the risk associated with holding bank stocks is still
informative about the risks to the banking system. Moreover, the current focus on increased capital requirements
for banks makes understanding bank stock risk particularly relevant. Common stock comprises the largest portion of bank capital and thus the value of bank equity
provides a good proxy for bank net worth.
In this paper, I use a time series, cross-section sample of
large U. S. commercial bank holding companies to examine the behavior of bank stock returns over the period 1979
to 1990. I consider first the overall volatility of these
returns. Then, drawing on theories of capital asset pIicing,
Economic Review / Fall 1991
I consider the influence of different systematic risk factors
on the behavior of U. S. banks' stock returns.
The results from this analysis indicate that the relationship of bank stocks to systematic sources of risk in the
economy has changed significantly during the past several
years. Certainly, some sources of bank equity risk increased during the 1980s. However, my analysis shows that
other sources of stock return variability actually declined
during this period. My results also indicate that there is
considerable variation among the banks in the sample
regarding their equity risk. For example, I separate the
banks in the sample by asset size. I find that the sensitivity
of stock returns of large banks to overall stock market risk
has increased relative to that of smaller banks. An understanding of such cross-sectional variations may help to
identify potential winners and losers arising from proposals to reform the banking system.
While the study of bank stock returns provides useful
insights into changes in bank risk, it is important to
recognize the limitations of these data. The variability of
bank stock returns reflects the market's perception of the
risks associated with all aspects of bank holding company
activities. These include asset risks, default risks, charter
value risks, the risks associated with the value of the
deposit insurance guarantee, and so on. It is not possible to
infer from these data what has happened to a particular
aspect of bank risk, say for example, to the riskiness of
bank assets. (For a study of bank asset risk, see Mark
Levonian's paper in this issue of the Review). The results
here identify how the systematic risk factors included in
asset pricing models influence the market's perception of
this amalgam of bank stock risks and how this perception
is reflected in bank equity returns.
I. Related Literature
According to the capital asset pricing model (CAPM,
Sharpe 1964 and Lintner 1965), the return on a firm's
equity can be explained as a function of a single factor,
namely, the return on the market portfolio of assets. In
empirical applications of the CAPM, the proxy for this
market return typically is taken to be a broad measure of
stock market returns (such as the S&P 500, or the AMEX
composite index). The CAPM splits asset risk into two
components. The first, called market or systematic risk,
represents that portion of asset risk that is related to the
riskiness of the market portfolio. The second component is
called residual, or nonsystematic, risk and is the portion of
total asset risk that is unrelated to the market portfolio.
Because an investor can eliminate the effects of nonsystematic risk by suitably diversifying his portfolio, the
CAPM argues that the expected returns on individual
assets reflect only their systematic risk.
Bank stocks have been a frequent object of analysis in
studies of equity risk and returns. Banks are of particular
interest to economists because of their role as financial
intermediaries. This role is believed to make bank stocks
especially sensitive to changes in interest rates. To test this
hypothesis, a number of studies have extended the basic
CAPM formulation to include a measure of returns on debt
in addition to the return on the market portfolio of stocks.
This "two-index model" was first proposed by Stone
(1974), and variations ofthis model have been investigated
in subsequent work by Martin and Keown (1977), Lloyd
and Schick (1977), Lynge and Zumwalt (1980), Chance
and Lane (1980), Flannery and James (1982, 1984a,
1984b), Beebe (1983), and Booth and Officer (1985). With
Federal Reserve Bank of San Francisco
the exception of the paper by Chance and Lane, these
studies have found that bank stock returns exhibit sensitivity to interest rates over and above their sensitivity to
stock market changes. Moreover, this sensitivity exceeds
that shown by most nonfinancial firms, confirming the
notion that the particular nature of bank assets and liabilities makes them especially sensitive to changes in
interest rates. 1
A number of studies have attempted to relate the market
and interest rate sensitivities of bank stock returns to some
aspect of bank balance sheet composition. Dietrich (1986),
for example, argues that the estimated coefficients in the
two-index model should depend on the balance sheet
proportions of broad categories of bank assets and liabilities. He embeds this hypothesis into the two-index
model and estimates portfolio composition effects on the
risk factors. Dietrich finds that market risk, the estimated
coefficient on the market portfolio of stocks, is most
heavily influenced by lending activity, time deposits, and
long-term debt relative to assets. Interest rate risk, he
finds, is most affected by the proportion of time deposits in
the balance sheet. While Dietrich's results suggest that
balance sheet composition may be important in explaining
the risk characteristics of bank stocks, his empirical results
suffer from serious econometric problems. The asset and
liability categories used in that study also are too broad to
be of much practical use in identifying specific sources of
bank risk.
In a similar avenue of research, Rosenberg and Perry
(1981) consider the determinants of bank risk in a singleindex CAPM. More specifically, they estimate the effects
19
on systematic and residual risk of a large number of asset
and liability ratios, operating characteristics, stock market
variables, and regional indicators. These authors find that
a number of their chosen indicators are significant determinants of bank risk. More interesting, they find that
different indicators help to explain systematic and nonsystematic risk of bank stock returns. For example, size,
dividend yield, equity capital, and the asset/long-term
liability ratio all help to predict market-related risk. For
residual risk, earnings variability and leverage are the most
important determinants. Rosenberg and Perry suggest that
bank risk can be predicted by focusing on a few significant
indicators, and that efforts to understand bank risk should
focus on understanding these aspects of bank behavior.
One weakness of the studies cited above is that they
provide little theoretical justification for the particular
empirical specifications used. A study by Flannery and
James (l984a) relies on a firmer theoretical foundation for
the analysis of bank risk and return. In this work, the
authors test the so-called "nominal contracting hypothesis" (French, Ruback, and Schwert 1983) on a sample of
bank and thrift stocks. This hypothesis suggests that a
firm's holdings of nominal assets and liabilities affect its
common stock returns through the redistributive effects of
unanticipated inflation and unanticipated changes in expected inflation. More specifically, the nominal contracting hypothesis suggests that the interest rate sensitivity
of a firm's stock will be larger the greater the amount of
net nominal assets (that is, nominal assets minus nominal liabilities) and the longer the duration of those net
nominal assets.
Flannery and James first estimate a two-index model of
stock returns on a time series, cross-section sample of bank
stocks. They then develop a proxy for the duration of a
bank's net nominal assets and regress the estimated interest rate coefficients on this duration measure. Nominal
asset duration is highly significant in explaining the size of
the interest rate sensitivity of bank stock returns. Kwan
(1991) extends this work by estimating the Flannery and
James model simultaneously in a random coefficients
framework. These studies confirm that the composition of
a bank's balance sheet, here as measured by the duration of
its net nominal assets, can influence the sensitivity of bank
stock returns to changes in interest rates.
II. Current Modeling Approach
Two Models of Asset Pricing
As the discussion of the related literature shows, most
researchers have employed a particular empirical model of
capital asset prices in order to focus on some aspect of bank
stock risk. Some debate persists among economists as to
the "correct" specification to use for describing equity
returns. In this paper, I investigate the behavior of bank
stocks in the context of two different models of asset
pricing: the single-index CAPM and a two-factor model.
The typical CAPM formulation is specified as follows:
(1)
where Rjt is the expected excess holding period return on
the equity of bankj in period t, RMt is the expected excess
holding period return on the market portfolio of stocks in
period t, 13Mj is a parameter to be estimated that represents
the sensitivity of the stock of bank j to changes in the
expected return on the market portfolio, cxj is another
estimated parameter that indicates deviations from equilibrium pricing, and Ejt is the residual left unexplained by
the expected return on the market portfolio. 2
The parameter 13 Mj is a measure of the covariance of
return on an individual stock with the return on the market
portfolio of risky assets. It thus represents the sensitivity of
20
that stock to systematic, or nondiversifiable, risk. 3 According to the CAPM, an "average" stock in the market portfolio will have a value of I3Mj equal to one. An asset with
13Mj greater than one carries above average nondiversifiable
risk, and must provide a greater than average expected
return in order to induce investors to hold it. The CAPM
predicts that only nondiversifiable risk is rewarded by a
higher expected return. Risk that is idiosyncratic to the
individual stock, and can therefore be diversified away, is
not associated in equilibrium with higher expected returns.
The model thus predicts that the expected value of cxj is
zero. Of course, realized or ex post values of cxj can differ
from zero if new information affects the asset's price and
return during the estimation period.
As mentioned in the previous section, the primary
hypothesis underlying the CAPM is that the return on the
market portfolio is a sufficient statistic to determine the
return on individual assets. One implication of this model,
therefore, is that no other variables should be significant in
explaining asset returns. Empirically, this prediction often
has not been supported, leading to asset pricing models in
which additional or alternative factors have been included
to capture missing influences on individual asset returns.
The two-factor model augments the CAPM by adding as
an additional explanatory variable the expected return on a
Economic Review / Fall 1991
debt security. The logic behind this model, as first proposed by Stone (1974), is that investors have two general
categories of assets to choose from: equity shares and debt
securities. As a result, expected returns on both types of
instruments should be relevant in setting the price of
individual financial assets. This same type of two-factor
model also can be derived more rigorously from Merton's
(1973) intertemporal version of the CAPM, or from Ross's
(1976) multi-factor arbitrage pricing theory. A number of
tests of the two~factor model using stock returns of industrial companies found little significance for debt returns.
However, stocks of companies in certain sectors, such as
utilities and financial intermediaries, typically exhibit significant sensitivity to changes in returns on debt securities.
The two-factor model takes the form
(2)
R jt =
(Xj
+
f3 Mj R Mt
+
f3ljRlt
+
Ejt ,
where R lt is the expected excess holding period return on a
selected debt security in period t, f3lj is a parameter that
captures the sensitivity of assetj to changes in the expected
holding period return on debt, and the other variables and
parameters are as defined in equation (1).4
Two modeling issues arise in empirical applications of
the asset pricing equations (1) and (2). First, time-series
regressions of these equations imply that the estimated
coefficients should be constant over time. Evidence suggests, however, that estimated f3s exhibit considerable
temporal variation. Moreover, efforts to relate the estimated coefficients to balance sheet composition variables
suggest that these coefficients will change with changes in
the asset/liability mix of banks. Recent evidence by Kane
and Unal (1988) using a switching regression methodology
and by Kwan (1991) in the context of a random coefficients
framework confirms the nonstationarity of the debt return
f3 in equation (2). Other work in a CAPM framework
likewise suggests that f3Mj varies over time. In order to deal
with this issue, I estimate versions of the two asset pricing
equations over different subsamples of the 1979 to 1990
period. This procedure generates statistics that enable me
to test for the constancy of the estimated regression coefficients. 5
The second modeling issue involves possible multicollinearity between the two returns series used as explanatory variables in equation (2). Chance and Lane (1980)
argue that returns on debt probably are influenced by the
same factors that determine the returns on the market
portfolio of stocks. One way to deal with this issue, they
suggest, is to orthogonalize one of the series by regressing
it on the other. The residual series from this regression,
which by definition is uncorrelated with the other explanatory variable, then can be used as a regressor in the equity
Federal Reserve Bank of San Francisco
returns estimating equation. This procedure eliminates the
estimation bias and isolates stock market from extramarket
effects on stock returns. Of course, the direction of causality in this first-stage regression is not clear. Chance and
Lane regress the debt return variable on the stock market
return while others, including Lynge and Zumwalt (1980)
and Flannery and James (1982), perform the opposite
regression.
This second issue may be important for hypothesis
testing .. Giliberto (1985) shows that the estimated standard
errors of the second-stage regression coefficients are unbiased only for the series that was used as the dependent
variable in the first~stage regression. This means that
studies regressing the stock market index on the debt
returns variable, like Flannery and James (1982), may
produce biased estimates of the significance of I3lj ' but will
yield unbiased estimates of the standard errors of I3Mj' To
determine the empirical significance of this bias, I reestimated all of the equations presented in the next section
using both orthogonalizations. While the two series did
exhibit significant cross correlation, the orthogonalized
results did not differ in a statistically significant way from
those reported here. 6 This suggests that any bias resulting
from the multicollinearity between the explanatory variables in the two-factor model is not substantial enough to
alter the empirical results.
The two asset pricing models described above predict
that different firms' equity returns will exhibit differing
sensitivities to stock market and debt returns. In terms of
the models' parameters, this means that each firm will have
its own specific values of (Xj' I3Mj and I3lj ' The estimation
results described in the next section are from pooled
regressions that combine time-series observations from all
the banks in the sample. In Section IV, I group the banks
into four size categories and describe regressions on these
subsets of banks. The estimated parameter values presented in Tables 2 and 3 are thus averages of the (xs and I3s
for different samples of banks. In this paper, I do not
present estimated parameters for individual banks. To
reflect this "averaging" in the discussion below, I drop the j
subscripts from all (X and 13 parameters (referring to
individual banks) when describing the estimation results.
Data
In the current study, I estimate monthly stock returns of a
sample of 84 large bank holding companies taken from the
Compustat Bank tapes. The monthly returns are derived
from end-of-month stock prices, and are adjusted for
dividends and stock splits. The Compustat tapes include
data on bank holding companies whose stocks trade on a
21
major exchange. This means that the sample includes
primarily large banks and is thus not completely representative of all U.S. banks. Of the 84 bank holding
companies considered in the current study, the smallest
held assets in the first quarter of 1990 of$2.3 billion, while
the largest had over $230 billion in assets. The sample was
chosen on the basis of availability over the entire interval
1979 to 1990. This period provides a number of observations prior to deregulation of bank interest rates, and also
encompasses several cyclical episodes. With 144 time
points and 84 banks, the sample includes over 12,000 data
observations.
The return on the market portfolio is proxied by the
monthly return series on the equal-weighted Standard &
Poor's 500 index of stocks. This variable was taken from
the Center for Research in Securities Prices (CRSP) tape
for the period 1979 to 1988, and from DRI's U.S. Central
database for 1989 and 1990. The debt return series is
an approximation of the monthly holding period return
on 30-year constant maturity U.S. Government bonds.
The approximation, as suggested by Flannery and James
(1984b), is
(3)
(Yt
-
Yt -
Yr -
1)
1
where Yt is the investment yield in month t on the bond.
This expression is the percentage change in the bond's
yield, multiplied by - 1. Note that monthly bond returns
fall as yields rise. Thus, a positive estimated coefficient on
this variable implies that bank stock returns are negatively
affected by increases in bond yields. The yield series used
in the construction of this variable was obtained from
Citibase.
III. Bank Stock Risk and Return Over Time
A First Look
In describing changes in bank stock risk, it is essential to
have an accepted measure of that risk. From the standpoint
of portfolio theory, expected or ex ante risk is the relevant
factor that determines asset prices. Unfortunately, such
anticipated risk is generally unobservable. As a proxy, it is
common to look at realized, or ex post, risk as the
appropriate descriptor of asset risk, with the belief that
past volatility is a likely indicator of future volatility. 7
Economists typically consider the total variance of historical asset returns (or its square root, the standard
22
deviation) as an appropriate measure of the overall volatility associated with asset returns.
Table 1 contains summary statistics of monthly holding
period returns for three different groups of assets for the
1979-1990 period, as well as for four subperiods of that interval. In the first two columns, I present the period averages of the mean and standard deviation of monthly returns
for the sample of 84 bank holding company stocks. The
second pair of columns contains comparable statistics for
the 30 Dow Jones Industrial firms. In both cases, the numbers presented in Table 1 are unweighted averages of the
Economic Review / Fall 1991
individual company means and standard deviations during
the applicable period. 8 The last two columns in Table 1
contain the mean and standard deviation of the monthly
return on 30~year constant maturity Treasury bonds.
The first row of Table 1contains statistics for the 12-year
period, 1979 to 1990. Over this interval, the mean monthly
return on both groups of stocks significantly exceeded the
mean return on bonds. At the same time, the total risk
associated with holding either of these groups of stocks
was more than twice the risk of holding Treasury bonds.
Between the two samples of stocks, the 30 industrial firms
provided a slightly higher mean monthly return and faced
somewhat less average risk than the sample of bank holding
company stocks, although the differences between the two
groups are small. During the full 12-year period, it does not
appear that bank stocks were significantly riskier than
other equities.
In the bottom portion of Table 1, I divide the full sample
period into four subperiods and present the averages of
mean monthly returns and standard deviations for the three
groups of assets during these different subperiods. The 30
industrial stocks show an upward trend in returns over the
four subperiods of the sample, while the bank stocks
exhibit a generally downward trend. Notably, in only the
1988-90 subperiod were bank stock returns below the
returns on both the 30 industrial stocks and the T-bonds.
While bank stock returns declined in the latter half of the
sample period, the variance of these stock returns rose over
the course of the 12-year sample period. The average
standard deviation of return on the 84 bank holding company stocks was 20 percent higher in the last two subperiods than it was in the first part of the sample. The
average risk of the 30 industrial stocks rose through the
1985-87 period, but then declined in the 1988-90 period.
The standard deviation of bond returns fluctuated during
the four quarters of the sample without any apparent trend.
Again, it is notable that, in the last subperiod of the sample,
the standard deviation of bank stock returns exceeded the
standard deviations of the other two groups of assets. Thus,
by the end of the 1979-90 period, bank holding company
stocks were more volatile than the other assets and offered
investors a lower rate of return.
The numbers presented in Table 1 provide support for
the perception that bank stocks have become riskier in
recent years. The volatility of bank holding company stock
returns increased during the 1980s, both in absolute terms
and relative to other portfolios of financial assets, including other equities. At the same time, the average returns to
holding bank stocks declined significantly. By the latter
half of the 1980s, it appears that investors in bank equities
suffered from both higher risk and lower returns.
Federal Reserve Bank of San Francisco
Risk in the Context of the 1\vo Asset-Pricing Models
The summary statistics of Table 1 confirm that the total
variability of bank stock returns increased over the 1979 to
1990 period. However, it is useful to determine if the
sensitivity of bank stocks to systematic sources of risk
changed during this period. Finance theory predicts that
(expected) asset returns should depend on systematic risk
and not on total risk. For example, the CAPM suggests that
only risk associated with returns on the market portfolio
will be compensated by higher expected asset returns.
Similarly, the two-factor model predicts that market risk
and interest rate risk should be compensated by higher
returns. Thus, the higher risks and lower returns on bank
stocks observed in the bottom portion of Table 1could still
be consistent with equilibrium asset pricing models if
returns fell because systematic risk declined. Estimation of
equations (1) and (2) in the previous section can help to
shed light on this point.
Table 2 contains regression results from estimating the
CAPMand the two-factor model on time series of the
monthly stock returns of the 84 bank holding companies in
the sample. The coefficients from these estimates correspond to equations (1) and (2) discussed above. The
parameter estimates presented in Table 2 are average
values across the 84 bank holding companies in the sample. The top part of Table 2 contains estimation results for
the full 12-year sample period, while the bottom portion of
the table contains estimates from the four subperiods. I test
the significance of the estimated coefficients against the
null hypotheses that a and 131 are zero and 13M is one.
The CAPM results for the whole sample show that the
average covariance of bank holding company stocks relative to the S&P 500 index was less than the "average" stock
during the 1979-90 period, as indicated by the estimated
13M of 0.92, which is significantly less than one. This
suggests that, over the 12 years of the sample interval,
changes in the stock market as a whole were associated
with less than one-for-one changes in bank stocks. A longrun value of 13M that is close to one is reasonable because
banks are expected to hold diversified portfolios of loans
and other assets whose returns should mimic the behavior
of the broader market. While this may not be true for small,
regional banks, it certainly should apply to the relatively
large banks included in the current sample. The positive,
significant value of a suggests that, on average, the sample
of bank holding company stocks was underpriced during
the 12-year period, yielding returns in excess. of what
would be predicted by the basic CAPM. The model explains only about 25 percent of the total variance of returns
during the sample period. This means that bank stock
returns contained a large portion of nonsystematic risk.
23
In the two-factor model for the 12-year sample period,
both factors were highly significant in explaining bank
stock returns from 1979 to 1990. This confirms previous
evidence regarding the sensitivity of bank equity returns to
changes in bond yields over and above their sensitivity to
the stock market. Moreover, the estimated coefficient, 13/,
is positive, indicating that bank stock returns were negatively affected by increases in long-term yields during the
sample period. Adding the debt returns variable to the
estimating equation reduces somewhat the stock market
sensitivity of bank equities. While the change in this
24
coefficient suggests that the two factors may be collinear,
the results were the same when the explanatory variables
were purged of their common influence. As in the CAPM
formulation, the positive and significant value of ex suggests that bank stocks were, on average, underpriced during the 12-year period. The expanded model explains about
27 percent of the variance of bank stock returns, only
slightly better than the CAPM, and again indicating substantial nonsystematic risk.
Several striking results stand out from the estimates of
the two models for the subperiods. First, in the context of
Economic Review / Fall 1991
the CAPM, market-related systematic risk of bank equity
returns, as embodied in 13M' increased during the four
subperiods of the 12-year interval. The estimated value of
13M rose from 0.72 in the 1979-81 period to 1.30 during
1988-90. 9 Investors who held bank equities faced more
market-related risk over the period and were rewarded for
assuming this additional systematic risk by receiving a
higher return.
The increase in market-related risk is even more striking
when viewed in the context of the two-factor model.
Estimated values of 13M more than doubled from the
beginning to the end of the sample period, from 0.60 in
1979-81 to 1.26 in 1988-90. 10 These estimates confirm that
the systematic, market-related risk of bank holding company stocks increased dramatically during the 1979 to 1990
period.
Perhaps the most striking result in the quarter-sample
estimates is the progression of the estimated coefficients
on debtreturns. The values of 131 decrease monotonically
over the four subperiods of the sample, from above 0.50
during both the 1979-81 and 1982-84 periods, to 0.26 from
1985 to 1987, to insignificantly different from zero during
the 1988-90 sample period. In contrast to stock marketrelated risk, the sensitivity of bank equity returns to bond
yields declined during the past decade. Moreover, bank
holding company stock returns showed no sensitivity to
changes in yields in the last three-year period of the
sample, the only subinterval for which this was true. While
bank stocks faced greater volatility with respect to the
stock market, they clearly became increasingly insulated
fromthe effects of bond yield changes.
Of course, systematic bank stock risk is only one aspect
of total risk. The remaining portion of risk represents
residual, or nonsystematic, bank equity risk. This, too,
changed significantly during the 1980s. The two-factor
model, for example, explains between 25 and 40 percent of
total bank stock returns during the first three subperiods of
the12-yearsample interval. By the 1988-90 period, this
model explains less than 20 percent of total returns. Thus,
the model leaves a large component of bank equity returns
unexplained. Clearly, bank stocks entail a substantial
amount of asset-specific risk that is not accounted for by
the systematic risk factors of these asset pricing models.
Finally, while bank stocks apparently were underpriced
on average during the 12-year period, as indicated by the
positive values of <X in the first two rows of Table 2, market
pricing of bank stocks changed during the course of the
1980s. Estimated intercepts were significantly positive
during the first two quarters of the sample period, were
statistically indistinguishable from zero in the 1985-87
period, and then turned significantly negative in the last
part of the sample interval. In terms of the asset pricing
models estimated in Table 2, this means that the stocks of
the 84 bank holding companies were overpriced in the
1988-90 period, yielding a lower return than the models
would predict.
IV. Some Cross-Sectional Comparisons
While the estimates presented in Table 2 contain important information about bank equity risks during the past 12
years, they also conceal substantial cross-sectional variation in bank stocks' responses to stock market and interest
rate risk. For example, I estimated values of 13M} and 131} for
each of the 84 bank holding companies during the various
subintervals of the sample period. I then generated summary statistics on these "samples" of coefficient estimates. The variance of these coefficients was by far the
greatest in the 1988-90 period. That is, there was considerably more variation across bank stocks in their stock
market and bond yield sensitivity during the last three
years of the 12-year sample period than in any other part of
the interval. This suggests that banks may have responded
in different ways to changes in their economic and regulatory environment.
One way to separate banks in the sample is by size. It is
reasonable to assume that the stocks of different-sized
banks may face differing sensitivities to systematic risk
factors. For example, the stock of a large bank holding
Federal Reserve Bank of San Francisco
company may reflect its enhanced opportunities for asset
diversification. Such a large bank thus may exhibit less
variability relative to the broader market than a smaller
bank whose opportunities for diversification may be more
limited. Similarly, a large bank may be able to exploit
possible economies of scale in hedging against interest rate
risk that a small bank cannot. These differences will show
up in the asset pricing models in terms of different values
of 131'. Moreover, if regulators implement, either explicitly
or implicitly, a policy of protecting large banks from failure
while permitting smaller institutions to go under, such a
policy may be reflected in estimates of the asset pricing
models and probably will differ across institutions.
To address this question, I split the sample of 84 bank
holding companies into four size categories according to
dollar amount of assets as of the first quarter of 1987. I then
estimated separate regressions for each category.11 The
estimates follow a distinct pattern where size clearly is
relevant to the banks' stock sensitivities to the two risk
factors. To highlight the differences between the various
25
groups, I present in the four panels of Table 3 the subsample results from the two-factor model fOr four sizes of
banks: assets less than $5 billion (13 banks), assets be~
tween $5 and $20 billion (37 banks), assets between $20
and $55 billion (24 banks), and assets greater than $55
billion (10 banks). As in Table 2, significance levels test
against a value of 13M equal to one and values of a and 131
equal to zero.
The results in Table 3 suggest that the greatest differences in estimated parameters are between the stocks of
the smallest banks in the sample and those of the remaining
banks; the three larger categories of banks show quite
similar estimation results. For example, the three groups of
larger banks all exhibited generally increasing values of
13M over the course of the four subperiods. In contrast,
there is no clear trend to the estimated values of 13M for the
smallest banks in the sample. Thus, the stocks of the larger
banks all became more sensitive to stock market-related
risk during the 1980s, while the smaller bank stocks
showed no tendency to entail higher market risk. It is
notable that the smaller bank stocks had the highest market
risk in the first portion of the sample period, 0.8 versus
values of 13M between 0.4 and 0.6 for the other three
categories of banks. By the end of the sample period,
however, the smallest banks had by far the lowest estimated
values of 13M' 0.7. The other groups of banks all had
estimates of 13M in the last period that exceeded one
(although only the largest two groups had parameter estimates that were significantly different from one). Moreover, the stocks of the largest group of banks exhibited the
greatest sensitivity to stock market risk of any banks in the
sample. The estimated parameter value of 1.8 in the last
period of the sample is larger than any other point estimate
in this study.
Bank stock sensitivity to bond yields also showed an
interesting pattern. Again, the stocks of the smallest group
of bank holding companies stand out from the others,
while the other three groups of bank stocks look very
similar. The stock returns of the three groups of larger
banks all exhibited significant sensitivity to bond yields in
the first subperiod of the sample, with estimated values of
26
131 near 0.6. In contrast, the group of smaller bank stocks
showed little sensitivity to yield changes, as indicated by
the coefficient estimate of 0.2. As the 1980s progressed,
t1le~ellsitivityof the. stock returns for the three categories
of larger. banks alL declined until, in the final three-year
period. of the sample, none of the banks' equity returns
showed any evidence of significant interest rate risk. The
stocks of the smallest banks in the sample continued to
exhibit little or no interest rate risk in the four subperiods of
thesarilple.Whilethepointestimates remain about the
same (0.2), the estimated standard errors increase over
time such that the coefficient on the debt return variable is
statistically insignificant in the last portion of the sample.
TheR2 statistics from these regressions indicate that the
estimates for each size group leave a large portion of bank
stock returns unexplained. Thus, stocks of the differentsized banks in the sample all have a significant component
of nOnsystematic risk. Moreover, the R2 for all four groups
declines in the last part of the sample interval, indicating
that the proportion of bank stock returns attributable to the
two systematic risk factors fell in the 1988-90 period. This
is particularly true for the smallest banks in the sample.
While the two-factor model explained about 20 percent of
stock returns for the other three size groups from 1988 to
1990, it provided less than 10 percent of the explanation for
the smallest group of banks. It is not ~urprising that the
stocks of the smaller banks in the sample exhibited the
most nonsystematic risk since these smaller banks may be
more heavily influenced by bank-specific events and local
market conditions. Nevertheless, all banks in the sample,
including the largest ones, exhibited significant nonsystematic equity risk.
Finally, the estimated values of a follow the same pattern
as for. the entire sample, and are roughly similar for all size
categories of banks. as are positive in all four cases early in
the 12-year sample period, and all tum negative in the last
subperiod. As mentioned above, this means that bank
stocks provided abnormally high returns (relative to. the
predictions of the theoretical asset pricing models) in the
late 1970s and early 1980s, and abnormally low returns in
the late 1980s.
Economic Review / Fall 1991
Federal Reserve Bank of San Francisco
27
V. Conclusion
The results presented above highlight a number of
interesting aspects of the behavior of bank holding company stock returns from 1979 to 1990. For example, the
total variability of bank equity returns increased during the
sample period relative to the returns on industrial equities
and on bonds. Moreover, this increased total volatility of
returns occurred at the same time that the level of average
bank equity returns fell relative to the other assets. By the
end of the 1980s, holders of bank stocks faced relatively
higher risk and relatively lower returns.
In the context of the asset pricing models estimated in
this paper, changes in the total risk and return of bank
equities were accompanied by a significant shift in the
sensitivity of bank stocks to systematic risk factors. The
covariance between bank equity returns and a broad stock
market index definitely rose on average during the 1980s.
In the latter part of the 1980s, average values of stock
market betas for the 84 bank holding companies in the
sample exceeded one. Thus, changes in returns on the S&P
500 stock index were associated with a greater than onefor-one movement in bank stock returns, whereas they were
less than one-far-one in the early 1980s. This increased
stock market sensitivity was especially pronounced for the
larger banks in the sample. Thus, the stock returns of large
bank holding companies became increasingly sensitive to
factors that influence the overall stock market.
One of the most striking findings in this paper is the
decline in the bond yield sensitivity of bank stock returns
during the estimation period. By the last three-year period
in the sample, banks stocks showed no statistically significant evidence of any effects of bond yields on their returns.
Moreover, this finding was consistent across banks of all
sizes in the sample. The recent lack of bond yield sensitivity contrasts sharply with the behavior of the same
bank stocks in the earlier part of the sample period as well
as with the findings of previous studies. It is possible to
interpret this reduction in interest rate risk as the result of
bank managers making greater use of adjustable rate
instruments and other hedging strategies to insulate their
stock returns from the effects of changes in yields. It is
reasonable to conclude that interest rate deregulation and
financial market innovations, such as interest rate swaps,
financial futures contracts, and adjustable rate mortgages,
helped to reduce the interest rate risk of bank stocks by
widening the sphere for banks to engage in risk hedging
activities.
Of course, there may be alternative explanations for the
apparent lack of interest rate risk in bank stock returns in
the last part of the 1980s. Shifts in the observed sensitivity
28
of bank equities can reflect changes not only in bank
behavior but also in the regulatory environment in which
banks operate. For example, in the late 1980s, bank regulators.from around the world were negotiating the structure
of international risk-based capital standards under the
aegis of the Bank of International Settlements. By 1987,
the likely future shape of these standards was becoming
cl~ar.. Under the new standards, risk adjustments to regulated capital levels would be made on the basis of credit
risk only and would downplay interest rate risk. While
banks might be expected to respond to this change in
regulation by increasing their interest rate risk exposure,
the change in the enforcement policies of regulators could
attenuate the impact of such actions on bank equity values.
The net result could be a reduction in the interest rate risk
embedded in bank stock returns.
Alternatively, the observed reduction in the debt return
sensitivity of bank stocks might be partially explained by a
statistical phenomenon. If the variance of debt returns fell
significantly from 1988 to 1990 while bank stock returns
behaved similarly to earlier subperiods, this might explain
the lack of significance for the coefficient on debt returns in
the last part of the sample. In fact, the variance of the debt
returns series did fall somewhat in the last three years of the
sample relative to earlier subperiods. However, this drop in
variance probably was not large enough by itself to account
for the dramatic decline in the estimated 131 values from
1988 to 1990. More likely it is a combination of factors
related to changes in bank behavior, regulatory shifts, and
statistical effects that contributed to reduce the measured
sensitivity of bank stock returns to changes in bond yields
in the last part of the sample period.
Finally, the results presented above support the conclusion that the proportion of nonsystematic risk in bank
stocks rose during the 12-year sample period. The asset
pricing models explain at most 40 to 50 percent of stock
return variability for certain size categories of banks during
certain subsamples of the estimation period. The proportion of total variance explained by the systematic risk
factors declined for the total and for each size group of
banks in the last three-year period of the sample. This
means that, in the late 1980s, bank stock risk was more
related to bank-specific factors than at any other time since
the late 1970s. The increase in nonsystematic risk was
greatest for the smaller banks in the sample. An accurate
assessment of the stock risk of these banks thus requires
less consideration of systematic risk factors and more
careful attention to factors specific to the individual
institutions.
Economic Review / Fall 1991
ENDNOTES
1. The two-index model, though proposed by Stone
(1974) in a somewhat ad hoc fashion, also can be derived
formally from the intertemporal CAPM of Merton (1973), as
well as from the Arbitrage Pricing Theory (APT) of Ross
(1976). The latter framework suggests thatthere may be
additional factors besides the two considered in these
studies that are relevant to explaining asset returns. For
example, Chen, Roll and Ross (1986) derive an APT model
in which five prespecified macroeconomic factors are
used to explain returns on several·· portfolios of· stock.
These authors find that several of the factors are important
in explaining the returns on diversified stock portfolios.
Campbell, Dietrich and Weinstein (1985) test the significance of these five factors on portfolios of financial
intermediary stocks. They find that banks stocks are particularly sensitive to measures of default risk and term
structure premia (both related to interest rates) as well as
to the stock market index. These findings provide some
support for the two-index formulation used so extensively
in the banking literature.
2. The two holding period return series are expressed in
the CAPM in terms of their return in excess of the return on
a risk-free security, usually assumed to be a short-term
riskless government bond. If no asset is considered riskfree, then it may be possible to construct an asset whose
rate of return has zero covariance with the market portfolio.
In this "zero-beta" version of the CAPM, the return on this
security is considered to be the risk-free rate of return. See
Fama (1976) for discussion of this point.
3. If changes in the stock market, and thus the return on
the market portfolio, mirror movements in the macroeconomy, then the stock market beta can also be interpreted as
measuring the sensitivity of the asset's return to changes
in general economic conditions.
4. Again, all holding period returns are expressed in
excess of the risk-free rate of return, where that rate is the
yield on a short-term Treasury bill.
5. There are, of course, alternative ways to test for timevarying effects on the estimated coefficients. For example,
a time trend could be included as an explanatory variable
in the regressions, although this would constrain time
effects to be linear and monotonic over the estimation
interval. Alternatively, it is possible to estimate a shift
parameter by interacting dummy variables for different
time periods with the explanatory variables in the regression. Beebe (1985) uses this methodology. Another
method is to assume that the estimated coefficients depend on some time-varying factor. Embedding this assumption into the regression equations translates into
Federal Reserve Bank ofSan Francisco
inclUding additional, interacted explanatory variables in
the estimates. See Kwan (1991) for an examplebfthis
latter approach. The methodology adopted here provides
considerable flexibility without imposing additional theoretical or empirical constraints, and generates easily interpreted test statistics.
6. The correlation coefficient between stock market and
debt returns was 0.28 during the 12-year sample period
and was significantly different from zero.
7. Some modeling approaches permit the use of more
direct proxies for ex ante risk. For example, Levonian,in an
article in this issue of the Economic Review, calculates
values ofex ante risk of bank stocks that are implied by the
prices of option contracts on those stocks.
8. I also considered weighting the individual stock returns
by the assets of the firms included in the groupings. This
weighting did not significantly alter the results presented
in Table 1.
9. I conducted Chow tests of the constancy of the set of
estimated regression coefficients in the various subintervals of the sample period. For the two halves of the 12-year
period, the F-value was 1.24. The critical value for the
F-distribution, at a 99 percent confidence level and with
(500, 1000) degrees of freedom, is 1.19. My half-sample
test had approximately 6000 degrees of freedom in both
numerator and denominator. Thus, the set of estimated
coefficients in the two half-intervals were significantly different from one another. On the quarter-interval estimates,
it was not possible to distinguish the first two quarters of
the sample period: the F-value was 1.12, with approximately (3000, 3000) degrees of freedom. The third and
fourth quarters of the sample were significantly different
from one another: the F-value for this test was 1.46.
10. Chow tests on the constancy of the set of estimated
coefficients in the two-factor model confirm that these
coefficients changed significantly during the sample. The
F-value between the two half-intervals was 1.36; between
the first two quarters of the sample, 1.23; and between the
last two quarters, 1.48. The critical value of the F-statistic at
the 99 percent level, with (500,1000) degrees of freedom,
is 1.19.
11. As mentioned in footnote 5, there are alternative ways
to estimate cross-sectional differences in risk sensitivity.
For example, size measures could be included as additional explanatory variables in the regression equations,
or as variables interacted with the two risk factors. The
method used here was chosen to highlight differences
between banks in the different size categories.
29
REFERENCES
Beebe, Jack H. 1983. "Bank Capital Risk in the Post1979 Monetary and Regulatory Environment," Federal
Reserve Bank of San Francisco Economic Review
(Summer) pp. 7-18.
______ . 1985. "Bank Stock Performance Since the
1970s." Federal Reserve Bank of San Francisco Economic Review (Winter) pp. 5-18.
Booth, James, and Dennis Officer. 1985. "Expectations,
Interest Rates, and Commercial Bank Stocks," Journal of Financial Research 8, pp. 51-58.
Campbell, Tim, J. Kimball Dietrich, and Mark Weinstein.
1985. "Some Evidence on Bank Holding Company
Regulation: The Question of Expansion intothelnsurance Business." In Conference on Bank Structure and
Competition, pp. 587-616. Federal Reserve Bank of
Chicago.
Chance, Don, and William Lane. 1980 "A Re-examination
of Interest Rate Sensitivity in the Common Stocks of
Financial Institutions." Journal of Financial Research
3, pp. 49-55.
Chen, Nai-fu, Richard Roll, and Stephen Ross. 1986.
"Economic Forces and the Stock Market." Journal of
Business 59, pp. 383-403.
Dietrich, J. Kimball. 1986. "Bank Stock Return Sensitivity
to Market and Term Structure Risk." Unpublished
manuscript. University of Southern California.
Fama, Eugene. 1976. Foundations of Finance: Portfolio
Decisions and Securities Prices. New York: Basic
Books.
Flannery, Mark, and Christopher James. 1982. "The Impact of Market Interest Rates On Intermediary Stock
Prices." In Conference on Bank Structure and Competition, pp. 520-538. Federal Reserve Bank of Chicago.
_ _ _ _ , and
. 1984a. "The Effect of Interest
Rate Changes on the Common Stock Returns of
Financial Institutions." Journal of Finance 39, pp.
1141-1153.
_ _ _ _ , and
. 1984b. "Market Evidence
on the Effective Maturity of Bank Assets and Liabilities." Journal of Money, Credit and Banking 16, pp.
435-445.
French, Kenneth, Richard Ruback, and G. William
Schwert. 1983. "Effects of Nominal Contracting on
Stock Returns." Journal of Political Economy 91,
pp.70-96.
30
Giliberto, Michael. 1985. "Interest Rate Sensitivity in the
Common Stocks of Financial Intermediaries: A Methodological Note." Journal of Financial and Quantitativ~Analysis 20, pp. 123-126.
Kane, Edward, and Haluk Unal. 1988. "Change in Market
Assessment of Deposit-Institution Riskiness." Journal
of Financial Services Research 1, pp. 207-229.
Kwan, Simon. 1991. "Re-examination of Interest Rate
Sensitivity Of Commercial Bank Stock Returns Using
a Random Coefficient ModeL" Journal of Financial
Services Research 5, pp. 61-76.
Levonian, Mark. 1991. "Have Large Banks Become Riskier?RecentEvidence from Option Markets." Federal
Reserve Bank of San Francisco Economic Review
(Fall) pp. 3-17.
Lintner, John. 1965. "The Valuation of Risk Assets ano the
Selection of Risky Investments in Stock Portfolios.and
Capital Budgets." Review of Economics and Statistics
47, pp. 13-37.
Lloyd, William, and Richard Schick. 1977. "A Test of
Stone's Two-Index Model of Returns." Journal of Financial and Quantitative Analysis 12, pp. 363-368.
Lynge, Morgan, and J. Kenton Zumwalt. 1980. "An Empirical Study of the Interest Rate Sensitivity of Commercial Bank Returns: A Multi-Index Approach." Journal
of Financial and Quantitative Analysis 15, pp. 731-742.
Martin, John, and Arthur Keown. 1977.' "Interest Rate
Sensitivity and Portfolio Risk." Journal of Financial
and Quantitative Analysis 12, pp. 181-195.
Merton, Robert. 1973. "An Intertemporal Capital Asset
Pricing ModeL" Econometrica 41, pp. 867-887.
Rosenberg, Barr, and Philip Perry. 1981. "The Fundamental Determinants of Risk in Banking." In Risk
and Capital Adequacy in Commercial Banks, ed.
Sherman Maisel, pp. 367-407. Chicago: University of
Chicago Press.
Ross, Stephen. 1976. "The Arbitrage Theory of Capital
Asset Pricing." Journal of Economic Theory 13, pp.
341-360.
Sharpe, William. 1964. "Capital Asset Prices: A Theory of
Market Equilibrium under Conditions of Risk." Journal
of Finance 19, pp. 425-442.
Stone, Bernell. 1974. "Systematic Interest Rate Risk in a
Two-Index Model of Returns." Journal of Financial and
Quantitative Analysis 9, pp. 709-721.
Economic Review / Fall 1991
Recession Probability Indexes: A Survey
Chan G. Huh
I wish to thank the editorial committee, Brian Motley,
Adrian Throop, and Bharat Trehan, as well as John Judd for
their helpful comments and Conrad Gann for his valuable
research assistance. I also wish to thank James H. Stock
and Glenn D. Rudebusch for providing data.
Specialized econometric models are designed to measure the likelihood of the occurrence of a recession in the
near future. This paper examines a selected group of
models that are distinct in terms oftheir theoretical underpinnings and also in terms of the scope of variables
included. The models' performance ofpredicting the onset
ofthe 1990 recession is mixed. In this case, it appears that
what distinguished the models was less the difference in
their theoretical underpinnings than whether or not the
models included financial variables.
Federal Reserve Bank of San Francisco
A wide range of methods is used to forecast recessions.
For example, one method is a rule-of-thumb that predicts a
recession following three consecutive declines in the
Department of Commerce's composite index of leading
indicators. At the other extreme are more advanced econometric models. This article will focus on the latter group,
and in particular on two advanced econometric models that
represent different theoretical approaches: the experimental recession probability index (XRI) model developed by
James Stock and Mark Watson at the National Bureau of
Economic Research (NBER), and a turning point forecasting model which implements a methodology proposed by
Salih Neftci.
The experimental NBER model is theoretically similar
to conventional linear regression models that are used for
forecasting in general, although it is also unique in terms of
the way information is extracted from data and in the
information the data provide. Implicit in the NBER's XRI
model and in other linear forecasting models is the assumption that expansions and contractions are part of the same
stable structure, and that they are responses to random
shocks (policy and otherwise).
Neftci-type turning point (TP) models depart from this
key assumption of a stable structure. TP models posit
multiple behavioral regimes that govern the movements of
output over time. Thus, the process that best describes the
behavior of output in an expansionary period is fundamentally different from the process describing the behavior of
output in a contractionary period. Consequently, forecasting a downturn is equivalent to predicting a switch in the
behavioral regime from an expansion to a contraction.
The recession of late 1990 provided the first out-ofsample opportunity to apply these models. The performances of the models in identifying this particular downturn
as of late 1990 were mixed, giving probabilities ranging
from 14 percent to 98 percent. Interestingly, the differences
among the forecasts do not appear to be related to differences in their theoretical underpinnings, but rather to
the types of variables used as the signaling source series.
The models incorporating several financial variables are
31
associated with low probability forecasts, and the models
that rely mostly on nonfinancial variables result in high
prob<i.bility forecasts; th<i.t is, financial markets were, in this
case, poor forecasters of the recession.
This result is not definitive, however, and must be placed
in perspective. By definition, a forecasting model of stochastic outcomes cannot be expected to have a perfect fit
repeatedly. One observation hardly provides enough information to judge the overall usefulness of the models. Or, as
Aristotle, the father of logic, put it, "One swallow does not
a summer make." To judge the accuracy, and thus the reliability, ofthese models requires a whole series of forecasts.
Brief overviews of different models for estimating the
probability ofeconomic downturns are provided in the next
three sections: a smndard linear regression model (Section
I), the NBER's XRI (Section II), and the Neftci turning
point forecast models (Section III). An overall assessment
oftheir past within-sample forecasting performances is provided in Section IV, and a discussion of out of sample performance is presented in Section V. Section VI concludes.
I. FRB San Francisco BVAR Model: A Conventional Regression Model
One easy and straightforward way to forecast a recession
is to use linear regression models designed to forecast key
macroeconomic variables. Any such regression model can
be used to forecast a recession once the "operational"
definition of a recession is determined in terms of variables
in the model. One example is the Bayesian Vector Autoregression (BVAR) model used as a part of the FRB San
Francisco in-house staff forecast. 1 The BVAR is designed
to forecast growth in real GNP, inflation, and other key
macro variables several quarters ahead. 2 The BVAR model
is specified in terms of a combination of log and level
differences of three real and seven nominal and financial
quarterly variables. 3 The Bayesian prior affects this otherwise ordinary VAR system in the form of a priori restrictions on the magnitudes of the coefficients. For example, a
simple prior restriction that the real GNP growth rate
follows a random walk is imposed on the real GNP equation. Of course, the final estimates would reflect both this
prior restriction and the sample information.
Suppose we are interested in finding the probability of a
recession occurring within the next three quarters, and that
we define a recession as two or more consecutive quarters
of negative real GNP growth. 4 The following formula
provides the necessary information to calculate the probability in period t:
(1)
Prob (recession within 3 quarters) = Prob {event
(output contracts in periods t + 1 and t + 2) u event
(output contracts in periods t+ 2 and t+ 3) u event
(output contracts in periods t + I, t + 2, and t + 3)}.
The actual calculation is in four steps. First, simulate a
large number of unconditional forecasts (e.g., 1,000) for
the next three quarters based on the model by repeatedly
drawing from the stochastic error terms of the system.
Second, count the number of simulated forecast triplets
that fit anyone of the three disjoint events that were defined
in (1). Third, calculate the probability measure by dividing
the sample numbers obtained from the second step by the
total number of simulations. Fourth, the total probability
of (1) is the sum of the three probability measures derived
in the second step. Actual probabilities calculated this way
from the FRBSF BVAR model are presented in Chart 1.
Chart 1
BVAR Recession Index
100
80
60
40
20
o
32
1970
1974
1978
1982
1986
1990
Economic Review / Fall 1991
n. The NBER's Experimental Recession Index
The experimental NBER models are also based on the
traditional regression method, and thus they share the key
assumption that output series over time can be described by
a single process. However, the experimental NBER models
(Stock and Watson 1989) are more specialized in terms of
their scope and of the econometric technique employed.
The NBER XRI is based on two artificial signaling
index variables that, in turn, are constructed from sets of
actual economic variables. The signaling variables are the
experimental indexes of coincident economic indicators
and of leading economic indicators. 5
The experimental index of coincident economic indicators (CEI) is designed to measure the level of current
economic activity. It involves a weighted average of four
series that are widely perceived to be coincidental: industrial production, real personal income less transfer payments, real manufacturing and trade sales, and employeehours in nonagricultural establishments. The index is
based on a dynamic factor model that measures the change
in an unobserved factor that is assumed to be a significant
Federal Reserve Bank of San Francisco
source of movement in all four series (for details, see
Sargent and Sims 1977). In term~ of both cyclical behavior
and historical trend, Stock and Watson's CEI is very close
to the CEI released by the Commerce Department, which
also was designed to reflect the general state of the economy. The main differences between the two are that Stock
and Watson use newer econometric technology to construct
the overall index from its components and that Stock and
Watson use the employee-hours series, while the Commerce department uses the number of employees.
The experimental index of leading economic indicators
(LEI) was designed to provide optimal forecasts of the
projected growth in the CEI over the next six months given
the information up to period t. There are two versions ofthe
LEI, namely, the XLI and the XLI-2, which differ in the
variables they use. The XLI uses seven variables-three
real and four nominal and financial variables-that were
selected after applying multiple sets of tests to a large
number of candidate variables. The XLI-2 replaces all
nominal and financial variables used in the XLI, except the
33
exchange rate, with additional real variables. (See Table 1
for the list of variables. For a detailed econometric description, see Stock and Watson (1989) or Watson (1991,
Appendix). )
Two related experimental recession indexes are based on
these models, the XRI and the XRI-2. These indexes are
designed to measure the probability that the economy
(gauged by the CEl) will be in a recession six months
hence. 6 Actual probabilities using a stochastic simulation
method that is similar to the procedure described in Section
I for XRI and XRI-2 are presented in Charts 2 and 3,
respectively.
This procedure is valid under a key assumption of linearity in the relationship between the variables involved. That
is, the underlying model that describes the behavioral
relationship between real GNP (or any variable of interest)
and its explanatory variables must remain stable and symmetric across both expansionary and contractionary phases
of business cycles. If this linear relationship does not hold,
one has to consider some alternative ways to describe the
behavioral relationship. Subsequently, calculating the
probabilities of the events defined in (1) would become
more involved.
Indeed, some economists think that there are fundamental differences in the behavioral patterns of key variables
across expansion phases and contraction phases of business cycles. We now turn to a specialized recession probability model that is based on such a view.
Chart 2
NBER Recession Index (XRI)
100
80
60
40
20
o
1970
1974
1978
1982
1986
1990
Chart 3
NBER Recession Index (XRI-2)
100
80
60
40
20
o
34
1970
1974
1978
1982
1986
1990
Economic Review / Fall 1991
III. Turning Point Recession Index: Process Switching Model
Many economists have observed asymmetric behavior
of some key macro variables between economic expansions
and contractions. For example, output tends to inch upward
during an expansion, but it tends to drop very sharply at the
beginning of a contraction. Thus, the behavior of the
economy in the two phases is best described as being
governed by two distinct stochastic structures instead of by
a single underlying structure (Neftci 1982). Consequently,
according to these views, forecasting a recession (the onset
of a contraction regime) amounts to predicting a behavioral
switch in the economy from an expansion to a contraction.
To putthis idea into practice, a forecaster needs a signal
variable that foretells changes in the behavioral structures.
This signal variable must meet several requirements: its
behavior should be systematically related to that of the
output in the economy; it should have some lead time with
respect to changes in output to be useful as a predictor of
changes in output; finally, it should be available frequently
enough to update the model in a timely manner in terms of
key developments that have a bearing on the potential shift
in the regime. Both the original turning point model of
Neftci (1982) and a model by Diebold and Rudebusch
(1989) use the monthly Composite Index of Leading Indicators published by the Department of Commerce
(henceforth, DOC LI) as such a signal variable.
The next step is to take the first difference of the series.
Then the data characteristics in upturns and downturns are
summarized by fitting simple normal distribution functions: first divide the overall historical period into expansionary and contractionary sub-periods using the historical
turning point dating in the DOC LI series. Then the DOC
LI observations belonging to expansionary and contractionary periods are respectively pooled into two groups of
upturn and downturn samples. Finally, two normal distribution functions Ne(fLe'(J'e)' Ne(fLe'(J'c) (where fL and (J'
denote the mean and standard deviation) are estimated
from the expansion and contraction samples, respectively.
Additionally, determine a prior transitional probability
for the signal variable. The transitional probability n is the
measure of the likelihood that the signal variable will
remain in the current regime at any given time. 7 Consequently, 1- n measures the probability of the signal variable switching from the current behavioral regime.
Given this information, one can apply the switching
time Bayesian probability formula that was developed by
Neftci (1982) as shown in Box 1. With each new observation in the DOC LI, the turning point recession index
(TPRI) model calculates the conditional probability that
the indicator is in the downturn regime. The probabilities
are shown in Chart 4.
Chart 4
Turning Point Recession Index
100
80
60
40
20
o
1970
1974
1978
1982
1986
1990
IV. Assessment
Recession probability indexes and turning point models
are more sophisticated than rule-of-thumb methods, which
typically forecast a recession after three consecutive declines in the DOC LI. They are also more systematic
because they account for the magnitude of change as well
Federal Reserve Bank ofSan Francisco
as the temporal direction of change in the leading indicators, and in general, they substantially outperform the ruleof-thumb predictions.
Stock and Watson (1989, pp. 382) applied a formal
econometric method to compare the predictive power of
35
the rule-of-thumb method and their method, and found
their method to be more accurate. They performed regression analyses that related consecutive movements in the
DOC LI numbers to actual historical recessions and expansions. For example, the R2 of the regression that related the
index to the occurrence of recessions or expansions six
months hence was 0.028 using the rule-of-thumb, whereas
it was 0.50 for the regression using the experimental
NBER XRI. Diebold and Rudebusch (1989) also found a
similar relative performance ranking of the rule-of-thumb
method compared to different methods, such as the Neftci
method. 8
However, assessing the" goodness of fit" of these models is conceptually difficult, because their forecasts are in
terms of probabilities, and "actual" probabilities are not
directly observable to evaluate the performance of these
models. In fact, low probability recessions may occasionally occur, while high probability recessions may occasionally not occur. Thus, over a limited sample period, simply
correlating the probability with the business cycle is not
necessarily a good way to judge the accuracy of the models.
Of course, the larger the sample, the more appropriate this
direct type of evaluation becomes. 9
One criterion that is often used to gauge reliability is the
frequency of false signals, a notorious problem for leading
indicators that led to Paul Samuelson's, famous remark,
"The stock market has predicted nine out of the last five
recessions!" The first type of false signal is analogous to
the Type II error of the usual hypothesis test; that is, the
model forecast of an imminent recession is not followed by
an actual recession within a reasonable period of time. For
example, suppose we interpret a model as signaling a
recession when the probability is above half of the maximum probability (observed over the sample period) of
each model. According to this criterion, the TPRI and
NBER XRI-2 models each have two instances of false
signals for the 1968-1989 sample period (1985 and 1988 for
TPRI and 1988 and 1989 for XRI-2); the very striking
spikes in the TPRI model in the late 1980s seem to have
been reflecting temporary slowdowns in the manufacturing
sector during those periods. The NBER XRI and BVAR RI
have no false signals.
The second type of false signal is analogous to the Type I
error of the usual hypothesis test; that is, the model fails to
predict an ensuing recession with some lead time (for
example, six months). Using the same cut-off probability
as in the first case, the NBER XRI-2 has failed four times
(1969, 1973, 1980 and 1982), the TPRI model has failed
twice (1974 and 1981), the BVARRIhas failed once (1969),
36
Economic Review / Fall 1991
and the NBER XRI has not failed at all. The performance
of the TPRI in this regard is most likely related to the fact
that it is based on the DOC LI which is notorious for having
widely varying lead times with the business cycle peaks
and troughs. For the past 30 years, for example, turning
points in the DOC LI have led the contractionary turning
points of the economy by anywhere from two to twenty
months. 10
VI. Recent Predictions
As in any of the forecasting models that have been
estimated using sample information, an important test of
the RPI models' forecasting power hinges on their out-ofsample performance. The only out-of-sample observation
we have is the most recent recession, which started in the
second half of 1990.
The models' various predictions of the probability of an
imminent recession as of the end of November 1990 are 14
percent for the NBER XRI, 21 percent for the BVAR, 53
percent for the NBER XRI-2, and 98 percent for the TPRI.
The sharp divergence between the forecasts of the NBER
XRI and XRI-2 suggests that different theoretical underpinnings alone do not explain the divergent forecasts. It is
natural to ask, then, what the most likely source of such
differences is.
One distinguishing feature is that low probability forecasts included a set of financial variables (interest rates and
associated spreads) but high probability forecasts did not.
This is particularly interesting in light of recent studies on
the changing role of financial variables in econometric
models of key macro variables.
Bernanke (1990), among others, found that various interest rates and spreads were substantially more useful in
explaining and forecasting key macro variables for the
pre-1980 sample period than for the post~1980 period. In
particular, he examined the spread between the commercial paper rate and the T-bill rate. This spread may reflect
the default risk of commercial paper, which, in turn, would
be very sensitive to an expected recession. However, if this
is the important channel through which the financial variables are useful in forecasting key variables, then they still
can be expected to have substantial explanatory power in
econometric models.
The spread may also reflect the monetary policy stance,
which affects the near-term economic condition by shifting
credit conditions. This may be particularly relevant when
there are deposit interest rate ceilings and when commercial paper and T-bills are imperfect substitutes as portfolio
assets. Monetary tightening would induce an outflow of
deposits from banks as market interest rates rise above deposit ceilings. This "disintermediation" creates a "credit
Federal Reserve Bank of San Francisco
crunch" and subsequently an economic contraction. At the
same· time, bank deposits will flow into T-bills because
T-bills can be purchased in relatively small denominations,
unlike commercial paper, which is typically in denominations too large for most small deposit holders. This inflow
of funds will depress T-biIl yields relative to commercial
paper rates in periods when the general level of interest
rates is higher. 11
According to this hypothesis, it is relatively easy to
explain the diminished role of the spread. Since the early
1980s when deposit rates were deregulated, more alternativefinancial assets have become available creating closer
substitutability among assets.
This conjecture seems relevant in explaining the divergent forecasts of the various models. The yield curve has
maintained a positive slope, and few noticeable changes
with respect to short-term interest rates and the rate-spread
have occurred in late 1990. Thus, the recession forecasts of
models that included these financial variables might have
picked up mixed signals of the likely conditions of the
economy, unlike the models with only real variables.
Consequently, according to this conjecture, the probability
of recession forecasted by models containing financial
variables did not increase as substantially as it did in
models relying entirely on real variables.
It is quite possible that the current recession is distinct
from preceding ones in terms of both its causes and the
way contractionary effects of the causal factors spread
across the economy. For example, some economists cite the
diminished credit availability which started in 1990 for
reasons related to the weakened condition of financial
institutions and stricter regulations while others point to
the special circumstances associated with the Middle East
confrontation, which increased short-term and near-term
uncertainties.
The question of whether business cycles are distinct
(and hence whether a single modeling strategy is appropriate) is not new. Blanchard and Watson (1986) examined the
nature of the sources of impulses behind business cycles
using U.S. time series data. Their findings suggest that
cycles are not alike; that is, each historical cycle can be
37
associated with several identifiable large single shocks
with different origins.
This result, however, does not necessarily make the
modeling approaches surveyed here inappropriate. The
existing models are still valid and applicable to the de-
signed task if there exist measurable similarities in the way
the original shocks propagate or dissipate throughout the
economy. Whether or not this is the case is an important
empirical issue, one on Which we can expect to see more
research in the future.
VII. Conclusion
Representative models designed to forecast prospects of
a recession in the near future have been examined. Specifically reviewed were the experimental NBER index models
and a model based on the Neftci method. They differ not
only in vari(}US operational aspects, but also in their
conceptual approaches to modeling the behavior of key
economic variables, such as output. The experimental
NBER models are based on the assumption that output
behaves symmetrically across both expansionary and contractionary phases of economic fluctuations, whereas the
Neftci method admits a shift in the behavioral regime
across the two phases. Whether this assumption of a symmetry in the behavior of the output is empirically appropriate is an issue currently being examined by economists.
The models performed well in terms of within-sample
historical predictions. They outperformed the common
rule-of-thumb that relies on three consecutive declines in
the DOC LI. However, their out-of-sample forecasts were
widely divergent, even for those that used the same modeling approach. The distinction is that models with a high
probability forecast .excluded a set of financial variables
while low probability forecasts included financial variabIes. This seems to reflect the fact that a recession is
defined to be a period of contractions in real variables such
as orders, sales, output and employment. Although the
amount of the lead time may vary, models that rely comprehensively on such real variables will necessarily provide indications of the onset of a serious downturn.
It is likely that the most recent downturn was unusual in
that its causal factors differed from the few factors that had
frequently been behind past recessions. In that sense, the
38
models that were designed to conform to the general average • characteristics of past economic fluctuations did
poorly in detecting the most recent economic downturn.
However, it is premature to draw any inferences from
this· single-sample observation of the current recession;
these results need to be considered in the properperspective. In most situations where we need to draw inferences
about an uncertain outcome, more information is preferred
tolessasa practical principle. This holds true with regard
to forecasting business cycle downturns, especially since
we do not have a well-understood, widely agreed upon,
and operationally feasible framework for describing evolutions of a large set of macro variables.
Such a framework could provide a theoretically wellfounded list of variables or a sequence of economic events
that could give rise to a "sufficient statistic" about a nearterm economic downturn, and would covsequently make
any additional information redundant. In this context,
systematic efforts to reduce our prediction errors involving
important aggregate economic variables such as the RPI
models can be useful.
The key contribution of the RPI models, however, essentially lies in providing another way to organize and use
information contained in the various leading economic
indicators. Consequently, their reliability is crucially
dependent on the reliability of the leading economic indicators that are used as the sources of information. Thus,
any further refinement and improvement of our stock of
knowledge on leading indicators will lead to commensurate improvement in the performance of the recession
forecasting models.
Economic Review I Fall 1991
ENDNOTES
1. For detailed explanations of this modeling strategy, see
Todd (1984) and Roberds (1988). For a more theoretical
discussion of this econometric methodology see Doan,
Litterman and Sims (1984).
2. This is done by weighing forecast accuracy at the oneyear horizon more heavily than the rest of the forecasting
horizon. This step is implemented during a model specification selection stage. Following .the BVAR modeling
practice, a model builder definesapriormatrix of parameters that control the dynamic interactions between variables .in each equation of the model. We adjusted these
prior parameters selectively to obtain the forecast accuracy configuration across different forecasting time
frames. See Roberds (1988) for detailed descriptions.
3. The variables are real GNP, business fixed investment,
the unemployment rate, fixed GNP price index, unit labor cost, producer price index, monetary aggregate M2,
trade weighted exchange rate,six~month commercial paper, and AAA corporate rates.
4. Applying this rule to post-war U.S. data (194701199003) we detect six out of the eight recessions that
occurred.
5. These indexes were developed as the result of efforts to
update the system of indicators that were developed in the
1930s and 1940s at the NBER by Mitchell and others; the
latter is still being used at the Department of Commerce.
6. This particular time horizon is related to the way the LEI
is constructed. That is, it was specifically designed to give
an optimal forecast of the CEI's relative growth over six
months. A more precise definition of the economy being in
a recession is as follows: A month is defined to be in a
recession pattern if the monthly growth of the CEI index is
either in a sequence of six consecutive declines below a
boundary point, or in a sequence of nine declines below
the boundary with no more than one increase during the
middle seven months.
7. There are different views regarding the question of
dependency between the duration of each phase (i.e., expansionary or contractionary) and the probability of transition from one regime to another. For example, in Neftci
Federal Reserve Bank of San Francisco
(1982), the transition probability is treated as dependent
on the duration, whereas Diebold and Rudebusch (1989)
use a transitional probability matrix that is independent of
the duration. For more details on this issue, see Hamilton
(1989), Neftci (1984), Diebold and Rudebusch (1990).
8. However, a recent study by Koenig and Emery (1991)
found that some relatively simple methods similar to the
rule of thumb did as well as the Neftci method when the
actual· real lime data that would historically have been
available to a forecaster were used, instead of the most
recent revised data on the DOC L1. These results point to
some potential problems with the DOC LI series, which
has. gone through major revisions, rather than..toa .devaluation of the Neftci methodology.
9. Diebold and Rudebusch (1989) propose and examine
a set of test statistics that can score a probability forecast
model in terms of different attributes such as accuracy,
calibration and resolution. Even though these proposed
methods are systematic, small-sample observations are
still problematic. However, the turning point forecast model seems more appropriate for such an evaluation method,
because it generates more observations both in terms
of switches from expansions to contractions and vice
versa, whereas a simple recession forecast model would
count only switches from expansionary to contractionary
regimes.
10. Koenig and Emery (1991) give a detail account of the
relative performance of the real time DOC LI series in
predicting expansions versus contractions. They find the
series to be a better predictor of expansions and a poorer
predictor of recessions in near future.
11. Financial institutions would have an opportunity to
arbitrage by selling T-bills in their portfolio and buying
commercial paper in those periods. However, for banks
those two instruments are not alike. For example, banks
can use T-bills but not commercial paper as collateral for
satisfying bank capital adequacy. Thus, due to the imperfect substitutability between T-bills and commercial paper, banks will not arbitrage and offset the widening
spread.
39
REFERENCES
Bernanke, Ben S. 1990.. "On the Predictive Power of
Interest Rates and Interest Rate Spreads," Federal
Reserve Bank of Boston New England Economic RevieW·pp .• 51-68.
Blanchard, Olivier J., and Mark W. Watson. 1986. "Are
Business Cycles All Alike?" In The American Business Cycles, ed. R.J. Gordon. Chicago. The Univer~
sity of Chicago Press.
Diebold, Francis X, and Glenn D. Rudebusch.1989.
"Scoring the Leading Indicators." Journal of Business
64, pp.369-391.
____________....... 1990.. "A NonpararTl~tric.lnvestigCltionof
Duration Dependence in the American Business.Cycle." Journal of Political Economy 98, pp. 596-616.
Doan, Thomas, R. B. Litterman, and C. A. Sims..1984.
"Forecasting and Conditional Projection Using Realistic Prior Distribution." Econometric Review 3, pp.
1-100.
Hamilton, James D. 1989. "A New Approach to the
Economic Analysis of Non-Stationary Time Series and
the Business Cycle." Econometrica 57, pp. 357-384.
Koenig, Evan F, and Kenneth M. Emery. 1991. "Misleading Indicators? Using the Composite Leading
Indicators to Predict Cyclical Turning Points." Federal Reserve Bank of Dallas Economic Review (July)
pp.1-14.
40
Neftci,SalihN. 1982. "Optimal Prediction ofCyclical
Downturns." Journal of Economic Dynamics and Contro/4, pp.225-241.
____-. 1984. "Are l:conomic Time Series Asymmetric over the Business Cycle?" Journal of Political
Economy 92, pp. 307-328.
Roberds, Will. 1988. "A Quarterly Bayesian VAR Model
of.theU . S.• E.conomy.".Working Paper 88-2. Federal
Reserve Bank of Atlanta.
Sargent, I. J., and C. A. Sims. 1977. "Business Cycle
Modeling without Pretending to Have Too Much A
Priori l:cgngrnic Theory. "JnNewMettlOcfSin BLJsine.ss
Cycle Research, ed.CA Sims, et al. Minneapolis:
Federal Reserve Bank of Minneapolis.
Stock, James.H., and Mark W. Watson. 1989. "New
Indexes of Coincident and Leadingl:conomiclndicators." •NBER. Mq,croeconomics Annual pp. 351·394.
Todd, Richard M. 1984. "Improving Economic Forecasting with Bayesian Vector Autoregression." Federal
Reserve Bank of Minneapolis Quarterly Review (Fall)
pp.18-29.
Watson, Mark W. 1991. "Using Econometric Models to
Predict Recessions." Federal Reserve Bank of Chicago Economic Perspectives (November/December)
pp.14-25.
Economic Review / Fall 1991
The Use of Equity Positions by Banks:
The Japanese Evidence
Sun Bae Kim
Economist, Economic Research Department, Federal
Reserve Bank of San Francisco. This paper is partly based
on a chapter of my dissertation submitted to the Department of Economics, University of Toronto. I would like to
thank the Center for Japanese Studies, Graduate School of
Business, Columbia University, for granting me access to
the NEEDS financial tapes. I am particularly indebted to
Profs. Hugh Patrick and Masako Darrough for kindly
making such an arrangement. Grateful acknowledgement
is also extended to Hang-Sheng Cheng, Mark Levonian,
Ramon Moreno, Brian Motley, and Randy Pozdena, for
their comments and suggestions. Able research assistance
was provided by Sean Kelly.
This paper draws on Japan's experience to analyze the
merits of conferring securities powers on banks. By issuing debt and equity jointly to a single outside investor, the
shareholder bank, firms will incur lower deadweight costs
associated with bankruptcy and monitoring than if these
claims are issued to separate entities. The level of Japanese banks shareholding in firms during the late 1960s is
generally consistent with this explanation of financing
decisions. Most notably, banks as a rule provided joint
debt-equity financing rather than pure debt financing.
Moreover, holding other things constant, the level of a
bank's equity holding increased in proportion to financing
it supplied the firm and to the riskiness of investment.
Federal Reserve Bank of San Francisco
A broad consensus now prevails that a firm in need of
external financing for investment may incur deadweight
losses that another firm, with sufficient internal funds but
otherwise identical, would not. The basic idea is that when
a firm knows more than outside financiers about its own
prospects and/or actions that affect its prospects, external
financing will engender deadweight or "agency costs"
which ultimately fall on the firm. Credit- and equityrationing, the need to meet strict collateral and other
financial requirements, and resources expended on monitoring, are-some of the manifestations of such costs.
One important conclusion from the literature is that the
more the corporate sector relies on external funds, the
greater will be the potential magnitude of agency costs. In
such a setting, the extent to which the market can devise
and implement contracts which attenuate these information-related costs will have a significant bearing on the
"real" performance of the economy. Financial contracts do
not materialize in a vacuum, however. The extent to which
agents can mitigate capital market imperfections is dictated by the legal and institutional parameters of the
financial system itself. Notably, we employ financial contracts with constraints idiosyncratic to the Anglo-American system, namely, the separation of commercial and
investment banking. There is no reason to believe, however, that such a systemic constraint should remain binding, much less be desirable, across time and space. If the
corporate sector's dependence on external financing is
sufficiently heightened, for instance, the constraint itself
may be subject to change.
The postwar Japanese experience is a case in point. The
rapid investment-led growth from the 1950s to the early
1970s put a formidable burden on Japan's financial system.
By virtue of the pace of growth, industries' demand for
external funds was large relative to their net worth or
collateral and hence, the potential agency costs in issuing
debt and equity were commensurately high. In such a
setting, the banks, which were the primary conduit of
investable funds, were legally sanctioned simultaneously
to extend loans and to hold shares of client firms. l The
predominant mode of financial contracts during Japan's
41
rapid growth period thus featured the major lenders as also
significant shareholders. Judging from the performance of
its economy, such a system appears to have met admirably
the task of underwriting Japan's growth.
Drawing on Japan's experience, this paper explores the
possible merits of conferring on banks ,securities powers. 2
It does so in two steps. Section I motivates the relevance of
financing choice on firm value under two types of capital
markets imperfections: costly bankruptcy and imperfect
information. Two points are established here. First, the
value-maximizing financial contract will optimally trade
off the agency cost of debt against that of equity. Second,
total agency cost of external finance will be lower when
debt and equity claims are jointly issued.
If agency costs do indeed matter in firms' financing
decisions, then firm-specific parameters affecting the relative severity of the agency costs of debt versus those of
equity should explain observed interfirm differences in
ownership structure. Section II explores this issue by
focusing on the determinants of the level of the bank's
equity holding for a cross-section sample of Japanese firms
during the period of rapid growth. The main contribution
here is the attempt to ascertain the effects of firm-specific
parameters on the level of the bank's equity claims that is
jointly held with debt claims. This approach contrasts with
previous studies that have focused on determinants of more
"conventional" measure of firms' capital structure such as
leverage ratio. 3
I. An Agency Cost Approach to Corporate Finance4
Deadweight Costs of External Financing
ness. Customers may desert financially distressed firms
Consider an entrepreneurial (i.e., owner-managed) firm
facing an investment that requires external financing. Its
return depends on a productive input we shall refer to as
"effort," whose level is set by the owner-manager. Higher
levels of effort enhance the return on the investment, but at
a cost of increasing the disutility incurred by the manager.
The investment is risky because it also depends on a
random variable the manager does not control. 5
The owner-manager can raise the required amount of
external financing by issuing debt and/or new equity.
Assume that banks are the only lenders in the system. 6
Furthermore, to serve as a benchmark, assume initially
that banks cannot own equity; that is, lenders in the system
cannot be shareholders. If the investment is undertaken
the firm can then be viewed as the nexus among three type~
of claimants: the original shareholder (the owner-manager), the new shareholder, and the lender (bank). As
Modigliani and Miller (1958) demonstrated, the value of
the firm will be independent of its financial structure if
capital markets are perfect. I motivate the relevance of the
financing decision by the owner-manager by positing two
types of imperfections.
First, bankruptcy is assumed to be costly in the sense
that the transfer of assets from the shareholders to the
creditors consumes some fraction of their total value.
These deadweight costs include lawyers' and accountants'
fees, and costs incurred in auctioning off the firm's assets.
Though more difficult to measure, bankruptcies also impose indirect costs which may tum out to be even larger. 7
Legal disputes or the perceived conflict of interest between
the shareholders and creditors of the firm can distract and
constrain the managers from properly running the busi-
and suppliers may exact more favorable terms. If lenders
are rational, these costs will be anticipated when negotiating the loans. Consequently, the expected deadweight cost
of bankruptcy will ultimately fall on the borrower.
The second set of imperfections relates to asymmetric
information between the firm and outside suppliers of
funds, the creditor (bank) and the new shareholder. This
gives rise to two types of incentive ~r moral hazard
problems. Consider first the case when new shares are
issued. As the owner-manager cedes larger proportions of
the firm's residual profit to the new shareholder, the effort
level, which is private information to the owner-manager,
8
will decline. This obtains from a standard assumption in
principal-agent models: The outside shareholder (principal) shares in the fruits of the insider's (agent's) effort, but
not in the level of effort itself. As a result, the agent
provides less effort than the principal deems optimal.
Insofar as the profitability of the firm depends on effort, the
prospective shareholder will impute the effect of this
adverse incentive when pricing the firm's equity. The inside
shareholder will therefore suffer a reduction in the value of
9
his equity.
Deadweight costs will arise with issues of debt as well.
First, the shareholder has an incentive to gain at the
expense of the lender by increasing the riskiness of the
investment the firm undertakes. This obtains because if a
risky investment turns out to be very profitable, the shareholder captures most of the gain, while the maximum
return to the lender is fixed to the contracted interest plus
principal. If, on the other hand, the investment fails
limited liability will shield the shareholder and the lende;
will bear the consequences. This asymmetry in the pay-
42
Economic Review / Fall 1991
off-bounded maximum downside loss but unbounded
upside return-creates an incentive for the shareholder to
invest in risky projects even if they have lower net present
value than a safer project. 10
The rational lender will anticipate the risk-taking propensity of the shareholder and demand an interest rate
commensurate with the maximum amount of risk that the
firm can undertake. In other words, by anticipating the full
extent of the moral hazard risk-shifting by the shareholder,
the lender will preempt any possible appropriation of his
wealth. But such a preemptive measure will prove costly to
the shareholder-and ultimately to society. Other things
equal, a higher interest rate implies a higher probability of
bankruptcy and hence, a higher expected cost of bankruptcy. In a competitive debt market, this higher expected
cost will be passed on to the shareholder.
When the level of effort is private information to the
insider, issues of fixed claims to outsiders will give rise to
yet another deadweight cost. The level of effort set by the
manager will decline as the probability of bankruptcy
increases. This is a rational response because when the
firm is bankrupt, its ownership will fall into the creditor's
hands and the manager will not reap any return to expanding effort. Accordingly, effort will decline as interest rates
rise, since the latter implies higher probability of bankruptcy. But reduced effort implies greater probability, and
hence greater expected cost, of bankruptcy. Again, this
deadweight cost will be passed onto the firm.
To summarize, the firm will incur deadweight losses
whether it issues debt or equity. Substituting debt for equity
substitutes one set of deadweight losses for another, but
does not eliminate them, so long as the firm needs external
financing. Under such circumstances, the firm's financing
decision will matter because by optimally trading off the
deadweight cost of debt against that of equity, total deadweight cost will be minimized. That firms do not exclusively rely on debt or on equity presumably reflects the fact
that such "corner solutions" are not optimal from the point
of view of minimizing agency costs.
Advantages of Joint Debt.Equity Financing
The joint issue of both fixed and residual claims to
a single outside financier-the lender-cum-shareholder
bank-can be motivated by two sets of considerations.
The first is reductions in bankruptcy costs, direct as well as
indirect. To the extent that the debtholder already owns a
fraction of the firm, the total cost that will be incurred in
transferring the firm's asset from the shareholders to the
creditor in the event of bankruptcy will be smaller than
when these claim holders are mutually exclusive entities.
The second set of advantages concerns the efficiency
Federal Reserve Bank of San Francisco
gains in monitoring. Up to this point, it has been assumed
that outside financiers anticipate the full extent of moral
hazard and price the firm's securities accordingly. However, the severity of the moral hazard problem, and hence
its deadweight costs, can be attenuated by monitoring the
activities of the insider. It will be ultimately in the interest
of the owner-manager to subject himself to such scrutiny if
the total monitoring cost is less than the reduction deadweight costs that it brings about, since the insider ultimately bears the agency costs in either case.
A commonly discussed pattern in the literature is that
the lender checks the borrower's propensity to undertake
risk through monitoring. 11 The outside shareholder monitors the effort of the manager, who acts in the interest of
inside shareholders, and thereby enhances the net return to
the investment. As in other forms of information production, however, monitoring exhibits economies of scope.
Needless duplication of monitoring costs will be eliminated by having a single outside financier, i.e., the lendershareholder, performing the monitoring. The idea can be
illustrated with a simple example.
Suppose that the outside shareholder incurs X units of
monitoring cost to increase the effort level of the manager
by de. Analogously, suppose that the lender also devotes X
units of resource to reduce the riskiness of the firm by da 2 .
This will have two effects. First, the reduction in risk will
lower the bankruptcy probability and hence the expected
cost of bankruptcy. Second, the lowered bankruptcy probability, in turn, will raise the marginal expected return to
effort for the owner-manager, and thus will elicit higher
effort. Thus, the shareholder's monitoring of effort, which
is costly, will be partly redundant as long as the lender's
monitoring of risk has some positive spill-over effect on
effort. By the same logic, the lender's monitoring of risk
will be redundant, in part or in whole, when the shareholder is monitoring effort, since higher effort lowers
bankruptcy probability and hence its expected cost.
Why can't the lender and shareholder coordinate the
task of monitoring so as to eliminate any duplication? One
obvious obstacle to such coordination is the agency conflict that prevails between the two. For example, while the
lender can safely rely on the incentive of the shareholder to
monitor the effort of the manager, he cannot trust the
shareholder to monitor risk with commensurate self-interest; the shareholder prefers higher to lower risk. So long as
a dissonance of interest prevails between the lender and the
shareholder, the bundling of debt and equity claims into a
single entity (i.e., the lender-shareholder bank) is a more
efficient way to capture the economies of scope in monitoring, and ultimately to reduce the deadweight costs of
external financing.
43
Hypotheses
While agency and bankruptcy costs provide a theoretical justification for the relevance of financing decision, are
these costs indeed significant in reality? This question can
be addressed more formally through a number of hypotheses suggested by the theoretical framework. The most
obvious hypothesis is: if issues of debt and equity do
impose deadweight losses, the prevalent mode of financing
should feature the lending bank as a shareholder in the
same firm, provided, of course, that the legal system
permits it. In addition to this broadly cast prediction, more
specific hypotheses emerge on interfirm differences in the
level of equity stake held by lenders ,12
HYPOTHESIS 1: the bank's shareholding will be larger the
higher is the magnitude of deadweight losses holding the
probability of bankruptcy constant. As the creditor holds
larger equity stake in the firm, we would expect these
deadweight costs to decline on sheer logistic grounds: a
smaller portion of the firm's assets need to change hands.
More significantly, perhaps, the greater coincidence of
interest between debt and equity that obtains by definition
in a lender-shareholder financing scheme will reduce the
indirect cost of bankruptcy, or even reduce the probability
that the firm encounters financial distress in the first place.
HYPOTHESIS 2: The higher is the firm's dependence on
the bank's funds, the higher will be the bank's equity stake
in the firm. All other things equal, the more the firm relies
on outside financing, the higher will be the agency costs of
debt as well as that of equity. 13 Greater equity holding by
the bank may attenuate these deadweight costs on two
grounds. First, by structuring a greater portion of the
bank's return through equity, the expected costs of bankruptcy will be reduced. Second, increased shareholding
may enhance the efficiency as well the clout of the bank in
checking both types of moral hazards discussed above, i. e. ,
risk-shifting and shirking on effort.
HYPOTHESIS 3: Holding the level of risk constant, the
higher the expected profitability of the firm, tht{ lower
should be the bank's equity holding in the firm. Higher
profitability implies lower probability of bankruptcy and
hence lower expected deadweight cost of debt. 14 On the
other hand, higher profitability will exacerbate the incentive problem associated with issues of (outside) equity:
Outside financiers share an enlarged pie while the original
owner-manager incurs all the cost of making it. The two
effects combined should lead to a lower reliance on equity.
HYPOTHESIS 4: the bank's shareholding will be higher in
riskier firms. Holding expected return constant, higher risk
implies higher probability of bankruptcy and hence higher
expected cost of bankruptcy. By structuring larger portions
44
of the bank's return through equity than debt, the probability of bankruptcy, and hence its expected cost, will be
reduced.
The collateral value of the firm is also germane here. The
more tangible is the form of the firm's investment, the less
opportunity is presumably available to the firm to engage
in asset substitution that increases risk. The fraction of a
firm's assets accounted for by tangible assets is therefore a
(negative) indicator of discretionary opportunities to shift
risk to lenders. The higher the firm's collateral value,
therefore, the lower will be lenders' shareholding. Empirically, however, it will be difficult to untangle this riskattenuating aspect of collateral from lowered bankruptcy
cost considerations discussed earlier.
Application to Japan
Postwar Japan provides a fertile ground to test the
hypotheses outlined above. As noted earlier, its legal
system has allowed banks to combine corporate lending
with equity participation. Moreover, the high reliance of
the corporate sector on external funds during the 1960s
through the early 1970s suggests that the magnitude of
agency costs, and hence the incentive to mitigate them,
would have been significant. Testing the hypotheses, however, requires some institutional background on the postwar Japanese financial system and industrial organization.
Japan's financial markets were tightly regulated until the
mid-1970s, when gradual deregulation was begun. One of
the main objectives of the authorities was to make industrial financing the virtually exclusive preserve of Japan's
financial institutions and to limit their number by strictly
controlling entry.I5 As a result, Japan's corporate bond
market has remained thin and the number of major corporate lenders limited. Excluding government financial institutions, major conduits of funds consist of a dozen city
banks, three long-term credit banks, seven trust banks, and
large life insurance companies,!6 According to Hodder
and Tschoegl (1985) fewer than 30 financial institutions
may control over 90 percent of private lending to large
industrial firms.
As is the case elsewhere, large Japanese firms typically
procure financing from a consortium of lenders. What
distinguishes the Japanese loan consortium, however, is the
special role played by the lead or "main" bank. Although a
precise and steadfast definition cannot be assigned to the
term, a typical main bank would be a city bank, which is
the largest lender as well as a significant shareholder of a
given firm. One important function of the main bank, as
Sheard (1989) put it, is to act as a delegated monitor among
lenders. It screens and monitors corporate borrowers on
Economic Review I Fall 1991
behalf of all lenders in a given consortium. 17 The main
bank also shoulders most of the burden of reorganization,
bail-outs or outright liquidation when a corporate client
encounters financial distress. IS
The main banking system typically occurs within the
organizational context of the keiretsu, loosely translated as
a corporate group. Firms belonging to these groups tend to
maintain long term relationships with one another. Intrakeiretsu ties are maintained through informal or implicit
commitments; they are also manifest in explicit financial
commitments of reciprocal shareholding. At the fulcrum
of each of these groups are the major city banks. Thus, for
example, the Mitsui Bank will most likely serve as the
main bank for most firms belonging to the Mitsui keiretsu.
Major city banks are themselves flanked by two or three
closely affiliated financial institutions. For example, the
Mitsui group includes at its financial core Mitsui Trust and
Banking, Taisho Marine and Fire Insurance, and Mitsui
Life Insurance Company. In view of the close coordination
that is said to prevail among the keiretsu financial institutions, it seems reasonable to regard them collectively as a
single economic agent; that is, for purposes of mitigating
the agency costs of external finance, it is the collective
shareholding of all keiretsu financial institutions that is
likely to matter. I therefore use this level of aggregation to
measure the bank's shareholding in the empirical analysis
to follow. For ease of exposition, the term "main bank"
throughout the remainder of the paper will refer to the
group of keiretsu financial institutions centered around the
city bank. 19
II. An Empirical Test
Variables and Empirical Proxies
Main bank's shareholding. This is the dependent variable in the estimated regression equations. Firm-level data
for this variable were compiled from Economic Research
Association's (Keizai Chosa Kyogikai) annual publication,
Keiretsu no Kenkyu (Research in Corporate Financial
Groups). ERA employs a primarily quantitative criterion
to define a financial group. If a firm has obtained the largest
amount of financing from the same bank for three or more
consecutive years to date, then that firm is classified as
belonging to the bank's keiretsu. As in any exercise in
taxonomy, ambiguities inevitably arise, and the ERA applies two additional criteria for inclusion where necessary:
(i) shareholding by group members exceed 20 percent; (ii)
historical ties.
Bankruptcy costs. Two set of proxies were considered.
The first is the collateral value of the firm-defined as the
proportion of tangible assets in the firm's total assets-as a
negative correlate of bankruptcy cost. 20,21 According to
Myers (1977), the deadweight losses of bankruptcy will be
more pronounced for intangible assets that are linked to the
health of the firm as a going concern; that is, the lower the
collateral value of the firm, the higher will be its expected
bankruptcy costs. For example, technical know-how, human capital, and brand image are likely to lose a greater
proportion of their values than tangible physical assets
such as plant and equipment, when the firm ceases, or is
threatened to cease, as a going concern. If this argument is
correct, one should observe a negative relationship between the level of shareholding by lenders and the ratio of
the firm's tangible assets to total assets.
Federal Reserve Bank of San Francisco
As is often the case, however, this empirical proxy may
not uniquely capture the theoretical attribute we wish to
measure. As already noted, collateral value may also serve
as a negative correlate of risk. An additional complication
concerns the so-called asset specificity effect suggested by
Williamson (1985). The idea is that as a firm's assets
become more "specific" to existing contractual relations,
and hence less redeployable outside these relationships, the
salvage value of the firm, given that bankruptcy occurs,
will decline; that is, bankruptcy costs rise with the degree
of asset specificity of the firm and the hypothesized effect
is a greater reliance on equity structuring the bank's return
through equity participation. One cannot rule out ex ante
the possibility that a firm's ratio of fixed to total assets also
proxies for the degree of asset specificity. The two will
exert opposite effects.
The second proxy tries to capture the indirect cost of
bankruptcy. The conflict of interest between shareholders
and creditors during financial distress may seriously impair the firm's capacity to take appropriate actions to stem
further deterioration. Appropriate action may entail timely
disposal of the firm's rapidly depreciating assets or, alternatively, new investment to boost its competitiveness. In
either case, the indirect costs of financial distress may be
more acute when the firm operates in a very dynamic and
rapidly growing market. For one, the failure to keep up
with market growth, let alone shutdowns, would exact a
high toll in terms of forgone output and, perhaps more
importantly, loss in market share. The expected industrywide growth level was therefore included in the regression
analyses as a possible correlate of the (expected) indirect
cost of financial distress.
45
External Financing Ratio. This variable is intended to
measure the extent to which a firm relies on the main bank
to finance its investments. I therefore computed the ratio of
financing obtained from the largest keiretsu financial group
to total assets.
Expected Profitability. The level of profitability was
proxied by the rate of business profit defined as:
RBP =
gross profit
+
receipts of interest plus dividends
::..-.......:-----=--------total assets
where gross profit is earnings before taxes and interest
payments. The choice of this proxy over other measures of
profitability is due to Nakatani (1984). He argues that since
total assets equal own capital plus debt, the rate of return
on total assets should include both current profits and
interest paid to financial institutions; counting current
profit alone will bias downward the rate of return for those
firms with a greater debt burden.
Risk. A natural proxy for risk is a measure of volatility
defined as the standard deviation of the rate of business
profit.22 In addition, three other possible proxies of risk
were considered. The first is the expected growth of the
firm. It has been argued that insiders may have greater
potential to obtain information about the prospects of a
more rapidly growing firm than outsiders do. A rapidly
growing firms may also be riskier because insiders potentiaHyhave greater scope and discretion to engage in risky
activities; for example, they have greater flexibility in the
choice of future investments. 23 The estimated model therefore included expected sales growth as a positive indicator
of risk.
Second, the age of the firm was included to explore the
possibility that the agency costs are less severe in older
firms than in new firms. Compared to relatively mature
firms. charting familiar waters, newer firms may face
greater uncertainty, for example, exploring new technology
or markets. 24 Furthermore, established firms may be more
cautious about jeopardizing their reputations for the sake of
short-term gain through morally hazardous behavior.
Finally, the size of firms may also proxy for risk. Larger
firms tend to be more diversified and hence less prone to
bankruptcy risk. This implies the opposite effect on the
firm's claim structure: banks should hold lower residual
claims in larger firms. 25
Table 1 takes stock of the arguments presented thus far.
Data aIidEstimation Procedure
The variables were analyzed for the period 1964-1970,
because it represents the last major investment boom
(56 months of uninterrupted growth from November 1965
46
to July 1970) before the first oil shock. Data on the sources
of loans and shareholder composition are from Keiretsu
no Kenkyu. The year of the firm's establishment was
taken from Kaisha Nenkan [Company Annual] published
by Nikkei. All other variables were compiled from the
NEEDS corporate financial data tape which includes balance sheet, income statement, and other supplementary
accounting data at the firm level. Since the financial
settlement of the majority of firms was on a semi-annual
basis until recently, the flow data were added up component by component. No problem was encountered on the
comparability of data across these different sources since
all of them were ultimately compiled from the same source,
the Yuka Shoken Hokokusho-financial reports that all
listed companies are required to submit on an· annual or
semiannual basis to the Ministry of Finance.
The sample is drawn from 635 firms that were continuously listed on the First Section of the Tokyo Stock
Exchange (TSE) from 1964 to 1970 inclusive. To exclude
regulatory and other related effects, sample selection was
limited to firms in manufacturing industries which reduced
the sample to 468. 26 The list was further pared down by
eliminating firms undergoing mergers or severance during
this period, firms with incomplete records on the variables
included in the analysis, and firms eliminated from the data
Economic Review / Fall 1991
tape by Nikkei because they were either involved in
mergers or severance in the period following 1970, or
because they simply went bankrupt. The sample therefore
contains a nonnegligible degree of self-selection with a
likely bias toward relatively larger, successful firms. 27
These rounds of elimination left a final tally of 338 firms.
Their breakdown according to Nikkei's industry classification is reported in Table 2.
business profit was measured using all seven years in the
sample in order to obtain the maximum efficiency in the
measure as possible.
Table 3 reports the summary statistics of the variables
analyzed. On average, the level of borrowing from the
group of keiretsu financial institutions represented a little
under 24 percent of the firms' total asset or over 35 percent
of total borrowing. A noteworthy finding is that for the vast
majority of the sample firms, the legal ceiling of 10 percent
did Ilotappearbin.ding: The average main bank's shareholding stood at under 11 percent. (Recall that is a collective measure which typically includes holdings of three or
more financial institutions.)
Though not reported in the Table, the second noteworthy
finding is that for close to 93 percent of the firms in the
sample, the main bank was simultaneously a lender and a
shareholder in the firm. Out of a sample of 334 firms, the
instance where the main banks held outstanding loans but
held n.o stock was limited to 25 firms (7.5 percent). The
prevalent mode of financing for the sample firms thus
featured principal lenders as shareholders. Though impressionistic, the finding is consistent with the postulated
efficiency of conjoining debt and equity claims.
Our next step is to ascertain whether the cross section
data reveal a systematic pattern in the level of shareholding. Since for a small but not negligible proportion of the
observations on the dependent variable assumed a limiting
The sampling period was divided into two subperiods1964-66 and 1967-70-over which sample averages were
calculated. Averaging was performed to reduce measurement error due to random year-to-year fluctuations in the
variables. The procedure should also serve to smooth the
effects of lumpy investments undertaken in a particular
year on accounting data. The 3-year averages of the dependent variable, firm size, asset structure, and external
financing ratio were measured for the contemporaneous
period 1964-67. The variables pertaining to expectations
-profitability and growth-were measured over the period 1967 through 1970; that is, I assume rational expectations and use the ex post realized values as proxies of the
values expected when the financing decision was made. 28
Finally, the standard deviation of the change in the rate of
Federal Reserve Bank of San Francisco
47
value-i.e., the bank's equity holding was zero-a maximum likelihood Tobit estimator was used. 29 For purposes
of comparison, an ordinary least squares estimation was
also performed.
The Results
As a preliminary step to running the regressions, a
Pearson correlation analysis was performed. The magnitude of collinearity among the explanatory variables was
minimal, so the results are not reported. To check for
possible industry effects on the model, a standard analysis
of variance was performed using industry dummy variables. 30 Surprisingly, no statistically significant industry
effect was detected in the data.
The main empirical findings of this paper are contained
in Table 4. 31 No material difference is discernible between
the estimated coefficients of the TOBIT and OLS regressions. This suggests that the censoring problem was minimal. Finally, different functional specifications were also
tried for possible non linear relationships between the
variables. The results turned out to be uniformly inferior to
the linear specification and are not reported.
To begin with the proxies for bankruptcy cost, the
collateral value of the firm yielded a positive coefficient.
The model thus predicts that as the proportion of tangible
assets in total assets increases, the lender's shareholding in
the firm will increase. This clearly runs counter to the
commonly subscribed view that tangible assets lose less
value relative to intangible assets in times of financial
distress. Several interpretations are possible. For example,
the obtained sign may reflect the asset-specificity problem
discussed by Williamson (1985), i.e., tangible assets, as
positive correlates of transaction-specific investment, impose higher bankruptcy costs. However, it is difficult to
reconcile this argument and the prediction that higher
collateral also means lower risk and hence leads to lower
shareholding by the main bank. In light of this, one cannot
dismiss the possibility that the "perverse" sign may be due
to the measurement problems discussed earlier, particularly with respect to the valuation of the firm's land
holdings.
The proxy for indirect bankruptcy costs-the expected
growth of the industry- yielded the predicted positive
sign; that is, the main bank tends to hold higher equity
stakes in firms expecting more rapid growth. The statistical
significance of the estimate is rather tentative, however. No
doubt, this reflects the considerable amount of statistical
noise that is likely to intrude on industry classifications of
the sample firms.
The most notable result is the positive and statistically
48
significant coefficient (at the 1 percent level) for the firm's
external financing ratio; that is, as larger fractions of the
firm's investment are financed by the main bank's funds,
the larger is the latter's equity stake in the firm. According
to the TOBIT estimate, an increase by 0.111 in the external
financing ratio-one standard deviation in the sampleincreases the main bank's shareholding in the firm by 2.7
percent. 32 Similar conclusions can be drawn on the basis of
OLS results. These findings lend support to an oft-noted
observation that Japanese banks exercise considerable
influence on the firm by virtue of their shareholding. 33
Economic Review / Fall 1991
Although an inverse relation obtained as was predicted
between the level of main bank's shareholding and the
expected profitability of the firm, the coefficient turned out
to he statistically i~significant.
As. pred.ict~d, a positive relation obtained between the
main bank's shareholding and the volatility of the firm's
profit which proxiedfor risk. The estimated relationship
predicts that an increase in volatility by the magnitude of
one standard deviation in the sample will increase the
bank's shareholding in the firm by nearly 1.7 percent. By
contrast, the second proxy for risk, the expected growth of
the.finn did not yield a significant result. Although an
inverse relation obtained between the level of the main
bank's shareholding and the firm's age, the coefficient was
statistically insignificant. 34 However, an inverse and statistically significant relationship did obtain between the
firm's size and the percentage of residual claims issued to
the bank.
III. Conclusions
OJl the basis ofpublished accounting data, this paper
investigated the benefits of joint debt-equity financing, by
examining the determinants of ownership structure of
Japanese firms during the era of rapid growth. Any test of
optimal financial structure, motivated in part or in whole
by information asymmetry, must necessarily be crude. By
definition, the researcher who must depend on publicly
available information is subject to the very type of information asymmetry faced by a firm's outside investor. In this
respect, the student of Japanese corporate finance is especially handicapped. The statistical noise due to the poor
quality of corporate disclosure in Japan no doubt accounts
for a significant portion of the sizable unexplained variance
that remains in the regressions. 35
These limitations notwithstanding, the empirical analysis did yield plausible results in support of the theoretical
model. For one, rarely did banks forgo the opportunity to
hold an equity stake in firms where significant lending
Federal Reserve Bank of San Francisco
lending occured. Thus, if any efficiency gains were made
possible by a legal system that conferred securities powers
to banks, they did not go unexploited. Furthermore, the
cross section evidence generally supports the view that
agency cost considerations indeed seem to matter in how
banks structure their claims in client firms. The most
notable results in this respect are that the amount of equity
stake that the bank held in the firm increased with the level
of financing the bank extended to the firm and with the
level of risk. The bank's capacity to participate in corporate equity is crucial in "reconciling" the aggressive
lending behavior of Japanese banks during the period of
rapid growth on the one hand, and on the other, the low
level of net worth and hence relatively high loan risks in the
corporate sector. These considerations may be relevant to
policymakers in the U. S. currently faced with the task of
overhauling its banking system.
49
ENDNOTES
1. In the process of dissolving the zaibatsu-the financial
"cliques" which allegedly precipitated Japan's entry into
war-the Occupation forces severely curtailed the power
of Japanese banks in addition to outlawing intercorporate
shareholding by nonfinancial corporations. These stiff
provisions were subsequently relaxed as Japan was
poised to embark from reconstruction to rapid peacetime
growth. Reciprocal shareholding became legal again in
1949, thus ushering the way for many of the former zaibatsu firms to regroup under the present day keiretsu.
And unlike in the United States, the city banks which form
the nuclei of these corporate groups, (along with trust
banks and insurance companies) were empowered to
hold corporate shares subject to a legal maximum. Until
1987, the legal limit was set to 10 percent of the outstanding stocks of any single company; the ceiling currently
stands at 5 percent.
2. This very question was addressed also by Pozdena
(1991).
3. See for example, Kester (1986), Allen and Mizuno
(1989) and Prowse (1990).
4. This section draws heavily from Kim (1991) which provides a more formal treatment on the subject. A compressed version of the formal model is sketched out in
Appendix A.
5. One can think of this variable as unforeseen events
such as bad weather, a technological discovery, or war in
the Persian Gulf.
6. This assumption abstracts the bond market (as well
non-financial credit intermediaries) from the analysis, thus
allowing us to focus on the implication of granting equity
powers to financial intermediaries. The implicit premise
here is that in the economy under consideration, intermediated debt finance (i.e., bank loans) are preferred to
direct borrowing (bonds). This could be because, as is
now widely recognized in the literature, banks possess a
comparative advantage in information production, such
as screening and monitoring borrowers. By implication,
this comparative advantage will be heightened in situations where information-related problems are acute in the
system, as is presumed here.
7. Empirical analysis on bankruptcy costs is scarce. Frequently cited is a case study of a railroad bankruptcy by
Warner (1977) which finds the direct costs to be rather
negligible. But a more recent case study of corporate
reorganization in the oil industry by Cutler and Summers
(1988) suggests that the indirect costs of financial distress
can be very substantial indeed. According to the authors'
estimate, the dispute between Texaco and Pennzoil over
the Getty Oil takeover imposed a deadweight loss equivalent to someone-sixth of the combined wealth of the two
companies.
8. We say residual profit because the profit accruing to
shareholders consists of what remains after creditors
have been paid off. For this reason, equity is sometimes
50
referred to as a "residual claim" to the firm. By contrast,
debtis a "fixed claim" since its return, provided the firm is
solvent, is invariant to the firm's profit; if the firm is insolvent, fixed claimants become residual claimants, i.e.,
creditors take over the ownership of the firm's assets.
9. It is for these reasons that the distinction between the
original and new shareholders is crucial. To reflect their
different access to information, the initial owner will sometimes be referred to as the "inside share" and the new
shareholder as "outside share."
10. The distinction between the inside and outside shareholder is not important here. The outside shareholder will
endup participating in the moral hazard of risk shifting to
debtholders, without necessarily being privy to the insider's information or his action.
11. The modern theory of financial intermediation critically
hinges on the postulated efficiency of banks as monitors
in the presence of moral hazard. For example, Diamond
(1984) argues that diversification within the intermediary
enables it to monitor at a lower cost than if scattered
principals (depositors) were to monitor individually. In a
related vein, in view of the bank's superior access to the
firm's information, Fama (1985) distinguishes bank loans
as "inside debt" from the open capital market "outside
debt" such as bonds.
12. I focus on the level of equity holding by Japanese
banks and omit discussion on the leveL of debt for the
following reason. Under the rubric of the so-called "low
interest rate policy," a usury regulation on corporate lending remained in effect throughout most of the postwar
period. There is now ample evidence that banks tried to
circumvent this regulation, most notably by requiring firms
to post compensating balances. Reported interest rates
are likely to diverge from the effective interest 'rate and
hence, measured levels of debt may diverge substantially
from actual levels. (See, e.g., Wakita (1983)).
13. By implication, a firm will try to finance an investment project out of internal funds whenever possible and
thereby avoid the deadweight costs of going to the external market. This option will be foreclosed, however, if
investment projects are "lumpy," i.e., project size rises in
discrete increments and the minimum.
14. Section II provides a discussion on the empirical
proxies for this and other firm-specific parameters.
15. For a concise survey of Japanese financial markets
and corporate finance, see Hodder and Tschoegl (1985).
16. The concentration ratio remains high in this industry.
At the end of 1980s, the top eight domestic life insurance
companies among a total of 21 controlled over 80 percent
of total assets (Hodder and Tschoegl1985, p. 176).
17. See also Horiuchi et aI., (1988), Horiuchi (1989) and
Hoshi et aI., (1990a).
18. See Hodder and Tschoegl (1985), Suzuki and Wright
(1985) and Hoshi et.al. (1990b). According to Nakatani
Economic Review / Fall 1991
(1984), the main raison d'etre of keiretsu and main banking is precisely to minimize the probability of encountering
financial distress through a mutual risk-sharing arrangement among member firms and financial institutions.
19. The membership of the various keiretsu financial institutionsas well as a list of "independent" ones, Le., financial. institutions without any keiretsu affiliation, are in
Appendix B.
20.· Another proxy for bankruptcy costs (as well as risk)
often used in the literature is the level of R&D and advertisingexpenditlJres as a proportion of the firm's total sa.les or
total assets. The presumption here is that these variables
measure the firm's growth opportunities, Le. they add
value to the firm but· cannot be collateralized. Unfortunately,Japanese companies were not required to disclose expenditures on these items until the 1970s; hence
this particular proxy could not be included in the estimated model.
21. Total tangible fixed assets consists of depreciable
and nondepreciable assets. Buildings and structures,
machinery and equipment, vessels and vehicles, etc.,
fall under the former category; land and construction in
progress fall under the latter. Inflation accounting was
virtually unheard of in Japan during the period under
review. Hence, assets reported in the balance sheet understate their prevailing value by a significant margin.
Corporate assets held in land are particularly problematic
given the steep increase in real estate prices during the
postwar period. This is doubly troublesome since land has
been one of the traditionally favored forms of collateral
required by banks. In the absence of more detailed information on corporate land holding, any attempt at market
value adjustment, however, is likely to introduce additional
measurement error. The empirical model was therefore
estimated using book values of assets.
22. This is a scaled measure of volatility, since business
profit was normalized by the firm's total assets.
23. See for example MacKie-Mason (1989) and Titman
and Wessels (1988).
24. These are some ofthe very reasons why de novo firms
often obtain financing through joint ventures rather than
bank loans.
25. The size of a firm will also have direct bearing on
how much bargaining power it has vis-a.-vis the bank. If
Japan's banking industries was not perfectly competitive,
greater bargaining power for the firm may imply lower
levels of residual and fixed claims issued to the bank.
26. Nonmanufacturing industries, such as communica"
tions or utilities, tend to be heavily regulated. Corporate
financing decisions will not be neutral to regulations. For
example, holding other things constant, a firm operating in
an industry which limits entry will be able to support a
greater amount of debt because entry barriers confer
oligopoly rent and lowers business risk. Regulated industries are also SUbject to greater public scrutiny and hence
are more limited in engaging in moral hazard.
Federal Reserve Bankof San Francisco
27. Admittedly, the moral hazard problem for these larger
firm would be much less severe than for smaller firms.
Unfortunately, as is the case elsewhere, access to data
a.boUt srna.ller (and hence unlisted) Japanese firms isvery
limited. Criticism of self-selection bias should be tempered on at least one count, however, namely, that the
dependence on external financing even for the largest
firms was very pronounced during the period under review. On this ground alone, one cannot dismiss thepotential moral hazard problem as trivial. The proof of the
pudding of course is in the eating.
2B. This also obviates possible multicollinearity problems
betwe.enprofitability and external financing requirement.
Ceteris paribus, external financing ratio are lower for more
prqfitC3.ble firm.s s.ince larger fractions of investments can
be financed through retained earnings. The collinearity is
avoided when forward values of profitability are used.
29. The TOBIT technique is designed to use all observations, both those at the limit (in our case, bank's shareholding equaling zero) and those above it, to estimate a
regression line. Tobin pioneered this technique in his
classic study of the influence income on household expenditures on durable goods, where a large percentage
of the sampled households made no durable purchases
during the survey period. The idea is that since durable
goods by nature are not divisible, a certain threshold
level of income must to be reached before one actually
observes positive levels of purchase. The coefficient estimated by TOBIT thus explains the change in the dependent variable y in terms of two components: (1) the change
in y of those above zero, weighted by the probability of y
being greater than zero; and (2) the change in theprobability of y being greater than zero, weighted by the
expected value of y given that it is greater than zero.
Generally speaking, when the dependent variable is censored, OLS estimation will yield biased estimates of coefficients. How significant this bias is will depend on the
severity of the censoring problem.
30. The data problem discussed in footnote 20 provides
one motivation. One would expect to find systematic interindustry differences in the relative importance of R&D and
advertising expenditures: for example, pharmaceutical
firms are likely to be more research-intensive than textiles
manufacturers. Any systematic variation that remains in
the error term due to the omission of this variable will be
picked up by the industry dummy.
31. Industry dummies were not included since they were
found to be insignificant.
32. Strictly speaking, the coefficient from TOBIT estimation overstates the effect of the explanatory variables. The
appropriate procedure is to weigh the coefficient by the
expected probability that a given observation has anonlimiting dependent variable. Since this weight turned out
to be virtually equal to unity, little harm is done by ignoring
this caveat. For a more l;lxtensive discussion on this issue,
see McDonald and Moffitt (1980).
51
33. For example, Japanese banks are said to wield much
influence on client firms' capital spending plans. Particularly noteworthy in regard tob~nks' corporate control
throughshareholdingis thelega.lprovisi()n thata.lI()ws
major shareholders to remove corpor~te directors at any
time, without cause by an ordinary resolution of a shareholder general meeting.
34. Regressions were also run with .the age variable
specified as a dummy variable, taking a value of 1 if the
firm was founded afterW.W.11 and ootherwise. This did not
yield a significant estimate eitheL
35. The poor quality of accounting data in Japan is not an
aberration; it should be expected. Throughout most of the
postwar period, corporate finance was the virtually exclusive domain of banks..By implication, banks monopolized
52
on corporate monitoring and used the information in allocating investable funds. In the absence of any active
open issue market to speak of, the lack of public disclosure as deep and broadas found in the U.S. or U.K. is
natural to expect.
36. To minimize notational clutter, the firm-specificparametersJ.!.and a will be suppressed unless called for in
the analysis.
37. Note that this amounts to saying that equity issues .do
not in themselves generate funds. This simplifying assurnptionisactuallyconsistenfWithJapanesecorp()ra.te
financing practice during the period under review. Virtually without exception, equity was issued at a par value
of 50 yen per share. Needless to say, this issue price
represented. a negligible. fraction of the market value of
equity for most of the listed firms.
Economic Review / Fall 1991
Appendix A
A Sketch of a Model of Optimal Financial Contracts
This Appendix outlines a simple model of optimal financial contracts between an entrepreneurial firm and a shareholder bank. The return to the firm's investment takes the
form X == e + 6 + f.L; e denotes effort, 6 is a random
variable, and f.L is a firm-specific parameter that indexes the
profitability. of investm.ent-Return increases. in all three
variables. Unless stated otherwise, assume that 6 is uniformly distributed over [~, 6] with E6 == O. Denote the
spre~~of •. • thedistributio~ •• (hence the riskiness of the
investment) by a, a == 6 -- ~ == 20. 36
To procure some fixed amount of external financing,
L, the owner-manager can issue the bank a fixed claim
(i.e. debt) equal to RL, where L is the amount borrowed
and R == (1 + r) is the gross interest rate, and/or cede a
portion of his equity A, retaining for himself the remaining
fraction (1 - A).37
Assuming risk-neutrality throughout, the expected profit
of the owner-manager is:
(A3)
<Pe == (1 - A)(1 - F(6*» - ue == O.
To ensure a maximum, assume <Pee < O. Implicit differentiation of (A3) yields the direction of adjustment in effort
with respect to the contract variables:
e~ ==
(A4)
(l-A)Lf(6*)/<Pee <0
e*
~
(l-F (6*) ) / <l>ee
<
0
In valuating the claims issued bythe firm, the rational b(lIl]c
will anticipate these effort responses in addition to changes
in the expected cost of bankrutpcy. Consequently,. the
problem facing the owner-manager is to choose a structure
of claims R (and hence RL since L is fixed) and A that
maximizes his expected profit (1) subject to the "budget
constraint" (A2) and the incentive constraints (A3) and
(A4). The relevant first-order condition for an interior
optimum is given by:
a
(AI)
<P
== (1 - A)
J [e + 6 -
RL ]dF (6)
u(e),
9*
where 6* == RL - e denotes the critical value of 6 below
which bankruptcy occurs, and u (e) measures the disutility
that the manager associates with effort. Assume ue > 0,
uee > O. Note that because of limited liability, the ownermanager cares about the expected return only over the
states where the firm is solvent.
The expected profit of the bank is given by:
8
(A2)
'IT
== RL(1-F(6*»
+
A
J [e+6
RL]dF(6)
9*
9*
+
J [e+6-B]dF(6)-pL ;;:: O.
9
The first term is the debt owed to the bank times the
probability that the firm will be able to honor it. The second
term is the return accruing to the bank through its equity
holding, while the third is the expected value of the firm
over states where the firm defaults. Bankruptcy is costly in
the sense that the value of the firm is eroded by some fixed
amount B when the bank takes over ownership. Finally, the
last term represents the opportunity cost the bank associates with providing L to the firm. Competition among
banks ensures that equation (2) equals zero.
For any given combination (R, A), the manager will set the
effort level so as to maximize his own expected profit; that
is, e * will be chosen to satisfy:
Federal Reserve Bank of San Francisco
The left-hand side (LHS) of (A5) is the ratio of the
marginal response in the firm's profit with respect to the
contract variables, <PR < 0, <P~ < O. The RHS is the ratio
of the marginal deadweight costs. For issues of equity
claims (A), this deadweight cost equals the marginal response of the bank's expected profit with respect to effort
times the change (decline) in effort induced by an increase
in A. For issues of debt (R), the deadweight cost divides
into two components: 'ITeeR < 0, which has a similar
interpretation as above, and BLf, the marginal increase in
the expected cost of bankrutpcy.
Because the optimization problem involves a nonlinear
constraint, the comparative static analysis turns out to be
quite complex. The discussion here highlights the basic
intuition underlying the adjustments in the equilibrium
value of the bank's shareholding A*, in response to changes
in firm-specific parameters. (See Kim (1991) for a more
complete treatment). From (A5), A* will depend on the
severity of the deadweight cost of equity relative to that of
debt. All other things equal, therefore, the direction of
adjustment in A* will depend on how a given parameter
affects the relative severity of these (marginal) deadweight
costs.
Consider first an increase in bankruptcy cost B which is
the most transparent case. Intuition suggests that this
increases the deadweight cost of debt relative to that of
53
equity and hence leads to the adjustment aA*/ aB
A necessary condition for this to obtain is:
> O.
('lT e eR - BLf) ['ITe ei\fL
(A8)
+ eR ('lTefLle + 1Tee e,.,,)] > O.
Itis relatively straightforward to show that efL > 0, eRfL
=0, ei\fL' 'lTefLle < 0 and hence that 'lTe ede ] < O. A
-
(A6)
a~
(7T
e
e:e
-
~i\ BLf)
7T e
< 0 --r (7T e eR-BLf)(ei\f)
ei\ (eRf - If) < O.
Rearranging and simplifying yields the inequality L [A (l F(6*)) + F + Bf] > BLf, and hence aA*/aB > O.
Following a similar procedure, the direction of adjustment for '11.* with respect to an increase in L, the extent to
which the firm relies on the bank's funds, will hinge on the
sign of
+ ei\('lTeLle + 'lTeeea]
1Te ei\ ['lT e eRL + eR('lTeLle + 'lT ee eL ) - Bf].
('lTee R - BIf)['lTeeu
(A7)
-
With some tedious algebra it can be shown that eRL> eL>
'lT ee < 0, 'lTeLle> 0 (hence 1Te ei\[e] > 0), and that 'lTe eu
+ ei\ (1T eL le + 'lT ee eL ) ~ 0 for all 'lTe ~ Ue (which holds for
all cases of interest). Therefore, the expression in (A7) is
negative, which in turn implies aA*/ aL > O.
In contrast to the previous two cases, an increase in the
profitability of investment f.L increases the relative deadweight cost of equity and hence leads to a lower '11.*. A
necessary condition for such an adjustment to obtain is:
+ ei\ ('lTefLle + 'lT ee e fL)]
'lT e
ed'lTe eRfL
negative (or zero) value for the expression inside the first
setaL square brackets is thus sufficient to establish the
inequality in (A8). After some manipulation this can be
shownJo hold unambiguously for cases where 'lT ee > <Pee'
i.e., the marginal return to effort diminishes faster for the
firm than the bank.
Finally, intuition suggests that increased riskiness
should lead to a greater issue of '11.*. It turns out, however,
thatthe actual direction of adjustment is sensitive to the
distributional assumption as well as to the initialequilibrium value of A* and R * (and hence to the initial default
probability). Full treatment on this issue exceeds the scope
of this paper. Instead, we simply state the result here that
aA*/ au > 0 obtains with the least degree of ambiguity for
cases af(e*)/au > 0 where u indexes the riskiness of the
distribution. The intuition is simple. All other things equal,
the relative severity of deadweight cost associated with
debt rises if greater riskiness increases the marginal deadweight cost of bankruptcy, BLf.
AppendixB
Keiretsu Affiliations of Financial Institutions, 1964-70
Affiliated Banks
Mitsui Group:
Mitsui Bank, Mitsui Trust and Banking, Taisho Marine
and Fire Insurance, Mitsui Life Insurance Company.
Mitsubishi Group:
Mitsubishi Bank, Mitsubishi Trust and Banking, Tokio
Marine and Fire Insurance, Meiji Life Insurance
Company.
Sumitomo Group:
Sumitomo Bank, Sumitomo Trust and Banking, Sumitomo Marine and Fire Insurance, Sumitomo Life Insurance Company.
Fuyo (Fuji) Group:
Fuji Bank, Yasuda Trust and Banking, Yasuda Fire and
Marine Insurance, Yasuda Life Insurance Company.
54
Sanwa Group:
Sanwa Bank, Toyo Trust and Banking, Daido Life
Insurance Company.
Dai-Ichi Group:
Dai-Ichi Bank, Asahi Life Insurance Company.
Unaffiliated Banks
Long-Term Credit Banks:
Industrial Bank of Japan, Long-Term Credit Bank of
Japan, Nippon Credit Bank
City Banks:
Hokkaido Takushoku Bank, Bank of Tokyo, Daiwa
Bank, Tokai Bank, Kyowa Bank, Kobe Bank, Nippon
Fudosan Bank, Norin Chuo Kinko
Economic Review / Fall 1991
REFERENCES
Allen, D.E., and H. Mizuno. 1989. "The Determinants of
Corporate Capital Structure: Japanese Evidence."
Applied Economics 21, pp. 569-585.
Cutler, D., and L. Summers. 1988. "The Cost of Conflict
Resolution and Financial Distress: Evidence from
the Texaco-Pennzoil Litigation." Rand Journal of Economics 19, pp. 157-172.
Diamond, P. 1984. "Financial Intermediation and Delega.ted Monitoring." Review of Economic Studies 51,
pp.393-414.
Fama, E. 1985. "What's Different About Banks?" Journal of
Monetary Economics 15, pp. 29-39.
Hodder, J. and A Tschoegl. 1985. "Some Aspects of
Japanese Corporate Finance." Journal of Financial
and Quantitative Analysis 20 (June) pp. 173-191.
Horiuchi, A, F. Packer, and S. Fukuda. 1988. "What Role
Has the 'Main Bank' Played in Japan?" Journal of
the Japanese and International Economies 2, pp.
159-180.
Horiuchi, A 1989. "Informational Properties of the Japanese Financial System." Japan and the World Economy 1, pp. 255-278.
Hoshi, T., A. Kashyap and D. Scharfstein. 1990a. "Corporate Structure, Liquidity, and Investment: Evidence
from Japanese Industrial Groups." Quarterly Journal
of Economics (February) pp. 33-60.
_ _ _ _ . 1990b. "The Role of Banks in Reducing the
Cost of Financial Distress in Japan." Journal of Financial Economics 27, pp. 67-88.
Kester, K. 1986. "Capital and Ownership Structure: A
Comparison of the United States and Japanese Manufacturing Corporations." Financial Management 15
(Spring) pp. 5-16.
Kim, S.B. 1991 "Modus Operandi of Lender-cum-Shareholding Banks." Working Paper. Federal Reserve
Bank of San Francisco.
Federal Reserve Bank of San Francisco
MacKie-Mason, J. 1989. "Do Firms Care Who Provides
Their Financing?" NBER Working Paper No. 3039.
McDonald, J.F. and R.A. Moffitt. 1980. "The Uses of Tobit
Analysis." Review of Economics and Statistics 62,
pp.318-321.
Modigliani, F., and M. Miller. 1958. "The Cost Capital,
Corporation Finance and the Theory of Investment."
American Economic Review 48, pp. 261-97.
Myers, S.C. 1977. "Determinants of Corporate Borrowing."
Journal of Financial Economics 5, pp. 147-175.
Nakatani, I. 1984. "The Economic Role of Financial Corporate Grouping." In The Economic Analysis of. the
Japanese Firm, ed. M. Aoki. New York: North Holland.
Pozdena, R.1991. "Why Banks Need Commerce Powers."
Federal Reserve Bank of San Francisco Economic
Review (Summer) pp. 18-31.
Prowse, S. 1990. "Institutional Investment Patterns and
Corporate Financial Behavior in the United States
and Japan." Journal of Financial Economics 27,
pp.43-66.
Sheard, P. 1989. "The Main Bank System and Corporate
Monitoring and Control in Japan." Journal of Economic Behavior and Organization 11, pp. 399-422.
Suzuki, S. and R. Wright. 1985. "Financial Structure and
Bankruptcy Risk in Japanese Companies." Journal of
International Business Studies pp. 97-110.
Titman, S., and R. Wessels. (1988). "The Determinants
of Capital Structure Choice." Journal of Finance 43
(March) pp. 1-19.
Wakita, Y. 1983. "Wagakuni no Kashidashi Shijo to Keiyaku
Torihiki" [Loan Markets and Contracts in Japan].
Kin'yu Kenkyu 2, pp. 47-76.
Warner, J. 1977. "Bankruptcy Costs: Some Evidence"
Journal of Finance 32 (May) pp. 337-347.
Williamson, O. 1985. The Economic Institutions of Capitalism. New York: Free Press.
55
@FedFRASER