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Economic
Review
Federal Reserve Bank
of San Francisco
Summer 1991
-
Number 3
REMINDER.
free
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tions) by October 1.
John P. Judd
and Brian Motley
Nominal Feedback Rules for Monetary Policy
Randall 1. Pozdena
Why Banks Need Commerce Powers
Frederick T. Furlong
and Michael C. Keeley
Can Bank Capital Regulation Work?
• Capital Regulation and Bank Risk-Taking
• A Reexamination of Mean- Variance Analysis
of Bank Capital Regulation
Table ©IFContents
Nominal Feedback Rmles ffor Monetary Policy
3
Joluni Po Jndd amd Priam Motley
WHuy Banks Meed Commerce Powers „
is
Kamdall Jo Pozdema
Cam Bank Capital Regulation Work?
32
Frederick T. Fmrloimg
Capital Eegnlatiom ami Bank Risk-Taking. A Note
34
Frederick T. Funrlomg and Michael C» Keeley
A Meexamimatnom off Mean-Variance Analysis off
Bank Capital Megunlatlom
4®
Michael C. Keeley and Frederick T. Furlong
Federal Reserve Bank off Sam Francisco
1
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2
E conom ic R eview / Sum m er 1991
Nominal Feedback Rules for Monetary Policy
John P. Judd and Brian Motley
Vice President and Associate Director of Research, and
Senior Economist. We would like to thank the editorial
committee, Mark Levonian, Chan Huh, and Jonathan
Neuberger, as well as Bharat Trehan and Carl Walsh for
valuable suggestions. We also would like to thank Rosalind
Bennett and Michael Weiss for research assistance and
Carol Healey for preparing the document.
We assess empirically how a particular set ofmonetary
policy rules (suggested by Bennett McCallum) would
operate in the transition to zero inflation, and in maintaining price stability thereafter. We do this through repeated
stochastic simulations ofprice and nominal income rules
within three different models of the economy. The price
rule leads to instability in some models. However, the
nominal income rule consistently works with high probability to reduce inflation from present levels to zero in five
years, without significantly raising the probability of a
recession. That rule also would ensure price stability in
the long run, but possibly at the expense of slightly more
volatility in real GNP.
Federal Reserve Bank of San Francisco
It now is widely accepted both outside and inside the
Federal Reserve that price stability is the appropriate longterm goal of U. S. monetary policy. This view has been
advocated by a substantial part of the economics profession for a long time. The issue recently became the subject
of Congressional debate when Representative Stephen
Neal proposed that the Congress instruct the Federal
Reserve to adopt policies to lower the inflation rate to zero
within five years, and to maintain constant prices thereafter. I This proposal was endorsed by Federal Reserve
Chairman Greenspan and a number of Federal Reserve
Bank Presidents (Greenspan 1989, Hoskins 1989, and
Parry 1990).
Despite the consensus on price stability as the main
long-term goal of monetary policy, the stabilization of real
economic activity remains an important short-term goal for
most central banks. The desire to achieve both of these
goals inevitably raises the issue of which should take
precedence at any particular point in time. Most economists would agree that monetary policy tends to have an
inflationary bias unless some institutional structure is in
place to ensure that the monetary authority achieves its
long-term goal of price stability. This consideration raises
the long-standing issue of rules versus discretion in the
conduct of monetary policy. 2 Proponents of monetary rules
argue that unless the monetary authority is required to
achieve prescribed values of a nominal variable under its
control (such as a monetary aggregate or the monetary
base), long-run price stability goals inevitably will be
sacrificed for short-run income stabilization objectives.
The main argument against rules, and in favor of discretion, however, stems from the belief that following a rule
would increase short- to intermediate-term volatility in
output, which is considered undesirable.
With the possible exception of three years in the early
1980s, the Federal Reserve has employed a highly discretionary approach in conducting policy. Since the move
away from the monetary targeting procedures used from
1979 to 1982, Federal Reserve policy actions have responded to a wide range of economic indicators, including
inflation, economic activity, the exchange rate, interest
3
rates, money, and other financial variables (Heller 1988).
Even though the Fed still establishes annual ranges for two
Illonetaryaggregates (M2 and M3) and a credit aggregate
(total nonfinancial debt), these ranges are not consistently
binding on its day-to-day operations. Thus, the process of
formulating and executing monetary policy in the U.S.
currently lacks an explicit nominal target that ensures that
discretionary policy actions taken in response to short-run
developments do not take aggregate demand off course in
the long-run.
In this paper, we review the theoretical arguments for
adopting rules for policy, and assess empirically how a
particular set of rules would operate both in the transition
to zero inflation and in the longer run after that transition
has been completed. The rules we examine are feedback
rules of the type proposed by Bennett McCallum (l988a,
1988b), in which the central bank adjusts the growth rate of
the monetary base in response to observed deviations of the
level of nominal income (or some alternative nominal
variable) from established target values. In order to assess
the risks of adopting different rules, we use numerous
stochastic simulations to determine the range of outcomes
for real GNP and prices that we could expect if these rules
were implemented and the economy experienced shocks
similar in magnitude to those in the past. Finally, we use
simulations of three different economic models to reflect
the alternative paradigms that currently have significant
followings among macroeconomists (as discussed in Mankiw 1990). Given the intense theoretical debate going on in
the macroeconomics profession, a rule should not be given
serious consideration unless it is robust across alternative
theories.
The remainder of the paper is organized as follows.
Section I presents a brief overview of the literature on
the theoretical basis for monetary-policy rules, and the
advantages and disadvantages of alternative target variabIes. Section II discusses the nature of, and rationale for,
McCallum's nominal feedback rules. Section III presents
the empirical results. The conclusions we draw from these
simulations are presented in Section IV.
I. The Role of Monetary Policy Rules
The basic argument in favor of rules in the conduct of
monetary policy is that discretion leads to time-inconsistent results. Even if the monetary authority has the same
objective function as the general public and acts to maximize that function at every point in time, the results of its
actions will be suboptimal in the long-run. The central
bank will produce more inflation (but no more real growth)
ex post than was desired ex ante (see Barro 1986, Barro and
Gordon 1983, and Kydland and Prescott 1977). This result
holds even if the central bank maximizes an objective
function that assigns negative weight to inflation while
putting positive weight on output above its full-employment level.
The key assumptions underlying this result are that there
is a positive relation between monetary policy surprises
and deviations of output from its full-employment level,
and that the public's expectations eventually are consistent
with the policy followed by the central bank. Thus, the
public can be "fooled" only temporarily. The assumption
that the public cannot be fooled permanently means that
output cannot deviate from its full-employment level in the
long-run, and therefore, that social welfare is maximized
by producing zero inflation. Under these circumstances,
therefore, if the monetary authority were to adopt a longrun policy rule, it would choose one that produced zero
inflation.
4
At any point in time, however, the monetary authority
takes the public's prevailing inflation expectation as a
datum. Thus, if it is not bound by a rule, the monetary
authority can add to social welfare in the short-run by
generating a policy surprise that raises output above its
full-employment level. But in the long-run, the authority is
unable to raise utility by producing surprises because on
average, real GNP cannot be raised above its full-employment level.3 Indeed, since the average rate of inflation is
raised by the authority's discretionary actions, social welfare is actually reduced by the discretionary approach
compared with the situation in which a rule is imposed.
The extent of the inflationary bias in discretionary policy is
affected by the central bank's rate of time preference. The
more weight it places on near-term, relative to more
distant, developments, the larger is the inflationary bias.
If it is to solve the time-inconsistency problem, a rule
must commit the monetary authority permanently and in
advance. This would ensure that the public would believe
that the rule would be followed into the indefinite future
and would form its expectations accordingly. The rule must
be stated in terms that the monetary authority is capable of
achieving, since otherwise the policymaker cannot be held
accountable. For this reason, proposals have been made to
require the central bank to stabilize the growth rate of some
easily observed and measured variable that is under its
Economic Review / Summer 1991
direct control, such as the monetary base or the narrow
money stock. Friedman's (1960) constant-money-growth
rule was an early example of a time-consistent policy
commitment.
Contingent rules, so long as they can be clearly defined
and enforced, also could solve the time-inconsistency
problem. For example, in principle, a time-consistent nominal rule that also specifies how the growth of the monetary
base temporarily would respond to business cycles might
reduce short-run swings in the economy while at the same
time ensuring that money growth would be noninflationary
over time. However, it may be difficult to enforce contingent rules, since the monetary authority may be tempted
to "cheat" on its longer-run price stability condition in the
expectation that the public will be unable to distinguish
between cheating and allowable responses to changes in
cyclical conditions. Thus it is especially important that
contingent rules be specified in terms of an easily observable variable that clearly is under the control of the
central bank.
Alternative Nominal Targets
Most analyses of monetary policy rules have begun with
the presumption that the target should be money, especially
Ml. The narrow money supply is appealing because it can
be controlled reasonably well by the central bank and
because ail credible theoretical models view money growth
as the unique causal factor in steady-state inflation. However, uncertainties about movements in the velocity of
money in the short to intermediate run, related to the
deregulation of the financial system, have been a central
feature of the U. S. economy and monetary policy since the
early 1980s (Simpson 1984). These developments have
raised serious doubts about the practical usefulness of
money as a target of monetary policy.
These concerns about instability in velocity have motivated proposals that the Fed should target nominal GNP.
Thus, this variable has been seen as a second-best solution
to the velocity problem (Hall 1983 and Tobin 1980).
Targeting nominal GNP would get around the problem of
velocity instability, since the money supply automatically would accommodate shifts in velocity under this
approach. 4
The following identity illustrates how nominal income
targeting can be used to achieve price level objectives:
where p = log of price level
x = log of nominal income
y
log of real GNP
Federal Reserve Bank of San Francisco
As this identity shows, a predictable relationship between
nominal income and the price level depends upon the
predictability of the level of real GNP. According to some
analyses, the level of real GNP has a long-run trend, called
potential GNP, which is determined by long-run supply
conditions in the economy, including labor force growth
and trend productivity (Evans 1989). Under this hypothesis, these factors evolve gradually over time, and thus trend
GNP growth should be relatively easy to predict; that is, it
is "trend-stationary." To the extent that this is the case, it is
straightforward to calculate the path of nominal GNP
required to achieve long-run price stability.
However, Haraf (1986) cites evidence that real GNP is a
nontrend-stationary time series. If this were the case, and
nominal GNP grew at a constant rate, the price level would
evolve as a random walk, and thus could drift over time.
This problem would arise if real GNP were affected by
supply shocks that had permanent effects on the level of
real GNP. As can be seen in the above identity, under
nominal income targeting, a positive (negative) supply
shock, which brings about a permanent increase (decrease)
in output, will induce an unnecessary price level decline
(increase). Such responses can be detrimental to macroeconomic performance by raising uncertainty about the
level of prices in both the short and long run. Unfortunately, statistical tests are not capable of distinguishing
accurately between random walks and trend-stationary
processes with autoregressive roots close to unity (Mankiw
1989). Thus, there is some inherent uncertainty concerning
possible problems caused by the behavior of real GNP for
nominal income targeting.
In part because of this concern, a number of authors have
argued that the Federal Reserve should target prices directly (Barro 1986 and Meltzer 1984), since under this
approach the price level would not be affected by the timeseries properties of real GNP. No matter what time-series
properties real GNP displays, direct price level targeting
obviously could avoid long-term price level drift. The
major potential disadvantage of price level targeting is that
in sticky price (Keynesian) models, attempts by monetary
authorities to achieve a predetermined path for prices
involve very sharp movements in real GNP in the short run,
which may not be desirable (Hall 1983). Essentially, if
prices are sticky, policy actions have their largest effects on
output in the short run. Of course, in flexible price (real
business cycle) models this would not be a problem because prices would be able to adjust to policy changes in
the short run, requiring no adjustment of output.
Concerns about volatility in real GNP motivate the socalled modified nominal income target proposed by Taylor
5
(1985), which is defined as the inflation rate plus the GNP
"gap" (the difference between real GNP and its full
employment level). This target differs from the others
discussed above in that it uses the inflation rate rather than
a nominal level. Thus it does not prevent the price level
from drifting upward or downward in the long run. For
example, if the inflation rate were to rise, the modified
nominal income target would call for a tightening of policy
only until the inflation rate returned to zero, whereas the
nominal income and price targets would require a longer
period of tightening until the previous price level was
restored. However, modified nominal income may have an
advantage over the two other targets discussed above in
terms of real GNP volatility. Taylor (1985) shows that, in
the context of a rational expectations Phillips curve model,
the rule would cause less volatility of real GNP than would
a nominal GNP rule.
II. McCallum-Type Rules
The preceding discussion makes it clear that the choice
of a nominal target variable cannot be determined from
theory alone. This choice depends on such factors as the
time series properties of real GNP and the degree of
flexibility of prices. An empirical investigation is needed.
McCallum (1988a, 1988b) has examined the empirical
properties of operational versions of nominal income and
price rules. These rules specifY a long-run equilibrium
growth rate for the monetary base plus a rule for adjusting
quarterly growth in the base in response to deviations
between the actual and desired values of the target variable.
They may be written in the form:
(1)
!lb t = [!lp/
+ !lyn - !lvt +
A[Zt-l -
Zt-d
where bt = log of the monetary base, Pt = log of price
level, y = log of real GNP, Zt = log of target variable,
* denotes a value desired by the central bank, and
1
!lvt = (16) [(x t - I - b t - I ) - (x t - I ? - bt - 17 )]·
The left side of (l) represents the growth rate of the monetary base, which serves as the policy instrument. The right
side has three components. The first term represents the
growth rate of nominal GNP the central bank wishes to accommodate in the long run, which is equal to the sum of the
desired inflation rate (!lp *) and the steady-state growth
rate of real GNP (!lyn. The second component, !lv, subtracts the growth rate of base velocity over the previous
four years, and is designed to pick up long-run trends in the
relation of base growth to nominal GNP growth. 5 The third
term specifies the feedback rule determining how base
growth is adjusted when there is a target miss in the
previous quarter. That miss is defined as [Z~-l - Zt-I],
while the term A defines the proportion of the miss the central bank attempts to offset each quarter. As such, values of
X can be chosen by the central bank between 0 and 1. In
steady-state, the feedback term drops out (since z* = z),
and the rule simply states that !lbt = !lPt* + !ly{ - !lvt.
McCallum's rules use the monetary base as the operat-
6
ing instrument on the grounds that it can be accurately
controlled by the central bank on a day-to-day basis, and
that this controllability is unlikely to be upset by financial
or regulatory innovations. Thus, when the base is used
as the policy instrument, the public can easily observe
whether the central bank is adhering to its rule and can hold
the central bank accountable for its actions. This feature
has the advantage that it provides an opportunity for the
central bank to develop credibility with the public. Such
credibility may substantially lower the costs, in terms of
lost economic output, of reducing inflation (see Blackburn
and Christensen 1989).
A drawback to using the base as an instrument is that its
velocity has tended to be unstable following the deregulation of the financial system in the 1980s. However, two
features of the rules under investigation tend to mitigate
the adverse effects of instability in velocity. First, the !lvt
term accounts for gradual movements in the relationship
between base growth and macroeconomic developments.
Second, under McCallum-type rules, shifts in the base
velocity are automatically offset by policy. For example, if
base velocity unexpectedly rises, nominal income will rise
relative to the target, which will induce a contraction in the
base growth rate under the McCallum rule. This contraction will tend to bring nominal income back to its target.
One of McCallum's main objectives is to test the robustness of the nominal income rule across alternative economic theories, which have different implications for the
correlations among !lb, !lp, and fly in the presence of
shocks. He argues that neither theory nor evidence points
convincingly to anyone of the competing models of the
dynamic interaction between nominal and real variables.
Because of this uncertainty about the true structure of the
economy, the monetary authority should adopt a rule that is
likely to work well in a variety of different economic
environments. McCallum tests his proposed rule by
conducting counterfactual simulations under several alternative macroeconomic models. The rule is designed to be
Economic Review / Summer 1991
model-free: that is, the monetary authority responds to
observed deviations from the target, and does not need to
base its actions on forecasts or judgments that would
require knowledge of the structure of the economy. McCallum's empirical results suggest that if the Fed had followed
the rule from 1954 to 1985, there would have been less
cyclical variability in nominal GNP and essentially zero
inflation, and that this conclusion holds true for all of the
models tested.
McCallum, of course, recognizes that these results are
subject to the Lucas (1973) critique: the estimated parameters in the models he estimates and simulates might have
changed significantly if the Federal Reserve actually had
followed the rules being tested. McCallum (1988a) attempts to deal with this issue in two ways. First, he cites
Taylor's (1984) finding of parameter stability across the
Fed's policy regime change in 1979, and argues that the
Lucas critique may not be empirically important in the
context of monetary policy rules. Second, he substantially
alters the coefficients in one of his e~timated models, and
shows that the simulation results are qualitatively unchanged (McCallum 1988a, pp. 192-194).
Extensions of McCallum's Exercise
We extend McCallum's results in a number of directions. First, we consider another target variable in addition
to nominal GNP and the price level, n3..t-nely, Taylor's
modified nominal income rule. Thus, three alternative
short-run target variables for the policy rules are considered: nominal income (equation 2), the price level
(equation 3) and modified nominal income (equation 4). In
addition, "no rule" simulations also are computed, in
which the monetary base followed the same path as in the
historical sample period:
(2)
flb t
[fly{
+
flp7] -
flv t
+
}..[x; - I
-
xt-d
(3)
flb t = [fly{
flp7] -
flv t
+ }..[P; - I
-
Pt- d
(4)
flb t = [fly{
+
+
flp7] -
flv t
=
+
}..[lY{-I-Yt-l)
+
(flp;
l.:..flPt-I)]·
Second, we conduct repeated stochastic counterfactual
simulations ofthe alternative models and rules. In McCallum's simulations, the monetary authority is assumed to
face. the same set of shocks that actually occurred in the
historical period. Below, we assume only that the shocks
have the same means and variances as the historical
shocks. Thus, rather than computing a single simulation of
the economy under each rule, we obtain a probability
distribution of alternative outcomes based upon numerous
sets of shocks. This enables us to compare different rules
in terms of the full range of alternative outcomes that each
might produce. Third, we examine how adoption of various rules might affect the volatility of real GNP. Since
concerns about such effects seem to be a major reason that
many central banks hesitate to adopt rules, we focus a good
deal of our attention on this issue. Finally, we examine how
alternative rules might be used to bring the inflation rate
down from its level in recent years to zero over the five-year
horizon specified in the Neal Amendment.
III. Empirical Results
Each of the policy rules was simulated under three
alternative sets of assumptions about the structure of the
economy: a Keynesian (or Phillips curve) model, a real
business cycle model, and an atheoretic vector autoregression (VAR). 6 We closely followed McCallum in specifying
and estimating these models, and our estimates are close to
those reported by McCallum (1988b). As will become
apparent, the models are not attempts to describe the
structure of the economy as precisely as possible. Rather,
they incorporate the fundamental features of the various
macroeconomic paradigms, and are meant to illustrate the
basic nature of the responses of the economy to the
implementation of the monetary-policy rules tested.
The Keynesian model consists of three equations. First,
the real aggregate demand equation embodies the direct
effects of monetary (and fiscal) policy on macroeconomic
activity. It specifies the growth rate of real GNP as a
Federal Reserve Bank of San Francisco
function of current and lagged growth rates of the real
monetary base, real government spending (g), and its own
lagged values (our estimates of the parameters of this
aggregate demand relation are shown in equation Al of the
Appendix):
!
(5)
flYt =
J
i~1 (XiflYt-i + j~O
Pj(flb t _ j -
flpt-)
The supply side of the Keynesian model is a simplified
Phillips curve, which embodies the essential "stickyprice" characteristic of the paradigm. It specifies that the
current inflation rate depends on past inflation and the gap
between actual and full employment real GNP (see equation A2 of the Appendix):
7
N
(6)
f:..Pi =
n~ohn(yt-n
M
- Y{-n)
+ m~lkmf:..Pt-m'
level of real GNP; see equation A5 in the Appendix for
econometric estimates):
L
where
M
2.k
m=1
(9)
1.
m
The coefficients on lagged inflation (km ) are constrained to
sum to 1, thus ensuring that, in steady state, real GNP will
be equal to its full employment level, and inflation will be
constant. Equation (7) defines yf , which is the log of full
employment real GNP and is measured as the fitted values
of a log linear time trend (T) of real GNP (see equation A3
in the Appendix):
y{ =
(7)
I)
+
~Tt·
In combination with anyone of the policy rules that
defines the growth rate of the base, equations (5), (6), and
(7) can be simultaneously solved for values of f:..p, f:..y, yf,
and f:..b as functions of the monetary policy target and other
variables. For the purpose of evaluating monetary policy
rules, the essential feature of this model is that monetary
policy affects real GNP with relatively short lags, while
inflation is affected with long lags. This means that attempts to exert precise control over inflation in the short
run inevitably involve a high degree of volatility of real
GNP. As noted above, it is this concern that has motivated
the vie\lJ that nominal Gl'lP or modified nominal Gl'-.JP
might be a better target variable, since neither requires
such precise short-run control of the price level.
The real business cycle model consists of two equations.
First, the price determination equation is obtained by
inverting equation (5) (see equation A4 in the Appendix):
-1
(8)
f:..Pt = (
~
f
) f:..Yt
13 _
+ j~1 ( 13~ ) (f:..bt _ j
(X-
+ i~1 ( ~~
)
f:..Yt-i
+
f:..bt
e + l~l f.Lz f:..Yt-z·
Any of the monetary policy rule equations and equations
(8) and (9) can be solved for values of f:..p, f:..y, and f:..b as
functions of values of the monetary policy target and other
variables. For present purposes, the key features of this
model are that prices respond immediately to changes in
the base and real GNP is unaffected by monetary policy.
Thus, short-run control of prices is much more appealing
than in the Keynesian model. Furthermore, the distinction
between controlling prices and nominal income is nonexistent, since real GNP does not respond to monetary policy.
Thus the Keynesian and real business cycle models
make opposite assumptions about the responsiveness of
prices and real GNP to monetary policy actions. The
Keynesian model assumes that real GNP responds relatively quickly but that prices lag; the real business cycle
model, however, assumes that prices respond quickly but
that real GNP does not respond at all. By testing the
various rules in both models, we have encompassed the
broad range of assumptions that potentially could be made
in this regard.
In addition to the two models just discussed, we also
conducted simulations using a four-variable VAR that
included growth rates of nominal GNP, the price level, and
the base, as well as the level of the Treasury bill rate (see
Appendix A for estimation results). In simulating this
model under a policy rule, the estimated equation for the
base was replaced by the equation defining the policy rule.
The VAR embodies no theoretical restrictions, and therefore is agnostic about the structure of the economy.
Simulating the Models
J
K
-
f:..Pt-)
'Yk
+ k~O ( ~o
) f:..gt -
k ·
This specification of the price equation follows from the
assumption that prices are flexible and that real GNP is
independent of aggregate demand. Thus inflation is directly determined by current and lagged values of monetary base growth, real GNP growth, and other variables.
Real GNP is determined by a simple time series model,
which is consistent with movements in real GNP being
determined by permanent technology and labor supply
shocks. Thus equation (9) specifies that real GNP has a
unit root (that is, shocks have a permanent effect on the
8
f:..Yt
Two basic questions were addressed with dynamic
simulations of the estimated models. First, how would
the principal macroeconomic variables (real and nominal
GNP, prices and the inflation rate) have evolved over the
historical sample period (1954 to 1989) if the monetary
authority had followed each of the three policy rules
throughout that period? We label these simulations as
"counterfactual experiments." The policy rules in these
simulations were specified to attempt to hold the price level
constant at its level in 1954. For each rule, within the
context of each model, we calculated 500 simulations in
which the shocks had the same variances as the error terms
Economic Review / Summer 1991
in the respective model equations. 7 Each set of 500 simulations is called an experiment. We calculated a 95 percent
confidence interval for each of these experiments.
Second, how might the economy evolve in the future if
the monetary authority adopted a policy rule beginning in
1990 with the objective of lowering inflation gradually to
zero by 1995 and holding the price level constant thereafter? For these disinflation experiments, we assumed that
the shocks to aggregate demand and aggregate supply in
the future would have the same variances as in the estimation sample period. Again, we calculated confidence intervals based upon 500 simulations for each experiment.
Counterfactual Experiments
In presenting the results from simulating the alternative
rules, we focus on three measures of economic performance that should reflect the concerns of policymakers-the
price level, the rate of inflation and the short-run growth
rate of real GNP. Ideally, a policy rule should deliver low
inflation, in both the short run and long run, without
causing unacceptable volatility in real GNP growth. Given
the conventional definition of a recession as two quarters of
declining GNP, we focus on the (annualized) two-quarter
growth rate of real GNP.
Federal Reserve Bank of San Francisco
Table 1 shows the performance of the various rules in
stabilizing the price level by reporting the 95 percent confidence intervals for average annual inflation over 1954.Q1
to 1989.Q4. With some notable exceptions discussed below, adoption of the rules could have stabilized prices in the
long run. In most cases, the confidence bands center
around an average inflation rate near zero. 8 Moreover,
these confidence bands are in most cases much narrower
under the rules than under the policy actually followed over
the period (the "no rule" case). For example, in the
Keynesian model with A = 0.25, average inflation would
have been between -0.67 and +0.48 percent (with 95
percent probability) under a nominal income rule, but
between 2.60 and 5.89 percent with no rule. Only the
modified nominal income rule under the real business
cycle model produced confidence bands wider than the no
rule case. This result confirms our speculation that this rule
would allow the price level to drift in the long run because it
targets the short-run inflation rate rather than the price
level. Price level drift is especially acute in the real
business cycle model because of its unit root in real GNP.
Several of the experiments summarized in Table 1 produced explosive cycles in the economy. In particular,
although the price rule works well in the real business cycle
9
model with its flexible prices, it produces instability in the
"sticky price" Keynesian model. The modified nominal
income rule works well in the Keynesian (Phillips curve)
context, for which it was designed, but causes instability in
the VAR.9 In fact, only the nominal income rule with
cautious policy responses (I\. = 0.25 and 0.50) was stable
in all three models.
Thus the results of these simulations show that the
nominal income rule is more robust across alternative
models than are the price and modified nominal income
rules. Within the context of uncertainty about the true
structure of the economy, the nominal income rule is the
only one tested that is not explosive in any of the macro
models (for suitably small values of 1\.) and so could be
considered a viable approach for policy. To illustrate the
effects of this rule (with I\. = 0.25), in Chart 1 we have
plotted the 95 percent confidence intervals for the price
level. In all of the models, the confidence intervals center
throughout the simulation period on· a price level near its
level at the beginning of the period, and the confidence
bands are relatively narrow. For comparison, the 95 percent confidence interval for the no-rule simulations, with
the monetary base taking on its actual historical values,
also are plotted. These results suggest that by following the
nominal income rule, monetary policy could have avoided
the inflation that occurred over this period with high
probability.
As noted in the introduction, one reason often given by
central banks for not taking advantage of rules to control
inflation is that nondiscretionary approaches tend to create
volatility in real GNP. To address this issue, Table 2 reports
the 95 percent confidence intervals for the two-quarter
growth rate of real GNP for the year 1989, under the rules
in the three models and for the no rule case. Since the width
of the confidence intervals varies somewhat over the simulation period, we show the results for 1989 as a representative year. In evaluating these results, we use the no rule
case as a basis for comparison, since it is an estimate ofthe
confidence band that actually obtained over the sample
period under the policies followed by the Fed. Of course,
the rules have no effect on real GNP in the real business
cycle model. In most other cases, the bands are wider
under the rules than in the no rule case, implying that rulesbased regimes may increase the short-run volatility of real
Chart 1
Simulated Price Level
Nominal GNP Rule
Versus No Rule
(95% Confidence Intervals)
1982 = 100
Keynesian Model
280
240
No Rule
200
D
Rule
160
120
80
40,. . . . . . . .
0+""'r-r-T"'T"T""'I-rT"T"T'T...-r'"'r'"TT'T"T""'Ir-r-T"T"T'T...-r'"'r'"TT"T"T"'I"TT"'I
54
59
64
69
74
79
84
89
84
89
Real Business Cycle Model
280
240
No Rule
200
D
160
Rule
120
80
40
__
1
0
280
54
59
64
69
74
79
Vector Autoregression Model
240
No Rule
200
D
Rule
160
120
80
r-I!!!~~=======
40
0+-r-.,..,....,i""T"T..,...,...,......,...,.....,...................,...,.....,i""T"T..........,....,...,r-r-r................
57
A. =
10
63
69
74
79
84
89
0.25
Economic Review / Summer 1991
GNP. An exception to this conclusion is the modified
nominal income rule in the Keynesian model. However, as
noted above, this rule produces unstable results in the VAR
and very wide confidence intervals for inflation under the
real business cycle model.
Rules that Explicitly Attempt to Smooth Real GNP
In an attempt to find a rule that might reduce short-run
real income volatility in the Keynesian model and the
VAR, we experimented with a rule in which the monetary
authority responded both to the level of nominal GNP (as in
the nominal income rule) and to the growth rate of real
GNP relative to its growth rate in the recent past. 10 In
steady state, this rule would yield the same results as the
nominal income rule, but it would induce a stronger
response to temporary fluctuations in real GNP growth:
- A[dYt-l - (
~ ) q~l dYt_q] ,
with Q equal to 20 quarters.
Federal Reserve Bank of San Francisco
We also tried a rule that replaced the growth rates of real
GNP in equation (IO) with levels, so that the final term in
the equation was: -A[Yt-1 - Y{-d. However, we found
that both nIles produced somewhat wider fluctuations in
real GNP than the simple nominal income rule in the
various models. These attempts obviously do not eliminate
the possibility that some other specification would reduce
real GNP volatility, but at least these simple, straightforward approaches do not seem to do the job.
Disinflation Experiments
In this section, we report the results of simulating a
policy rule specified so as to lower the inflation rate to zero
within five years. We chose this time interval because the
Neal Resolution proposes this objective for the Federal
Reserve. In view of the results of the counterfactual experiments, these disinflation simulations were computed only
for a nominal income rule with A equal to 0.25.
In these simulations, the policy rule (equation (2» was
specified so that both the equilibrium growth rate of the
base (db* = dp* + dyf ) and the targeted level of
nominal income (x7-1) allow for a gradual decline in
11
inflation over a period offive years. This requires that Ap *
declinegradllallyJromtheactual inflationrate in J989 to
zero in 1994.Q4. Frolll1994.Q4 pllwarda.p* = 0, and
thus. Ab *.= a.yf. Atthesallle. time, the target level of
nominaJGNP (xT-l) is set equal to the actual lagged value
of nominal GNP in J990.Ql,after which itgrows at arate
that declines steadily until, after twenty quarters, it grows
Chart 2
Simulated Inflation Rate
(95% Confidence Intervals)
Percent
12
Keynesian Model
ata.yf.
The re~~ltspfthis.simulationare.shown in Charts 2
through 4. /Chart2sho\Vs. the path ofthe inflation rate
under the rule in the threealtemative models, while Chart
3 sQows the results for the price level. These charts suggest
that inallthreemodels,adoptionof the rule would have a
good chance ofreducing illflationto zero within five years
and ofmailltaininggenerallystable prices thereafter. The
confidence .bands for inflation are wide because they apply
to inflation rates in individual quarters. However, the
relatively narrow bands in the price level charts make
it clear that average inflation over an extended period of
time would be held close to zero with a high degree of
confidence. 11
Chart 4 shows the simulated two-quarter GNP growth
rate in the three models. Even during the period in which
the inflation rate is being brought down, there is a better
than even chance that a recession can be avoided. Although
the mean simulated GNP growth rate declines below the
trend growth rate in the early years of the simulations, it
does not become negative. Perhaps more significant is the
observation that the confidence intervals on real GNP
growth are no wider during the period in which inflation is
coming down than they were during the historical sample
period. Thus a policy of aiming for zero inflation by
following a nominal income targeting policy rule would not
significantly worsen the probability of the economy falling
into a recession.
-12
1990
1995
2000
2005
2009
1995
2000
2005
2009
12
8
4
0
-4
-8
-12
1990
12
Vector Autoregression
Model
8
4
0
-4
-8
-12
2000
2005 2009
1990
1995
Nominal GNP Rule
A= 0.25
12
Economic Review / Summer 1991
Chart 3
Simulated Price level
(95% Confidence Intervals)
1982
Chart 4
Simulated Two-Quarter
Growth of Real GNP
(95% Confid.ence Intervals)
=100
Percent
200
18
Keynesian Model
180
12
160
6
140
o
120
·6
100
1990
1995
200
2000
2005
2009
1995
18
Real Business
Cycle Model
180
12
160
6
140
o
120
·6
1001+9""T90......,r--r-"""-"19r-9+-5..,......,-r-2"""0""T00""-""""'2""0-0"'-5""""""""20""09
200
Vector Autoregression
Model
18
12
160
6
140
o
120
·6
1995
A= 0.25
2000
2005
2009
Real Business Cycle Model
-12 +-,....,-,.....,.....,-,.......,......,-1"'"'""'1'""....,.......,.--.-..,......,-,..-..,......,............
1990
1995
2000
2005
2009
180
1001990
Keynesian Model
Vector Autoregression Model
-1 2 +-r-,--,.....,......,.......,r-r-.,....,....,-,.......,.....,......,,..-,-.,....,....,-,....,
2000
2005
Nominal GNP Rule
Federal Reserve Bankof San Francisco
2009
1990
1995
A. = 0.25
2000
2005
2009
Nominal GNP Rule
13
III. Conclusions
In this paper, we have extended the work of Bennett
McCallurn.on the usefulness ofnolllinalfeedback rules for
linking short-run monetary policy actions to the goal of
achieving and maintaining price stability. Given present
uncertainties about the structure of the economy, these
rules are designed to be modeHree; that is, the monetary
authority does not need to rely ona model to implement
thern,andtheyperlormwelLinseveralpossible models. In
addition, therulesareop~r<\tion<\l in the .sense that they
define movements in a variable (the monetary base) that
can be controlled by the central banle
We have ex,aminedthe properties ofthree •s"Uch rules~
with short-run targets of nominal GNP, the price level, and
inflation plus the GNP "gap"-in the context of three
alternative views of the structure of the economy. Our tests
involved numerous stochastic simulations of these models
and rules. We examined the behavior of prices and real
GNP during a transition from the current prevailing inflation rate to price stability, and during an extended period in
which price stability is maintained.
This analysis leads us to a number of conclusions. We
find that the nominal income rule is successful at maintaining price stability, in the sense that at the end of the
simulations, 95 percent confidence intervals for the simulated price level are centered on the level of prices that
existed at the beginning of the simulation period. Moreover, the nominal income rule provides tight confidence
intervals, suggesting a high level of certainty about where
prices will end up under the rule.
The price level and modified nominal income rules
produce dynamic instability in some of the models tested.
Only the nominal GNP rule, with relatively cautious adjustment parameters of 0.25 and 0.50, was nonexplosive in
all the models. Given the uncertainty about which model is
most appropriate, this would appear to be the only rule
14
tested with suffident robustness tobe consideredseriously
as a target. This rule, however, does present the problem
that it appears to increase real income volatility in some
models. In interpreting the results for real income v<\riability, however, it is important to. bear in.rnindthat the
estimates we have obtained probably represent .upper
bounds on the detrimental effects of following the rules.
These roles most likely. would have. beneficial effects on
Fed credibility and would reduce uncertainty in the economy, .which most likely would have beneficial effects on
real.income volatility (Blackburn and Christensen 1989).
These. beneficial effects are not captured in our simulations, and we have noway of measuring their signifiCance.
Finally, we simulated the possible effects of· moving
from the present inflation rate to zero inflation in five
years. We limited these experiments to the nominal income
rule for reasons given above. Under all three models, this
rule achieved zero inflation in five years in the sense that
the confidence intervals for inflation were centered on zero.
Moreover, even without beneficial credibility effects, none
of the models suggested that the disinflationary process
would noticeably increase the chances of a recession compared with the experience over the past 35 years under
actual policy.
Thus, our results suggest that the nominal income rule
could work effectively in reducing inflation from current
rates to· zero. Moreover, this rule would ensure price
stability thereafter, although possibly at the expense of
more volatility in real GNP. Whether a rule seems worth
trying (ex ante) depends on how important achieving and
maintaining zero inflation is to the policymaker, compared
with the possible benefits of attempting to smooth real
GNP. This paper has attempted to put some parameters on
the nature of the tradeoff the policymaker would face in
making this choice.
Economic Review / Summer 1991
ENDNOTES
1. This legislation was called the "Zero-inflation" Amendment, H.R. 2795, 101st Congress, 1st session.
2. See Englander (1990) for a review of these issues and
an extensive bibliography.
3. This argument assumes away the possibility that the
central bank may be able to use discretion to reduce the
size offluctuations of real GNP around its full-employment
level. If this were possible, and if stability had utilityfor the
publiG, then there could be some positiveutiiity from
discretion in the long"run, which couldoffsetthe loss of
utility from higher inflation.
4. Hence, Tobin's observation that nominal income targeting is nothing but "velocity-adjusted moneytargeting. "
5.. McCallum selected the 16-quarter average to be long
enough to avoid dependence on cyclical conditions. As a
consequence, the term can take account of possible
changes in velocity resulting from regulatory and technological sources.
6. McCallum also examines the properties of a rational
expectations inflation surprise model (Lucas 1973). We
decided not to pursue this approach because it no longer
receives much support from macroeconomists.
7. In the Appendix, we reproduce some of McCallum's
simulation results. Following his approach, in this table we
used only one set of shocks, equal to the actual historical
errors in the estimated equations. Our results are similar to
his.
8. The simulation of the V}i,R under the nominal income
rule produced a gradual decline in the price level. At the
Federal Reserve Bank of San Francisco
same time, the model predicts that real GNP would have
risen more rapidly than actually occurred historically. This
result implies that to produce zero inflation, the rule should
have specified a faster steady-state growth rate oUhe
base. It appears that the VAR model embodies an inverse
correlation between the inflation rate and the real GNP
growth rate. This correlation also is found in Lebow, Roberts, and Stockton (1990) and Selody (1990VThus if the
growth rate ofthe base is reduced to holddowninflation,
thetrend growth rate of real GNPis higher.Oneofthemain
arguments in favor ofprice stability is that itwquld boost
real growth by facilitating long-range planning and eliminating the need for economic agents to waste resources
in efforts to avoid the effects of inflation. The VAR appears
to be consistent with this view. By experimentation, we
found that if the base growth rate was set to prOduGe zero
inflation, the trend GNP growth rate was 4 percent,rather
than the actual trend rate of 2% percent over the historical
sample.
9. Simulations also were computed with an inflation rule,
but this procedure produced instability in all models and
so was abandoned.
10. Recall that policy does not affect real GNP in the real
business cycle model.
11. Prices are more volatile in the real business cycle
model than in the other models, because holding nominal
income stable implies that independent fluctuations in
real GNP are mirrored in opposite fluctuations in prices.
15
APPENDIX
Regression Results
Aggregate Supply:
1954.1~1989.4
The variables in the regressions below are defined as follows:
+
b
log of monetary base
(adjusted for reserve requirement changes)
log of high-employment government expenditures
g
P
log of GNP deflator
log of 3-month Treasury bill rate
Y
log of real GNP
yf = log of real GNP trend
T = time trend
R2
SEE
Q
D.E
+ 0.30 aYt- I
aYt = 0.0051
(4.59)
(A5)
(3.60)
0.14 aYt-2 0.13 aYt-3
(1.65)
(- 1.54)
0.11
0.0093
25.23
140
Vector Autoregression
Marginal Significance Levels
Keynesian Model
Aggregate Demand:
(Al)aYt =
+
R2
SEE
Q
D.E
Dependent Variables a
(3.29)
(2.17)
0.18 (abt-1-apt_I)+ 0.091 ag t - 0.091 ag t (1.51)
(2.20)
(-2.20)
l
0.19
0.0091
26.08
139
ilpt
R
db
0.300000
0.300000
0.000016
0.007800
0.700000
0.000015
0.035000
0.008000
0.005000
0.091000
0.000000
0.051000
0.018000
0.180000
0.000000
0.000000
0.300000
0.008400
23.920000
120
0.673000
0.003900
38.910000
124
0.930000
R
db
R2
SEE
Q
D.E
0.026 (Yt-Y{)+ 0.35 apt-l+ 0.23 !i.Pt-2
(2.71)
(4.22)
(2.66)
=
ap
ay
ap
Aggregate Supply:
(A2)
ay
+ 0.26 aYt-1 + 0.25 (db t - apt)
0.0044
(4.64)
0.710000
0.003700
34.990000 29.880000
119
121
0.95ססOO
aLags chosen by Final Prediction Error procedure (Judge, et al.
1985).
+ 0.23 apt-3 + 0.20 apt-4
(2.46)
R2
SEE
Q
D.E
(A3)
R2
SEE
Q
D.E
(2.38)
Simulations of Alternative
Target Variablesa
0.62
0.0041
26.97
140
y{ =
1954.1~ 1989.4
7.05
(855.16)
+ 0.007557 T
+ (99.71)
t
0.99
0.Q38
982.64
142
Real Business Vector
Keynesian Cycle Autoregression
Thrgets
Real Business Cycle Model
Aggregate Demand
(A4)
RMSE Values
apt = 0.017
3.94aYt
+ 1.01aYt_1
+ abt + O.72abt _ 1 O.72apt_1
+ 0.36ag t - 0.36agt _ 1
Nominal GNP
"-=0.25 b
"- = 0.75
Price Level
"-=0.25b Explosive
"-=0.75 Explosive
Modified
Nominal GNP
"-=0.25
"-=0.75
0.0268
0.0171
0.0279
0.0196
0.0167
0.0115
0.0237
Explosive
0.0161
0.0080
0.0293
0.0490
0.0317
0.0240
Explosive
Explosive
aShocks equal residuals in estimated model equations.
bSee Tables 1 and 2 in McCallum (l988b).
16
Economic Review / Summer 1991
REFERENCES
Barro, Robert J, 1986, "Recent Developments in the
Theory of Rules Versus Discretion," The Economic
Journal Supplement, pp, 23-37,
_--.-,---.--_, and David B,Gordon, 1983, "A Positive
Theory of Monetary Policy in a Natural Rate Model."
Journal of Political Economy pp, 589-610,
Blackburn, Keith, and Michael Christensen, 1989, "Monetary Policy and Policy Credibility: Theories and
Evidence," Journal of Economic Literature (March)
pp,1-45,
Englander, A Steven. 1990. "Optimal Monetary Policy
Design: Rules versus Discretion Again." In Intermediate Targets and Indicators of Monetary Policy, Federal Reserve Bank of New York,
Evans, George W 1989. "Output and Unemployment Dynamics in the United States: 1950-1985," Journal of
Applied Econometrics 4, pp, 213-238,
Friedman, Milton, 1960, A Program for Monetary Stability,
New York: Fordham University Press,
Greenspan, Alan. 1989, "A Statement before the Subcommittee on Domestic Monetary Policy of the Committee
on Banking, Finance and Urban Affairs, U,S, House of
Representatives, October 25,1989," Federal Reserve
Bulletin (December) pp. 795-803,
Hall, Robert E.1983. "Macroeconomic Policy Under Structural Change." In Industrial Change and Public Policy,
pp. 85-111, Federal Reserve Bank of Kansas City,
Haraf, William S, 1986, "Monetary Velocity and Monetary
Rules," Cato Journal (Fall) pp, 641-662,
Heller, Robert H, 1988, "The Making of U,S, Monetary
Policy," Paper presented at Seminar for Economic
Policy, April 27, The University of Cologne, West
Germany.
Hoskins, W Lee, 1989, "Monetary Policy, Information, and
Price Stability," Federal Reserve Bank of Cleveland
Economic Commentary (February),
Judge, C,G" WE. Griffiths, R,C, Hill, H, Lutkepohl, and TC,
Lee, 1985, The Theory and Practice of Econometrics,
New York: John Wiley,
Kydland, Finn E" and Edward C, Prescott. 1977, "Rules
Rather Than Discretion: Time Inconsistency of Optimal Plans," Journal of Political Economy pp, 473-491,
Federal Reserve Bank of San Francisco
Lebow, David E" John M, Roberts and David J, Stockton,
1990. "Economic Performance under Price Stability,"
Unpublished paper, Board of Governors of the Federal Reserve System (December).
Lucas, Robert
1973. "Some International Evidence on
Output-Inflation Trade-offs. American Economic Review pp, 326-334,
Mankiw, N. Gregory, 1989, "Real Business Cycles: A New
Keynesian Perspective." The Journal of Economic
Perspectives (Spring) pp. 79-90,
_ _ _ _ , 1990, ",A. Quick Refresher Course in Macroeconomics," Journal of Economic Literature (December) pp. 1645-1660,
McCallum, Bennett T 1988a, "Robustness Properties of a
Rule for Monetary Policy," Carnegie-Rochester Conference Series on Public Policy 29, pp, 173-204,
_ _ _ _ , 1988b. "Targets, Indicators, and Instruments
of Monetary Policy," In Monetary Policy in an Era
of Change, Washington, D,C,: American Enterprise
Institute,
Meltzer, Allan. 1984, "Credibility and Monetary Policy," In
Price Stability and Public Policy, pp, 105-128, Federal
Reserve Bank of Kansas City.
Parry, Robert T 1990, "Price Level Stability," Federal Reserve Bank of San Francisco Weekly Letter (March 2),
Selody, Jack C. 1990, "The Benefits and Costs of Price
Stability: An Empirical Assessment." Unpublished paper, Bank of Canada (December),
Simpson, Thomas C. 1984, "Changes in the Financial
System: Implications for Monetary Policy," Brookings
Papers on Economic Activity 1, pp, 249-272,
Taylor, John B, 1984, "Recent Changes in Macro Policy
and Its Effects: Some Time Series Evidence." American Economic Review Papers and Proceedings,
pp, 206-210,
_ _ _ _ , 1985, "What Would Nominal GNP Targeting
Do to the Business Cycle?" Carnegie-Rochester Conference Series on Public Policy 22, pp, 61-84.
Tobin, James 1980, "Stabilization Policy Ten Years After,"
Brookings Papers on Economic Activity 1, pp, 19-49,
17
Why Banks Need Commerce Powers
Randall 1. Pozdena
Vice President, Banking and Regional Studies, Federal
Reserve Bank of San Francisco. The author wishes to thank
Deborah Martin for her very effective research assistance,
Ester Schenk for assistance in some German translating,
and Hambrecht and Quist for permitting access to their
library. Roger Craine provided very helpful references for
the theoretical portion of the paper. I also have benefited
from conversations with Volbert Alexander (Giessen University) and Theodor Baum (Osnabrock University). Helpful comments on an earlier version of this paper were
received from Robert Eisenbeis, Sun Bae Kim, Mark
Levonian, Paul Spindt, and Bharat Trehan.
Commercial banks are important intermediaries of
credit for the commercial and industrial sector. Their
power to finance commercial and industrial activity, however, is limited sharply by the restrictions imposed by law
and regulation. In particular, banks are limited in their
ability to hold corporate equity in commercial firms. The
author argues that these restrictions on banks' commerce
powers likely impair the ability of banks to effectively
intermediate credit, particularly to riskyfirms. In addition
to a theoretical presentation, the paper provides empirical
evidence consistent with the importance of lender equity
powers.
18
The powers of commercial banks in the United States
are circumscribed sharply by law and regulation. The main
source of these restrictions is the Banking Act of 1933
("Glass-Steagall Act"). The act's restrictions on bank
underwriting powers are its best known features. These
restrictions effectively separate investment banking from
commercial banking and limit the ability of banks to
operate mutual funds or issue other asset-backed liabilities.
In addition to the underwriting limitations, however, the
act restricts a bank's ownership of securities for its own
account. Specifically, most banks in the United States
generally may hold only debt securities of other companies, unless otherwise authorized. This has come to
mean that banks may hold only small amounts of nonfinancial firm equity, and in no case may banks exercise control
over commercial companies. 1 Banks also generally may
not hold the debt and equity simultaneously of a client
commercial firm because of this restriction. 2 In general,
therefore, the Banking Act of 1933 confines banks to the
role of portfolio lender, and the ownership of shares in
commercial enterprises by banks is limited severely.
The separation of banking and commerce is a seldom
debated restriction on bank powers. While there has been
much debate in recent years over the investment banking
powers restrictions, removal of the commerce restrictions
is considered to be much more difficult politically. The
ownership and control of commercial enterprises by banks
raises questions of concentration of economic power. In
addition, in an environment of underpriced deposit insurance, it raises important questions about propagation of the
safety net.
This paper argues that there are important arguments in
favor of the removal of the commerce restrictions. In
particular, it is argued that the ability to simultaneously
hold the equity of and lend to commercial firms is important to successful intermediation of risky credits. To the
extent that banks are special intermediaries whose function
is not costiessly replaced by other types of firms, the
commerce restrictions may have significant macroeconomic consequences. 3 In particular, costs of capital may
Economic Review I Summer 1991
be higher and total investment lower than would be the case
if banks were permitted to hold corporate equity.
In subsequent sections of the paper, the theoretical
analysis is developed using a simple theoretical representation of the firm in the context of information asymmetIy
(For exposition purposes, the analysis abstracts from problems caused by underpriced deposit insurance.) The paper
goes on to look for data verifYing the theoretical notions.
Direct empirical verification of the effects of expanded
powers hypothesized is difficult because U. S. banking
exists in the context of restricted powers. However, international comparisons, and scrutiny of the contracting
processes of nonbank U. S. financial intermediaries provide anecdotal evidence that is generally consistent with
the hypothesized effects. The paper concludes with some
broad policy observations.
I. The Theoretical Advantages of Mixed Finance
In recent years, the finance literature has come to
recognize the importance of information asymmetries in
financial relationships. If one party is better informed than
another about events affecting the relationship, a financial
relationship may be infeasible or handicapped unless the
contractual agreement controls the ability of one party to
exploit the other.
A primary instance of such a problem can arise in the
context of a firm and its external financiers. It is probably
reasonable to assume that the insider/management of the
firm knows more than outside financiers about the firm's
projects and prospects. This is likely because it is costly to
make the firm transparent to outside investors, and because
information is fungible, so that its general release would
dissipate rents enjoyed by the firm in its markets. In such
an atmosphere of information asymmetry, there is no
assurance that the self-interested behavior of the firm will
conform to that expected by its outside financiers. The
result may be failure to fund socially desirable activities, or
financial contracts that do not allocate resources optimally.
In the following discussion, we demonstrate formally
that pure debt is not the socially desirable form of finance
under many conditions. Rather, outside financiers may
need to hold some form of equity claim on the firm
simultaneously with the debt claim if the firm's value is to
be maximized. We will call this type of financing "mixed"
financing.
A Model of the Financing and
Strategy Choices of the Firm
We examine the financing arrangements for a firm that
faces uncertainty about its future payoffs. 4 Let P be the
nonnegative payoffs ranging from 0 to m and x be a
parameter representing different "strategies" that indexes
various payoff distributions. Using Lucas/Breeden-type
capital asset pricing, the market value (in a competitive
market) of the firm can be derived from information on
the distribution of payoffs. s As Ross (1987) has shown,
a distribution function f(P ,x) can be derived that has
the property
Federal Reserve Bank of San Francisco
m
f
o
f(P,x)dP = 1. 6
Thus the discounted expected value of the firm, MV (x)
can be written as
m
MV(P,x) = r- 1
f
I
MV(x) = -
[1 - F(P,x)]dP,
Pf(P,x)dP
o
or
r
m
f
0
where r is the return on a certain payoff (the "risk-free"
return) and F (P ,x) is the cumulative distribution associated withf(P ,x). 7 We assume that the firm has a maximum
discounted expected value at some strategy x*, and that its
value function is strictly concave in x. In addition, we
assume that the firm borrows in external debt markets an
amount equal to D.
The value of the firm can be partitioned into those
payoffs that accrue to debt holders, B (x), and those that
accrue to equity holders, V (x). Specifically, if the coupon
payment on the debt is R, the market value of the firm can
be partitioned as
I
R
MV(x) = B(x) + Vex) = [l - F(P,x)]dP
r
I
+r
f
0
m
f
R
[1 - F(P,x)]dP.
That is, the discounted expected value of the payoffs
between 0 and R accrues to bondholders, while the portion
in excess of this accrues to equity holders.
Note that x indexes not only the firm's value, but also the
"risk" of the strategy. Bankruptcy occurs if P < R. The
strategy x' will be considered riskier than x if the probability of bankruptcy is greater. That is, if F (R ,x') > F (R ,x).
If the distribution function has a single-crossing property,
then this also suggests that when x' is greater than x, x' is a
riskier strategy than x. 8
19
The Moral Hazard Problem
Having structured the basic valuation model, we can
now model how information asymmetry can influence the
viability of external finance for this firm. It is assumed that
only outside financiers hold the debt of the firm, and that
outside financiers are informationally handicapped relative
to the insider/equity holders of the firm. This information
asymmetry takes the form of uncertainty about the strategy,
x, that will be chosen by the insiders.
We look first at the case when outside financiers can only
hold the debt the firm (and thus the insiders hold all the
equity). For a given coupon, R, on the debt, insiders have
an incentive to chose a riskier strategy than the one
incorporated in R. This is because for x' > x, for a
given coupon
Vex') =
1
-
r
I
[1 - F(P,x')]dP
>
Vex)
R
I
[I
F(P,x)]dP
R(x+)
I
R
r
B(x')
1
I
R
I
r
0
r
f
0
[1 - F(P,x' )]dP
<
[1 - F(P,x* )]dP = D.
o
[1 - F(P,x)]dP,
by the earlier definition of a riskier strategy. In essence,
riskier strategies add to the "upside" value captured by
equity holders while decreasing the value of the position of
the bondholders (for a given amount of outstanding debt).
This implies that aB (x )/ ax < O.
The Effect on Risk-Thking
The equilibrium effect of the moral hazard problem on
risk-taking and the value of the firm requires consideration
of how the parties to the transaction will respond to these
incentives. Since the value of the firm is assumed to be a
concave function of the strategy x, by definition it is
maximized when aMV(x)/Jx = 0, which will occur by
definition at x*. The insider/borrower, however, will have
his equity stake maximized when the first order condition
for a maximum value of V(x) is met. This is when
JV(x)
[1 - F(P,x+ )]dP
R(x*)
-r I
B(x)
R
~ =
[1 - F(P,x+ )]dP = D.
o
This will be a higher coupon than at the value-maximizing
strategy, since for x + > x *, R (x + ) must be greater than
R (x *) in order to make
and
JMV(x)
ax
JB(x)
-~ =0,
at a given coupon rate, R. But since JB(x)/Jx < 0, the
value of the first-order condition will be zero only for
strategies for which JMV(x)/Jx < O. By the assumed
20
I
B(x+) = ~
m
m
r
concave nature of the firm value relationship, this requires
selection of a strategy, x + , that is greater than the valuemaximizing strategy, x*. Thus, the strategy, x+, that
would be chosen by the insider would result in a less than
maximum firm value, and strategies riskier than the valuemaximizing strategy.
A rational lender, of course, will anticipate the tendency
for the insider to take on riskier projects, and will charge a
risk-adjusted bond coupon rate that accommodates this
expectation. Thus, he will charge a risk-adjusted rate
R (x + ) so that the value of the debt' is equal to D, the given
amount of outside debt financing obtained by the firm.
That is, in equilibrium R (x + ) will be chosen so that
I R(x+)
In equilibrium, therefore, lenders price debt in the above
manner so that its discounted value is always equal to the
amount borrowed, D. As a result, if a strategy, x, is
pursued where x * ~ x < x +, it is immediately implied that
V(x*)
= MV(x*)
- D;:: Vex)
= MV(x)
- D> V(x+)
= MV(x+) - D.
That is, the value of the insider's equity would be greater if
the strategy, x, which is less risky than the strategy x+ ,
were employed.
Mechanisms to Control Risk-Taking
Thus, the insider has an incentive to find some way to
persuade outside financiers that the riskiest strategies will
not be pursued. The mechanism could involve, for example, covenants in the financial agreement to bind the
insiders' behavior. Covenants that restrict additional borrowing by the firm, or give borrowers seats on boards of
directors (thereby giving them access to inside information) may be thought of in this light.
Alternatively, the outside financiers could be given a
share of the equity of the firm in return for their lending the
funds, D. Let us say, for example, that the insiders give
Economic Review / Summer 1991
away a portion, t, of V (x) so that the insider's share is now
(l-t)[MV(x) - B(x)]; O:oS t:oS 1.
The insider will now have to find a strategy, x+
maximize
(1- t)
aMV(x+ +)
ax
- (1- t)
+,
to
aB(x+ +)
ax
= 0,
which will have the same optimum for a given R as before
since it is just a scalar of the first order condition in the alldebt finance case. However, the reaction of the bondholders
will change. Since they now hold a share of the equity of the
firm, everything else being equal, they will require a lower
coupon on competitively priced debt, D. 9
It can be shown that the optimal strategy, x+ + , in this
situation will be less risky than the strategy pursued when
only all-debt positions were permitted. That is, x+ + will
be less than x +. This can be demonstrated by recognizing
that if the new strategy, x+ + , is in fact better for equity
holders than x + , then V (x + + , R + + ) > V (x + , R + + ). It
also must be the case that it was not the preferred strategy
when all-debt finance was used. That is, it must be the case
that V (x + , R + ) > V (x + + , R + ). With the knowledge that
R + + is less than R +, these two relationships together
imply that
R+
J
[F (P,x + ) - F(p,x+ + )]dP
> 0.
R++
This will be the case only if x + + is a lower risk strategy
than x + .10 Thus, if outside financiers are offered the
opportunity to simultaneously hold the debt and equity of a
firm, the firm will adopt less risky strategies. These
strategies more nearly maximize the value of the firm.
The same result, it should be emphasized, can be
obtained by directly monitoring and controlling the firm's
risk-taking via restrictive covenants, participation inside
the firm, and other techniques. Monitoring efforts are
costly, however, because they involve expenditure of resources by the outside financier, and because they require
the firm to reveal information that it might otherwise prefer
not to circulate outside the firm. If the outside financiers
are given some control over the firm (through seats on
boards of directors, for example), there also may be a cost
burden in the form of less efficient management (because
the outsiders, by definition, may be less expert in the
business of the firm than the firm itself). Whether monitoring and control approaches will be used with (or instead of)
mixed financing depends upon the balance of the costs and
benefits of each approach.
In summary, however, we have found that, for a firm with
Federal Reserve Bank of San Francisco
a given face value of debt, D, and a given distribution of
payoffs, allowing outsiders to simultaneously hold debt
and equity increases net firm value over all-debt finance.
Thus, if an artificial restriction limits outside financiers to
all-debt claims, net social value of the firm's activities will
be enhanced if nonzero equity shares are permitted. Since
the moral hazard problem is greatest in the case of a
borrower who has little equity at stake, or whose risktaking cannot be controlled or monitored accurately, the
remedy of mixed financial contracts likely is of particular
value in these cases. II
Needless to say, various forms of mixed financing
besides the simple mixed finance form used here can
produce this result. Convertible debt, debt plus warrants or
rights, collateralized lending, and other forms of mixed
debt and equity financial structures are essentially ways of
sharing equity claims with lenders.
The Role of Banks in Mixed Finance
Thus far, the discussion has emphasized the importance
of mixed financing generally in the relationship between a
firm and its outside financiers. An obvious question,
however, is whether mixed financing needs to be done by
financial institutions that accept deposits. There would
appear to be a simple answer to this question, one that
relies again on the notion of asymmetric information.
A bank is distinguished from other intermediaries because it issues debt, redeemable on demand, that may be
used in lieu of currency to effect household transactions.
The depositors of a bank thus are holders of par-value, demand debt. Because depositors consist of ordinary households, they may be assumed to be informationally deprived
relative to the managers of the bank. Thus they, like the
outside financiers of our previous discussion, need to be
able to observe behavior on the part of the bank that is
consistent with control of risk-taking. In essence, this is an
extension of the argument made by Diamond (1984) and
Gorton and Haubrich (1987) that a bank has an incentive to
structure the portfolio so as to simplify the depositors' own
monitoring problem.
From our earlier analysis, a bank that holds a pure-debt
position in firms has a claim that will be used to finance a
riskier strategy than it would be if it employed mixed debt
and equity finance. To the extent that such mixed financing
improves the lender's control over the moral hazard problem, it is a superior claim to the pure-debt position. It is
likely that depositors, everything else being equal, would
prefer their deposits be invested in such superior claims.
Thus, depositors desiring a risk-free rate of return would
prefer banks with investments structured as mixed finance
21
for the same reason that a lender would prefer such an
investment itself.
The Specialness of Banking
This line of reasoning suggests that banks with commerce powers would dominate banks restricted to all-debt
financial contracting with loan clients. It does not say,
however, that fully empowered banks necessarily dominate
other types of financial institutions with the ability to hold
the equity and debt of a firm. For this to be the case, there
must be something" special" about the banking firm in the
first place.
The" specialness" of a bank can be either on the assets
or liabilities side of its activities. That is, depository
institutions may be special because the provision of deposit
services lowers the cost of accessing the savings of certain
types of individuals in the economy. Households, for
example, may have little in the way of resources to devote to
financial management. Hence, they may seek demand debt
as an investment because it offers a bankruptcy covenant
that is inexpensive to exercise (they can just demand
repayment of their debt, without any legal costs), and
demand debt simultaneously provides liquidity and investment services.
Alternatively, banks may be special because they are
superior monitors of loan credits. This is an argument that
has been made by James (1987) and others. For this to be an
advantage of depository loan monitors, however, this technological advantage must flow from some advantage of
jointly providing this service and deposit services. Conceptually, this could be because holding deposit accounts
provides monitoring information about loan clients, or
because banks enjoy scale economies because deposit
liabilities provide a large liability base.
Although economists continue to debate the issue, the
empirical importance of banking in virtually all financial landscapes strongly suggests that banks play special
roles.l 2 By extension, therefore, restricting the equity
powers of commercial banks will have important consequences to the extent the powers restrictions have the
adverse effects modeled above.
II. Empirical Support
The arguments made in this paper suggest a number of
testable hypotheses about the use of mixed financing and
the role of banks:
1. Mixed debt-equity financing will be used when the
riskiness of projects is difficult for outsiders to monitor
or control.
2. Preference for such financing also will be higher where
the equity stake of the firm is small or collateral is not
available.
3. Banks that must hold only debt will be dominated by
intermediaries without such restrictions. As a corollary
of this, banks will be more prominent intermediaries in
financial systems that grant banks equity powers.
4. In economies where external finance is handicapped by
instrumentation powers, there will be greater reliance
on financing generated internally by the firm, despite
the inefficiency of such finance.
Because mixed debt-equity financing by banks is not
permitted in the U.S., however, it is necessary to look to
other financial sectors and other financial systems to see if
these hypothesized effects are observed.
Evidence from Venture Financing
Hypotheses 1 and 2 above can be tested by examining
financings that clearly involve risky projects and asym-
22
metric information. Mixed debt-equity financing should
be prevalent in these types of circumstances.
The Nature of Venture Activity. An examination of
U.S. venture capital activity helps test these hypotheses.
The venture capital business in the United States provides
financing in an environment of particularly severe information asymmetry on project risk. Venture projects, because of their novelty, are risky and difficult to evaluate
externally. In addition, venture firms, by definition, are
firms with low collateral and market value net worth.
Thus, start-up firms offer little in the way of receivables or
other sources of collateral to protect the financier's position; and the entrepreneur typically has little equity in the
enterprise to moderate the moral hazard problem faced by
the lender. As Table 1 demonstrates, the result is a class of
investments with very high risk, relative to other types of
assets in the economy.
The Type of Instrumentation. The type of financial
instrumentation typically employed in the high-risk setting
of venture finance as displayed in Table 2 supports the
theoretical notions offered earlier. l3 As is apparent from
this table, simple coupon debt instruments ("notes" in
Table 2) are very uncommon in venture financing. 14 When
pure debt is used, it is typically very short term, usually to
provide a new firm with interim working capital or other
temporary needs. Consistent with the model above, both
Economic Review / Summer 1991
the monitoring problems and the high risk of the projects
predispose against the use of pure debt.
The most common form of venture finance instrument
appears to be convertible preferred stock, which is essentially a mixed debt-equity position similar to the simpler
equity share modeled above. The preferred stock dimension gives the venture capitalist some debt-like returns,
while the convertibility feature provides opportunities to
enjoy the greater upside potential of common stock. Less
commonly, straight debt with equity conversion or detachable stock warrant features are employed. These, too, have
elements of a mixed financial structure.
The venture finance positions are augmented by other
covenants that serve the role of direct risk-capping, that is,
permitting the financier to control his losses should he
perceive a deterioration in his position. The convertible
preferred positions, for example, often include liquidation
priority and redemption rights. Liquidation priority, provides the venture capitalist with a worst~case downside
protection; redemption rights require that the firm cash out
the venture capitalist at a premium over the value of the
initial investment if, by a certain time, performance has
been less than anticipated. In addition, various antidilution
and stock sale restrictions are frequently imposed to prevent the firm from increasing its leverage or diluting the
claims of the venture capitalist. Table 3 presents the
frequency of such features from a survey of venture
partnerships.
In addition to embedding these control features in their
outside positions, venture capitalists often obtain inside
(management) rights in return for their significant outside
funding. These rights may include the opportunity to
appoint one or more directors or to serve as an officer of the
company. In addition, financing to venture firms usually is
provided in stages, to give the venture financier additional
control.
Evidence from Recent Changes in
Tax Law and Venture Activity
All of these contracting conventions observed in the
venture capital industry lend further support to the notion
that mixed debt-equity positions are useful in intermediating these types of risky credits. This observation is further
supported by the effect of recent changes in tax law on the
Federal Reserve Bank of San Francisco
23
level of venture finance activity. Recent changes in tax law
have increased effective capital gains tax rates and increase
the benefits of tax-deductible debt finance. Specifically,
with the passage of the Tax Act of 1986, personal income
tax rates were made lower than the corporate income tax
rate, and the rates at which capital gains and ordinary
income are taxed were equalized. Both have the effect of
favoring debt over equity finance.
In the venture capital industry, this appears to have
resulted in a reduction of venture commitment flows by
about 60 percent, and to have skewed venture finance
activity toward lower-risk, more conventional intermediation. ls This recent experience underscores the selective
importance of equity and mixed finance positions in financing risky ventures.
Evidence from Other Banking Systems
Hypotheses 3 and 4 state, respectively, that in economies
that do not restrict bank commerce powers, banks will be
the dominant form of intermediation and, by extension,
that external finance thus will be facilitated. Although the
commerce powers of commercial banks are limited today
in the United States, banks in some other countries enjoy
greater flexibility in this regard. This permits us to see
whether mixed financing emerges as a common financing
technique in such systems, and how banks fare versus other
intermediaries when these powers are available.
German and Japanese Banking. Commerce powers
are generally less restricted in most European countries
and in Japan as well. Of the major European countries,
Germany has the most liberal policies regarding combinations of banking and commerce. So-called universal
banking is practiced, and banks enjoy virtually complete
flexibility in the relationships that they may have with
commercial firms. 16 These powers are of long standing in
Germany, having been acquired with the introduction of
joint-stock banking that occurred in 1848. These so-called
Kreditbanken enjoyed both investment and commercial
banking powers. In addition, historically there have been
no antitrust laws or restrictions against interlocking directorates in Germany, and banks were permitted, as needed,
to require representation on supervisory boards of the firms
to which they lent funds.
Japanese financial regulation is nominally similar to the
U.S., since restrictions similar to Glass-Steagall were
imposed in the postwar period. In practice, however, as
Kim (1988) has pointed out, the keiretsu industrial relationships and mochiai cross-shareholding relationships
function to permit considerable exercise of mixed financing. Thus, both Germany and Japan offer interesting
24
Chart 1
Use of Bank Debt
by Commercial Firms
(Share of Outside Financing
Obtained from Banks)
Percent
90
80
70
60
50
40
30
20
10
O+-----T--I----------
·1 0 ;-'r--r-r-""";i"--r-r-..,........,r--r-r-..,........,r--r-r-..,........,r--1
72
76
80
84
88
opportunities to examine the effects of liberal commerce
powers.
Dominance of Bank Intermediaries. In both countries,
commercial banks are the dominant intermediaries. In
sharp contrast to the 0. S., the major share of external
finance is obtained in the form of bank loans, rather than
the direct placement of debt or equity securities. Chart 1
depicts the level and trend of bank loan share in the 0. S. ,
Japan and Germany.
The pattern of finance in both Germany and Japan
appears to emphasize mixed debt and equity finance.
Unlike banks in the US., banks in both Germany and
Japan hold major equity positions in their corporate credit
clients. In Germany, it is estimated that banks hold between 5 and 10 percent of total banking assets in the form of
corporate equity, or about 10 to 20 percent of total corporate equity in Germany. Complete data are not available on
the equity positions of German banks. Special antitrust
studies conducted in the 1970s, however, reveal the role of
German banks in large corporations. As Table 4 shows,
German banks have very significant positions in these
companies, with 28 percent of the largest companies
having 10 percent or more of their equity capital held by
financial institutions. Commercial banks appear to use this
practice the most, but a wide variety of universally empowered financial institutions hold corporate equity.
In addition to significant equity positions, German
banks obtain additional corporate control capability because of stock voting practices permitted in Germany. In
Economic Review / Summer 1991
particular, German banks also are the major provider of
stock brokerage and dealing services. As a result, most
shares are held on deposit by banks. German law and
regulation permits the shareholder to delegate voting authority to the bank of deposit.
These delegated voting rights add to the ability of
German banks to control risk in the corporations to which
they have lent; in the parlance of our earlier model, they are
able to directly limit selection of risky projects through
their corporate affiliations. Referring again to Table 4,90
percent of the large-company sample had 10 percent or
more of their equity voted by banks in 1974175. These
control channels are further implemented through bank
memberships on boards of directors and management committees of commercial firms. A 1979 report by the German
Monopolies Commission, (Bericht der Studiet Kommission 1979) for example, found that banks had representatives on the boards of two-thirds of the top 100
corporations.
For reasons given earlier, we would expect the use of
mixed financing to be less common in the financing of
well-established firms with substantial net worth since they
pose more modest monitoring and control challenges than
new, low-net worth firms. Indeed, over time the amount of
equity held by German banks in large corporations has
declined (Bericht der Studiet Kommission 1979).
Similar patterns of significant stock ownership and
control have been found in Japan in recent decades. As
Table 5 indicates, for example, the six major industrial
keiretsu all have had significant ownership by financial
Federal Reserve Bank of San Francisco
institutions. Although banks are nominally limited to 5
percent equity positions in nonbank corporations, through
cross-shareholdings with insurance companies and securities firms, the effective position of the main banks of
keiretsu is enlarged considerably.
Alternative Explanations. It could be argued that the
dominance of banks in these two countries results not from
more efficient bank intermediation, but from less efficient
direct placement markets. Indeed, German stock and bond
markets in particular are notoriously undeveloped. (The
German stock exchange, for example, is open only 2 hours
25
a day for public trading.) Similarly, corporate debt markets
in Japan are said to be poorly developed.
Poorly developed external financial markets however,
would lead us to expect to see relatively greater reliance on
internal financing. (As Myers and Majluf 1984 have suggested, firms rely on internal finance when information
asymmetries cannot be managed by outside intermediation
processes.) Yet in both Germany and Japan, there is less
reliance on internal financing than in the United States,as
illustrated by Chart 2. The comparative reliance of U.S.
firms on internal finance is consistent with the notion that
bank intermediaries are handicapped in their ability to
manage risk in an information-asymmetric environment.
The relatively heavy reliance in the U.S. on a distinct
venture capital industry also suggests that banks may be
handicapped in financing certain types of credits. In essence, in the United States, the venture capital industry or
some institution like it is necessary because of constraints
on mixed financing by banks. With no such constraints, we
would hypothesize greater bank involvement in venture
capital. Indeed, this appears to be the case in Germany,
where banks provide between 45 and 55 percent of all
venture capital. In fact, similar high percentages are
observed by Oohge, et al. (1989) in all other European
nations with liberal bank equity powers, such as France (35
percent) and Italy (70 percent). The fact that U.S.-style
venture capitalism has had difficulty operating in Japan
also may be consistent with this view.
Chart 2
The Use of External
Financing by Commercial Firms
(Percent of Financing
Obtained Externally)
4
Germany
70
26
Evidence from U.S. Bank Portfolio Behavior
The evidence above suggests that the presence or lack of
bank equity powers can have a significant effect on the
structure of financial intermediation. In particular, banks'
rolein.financial intermediation of risky credits is likely to
be less without equity powers. At issue, however, is not just
the specific institutional form of financial intermediation,
but rather the efficiency of its provision in the economy.
Portfolio. Effects. To the extent that strip finance by
deposit-taking intermediaries is the most efficient form of
intermediation, of course, the market share implications of
powers restrictions have direct efficiency effects. Moreover, restricting the type of financial contracting that a
bank may use will result in a self-selection of the types of
credits able to be served by a bank. This reduces the
diversification opportunities that banks may enjoy, and
with it, the ability to attract (uninsured) depositors.
In the U.S. context, it seems clear that firms with
significant equity and relatively transparent portfolios are
increasingly able to go to investors directly to raise new
funds. Underwriting and information systems clearly have
improved in the computer age. Yet these are precisely the
types of credits that banks, under their current restrictions,
are best suited to serve. Without the ability to hold corporate equity, banks cannot reasonably expect to serve efficiently firms with low net worth, low collateral, or novel
and risky projects. There seems no doubt that, in the
United States, the portfolios of commercial banks have
become less diversified, and more dependent upon "middle market" credits and remaining high collateral credits.
Having lost the short-term corporate debt market to the
commercial paper market in the 1970s, U.S. commercial
banks began losing other lines of industrial finance in the
1980s. Call report data reveal that the result has been a decline in the share of commercial and industrial loans relative to total assets. In 1984, for example, C&I loans were
17.5 percent of total assets; as of the first half of 1990, this
had declined to less than 15 percent. In absolute, inflationadjusted terms, lending by U.S. banks to nonfinancial
corporations has declined by two-thirds since 1978.
In place of C&I lending, banks have increased substantially their holding of real estate credits. The share of real
estate-collateralized loans in U.S. bank portfolios has
increased from 14 percent in 1984 to about 23 percent
today. In contrast, U.S. Flow of Funds data show that the
flow of directly placed corporate debt has increased 500
percent since 1978, and the real value of venture capital
commitments by a similar amount since 1980. In sharp
contrastto this experience of U.S. banks, real bank lending
Economic Review / Summer 1991
to business, in absolute terms has increased in the same
period in both Germany and Japan, according to flow of
funds data from those countries.
Mixed Financing and Corporate Discipline
An additional source of efficiency effects is the possibility that mixed financing provides a superior mechanism for
resolving intracorporate conflicts. In a financial structure
composed of separate debt or equity positions, conflicts
arise during times of financial stress between equity
holders and debt holders. No such conflicts arise, by
definition, in a mixed finance position. Workouts thus may
not need to result in bankruptcy, takeover, or other costly
external control mechanisms.
The data on the incidence of corporate takeovers in
Germany and Japan are consistent with the view that
mixed financing affords an opportunity to effect significant
corporate change without formal bankruptcy or takeover
and the deadweight costs associated with such processes.
InGermany, forexample, where this phenomenon has been
studied in detail, there has been only one hostile takeover
(the takeover of Feldmuehle Nobel in 1989 by Flick), and
other types of .• takeovers have been similarly rare, when
cQIUpared to the U. S. and the U. K. Rather, the banks have
used their strip financier position to press for management
changes in advance of serious deterioration of the firm's
condition. Similar practices are reported for Japan by
Kim (1988).
III. Concluding Observations
This paper has argued that restrictions on the instrumentation powers of commercial banks is a potential handicap
to both the U. S banking industry and to financial intermediation processes in our economy generally. The theory
presented in the paper argues that mixed debt-equity
finance is a potentially important means of resolving the
moral hazard problem that all outside financiers face. Only
casual data were presented in this paper, but the pattern of
instrumentation is consistent with that implied by the
model presented.
The more difficult issue is whether the lack of instrumentation powers of U. S. banks has any important macroeconomic consequences. For this to be so, one must first
accept the notion that the handicap of limited commerce
powers is significant and, second, that banks have special
capabilities not easily provided by other intermediaries. If
both of these observations are true, then the lack of
universal bank-like powers may result in a handicap to the
overall economy.
In concluding this paper, therefore, it is interesting to
offer additional, casual observations. The banking systems
in at least two major economies, Germany and Japan,
follow some variant of mixed finance. In both of these
economies, the introduction of bank equity powers is
associated with their rapid subsequent development.
In the case of Germany, the introduction of universal
banking in 1848 was followed by rapid growth through the
turn of the century and the advent of the First World War.
Historians and economists such as Riesser, Gerschenkron,
Federal Reserve Bank of San Francisco
and Schumpeter have attributed the rapidity of German
growth in this period in large part to the intermediation
services provided by the Kreditbanken universal banking
system. (See Pozdena and Alexander 1991.) The universal
banking system appears to have served modern Germany
equally well. The German economy has enjoyed higher
average real growth rates than the U. S. in the last three
postwar decades. In addition, spending on plant and equipment in Germany is roughly twice as great (as a percentage
of GNP) in Germany as in the U.S. Nonmilitary research
and development expenditures in Germany also exceed
those in the U.S. by only a slightly smaller fraction.
In Japan, as Hodder, et a1. (1985) point out, the prewar
zaibatsu and direct placement markets had managed to
provide a volume of external financing of only 2 to 4
percent of GNP. In contrast, the World War II and postwar
intermediation by banks is associated with a rate of external finance of as much as 20 percent of GNP. Today,
investment in plant and equipment in Japan exceeds that of
the U. S. in absolute terms, and at 23.5 percent of GNP is
approximately twice the U. S. rate. Research and development spending, at 3.1 percent in Japan, is 50 percent higher
than in the U. S. 17
Obviously, considerable additional research is needed to
demonstr<ite more robustly the effects of restricted banking
commerce powers. In addition, before banks receive additional powers of any kind, powers reform must be coordinated with the reform of the deposit insurance system. IS
27
ENDNOTES
1. Section 16 of the Banking Act of 1933 prohibits national
banks from purchasing corporate stock [12 USC 24], a
prohibition that has been extended to state-chartered
banks that are members of the Federal Reserve System
[12 USC 335J. Section 4 of the Bank Holding Company Act
prohibits a bank holding company (BHC) from owning or
controlling, directly or indirectly, the shares of any company that is not a bank [12 USC 1843J. The act exempts
investments by BHCs that involve less than 5 percent of
the voting shares of another company [12 USC 1843 (c)
(6)]. In addition, Congress at various times has made
exceptions that permit share ownership in selected organizations, such as Small Business Investment Corporation~, which provide a limited form of debt financing to new
bUSiness ventures [15 USC 682(b)J and state housing
corporations [87 Stat. 269J.
2. The Banking Act does not generate this restriction
specifically. It restricts equity ownership, but generally
allows incidental banking powers related to lending. The
Office of the Comptroller of the Currency has interpreted
this to mean that a bank may take as consideration for a
loan a portion of the company's profits or earnings, but not
shares of its stock [12 CFR 7.7312J. The Board of Governors of the Federal Reserve System typically has interpreted this restriction conservatively as well, and does not
permit a bank to be the lead lender to a commercial firm in
which it or other BHC subsidiaries hold shares even if
those shares are nonvoting and thus do not c~nstitute
controlling positions. See Taylor (1987) and Bostrom
(1989) for a further discussion of these issues.
3. The macroeconomic importance of banks as intermediaries is emphasized by a number of authors studying
the relationship between banking activity and business
activity. See, for example, Bernanke and Gertler (1989)
and Greenwald, Stiglitz, and Weiss (1989).
4. This section draws very heavily on an approach suggested by Roger Craine, and applied by Craine and
Steigerwald (1989). Craine and Steigerwald's approach
makes very compact a demonstration that otherwise is
quite cumbersome.
5. See, for example, Lucas (1978).
6. This need not be the underlying payoff distribution; that
will be the case only if agents are risk-neutral.
7. The discounted expected value of the firm is MV (P,x)
= (-1 f'(;Pf(P,x)dP. However, this can be shown to be
equal to (-1 f8 [1 - F(P,X) JdP by application of the rule of
integration by parts. Specifically, suppressing the x index
for simplicity, let u = [1 - F(P)J and v = P. Then
b
(-1
f
b
[1 - F(P,x)JdP
=
(-1
o
0
(-1
28
f
uv I ~:'(;
b
- (-1 f
vdu
udv
This can be written as
(-1
{[1 - F(P)JP} I ~:'(; -
m
(-1
f
m
=
-(-1
f
Pd[1 - F(P)J
o
m
-PdF(P)
=
(-1
o
f
Pf(P)dP
0
since
r- 1 {[1 - F(P)JP} I ~:'(;=
o.
8. The single. crossing property is that F(P,X1) > F(P,x)
for X1 > X. ThiS ensures that a shift in the distribution has
an unambiguous effect on the weight in the tails of the
distribution.
9. That is, the R(x+ +) needed to solve
R(x++)
f
-
(
+
[1 - F(P,x+ + )JdP
o
t
m
r f
[1 - F(P,x+ + )]dP
R(x++)
R(x+ )
-( 0f
[1 - F(P,x+ )JdP
=D
is less than R(x+ ), if the expected value of the equity share
is positive.
10. And the two distributions behave so that F(P,x+) >
F(P,x+ +) for all P, the so-called "single crossing property" of simple cumulative distributions.
11. The model presented above can be used to show that
bigger coupons (such as might arise as the firm enlarges
the amount of debt, D, it wishes to borrow) induce greater
risk-taking. Thus, the more leveraged a firm becomes, the
greater the moral hazard problem and the potential for a
significant effect of a mixed financing mechanism.
12. See, for example, Black (1985).
13. Venture firms may have other sources of finance as
well, such as funds raised from family or other direct
investor sources. Typically, however, the venture capitalist
is the major source of the funding of start-up industrial
firms. Because such firms usually are closely held, data
are not publicly available to characterize accurately the
liabilities of the typical venture firm.
14. For a more complete description of venture financing
mechanisms, see Testa and King (1989).
15. See Pozdena and Martin (1990).
16. See Pozdena and Alexander (1991), for a more complete description of the institutional features of the German banking system. This section draws heavily on that
source.
o
Economic Review / Summer 1991
17. Restricted equity powers thus may be at the root ofthe
often lamented high cost of capital in the U.S. Indeed, in
their recent study of Japanese and U.S. costs of capital,
Ando and Auerbach (1990) conclude that the measured
Japanese cost-of-capital advantage may be due to the
"lower risk" of comparable investments in Japan. This is,
of course, simply another way of saying that Japanese
financial intermediation methods better accommodate
risk.
18. It is not clear, however, that expanded commercial
powers necessarily translates into expanded opportuni-
Federal Reserve Bank of San Francisco
ties to exploit the bank safety net. Giving banks additional
tools to manage asset risk should offer them the opportunity to enhance bank profitability and net worth, which in
turn quells the desire for risk-taking at the expense of the
deposit insurance fund. Even for banks with very low
market value net worth (and, hence, a strong preference
for risk taking at the expense of the deposit insurer), a
method of controlling the cost of risky credits would be
used positively to enhance net worth.
29
REFERENCES
Ando, A, and A J. Auerbach. 1990. "The Cost of Capital in
the United States and Japan: A Comparison." The
Journal of Japanese and International Economies 2,
pp. 22, 134-158.
Bank of Japan. Economic Statistics Annual. Various
issues.
Benston, G. 1976. "A Transactions Cost Approach to the
Theory of Financial Intermediation." Journal of Finance 31, pp. 215-231.
Bernanke, B. and M. Gertler. 1989. "Agency Costs, Net
Worth, and Business Fluctuations." American Economic Review 79, pp. 14-31.
Bericht der Studienkommission, Frankfurt. 1979.
Black, F. 1985. "The Future for Financial Services." In
Managing the Service Economy, ed. R.P. Inman,
pp. 223-233. Cambridge University Press.
Bostrum, R. E. 1989. "Non-voting Equity Investments by
Bank Holding Companies." The Review of Banking
and Financial Services (March 1) pp. 43-52.
Campbell, T. S., and W Kracaw. 1980. "Information
Production, Market Signalling, and the Theory of
Financial Intermediation." Journal of Finance 35.
pp. 863-882.
Chiampou, G. and J. Kallet. 1989. "Risk/Return Profile
of Venture Capital." Journal of Business Venturing
(January).
Commerzbank.1985. \lI/erGehortZu \II/ern. Hamburg, West
Germany.
Craine, R., and D. Steigerwald. 1989. "Raiders, Junk
Bonds, and Risk." Mimeo.
Diamond, D. W 1984. "Financial Intermediation and
Delegated Monitoring." Review of Economic Studies,
pp.393-414.
Franks, Julian, and Colin Mayer. 1990. "Capital Markets
and Corporate Control: A Study of France, Germany,
and the U.K." Economic Policy (April) pp. 191-231.
French, K. R., and J. M. Poterba. 1990. "Are Japanese
Stock Prices Too High?" Mimeo.
Gorton, G., and J. Haubrich. 1987. "Bank Deregulation,
Credit Markets, and the Control of Capital." CarnegieRochester Conference Series on Public Policy 26,
pp.290-348.
Greenwald, B., J. Stiglitz, and A Weiss. 1984. "Informational Imperfection in the Capital Market and Macroeconomic Fluctuations." American Economic Review
74 (May) pp. 194-200.
Hodder, J., and A. E. Tschoegl. 1985. "Some Aspects of
Japanese Corporate Finance." Journal of Financial
and Quantitative Analysis 20, pp. 173-191.
James, C. 1987. "Some Evidence on the Uniqueness
of Bank Loans." Journal of Financial Economics 26,
pp. 217-236.
30
Jensen, M. C. 1987 "Corporate Takeovers: A Financial
Perspective on Mergers and Acquisitions and the
Economy." In The Merger Boom: Proceedings of a
Conference at Melvin Village. Federal Reserve Bank
of Boston.
_ _ _ _ . 1989. "Eclipse of the Public Corporation."
Harvard Business Review (November).
_ _ _ _ , and W H. Meckling. 1976. "Theory of the
Firm: Managerial Behavior, Agency Costs and Capital
Structure." Journal of Financial Economics 12, pp.
541-552.
Kim, Sun Bae. 1988. "Industrial Financing in Postwar
Japan." Mimeo. University of Toronto (November).
_ _ _ _ . 1989. "Modus Operandi of Lender-cumShareholders Banks." Mimeo. University of Toronto
(November).
Leland, J., and D. Pyle. 1977. "Information Asymmetries,
Financial Structure, and Financial Intermediation."
Journal of Finance 32, pp. 371-387.
Lucas, R.E. 1978. "Asset Prices in an Exchange Economy." Econometrica 46, pp. 1429-1445.
McDonald, J. 1989. "The Mochiai Effect: Japanese Corporate Cross-Holdings." The Journal of Portfolio Management (Fall) pp. 90-94.
Myers, S.C., and N. S. Majluf. 1984. "Corporate Financing
and Investment Decisions When Firms Have Information that Investors Do Not Have." Journal of Financial
Economics 13, pp. 187- 221.
Nakatani, I. 1984. "The Economic Role of Financial Corporate Grouping." In The Economic Analysis of the
Japanese Firm, ed. M. Aoki. Amsterdam: Elsevier
Science Publishers.
Ooghe, H., A Bekaert, and P. van den Bossche. 1989.
"Venture Capital in the U.S.A., Europe, and Japan."
Management International Review 29, pp. 29-45.
Pozdena, R. 1987. "Tax Policy and Corporate Capital
Structure." Federal Reserve Bank of San Francisco
Economic Review (Fall) pp. 37-51.
_ _ _ _ .1987. "Commerce and Banking: The German
Case." Federal Reserve Bank of San Francisco Weekly
Letter (December 18).
_ _ _ _ .1989. "Do Banks Need Securities Powers?"
Federal Reserve Bank of San Francisco Weekly Letter
(December 29).
_ _ _ _ .1990. "Banking and Venture Capital." Federal
Reserve Bank of San Francisco Weekly Letter (June 1).
_ _ _ _ , and V. Alexander. Forthcoming. "Bank Structure in West Germany." In Bank Structure in Major
Countries, ed. G. Kaufman. Kluwer.
_ _ _ _ , and D. Martin. 1990. "Is Tax Policy Hurting
Venture Capital?" Federal Reserve Bank of San Francisco Weekly Letter (August 24).
Economic Review / Summer 1991
OED Survey of Venture Partnerships. 1989. Palo Alto.
Ross, SA 1987. "Arbitrage and Martingales with Taxation." Journal of Political Economy 95, (November 2)
pp. 371-393.
Smith, C.w., Jr. 1979. "Applications of Option Pricing
Analysis." In Handbook of Financial Economics, ed.
J.L. Bicksler, pp. 288-327.
Stiglitz, J. and A. Weiss. 1981. "Credit Rationing in Markets
with Imperfect Information." American Economic Review 71, pp. 393-410.
Federal Reserve Bank of San Francisco
Taylor, A.M., III. 1987. "Equity Investment Opportunities
Available to Banks and Bank Holding Companies."
The Banking Law Journal (January) pp. 127-153
Testa, Richard J., and Rufus C. King. 1989. "Venture Capital Investment." Securities and Commodities Regulation (September 27) pp. 171-180.
31
Can Bank Capital Regulation Work?
Research Revisited
Frederick T. Furlong
The following two articles are reprinted here because they provide important theoretical analysis
on the effectiveness of capital regulation. Over the past several years, regulatory policy has placed an
increasing emphasis on the adequacy of bank and thrift capital. The argument is that raising bank
capital is an effective way to protect the insurance system and taxpayers, since capital represents a
buffer for absorbing losses. With higher levels of capital, banks should be safer and pose less of a risk
to the deposit insurance system. This view is reflected in Modernizing the Financial System (U.S.
Treasury 1991). That study states that "The single most powerful tool to make banks safe is capital."
However, the capital position of a bank is only one dimension of risk. The safety of a bank and the
expected cost to the deposit insurance system also depend on a bank's portfolio risk, which reflects
several factors such as credit risk, the degree of diversification, and interest rate risk. The controversy
addressed in the following two articles is whether banks, when forced to hold more capital, can be
expected to adjust their portfolio risk so as to offset, or even more than offset, the potential for higher
levels of capital to reduce the risk exposure of the deposit insurance system.
The first article, "Capital Regulation and Bank Risk-Taking," concludes that when banks act to
maximize their value, forcing them to hold more capital should reduce the risk exposure of the deposit
insurance system. This is the case even though banks have an incentive to increase portfolio risk with
subsidized deposit insurance. As shown in the article, a solvent bank's incentives to increase portfolio
risk to exploit the insurance subsidy decline as its capital-to-asset ratio increases. Therefore, as long
as the rise in the bank's capital ratio is not accompanied by a relaxation of regulatory efforts to
constrain its portfolio risk, a higher level of capital at the bank should mean more protection for
taxpayers.
This conclusion for risk-neutral, value-maximizing banks is at odds with the conclusions reached
in earlier studies concerning the effectiveness of capital regulation on risk-averse, utility-maximizing
banks. These earlier studies use a mean-variance framework and conclude that banks might react to
more stringent capital standards by increasing portfolio risk to such an extent that the probability of
failure increases. That is, these earlier studies argue that forcing banks to hold more capital could be
counterproductive.
The second article, "A Reexamination of Mean-Variance Analysis of Bank Capital Regulation,"
demonstrates that the analyses in the earlier studies that rely on the mean-variance framework cannot
be used to support the conclusion that capital regulation could be counterproductive.! These studies
inappropriately apply the Markowitz two-period portfolio model, which assumes that the probability
of failure is always zero, to address the question of how capital regulation affects the probability of
failure. More specifically, the analyses in these studies leave out the option value of deposit insurance
and use an inappropriate measure of risk, and, thus, misrepresent the return frontiers facing banks.
The two theoretical articles on capital regulation in this Review support the view that capital
regulation can be effective. That is, banks operating with higher levels of capital should reduce the
exposure of the deposit insurance system to losses. Moreover, the authors are not aware of any other
theoretical or empirical studies that show that banks forced to hold higher levels of capital would
adjust portfolio risk so as to actually increase the probability of failure. 2
NOTES
REFERENCES
1. Keeton (1988) considers the effects of capital regulation on risk-averse banks in a more
general framework. That study finds that for
poorly capitalized banks, increases in capital
ratios would be effective. For banks with relatively high capital ratios, further increases in
capital could induce a bank to substitute asset
risk for capital risk. However, the analysis does
not indicate that the substitution would be such
that capital regulation would be counterproductive.
Furlong, Frederick 1. 1988. "Changes in Bank
Risk-Taking." Federal Reserve Bankof San
Francisco Economic Review (Spring) pp.
45-56.
2. Empirical work by the authors supports the
proposition that capital regulation is not counterproductive. Furlong (1988) finds that for
bank holding companies in the 1980s whether
an institution was required to increase capital
in order to meet minimum regulatory requirements did not have a bearing on its change in
asset risk. Keeley (1990) finds that for bank
holding companies risk is negatively related to
the charter value of the holding company. This
is consistent with the view that banks with more
at stake tend to be less risky.
Keeley, Michael C. 1990. "Deposit Insurance,
Risk, and Market Power in Banking." American Economic Review (December) pp.
1183-1200.
Keeton, William R. 1988. "Substitutes and
Complements in Bank Risk-Taking and the
Effectiveness of Regulation." Unpublished
paper. Federal Reserve Bank of Kansas
City.
Capital Regulation and Bank Risk-Taking: A Note
Frederick T. Furlong and
Michael C. Keeley
Federal Reserve Bank of San Francisco
Reprinted from Journal ofBanking and Finance, 13(1989)
by permission of Elsevier Science Publishers.
This paper examines theoreticaUy the effects of more
stringent capital regulation on bank asset portfolio risk.
The analysis shows that, for a value-maximizing bank,
incentives to increase asset risk decline as its capital
increases. Thus, as long as regulatory efforts to contain
asset risk and size are not reduced, more stringent capital
regulation unambiguously reduces the expected liability of
the deposit insurance system.
34
Concern over the risk exposure of the federal deposit
insurance system has been a major factor behind the
increase in capital standards in banking in the 1980s. A
central issue in bank capital regulation is whether the
enforcement of higher capital ratio requirements gives
banks greater incentive to increase asset risk, thereby
partially or even fully offsetting the effect of a higher
capital ratio on default risk. Indeed a major criticism of the
regulatory attempts to raise bank capital ratios in the 1980s
is that these efforts "drove" banks to seek out more risky
activities. This view that more stringent capital regulation
will exacerbate the problem of risk-taking appears to be
held widely among commercial bankers and is evident in
the financial press as well as in the academic literature. 1
In this note, we address the question of how more
stringent capital ratio requirements affect the incentives of
a fully insured bank to increase the riskiness of its asset
portfolio. The analysis builds on that of studies such as
Sharpe (1978), Kareken and Wallace (1978), and Dothan
and Williams (1980), which use state-preference models to
examine the effects of deposit insurance, and those such as
Merton (1977) and Pyle (1984), which model the deposit
insurance guarantee as a put option. These studies show
that, for a value-maximizing bank with subsidized deposit
insurance, regulations are required to control both leverage
and asset risk. What is not addressed fully is how a bank's
incentives for increasing asset risk vary with changes in
capital ratio requirements. It is important to fill this gap in
order to assess the effect of bank capital regulation on bank
default risk and the risk exposure of the deposit insurance
system.
Economic Review / Summer 1991
I. A State-Preference Model
In this section, a state-preference model is used to
analyze the portfolio and leverage decisions of an insured
bank that maximizes its current value (the market value of
its equity). We use a two-period model with two possible
future states. The current prices of a dollar payout in the
future states are PI and Pz , for State 1 and State 2,
respectively. These prices are taken as given and are
unaffected by the portfolio decisions of banks.
To fund its current assets, A o, a bank has an initial
amount of capital, Co, and issues insured deposits, Do, so
thatA o = Do + Co' z A unit of deposits pays off $1 in each
state and is summarized as D(I,I). The current price of a
unit of deposits is:
PD = PI
(1)
is summarized as Y(YI' Yz). Security X is the riskier
security such that Xl < YI and X z > Yz. The current prices
of Securities X and Yare:
(2)
and
(3)
respectively. Without loss of generality, the payouts in each
state are defined to be such that the price of a unit of each
security is the same, that is,
(4)
Px = Py = PD = P.
The equalities in (4), along with the assumption that
Security X is riskier than Security Y, imply that Xl < YI <
+ Pz·
Deposits then earn the risk-free real rate, lI(PI + Pz ) - 1.
A bank can invest in two risky assets, Security X and
Security Y. One unit of Security X represents a promise by
the issuer to pay Xl dollars if State 1 occurs and Xz dollars if
State 2 occurs, and is summarized as X (x I' X z ). Security Y
1 < Yz < X z ·
The share of a bank's assets allocated to the riskier asset,
Security X, is S, and the share allocated to Security Y is
(l - S).
II. Value of Deposit Insurance
For a bank that is capitalized such that it can meet its
obligations to depositors in all future states, deposit insurance is redundant, and, thus, has no value. The current
value, Vo , of a bank that can meet its obligations to
depositors in both State 1 and State 2 equals the sum of the
current value of the payoffs on assets in each of two states
minus the current value of depositors' claims:
(5)
Vo
=
Co+D o
P
+
[Sx I
Co+D o
P
+
[Sx z
(l - S)ydPI
+
(l - S)Yz]Pz - Do·
(5) simplifies to Vo = Co' That is, the value of a bank that
can meet its obligations to depositors in both states is equal
to its initial capital; there is no deposit insurance subsidy.
However, a bank that can fail-that is, one that cannot
meet its obligations to depositors in one state-benefits
from deposit insurance. Given that the initial capital position and asset risk of a bank is such that bankruptcy occurs
Federal Reserve Bank of San Francisco
in State 1, and the deposit insurance premium rate is zero , 3
the current value of the deposit insurance subsidy, 10 , from
(5) is
C
D
Do
0+ 0
(6) /0 = P PI P
PI [SX I + (l - S)YI] > O.
In (6), (Co + Do)/P is the number of units of asset
securities held and PI [SX I + (l - S)YI] is the current
value of the asset payoff in State 1 per unit of security.
(DolP )PI is the current value of depositors' claims in State
1. For deposit insurance to have a value to the bank, the
value of the bank's assets in State 1 has to fall short of the
claims of depositors. The current value of that short-fall,
which corresponds to the option value of deposit insurance,
is equal to the current value of the payout to depositors by
the insurance fund in the bankruptcy state. Given Co, a
bank seeking to maximize the current value of its equity,
which is Vo = Co + /0' will try to maximize the value of
the deposit insurance option, /0'
35
III. Leverage and Risk
It is well known that a bank can maximize 10 by
maintaining the highest degree ofleverage (the lowest ratio
of initial capital to initial assets) allowed by regulation and
by increasing asset portfolio risk as much as possible.
Under the traditionally invoked assumption that Co is fixed
(an assumption that will be dropped shortly) the effect of a
change in leverage (a change in DolA o ) on the value of the
insurance guarantee is obtained by differentiating (6) with
respect to Do. Doing so yields
(7)
alo
aD
o
I Co = PI
p
{I - [Sx 1
+
(l - S)YI])
> O.
The partial derivative is positive since, as stated above,
< YI < 1, which means that [Sx I + (1 - S)Yd < 1.
Thus, the current value of the deposit insurance subsidy
increases with leverage. With subsidized deposit insurance, a value-maximizing bank would limit its leverage
only if forced to do so by regulation.
Constraints on bank asset risk also are required. In this
model, increased asset risk is associated with a higher
value of S. The effect of a change in risk-taking on 10 , as
determined from (6), is
Xl
(8)
alo
as = -
PI
A o P (x I
-
Y I) > O.
The partial derivative is positive since Xl < YI' The
positive relation between asset risk and the value of the
deposit insurance guarantee indicates that a value-maximizing bank with underpriced deposit insurance would
want to have S = 1. To prevent this, regulators would have
to control asset risk, which in this model could mean
limiting S to some maximum S or imposing regulatory
costs that are a positive function of S. For a bank to be at
S < 1, regulatory cost would have to be such that the
marginal cost of exceeding that particular value of S was at
least equal to the marginal value (in terms of increased
value of deposit insurance) from doing so.
This condition for asset risk regulation to be effective is
precisely the reason that the question of how capital
regulation affects the incentives for increasing asset risk is
important. Those who maintain that capital regulation
leads to more asset risk implicitly argue that the marginal
value from increasing asset risk is negatively related to
changes in leverage (Le., positively related to changes in
the capital-to-asset ratio). This position implies that for
higher capital standards to be fully effective they likely
would have to be accompanied by the imposition of higher
regulatory costs for violating asset-risk constraints. On the
other hand, if the marginal value is either not related to or is
positively related to changes in leverage, the enforcement
of higher capital standards would not lead to greater asset
risk, unless the restrictions on asset risk themselves were
relaxed.
(8) indicates that the gain from increasing asset risk
depends on asset size but not on the bank's leverage per se.
Under the assumption of fixed capital, however, a change
in leverage directly affects the volume of assets. A reduction in leverage can only be accomplished by selling assets
and using the proceeds to retire liabilities. From (8), the
marginal gain from increasing asset risk is positively
related to a change in leverage. That is,
2
a 10
aSaD
I
PI
-p
(Xl - YI) > O.
o
This means that a reduction in leverage achieved via
retiring debt and shrinking assets would reduce the marginal gain from increasing asset risk. In other words, a bank
would not be expected to respond to higher capital requirements by increasing the riskiness of its asset portfolio.
(9)
Co
=
IV. Allowing Capital to Vary
While the assumption of fixed capital may be suitable
for certain banks, it is not appropriate for many larger
banking organizations with access to capital markets. The
ability of a bank to issue new capital is a potentially
important consideration since, as we show below, a bank
would prefer to do so when it reduces leverage in response
to more stringent capital requirements. The reason for this
preference is that, for a given degree of leverage, the total
value of the insurance subsidy, 10 , is positively related to
the volume of assets, holding leverage constant. This can
be seen from the derivative of the value of the insurance
36
guarantee, in (6), with respect to assets, holding leverage
constant, which is
(10)
The term in the braces is the expression for the value of the
deposit insurance, which is positive given the bankruptcy
conditions for State 1.
Economic Review I Summer 1991
(10) indicates that, when a bank reduces leverage, it
would receive a larger insurance subsidy by increasing Co
than by selling assets and reducing deposits. This is
relevant to the analysis since the extent to which a bank
alters its leverage by issuing new equity affects the volume
of assets, which from (6) determines how the gains from
increasing asset risk are affected. As we show next,
however, allowing capital to vary does not change the
earlier conclusion from (9) regarding the effects of leverage on the change in the value of the insurance subsidy with
respect to changes in asset risk. The reason is that, even
when a bank can increase Co, requiring the bank to reduce
leverage will result either in a net contraction in A o or no
change in A o .
To see why initial assets would not expand, first note
that from (10) a bank, as well as the banking industry as a
whole, will expand as A o much as possible, independent of
any requirement to reduce leverage. Specifically, a bank
would have expanded assets to the point where the marginal gain from increasing assets was balanced by the
marginal cost of doing so. The main source of such a cost
would be regulatory constraints.
Next, assuming no change in the marginal cost of
increasing assets when leverage is reduced (that is, regulatory restrictions are not relaxed), a bank would expand
assets only if the change in the value of the insurance
subsidy with respect to assets declines as leverage increases. However, from (10) the opposite is the case-that
is: [a 2I o / aA a(Do /A o )) > O. Therefore, a bank would not
hold more assets when required to reduce leverage, even if
the bank can increase Co.
Given this result, the effect of leverage on the gains from
increasing asset risk for a bank that can issue new capital
(increase Co) are similar to those for a bank with fixed
initial capital. That is, from (8),
(ll)
a2I o
aSAa(Do/A o )
aA o
PI
a(Do/A o ) P
(Xl
-YI)
> 0,
given that [aAo/a(Do/A o )) > 0, which holds if A o contracts when a bank is required to reduce leverage. In the
limiting case in which Ao is unchanged, the partial derivative in (11) is equal to zero. Therefore, the incentives for a
bank to increase asset risk do not rise as leverage falls.
The conclusion we draw from the state-preference model
is that, if the costs to a bank from expanding asset risk and
size are not reduced due to a relaxation of regulatory
constraints, a value-maximizing bank, whether or not it
can issue new capital, will not respond to more stringent
capital requirements by increasing the riskiness of its
assets. Thus, more stringent capital regulation unambiguously reduces the risk exposure of the deposit insurance system.
V. Options Model
Options models also have been used to analyze the
effects of leverage and asset risk on the equity value of a
bank when deposit insurance is mispriced. One advantage
of options models is that they are more general than the
two-state model presented above. However, as with the
studies using state-preference models, the studies modeling deposit insurance as a put option do not address fully
the question of how capital regulation affects the gains
from increasing asset risk nor do they discuss why this
issue is important. In this section, we show that an options
model yields conclusions similar to those derived from the
state-preference model concerning the implications of
capital regulation for asset risk among value-maximizing
banks.
Following Merton (1977), the Black-Scholes formula for
a European put option can be adapted to apply to the
federal deposit insurance guarantee. Assuming all earnings are retained and a zero insurance premium, the
current value of the insurance guarantee is
(12)
10 = DoF(a-vt - X) - AoF( -X)
Federal Reserve Bank of San Francisco
where:
10
the value of the option.
the current value of insured deposits, which are
assumed to constitute all deposits.
the current value of assets (excluding the value of
Ao
the insurance option).
the standard deviation of the rate of return on
a
assets, which is the measure of risk.
t
= the interval to the next examination.
Do =
X
F( ) is the standard normal cumulative density function.
Assuming that capital is fixed, the familiar results
regarding the effects of leverage and asset risk on the value
of deposit insurance, the put option, can be derived from
(12) as follows:
37
(13)
aIo
I
aDo c
. . r:=F(ervt -X)-F(-X»O
0
and
aJ
-..2 = A oYf F'(X)
(14)
aer
> 0
where F' ( ) is the standard normal density function. 4 From
(13), it follows that a value-maximizing bank will increase
leverage indefinitely unless constrained by regulation. (14)
indicates that a bank has an incentive to increase asset risk.
How the incentives for increasing asset risk, holding Co
constant, would be affected by changes in leverage induced
by regulation can be determined by taking the partial
derivation of (14) with respect to the current value of
deposits. This yields the result:
(15)
a2I
aera; o
I Co
=
. . r:-"
ax
A o v t F (X) aD
o
+
F'(X)Yf> O.
As long as a bank has positive initial capital, this last
partial derivative will be positive because F"(X) < 0 and
ax/ aDo < 0 and F'(X) > O. This result is qualitatively the
same as that obtained from the state-preference model. The
marginal gain from risk-taking increases with leverage,
holding capital constant. Therefore, higher capital standards by themselves would not increase the incentives for
insured banks to increase asset risk.
As in the state-preference model, this conclusion also
holds for a bank that can increase Co in order to reduce
leverage. Again, under the options model, a bank would
expand assets, holding leverage constant, as much as
possible, independent of any required change in leverage,
since from (12)
aIo I
aA o (Do/A o ) > O.
However, regulatory costs that are sufficient to limitAo at a
given level of leverage will be sufficient at any lower level
of leverage since
a2I o
----=---> o.
aA o a(Do/A o )
Therefore, a reduction in leverage will not lead to an
increase in A o, everything else equal.
With an increase in A o ruled out, it follows from (14)
that the effect of leverage on the gains from increasing asset
risk is
(16)
=
. . r:- ,
aI
+ Ao v t F' (X) a(Do/A ) > O.
o
since [aAo/a(Do/A o )) ~ O. Thus, whether or not is Co
constant, higher capital requirements reduce the marginal
gains from increasing asset risk. This in turn means that the
risk exposure of the deposit insurance system is lower.
VI. Conclusion
This note analyzes the theoretical relationships between
capital regulation and bank asset risk. The key finding is
that regulatory increases in capital standards by themselves
will not require greater efforts to restrain asset risk. Higher
capital requirements reduce the incentives for a bank to
increase asset risk. Our results also indicate that a valuemaximizing bank prefers to meet higher required capital
ratios by raising additional capital, rather than merely by
selling assets and retiring deposits. In this way the bank
38
maximizes its volume of assets and thereby the value of the
deposit insurance subsidy.
The implication is that regulatory efforts to raise capital
standards do not lead a value-maximizing bank to hold a
more risky asset portfolio, as long as regulators do not also
relax efforts to limit asset risk and size. Thus, a more
stringent capital regulation will reduce the risk exposure of
the deposit insurance system.
Economic Review / Summer 1991
NOTES
1. In a New York Times article on March 5, 1987, concerning a Federal Reserve proposal to require banks to
hold capital in connection with interest rate and currency
contracts, William McDonough, vice chairman of First National Bank of Chicago, is quoted as saying that" ... the
proposal could lead banks to take on riskier business to
compensate for the lower returns they would almost assuredly get by having to maintain more capita!."
In the academic literature, studies such as Kahane (1977)
and Koehn and Santomero (1980), applying a meanvariance model to utility maximizing banks, conclude that
higher capital ratios can lead to greater asset risk. In a
recent article in this journal, Keeley and Furlong show that
the previous studies using such a framework are internally
inconsistent and the models cannot be used to support
the conclusion that a higher bank capital ratio can lead to
greater risk-taking.
2. Thus, Ao and Co exclude the value of any deposit
insurance subsidy, which will be introduced shortly.
3. The conclusions from the analysis would be unchanged if the rate were a positive, fixed-rate premium.
4. See Jarrow and Rudd (1983).
REFERENCES
Dothan, Uri, and Joseph Williams. 1980. "Banks, Bankruptcy, and Public Regulation," Journal of Banking
and Finance 4, pp. 65-87.
Jarrow, Robert A., and Andrew Rudd. ·1983. Option Pricing. Homewood, IL: Richard D. Irwin.
Kahane, Yehuda. 1977. "Capital Adequacy and the Regulation of Financial Intermediaries." Journal of Banking and Finance 1, pp. 207-218.
Kareken, John H., and Neil Wallace. 1978. "Deposit Insurance and Bank Regulation: A Partial Equilibrium Exposition." Journal of Business 51, pp. 413-438.
Keeley, Michael C., and Frederick T. Furlong. 1990. "A
Reexamination of the Mean-Variance Analysis of Bank
Capital Regulation." Journal of Banking and Finance
14, pp, 79-84,
Federal Reserve Bank of San Francisco
Koehn, Michael, and Anthony M. Santomero. 1980. "Regulation of Bank Capital and Portfolio Risk," The Journal of Finance 35, pp. 1235-1244.
Merton, Robert C. 1977. "An Analytical Derivation of the
Cost of Deposit Insurance' and Loan Guarantees."
Journal of Banking and Finance 1, pp, 3-11,
Pyle, David H. 1984. "Deregulation and Deposit Insurance
Reform" Federal Reserve Bank of San Francisco Economic Review (Spring) pp. 5-15.
Sharpe, William F. 1978. "Bank Capital Adequacy, Deposit
Insurance and Security Value." Journal of Financial
and Quantitative Analysis (November) pp. 701-718.
39
A Reexamination of Mean-Variance Analysis
of Bank Capital Regulation
Michael C. Keeley and
Frederick T. Furlong
Cornerstone Research, Menlo Park, CA and Federal
Reserve Bank of San Francisco, respectively. Comments
on a previous draft by Christopher James and an anonymous referee are much appreciated.
Reprinted from Journal ofBanking and Finance 14(1990)
by permission of Elsevier Science Publishers.
The mean-variance framework has been used to analyze
the effects of bank capital regulation on the asset and
bankruptcy risk ofinsured, utility-maximizing banks. This
literature claims that more stringent capital regulation
will increase asset risk and can increase bankruptcy risk.
These conclusions are notable because they are opposite to
those obtained for insured, value-maximizing banks. In
this paper, we show that the utility-maximization literature
does not support its conclusions regarding the effects of
bank capital regulation because it has mischaracterized
the bank's investment opportunity set by neglecting the
option value of deposit insurance.
40
In recent years, federal bank regulatory agencies have
increased reliance on bank capital regulation, in part,
because of heightened concerns over the risk exposure of
the deposit insurance system. Indeed, the primary rationale for existing capital regulations, as well as proposals
for more stringent capital regulation, is to reduce the
insurance system's risk exposure by reducing leverage.
The idea that capital and other restrictions might be
needed by liability holders in general to protect themselves
from equity holders has been discussed extensively in the
theoretical corporate finance literatl:re. For example, Jensen and Meckling (1976), modeling the equity of a firm as a
call option on its assets, show that equity holders have an
incentive to increase the non-systematic risk of assets once
debt has been issued or to issue additional debt. The reason
is that increasing asset risk or issuing new debt increases
the value of their option on the firm's assets and hence
decreases the value of outstanding debt. As a result,
bondholders often impose covenants constraining such
things as future debt issues, dividend payments, and
leverage.
In banking, the interests of the deposit insurance system
parallel those of a private bondholder because the deposit
insurance system, not the insured depositors, stands to lose
in the event of a bank failure. In this vein, regulatory
capital requirements and other portfolio restrictions could
be viewed as similar to private bond covenants. 1
It is within this context that a number of articles have
analyzed the need for bank regulation. One strand of the
literature has shown that when deposit insurance underprices risk, banks seeking to maximize the value of their
stockholders' equity will attempt to maximize the value of
the insurance subsidy by increasing asset risk and leverage
(see Sharpe 1978, Kareken and Wallace 1978, and Dothan
and Williams 1980). The reason is that the option value
of deposit insurance increases as leverage or asset risk
increases (see Merton 1977). As a result, with fixed-rate
deposit insurance both capital and asset portfolio regulation are needed to limit the liability of the deposit
insurance fund.
Moreover, as we have shown elsewhere (Furlong and
Keeley 1989), the marginal value of the deposit insurance
Economic Review / Summer 1991
option with respect to increasing asset risk declines as
leverage declines. Consequently, value-maximizing banks
would have less of an incentive to increase asset risk as a
result of more stringent capital regulation. Thus, more
stringent capital regulation will reduce the risk exposure of
the insurance system as long as the stringency of the
regulation of asset portfolio risk remains unchanged. (That
is, as long as the resources devoted to enforcing, and the
penalties for evading, asset regulations remain unchanged,
more stringent capital regulation will cause the probability
of bank failure to decline.)
In contrast, another strand of the literature focusing on
utility-maximizing banks questions the effectiveness of
capital regulation. The original contributions to this literature perhaps are best typified by Kahane (1977) and Koehn
and Santomero (1980), hereafter referred to as KKS.
Moreover, the basic framework developed by KKS continues to be used, as in the work of Kim and Santomero
(1988) and others. 2 KKS claim to show that, in the context
of a Markowitz two-parameter portfolio model, more
stringent bank capital regulation will cause a utilitymaximizing bank owner-manager to increase asset risk and
may, as a result, increase the risk of bank failure (and thus
implicitly increase the expected liability of the deposit insurance fund).3 These results are notable in large part because they run counter to the general finance literature and
suggest that capital regulation may be counterproductive. 4
In this paper, we show that KKS's use of the Markowitz
two-parameter portfolio model to analyze the effects of
bank capital regulation on bankruptcy risk is inappropriate
because of the model's assumption of constant borrowing
rates and costs independent of portfolio (default) risk. 5
While this assumption is appropriate for certain investment decisions where the probability of bankruptcy (default on debt) is zero or can be ignored, it is logically
inconsistent to use it to analyze the effects of bank capital
regulation on bankruptcy risk.
First, in a world without deposit insurance when the
probability of bankruptcy is nonzero, the promised deposit
rate demanded by uninsured depositors will depend on the
risk of the bank's portfolio, which in turn depends on
leverage and asset risk. Also, if default is possible, the cost
of deposits will be a random variable. Moreover, if depositors are risk-averse, the expected cost of deposits (per
dollar) will rise with risk. Thus, the models ofKKS, which
Federal Reserve Bank of San Francisco
assume constant borrowing rates and costs, are not applicable to uninsured banks.
Second, and more importantly, while it might appear
that the Markowitz assumption ofconstant borrowing costs
employed by KKS is applicable to insured banks since
insured depositors will supply funds at a constant risk-free
promised rate, we show below that it is not. 6 The reason is
that the expected net marginal cost (expected interest cost
plus an assumed fixed-rate premium) of deposits (per
dollar) to the bank declines as the quantity of deposits
increases, because the option value of the deposit guarantee increases as leverage increases. In effect, KKS confuse
the expected cost of deposits with the promised return under situations where the probability of default is nonzero.
By assuming that changes in the probability of bank
failure do not affect deposit rates or costs, KKS mischaracterize the risk-return tradeoff even for a bank with fixedrate deposit insurance by neglecting changes in the value of
the insurance subsidy that occur when leverage or asset risk
changes and by using an inappropriate measure of risk
when bankruptcy is possible. These oversights are crucial
since limiting the deposit insurance subsidy is the main
reason for capital requirements in the first place. 7
In Section I we first construct a prototype of the Markowitz portfolio model used by KKS to analyze the effect of
bank capital regulation on asset risk. We show that when
bankruptcy is not possible, and, thus, when there is no
deposit insurance subsidy, the results from our prototypical
model parallel those of KKS regarding the effects of
capital regulation on increasing asset risk. However, increases in asset risk due to more stringent capital regulation cannot increase the probability of bankruptcy under
the assumptions that KKS use to derive the model since
these assumptions imply that the probability of bankruptcy
must be zero.
In Section II, we demonstrate that accounting for deposit
insurance and the possibility of bankruptcy markedly
changes the bank's opportunity set. Moreover, the variance
of return no longer adequately characterizes risk. As a
result, KKS mischaracterize the risk-return tradeoff absent
capital regulation as well as the effect of capital regulation
on the risk-return tradeoff when bankruptcy is possible or
when deposit insurance is subsidized. Because of this,
KKS's model cannot be used to support their results.
Section III presents our summary and conclusions.
41
I. A Prototypical Model of an Uninsured Bank's Portfolio Decisionmaking
KKS analyze bank risk-taking as a portfolio management problem for a risk-averse bank owner-manager whose
entire net worth is invested in the bank. The ownermanager's equity risk depends on the bank's asset portfolio
risk and on leverage. We assume that, in the absence of
regulation, banks will leverage only efficient asset portfolios (those with maximum expected return for any given
level of risk). 8 Given the owner's preferences towards risk,
expected utility will be maximized subject to a constraint
that relates the gross expected return (one plus the expected
rate of return) on capital, E(Z), to the standard deviation of
that return, a(Z).
To derive this risk-return constraint, we assume that the
bank's deposits are not insured but that the bank can attract
deposits at a fixed promised deposit rate unrelated to the
bank's risk. This implies that the bank has to choose a
combination of leverage and asset risk to make bankruptcy
impossible (that is, the realized return on assets will be
such that the promised obligations to depositors always
will be met). With bankruptcy not possible, the gross return
on capital, Z, is given by the gross return on assets, AoP,
minus the promised (which equals the actual) obligation to
liability holders, LoR, divided by initial capital, Ko, or
Z
(1)
__ AoP - LoR
Ko
where
Ao
Lo
Ko
P
Z
R
initial assets,
initial liabilities (deposits),
initial capital,
gross return on the bank's pqrtfolio of assets,
assumed to be random, which equals one plus the
rate of return,
= gross return on capital, which is random, which
equals one plus the rate of return,
promised (which equals actual) gross certain return paid on (and per dollar cost of) liabilities,
which equals one plus the rate of return.
(1) may be rewritten by noting that Lo
(2)
Z
Ao - Ko to give
A
= [ Ko ] [P - R] + R.
o
The expected gross return on capital, E(Z), may be found
by taking expected values of both sides of (2). As long as R
is fixed and not random, which it would be as long as
bankruptcy were not possible, this gives:
(3)
A
] [E(P) - R]
E(Z) = [ /
o
42
+ R.
Thus, increasing leverage, as measured by the asset-tocapital ratio, increases the owner's expected return on
capital linearly when default is not possible for any given
asset portfolio.
Similarly, the standard deviation of the return on capital,
a(Z), may be derived from (2). When bankruptcy is not
possible, the covariance of Rand P is zero and
(4)
a(Z) =
A
[Ko ] a(P).
o
so that the standard deviation of return on capital also
varies linearly with leverage for a given asset portfolio.
(3) and (4) may be jointly solved to eliminate the
[Ao/K o] term to give
(5)
E(Z) = [
:~~~
] [E(P) - R] + R
In other words, the expected (gross) return on capital varies
linearly with the standard deviation of return on capital for
a given expected asset return and asset standard deviation.
This is a standard result in the CAPM models of the finance
literature on investment (see Sharpe 1970).
In general, it is assumed that a bank faces a variety of
different asset portfolio risk-return combinations (the asset
risk-return frontier). Asset portfolios with more risk are
assumed to yield larger expected returns and thus the asset
risk-return frontier is convex (see Figure 1). Moreover, it is
assumed that the banking sector is small enough that the
asset risk-return frontier is unaffected by banks' behavior.
Thus, the frontier is taken as given by banks in their
optimizing decisions.
An unconstrained bank's efficient investment frontier
consists of linear combinations of a particular asset portfolio and the single risk-free liability. As is well known (see
Hirshleifer 1970, chap. 10, or Fama and Miller 1972, chap.
7), the most efficient asset portfolio is the one where a line
from the constant (gross) borrowing rate, R, is tangent to
the asset risk-return frontier. (This is depicted as point
E(po), a(Po ) in Figure 1.) By leveraging this asset portfolio the bank can obtain the highest expected return on its
capital for any degree of risk. Since this tangency at point
E(Po ), a(Po ) does not depend on the bank owner's risk
preferences, the asset portfolio chosen depends only on the
risk-free interest rate and the asset risk-return frontier.
An unconstrained bank's optimal position on this linear
investment (or capital) risk-return frontier is the point at
which the marginal rate of substitution between risk and
expected return, da 2(Z)/dE(Z) I U= (j, is equated with the
tradeoff between risk and expected return along the effi-
Economic Review / Summer 1991
cient investment portfolio frontier. Following Koehn and
Santomero, assuming the distribution of portfolio returns
(Z) is symmetric (as it would be for a diversified portfolio
in which bankruptcy was not possible), and taking a second
order Taylor-series expansion of the utility function, V,
around the initial capital, K o, of the bank, and then taking
expected values gives:
(6)
E(V)
although the assumption is that the unconstrained bank
would choose a degree of leverage for which bankruptcy is
not possible.
When capital constraints are imposed, the bank owner
generally will be able to increase utility by leveraging asset
portfolios with more risk than the one characterized by the
parameters E(P0) and <r(P0). The reason is that a binding
capital constraint changes the shape and location of the
capital risk-return frontier, making it convex once the
constraint becomes binding. The capital risk-return frontier under binding capital regulation is convex because it
represents a linear mapping of the asset risk-return frontier
which is assumed convex. 9
In Figure 1, the effect of such a binding capital constraint on the capital risk-return frontier is depicted. As
Koehn and Santomero point out, a reduction in permissible
leverage reduces expected return on capital and investment
risk over the entire constrained frontier for any given asset
portfolio. Moreover, A is larger on the constrained frontier.
Thus, if a binding capital constraint were imposed on a
previously unconstrained bank (at VO), the bank would
choose a more risky asset portfolio (and move to VI). (The
bank could have chosen a less or equally risky asset
portfolio when not constrained, but did not, which precludes a new equilibrium on the old capital frontier.) It
= V(Ko ) +
V'(Ko){E(Z) - b[(E(Z))2
+ <r2 (Z)2]}
where
V"(Ko)Ko
2V'(Ko )
b = -
is the coefficient of relative risk aversion of the underlying
utility function and V' and V" are the first and second
derivatives of V. For this utility function the marginal rate
of substitution is:
(7)
d(<r2 (Z))
d(E(Z))
I U= (;
1
=
b -
2E(Z) = MRS.
Thus, the optimal portfolio requires that MRS = A, where A
is the tradeoff between variance and expected return on the
efficient investment frontier. Thus, the degree of leverage
chosen is determined by the owner's risk preferences,
Figure 1
E(z)
Unconstrained Capital
Risk-Return Frontier
~
More Constrained Capital
Risk-Return Frontier
Asset Risk-Return Frontier
E(PO)
R
o(PO)
Federal Reserve Bank of San Francisco
o(z)
43
should be emphasized that this result of an unambiguous
increase in asset risk depends critically on the assumption
that capital regulation alters the bank's risk-return frontier
from a linear to a convex constraint, thereby increasing "and reducing expected return on capital. However, as we
demonstrate in the next section, in the absence of capital
regulation the capital risk-return frontier of a bank that can
fail is not linear; nor does leverage have a linear effect on
risk and return. 10
The effects of further reducing leverage through regulation are ambiguous, however, and depend on the shape of
the bank's (owner's) utility function. The case depicted in
Figure I is one with constant relative risk aversion, where
increasing the stringency of capital regulation (lowering
the permissible degree of leverage) leads the bank to
choose a more risky and higher-return asset portfolio (by
moving to U2).1I This result too, however, depends critically on the assumption that leverage affects the riskreturn frontier linearly-a result that does not hold for
banks that can fail.
This basic result of increased asset risk caused by more
stringent capital regulation is one result emphasized by
KKS. More important is their claim that the increased
asset risk caused by more stringent capital regulation could
increase the probability of bank failure and thus could be
counterproductive. However, under the constant borrowing
cost assumption they use to derive their model, an increase
in asset risk due to more stringent capital regulation cannot
affect the probability of failure, which remains zero.
The reason is that the probability of failure must be zero
in order for borrowing costs to be constant and for the effect
of leverage on risk and return to be linear. As we show
below, neither insured nor uninsured banks that can fail
have constant borrowing costs, and thus there is not a linear
effect of leverage on risk and return as KKS suppose.
Moreover, with underpriced deposit insurance, the capital
frontier may be nonconvex. Thus, KKS's model is not
applicable to assessing the effects of capital regulation on
the probability of bankruptcy. In the next section we show
how the constraint changes and why KKS's analysis of
capital regulation is inappropriate when a nonzero probability of bankruptcy and deposit insurance are introduced.
II. Introducing Bankruptcy and Deposit Insurance
The analysis above, which is consistent with KKS,
assumes that a bank always would mak.e asset and leverage
choices such that bankruptcy could not occur. Such a bank
could attract deposits at the risk-free rate because it always
would make the payments promised regardless of the
return on assets realized. Consequently, the cost of deposits (per dollar) to such a bank would equal the promised
risk-free deposit rate and would not be a random variable
so that the capital risk-return frontier in the absence of
capital regulation would be linear.
In the absence of deposit insurance a bank's expected
borrowing cost would rise as leverage (and thereby the
probability of bankruptcy) increases if depositors are riskaverse. Thus, leverage does not have a linear effect on risk
and return for uninsured banks that can fail.
More importantly, even with fixed-rate deposit insurance (under which a bank could attract deposits at a
promised risk-free rate even though bankruptcy is possible), the per dollar deposit cost is random and the
expected per dollar cost of deposits to the bank would vary
with default risk and would no longer be equal to the
promised risk-free deposit rate plus the deposit insurance
premium rate. 12 As a result, leverage would not have linear
effects on risk and return. The reason is that a fixed-rate
deposit insurance guarantee represents an option to the
bank to put the bank's assets to the insuring agency at a
striking price equal to the promised maturity value of its
44
liabilities. The value of the option (per dollar of deposits)
increases as leverage (deposits) increases, but its price (per
dollar of deposits) is fixed. This increase in the option's net
value, in effect, lowers the expected marginal cost of
deposits. As a result, the expected cost of deposits to the
bank is less than the risk-free rate plus the deposit insurance premium. Moreover, the expected cost of deposits is
not independent of the bank's asset portfolio risk-in fact,
the expected cost of deposits also declines as asset portfolio risk increases because the net value of the deposit
insurance option also increases as asset risk increases.
To demonstrate how the deposit insurance guarantee
affects the risk-return tradeoff, it is assumed that a minimal
form of capital regulation is in place (a bank owner must
invest his or her entire net worth in the bank), and that the
deposit insurance premium is zero. 13 ,14 The expected
gross return on capital, then, is given by:
00
A P - L R
(8)
E(Z)
0
K 0 ] f(P) dP,
o
t[
where
R
f(P)
p*
the promised gross rate on deposits,
the probability density function of P,
[Lo/Ao]R, which is the lowest asset return for
which depositors are repaid in full, that is, when
bank capital is exhausted.
Economic Review / Summer 1991
(8) indicates that the expected gross return on capital is the
expected value of gross asset returns minus liability obligations, conditional on nonbankruptcy. (If P < P *, bankruptcy occurs and the gross return on capital is zero.) (8)
can be rewritten by adding and subtracting the same term
to give:
I [A
00
(9)
E(Z) =
0
P-L R
K 0 ]f(P)dP
0
-00
P*
I [
A P-L R
0 K 0
J!(P)dP.
LoF(aVt - x) - AoF( -x)
(11)
10 =
0
-00
v
AO
E(Z) = ([ K ][E(P)
o
R]
where
10
the value of the option per dollar of capital invested, which equals
+ R}
p*
I [
L R - A P
0
K 0 ]f(P)dP,
0
00
+
p*
I [
L R-A P
0 K 0
]f(P ) dP.
the current value of insured deposits, which earn
the risk-free interest rate and are assumed to
constitute all deposits,
= the current value of assets (excluding the value of
the insurance option),
= the standard deviation of the rate of return on
assets, which is the measure of risk,
= the interval to the next eXfu'l1ination,
=
0
-00
Note that the first term of (10) in braces is identical to the
right-hand side of (3), the formula for the expected gross
returns on capital of a bank that cannot go bankrupt.
However, the second term of (10) represents an integration
over bankruptcy states of the obligations to depositors in
excess of returns on assets, which, by definition, are
positive in each bankruptcy state (since if P < P *, LoR AoP > 0). The value of this integral, however, depends
positively on leverage. (That is, the derivative of the
integral with respect to liabilities holding constant equity
is
p*
I
-00
[R
-
Ko
'
1\.0
Noting that L o = A o - K o and taking the integral of the
first term of (9) and rearranging terms in the second
integral gives:
(10)
ance is the sum of the expected return posited by KKS plus
the expected return of the option. Below, the implications
of these changed relationships for the· effects of bank
capital regulation on the relationship between leverage and
expected return are explored.
Following Merton (1977), under the stochastic assumptions employed by Black and Scholes (1973), the value of
the integral neglected by KKS-the option value of deposit insurance per dollar of capital invested-is:
P]
A
log ( ~ )
a 2t
+ (2 )
x
, and
aVt
F() = the standard normal cumulative density function.
f(P)dP
which is positive since R > P for P < P *.) This means
that the cost of an additional dollar of deposits holding
equity constant (which increases leverage), is not R, but is
R minus the increase in the value of the integral.
This second term of (10), the expected value (conditional
on bankruptcy) of the obligations to depositors in excess of
returns on assets per dollar of invested capital, corresponds
to the option value of deposit insurance as described by
Merton (1977). This is the term that is neglected by both
Kahane and Koehn and Santomero. By neglecting the
option value of deposit insurance per dollar of invested
capital, the linear relationship between expected return
and leverage assumed by KKS no longer holds, nor does
the linear relationship between risk and leverage. 15 In
effect, the expected return on capital with deposit insur-
Federal Reserve Bank of San Francisco
First, consider how the value of the option varies with
leverage, holding initial capital constant. (We chose this
method of varying leverage since it corresponds to KKS's
assumption that the bank owner's capital is fixed.) Using
the results in Jarrow and Rudd (1983),
(12)
dlo
dL
o
I
_
Ko -
[
alo
aLo
alo
1
+ aLo ] [ K ]
o
or
(13)
1
[F(aVt - x) - F( -x)] [ K
o
] > O.
That is, increasing deposits, holding capital constant,
increases the option value of deposit insurance. Moreover,
the second derivate of 10 with respect to L o is positive.
45
Thus, the overall expected return increases more rapidly
and nonlinearly with leverage than the linear relationship
posited by KKS, thereby making the relation between
leverage and expected return nonconvex. Because of this,
risk-aversion would no longer necessarily constrain bank
risk-taking. In fact, as we have shown elsewhere (Furlong
and Keeley 1987), for a binomial asset return distribution,
as long as the bank owner is willing to risk bankruptcy,
absent regulation, optimal leverage is infinite even though
the bank owner is risk-averse. 16
Moreover, consider how the expected return varies with
increased asset portfolio risk. The value of the option
varies with asset risk as
(14)
dIo
A o '\/"t F'(x)
da K
> O.
o
Thus, independent of the positive market relationship
between asset risk and return presumed by KKS, the value
of the option also increases with asset risk, thereby changing the shape of the capital risk-return frontier holding
leverage constant. That is, the capital risk-return frontier is
no longer a linear mapping of the asset risk-return frontier.
Finally, as we have pointed out elsewhere (Furlong and
Keeley, 1989), the gain from increased risk-taking (in terms
of increased option value) increases as leverage increases
because:
(15)
[A o '\/"t F"(x)
dx
dLo
+
K] >
F'(x)'\/"t][
1
0
o
(which is positive because F"(x) < 0, dx/dL o < 0 and
F'(x»O). (15) implies that the gain from increased risktaking is not independent of leverage as KKS assume.l7
As the above results demonstrate, the relationship between expected return, leverage and asset risk is straightforward, but the relationship between true capital risk and
return is not. Although the variance of Z under subsidized
deposit insurance is easily calculated, a(Z) alone no longer
adequately characterizes risk for the bank owner when
bankruptcy is possible. Specifically, it is well known that
variance alone is an unreliable measure of risk for truncated, skewed distributions such as that of Z when bankruptcy is possible. Since the equity of the bank is a call
option on its assets at a striking price equal to the promised
maturity value of the deposits, the return on equity will
be positively skewed. As Cox and Rubinstein (1985,
pp. 317-342) show, for utility functions with constant
proportional risk-aversion, expected utility depends on the
skewness as well as the mean and variance of the return. By
neglecting the skewness of the return distribution, KKS
mischaracterize the shape of the capital risk-return tradeoff
absent capital regulation and how that shape is affected by
leverage and capital regulation.
Thus, KKS's analysis does not demonstrate that more
stringent capital regulation would lead a utility-maximizing bank with fixed-rate deposit insurance to take on more
asset risk. Moreover, from the analysis above, risk-aversion alone will not necessarily be sufficient to limit leverage and asset risk as is concluded by KKS. As a result,
KKS's analysis cannot support their claim that more
stringent capital regulation will be counterproductive for
bank owners with certain preference structures. For example, Furlong and Keeley (1987) demonstrate that for a
binomial asset return distribution, the probability of bankruptcy declines as the stringency of capital regulation is
increased as long as the stringency of asset portfolio risk
regulation remains unchanged regardless of the bank
owner's preference structure.
III. Summary and Conclusions
Two inconsistent strands of the finance literature come to
In this paper we show that the KKS model does not
opposite conclusions regarding the effects of capital reg-support its claimed results. KKS apply the Markowitz twoulation on bank risk-taking. On the one hand, the options
parameter portfolio model to analyze bank risk-taking
literature suggests that for risk-neutral or value-maximizunder a nonzero probability of bankruptcy inappropriately.
ing banks capital regulation will reduce the risk exposure
Specifically they neglect the option value of the deposit
of the deposit insurance system under a given stringency of
insurance subsidy and use an inappropriate measure of
asset regulation. On the other hand, the utility-maximizarisk, thereby mischaracterizing both the risk-return frontion literature utilizing the Markowitz two-parameter porttier absent capital regulation and the shift in the risk-return
folio model, as typified by KKS, claims that forrisk-averse
frontier due to capital regulation. Because of these overbanks more stringent capital regulation may increase the
sights, the models used by KKS are not applicable to
probability of bank failure (and hence implicitly the risk
analyzing the effects of bank capital regulation on asset
exposure of the insurance system) and thus be counrisk and cannot be used to support their results.
terproductive.
46
Economic Review / Summer 1991
NOTES
1. See Black, Miller, and Posner (19.78) for a discussion of
why bank regulation is analogous to the contractual enforcement of private lending agreements by private debtholders.• Black, Miller, and Posner also argue, but do not
formally prove, that the less capital the bank has, the
greater its incentives for risk-taking. As aresult, they call
for more stringent capital requirements to protect the
insurance fund.
2. Also, see articles by Wall (1985), Lam and Chen (1985)
and Hanweck (1985).
3. As Koehn and Santomero (1980, p. 1244) put it, "In fact,
a case could be argued that the opposite result can be
expected to that which is desired when higher capital
requirements are imposed."
4. Although Kahane and Koehn and Santomero conclude
that both capital and asset regulation are necessary, as
does the value-maximizing literature typified by Sharpe,
Kareken and Wallace, and Dothan and Williams, it is
important torecognize that KKS's models cannot support
this conclusion. (It is true that, under the assumption of
value maximization, both capital and asset regulation are
needed to limit the liability of the deposit insurance system.) KKS claim that both capital and asset regulation are
needed because more stringent capital regulation leads
to greater asset portfolio risk, which in turn can increase
the probability of failure. However, as we show later, KKS's
models cannot be used to show that more stringent regulation will lead to an increased probability of failure.
5. Koehn and Santomero explicitly assume a constant
deposit rate and corresponding constant borrowing cost
per dollar of liabilities. Similarly, Kahane, following Hart
and Jaffee (1974), assumes that the deposit rate is stochastic but unrelated to the bank's portfolio risk. For
example, Kahane (1977, p. 209) states that "... the distributions of the random variables (the returns on assets
and liabilities) must be exogenously given and independent of the value of the vector x (the portfolio allocation) ... " (parenthetical statements added).
6. In private correspondence Anthony Santomero indicated that the Koehn and Santomero model was properly
interpreted as applying to insured banks. Moreover, the
more recent Kim and Santomero (1988) model specifically
is claimed to apply to insured banks.
7. It should be noted that the analysis of KKS is not
applicable to uninsured banks either. To analyze uninsur(:')d banks, one. would have to account for the increase
in expected borrowing costs as bank risk increased and
the variance of deposit returns increased, which would
result from the behavior of risk-averse depositors.
8. See Merton (1972) for a discussion of how quadratic
programming can be used to solve for the efficient asset
portfolio.
9.To derive the shape of the capital risk-return frontier,
the risk-return combination resulting from leveraging each
asset portfolio to the maximum degree allowed may be
Federal Reserve Bank of San Francisco
traced out. As (3) and (4) show, both expected return,
E(Z), and risk, Ri , are linear functions of leverage. Thus,
the risk and return on capital fora given asset portfolio and
leverage canb(:')found geometrically by extending a ray
from the constant borrowing rate through the particular
asset portfolio up to the maximum leverage allowed. The
locus of such points is the constrained capital risk-return
frontier. Also, note that a particular point on a capital riskreturn frontier has greater ass(:')t risk than anotherpoint on
the same orOn a different frontier ifthe slope of a line from
R through th(:')point is smaller.
10. Although the shape of the risk-return frontier depends
on whether the bank's deposits are insured at a fixed rate,
neither insured nor uninsured frontiers are linear.
11. Foraformal proof see Koehn and Santomero(1980).
12. An anonymous referee noted that once it is realized
that the deposit rate (from the bank's perspective) is
random, the nonlinearity of the investment frontier is selfevident since it is simply a combination of positive and
negative risky assets. While this is true, our point is that a
fixed-rate deposit insurance guarantee alters the riskreturn frontier in a specific way so as to subsidize risktaking.
13. The assumption implicit in the utility maximization
framework is that a (potential) bank owner has an exogenously given initial capital (wealth) Ko, all of which
must be invested in the bank in order to obtain deposit
insurance. However, this assumption implies some form of
capital regulation since a risk-averse bank owner generally would prefer to segregate his capital (and make a
relatively safe investment) and start a bank with no capital,
thereby acqUiring an option of potentially unlimited value.
This suggests that the utility-maximization model may not
be applicable to many actual banks since even owners of
small banks have limited liability, and, absent capital
regulation, would not have to risk all of their own funds. It
also suggests that this limited form of capital regulation
must reduce the probability of bank failure-a result
opposite to KKS.
14. Since we are interested in fixed-rate deposit insurance systems, the analysis of a zero-premium rate system
is essentially the same as a positive fixed-rate system.
15. With fixed-rate deposit insurance, a more risky asset
portfolio, even if it has the same expected return, increases the expected return on capital because the option value of deposit insurance increases. Similarly, by
increasing leverage, the owner can increase without limit
the expected return on capital as long as some part of the
asset distribution exceeds the promised rate. Under these
circumstances, even if the expepted rat(:') on assets were
less than the promised rate on deposits, a bank with
underpriced deposit insurance would gain from lev(:')rage.
This is in sharp contrast to the results without deposit
insurance when bankruptcy is not possible. In that case,
leverage can increase expected return only if the expected return on assets exceeds the expected cost of
47
deposits (see (3)). Thus, the provision of underpriced
deposit insurance can cause risk-averse bank owners to
assume more risky portfolios.
16. Rationality implies that a lottery that costs $1 and pays
$100 with a 50 percent chance and $0 with a 50 percent
chance will be preferred to one that also costs $1 but pays
$10 with a 50 percent chance and $0 with a 50 percent
chance, even though the variance of the first lottery's
outcomes is higher. Thus, for some asset distributions,
such as the binomial, a bank owner's true risk is limited (for
sufficiently high leverage there is a constant probability,
which is invariant with greater leverage and is less than
one, that he will lose his capital), but his (certain) return if
failure does not occur (and thus his expected return) is
unlimited as leverage increases. (That is, as leverage
increases, end-of-period capital increases without limit as
long as bankruptcy does not occur and is zero if bankruptcy does occur, See Furlong and Keeley (1987, p. 39)
for a more detailed discussion.)
Thus, even a risk-averse bank owner (willing to risk
bankruptcy in return for a sufficiently high payoff) might
prefer unlimited leverage. A similar result applies to asset
risk. In contrast, KKS argue that risk-aversion necessarily
limits bank risk-taking. While this may be the case in the
absence of subsidized deposit insurance, it need not be
so with subsidized deposit insurance. It may be the case
that even a risk-averse bank owner-manager will try to
maximize the option value of deposit insurance. Thus, in
general it is not meaningful to analyze the effects of capital
regulation absent asset regulation as do KKS.
17.(15) also implies that, for value-maximizing banks,
more stringent capital regulation will reduce the risk exposure of the deposit insurance system as long as the
stringency of asset portfolio regulation is not reduced.
See Furlong and Keeley (1989) for a more complete
discussion.
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Economic Review / Summer 1991
@FedFRASER