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A Series of Occasional Papers in Draft Form Prepared by Members o
THE IMPACT OF MARKET, INDUSTRY, AND
INTEREST RATE RISKS ON BANK STOCK RETURNS
Elijah Brewer II and Cheng Few Lee
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The Im pact o f M a rk e t, Industry, and Interest R ate
Risks on B ank Stock Returns
Elijah Brewer III a n d C h e n g F e w Lee*
In structuring their investment portfolios, bankers choose their risk expo
sure with the expectation of earning a return commensurate with the ex
pected risk. Current Financial theory suggests that the risk sensitivity of
banks are being evaluated by financial markets, especially the market for
ba n k equity. B a n k s ’ equity values are sensitive to all of the factors that
affect the overall stock market.
For example, banks are sensitive to
changes in interest rates, inflation, economic growth, an d so forth. Banks
are also sensitive to risks specific to themselves, such as “earnings risk”
through possible defaults o n their loans and investments, changes in loan
demand, an d potential variability in growth and profitability of their n o n
portfolio operations. T h e one-period capital asset pricing mod e l ( C A P M )
developed by Sharpe (1963, 1964) a n d Lintner (1965a, 1965b) has been used
to quantify the sensitivity of firms. According to the C A P M , the required
return o n an asset equals the risk-free rate of interest plus a risk p r e m i u m
that is proportional to the asset’ “beta” coefficient— a measure of the de
s
gree of c o m o v e m e n t between the asset’ returns an d returns o n a market
s
bundle of risky assets.1 T h e specific form of this risk p r e m i u m is based o n
the assumption that optimizing risk-averse investors diversify their risks,
and require compensation only for bearing systematic, or market risk, as
measured by beta, which cannot be diversified away.
T h e C A P M assumes that systematic m o v e m e n t s in security returns are
caused by market influences, such as economic growth, interest rates, in
flation, an d so forth. It is unlikely, however, that the market portfolio
captures all of the determinants of individual returns, such as changes in the
prospects of an industry. If so, an industry factor m a y be justified. T h e
use of an industry factor controls for the nume r o u s and complex factors
that wou l d have effects o n the entire set of firms in the industry, not just
o n stocks in general. Lastly, Stone (1974) has suggested the possibility of
an “interest rate” factor in security returns, separate from that for the
market as a whole, which varies in importance a m o n g individual firms.2
♦Elijah Brewer III i Economist, Federal Reserve Bank of Chicago; and Cheng Few Lee i
s
s
Professor of Finance, University of Illinois, Urbana-Champaign. The authors would like to
thank Herbert Baer and George Kaufman for many ideas, helpful comments and assistance.
The views expressed herein are solely those of the authors and do not necessarily represent the
views of the Federal Reserve Bank of Chicago or the Federal Reserve System.
FRB C H IC AG O Staff Memoranda
1
Specifically, Stone hypothesizes that the returns for equities in individual
industries, such as b a n k stocks, should exhibit a strong sensitivity to interest
rate movements.
M o r e recently, there have been attempts to explain b a n k stock price re
sponse to m o v e m e n t s in interest rates in the context of nominal contracting
hypothesis (e.g. Flannery an d James (1984a) and Booth an d Officer (1985)).
Unexpected m o v e m e n t s in interest rates affect ban k stock prices because
banks typically engage in interest rate intermediation in which the interest
sensitivity of their assets differs from that of their liabilities. A s a result,
m o v e m e n t s in interest rates will affect the market value of the two sides of
banks’ balance sheets differently and affect both their net worth a n d their
stock value. T h e relation between ba n k stock returns, and market risk,
industry risk and interest rate risk is examined in this paper. T h e results
indicate that, in general, industry and interest rate risks are important in
explaining b a n k stock returns.
Section I of this paper discusses the multi-factor C A P M m odel which is
used to examine the relationship between c o m m o n stock returns an d m a r
ket risk, industry risk, a n d interest rate risk.
Section II describes the
methods a n d data used in the tests. Section III presents the results. T h e
relationship between the interest rate sensitivity measure and a balance
sheet measure of ba n k maturity mismatch is reported in Section IV. T h e
last Section contains a brief s u m m a r y of the results.
I. The Theory
According to the one-factor C A P M developed by Sharpe and Lintner, in
equilibrium, the rate of return an investor expects to realize from any risky
asset j E (R f , is related to the excess expected return on the market port
,
)
folio, \_E{Rm — / y], by equation (1)
)
f
[ E ( R J - Rf n
E(R j) = R f + ------- ^--- —
am
[ Cov(Rr R J -]
(1)
where: R f is the risk-free rate for borrowing and lending3; oJ„ is the variance
of the return on the market portfolio; an d C o v ( R h R m) is the covariance of
the return o n asset j with the return on the market portfolio. Alternatively,
equation (1) can be defined as in equation (2)
E(R j) = Rf + p jlE (R m) - R f i
FRB C H IC AG O Staff Memoranda
(2)
2
where
[ C o v { R j, R m) ]
A n empirical issue surrounding the C A P M is whether beta captures all an
asset’ nondiversifiable risk. Several empirical studies have suggested that
s
investors m a y actually require compensation for bearing industry risk in
addition to market risk.
K i n g (1966) found a significant extramarket
source of covariation which wa s attributable to product-industry class.
Farrell (1974) tested for non-industry-related extramarket factors in secu
rity returns an d found that significant groupings could be defined in terms
of growth, cyclical, stable, an d oil stocks. Farrell was able to minimize the
industry effects found by K i n g by sampling from a broad array of industrial
classifications. H e concluded that the appropriate model for describing
security returns might well include four factors; (1) a market factor, (2) an
industry factor, (3) a group factor, and (4) a firm-unique factor. In a sub
sequent study, Martin an d K l e m k o s k y (1976) found significant extramarket
covariation in c o m m o n stock returns related to the stock membership in a
growth, cyclical, stable, oil group. T h e group effects accounted for as m u c h
as 35 percent of the risk in portfolios containing ten oil stocks and as little
as 8 percent in a 10-stock portfolio of cyclical stocks. In a m o r e recent
study, Fogler, John and Tipton (1981) estimate a three-factor model for
nonflnancial firms and find that c o m m o n stock returns from groups such
as Farrell’ stable-cyclical-and-growth were related to interest rates in the
s
G o v e r n m e n t b o n d market and to corporate bonds with default risk.
Schwert (1981) found that returns on different securities in the same in
dustry are highly correlated. Davidson (1984) and Glascock and Davidson
(1985) used an industry factor along with a market factor to describe secu
rity returns.
A n u m b e r of empirical studies have related returns on b a n k stocks to in
terest rate changes (Booth and Officer (1985); Flannery and James (1984a);
and Lyn g e and Z u m w a l t (1980)). Lynge and Z u m w a l t (1980), using several
expanded versions of the market model,4 found that a large portion of
commercial b a n k equity returns is explained by interest rate indices on
corporate debt. Flannery and James (1984a), employing a version of the
market mod e l used by Lynge an d Zumwalt, found a statistically significant
relationship between bank and S & L c o m m o n stock returns and unantic
ipated changes in long-term interest rates. Booth and Officer (1985) extend
the previous two research studies by considering the effects of investors’
expectations of interest rate changes by using a Meiselman-type (1962)
error-learning mod e l of m o v e m e n t s in the term structure of interest rates.
A n error-learning approach suggests that interest rate expectations are a
function of past and present interest rate forecasting experience. A s n e w
FRB CH ICAGO Staff Memoranda
3
information is received about the errors m a d e in forecasting the current
interest rate, interest rate expectations are adjusted in keeping with the
learning process.
Booth a n d Officer results indicate that b a n k holding
c o m p a n y stock returns are sensitive to unanticipated changes in short-term
interest rates, an d that the degree of this sensitivity i , in turn, related to the
s
holding c o m p a n y ’ bank balance sheet composition.
s
If the dollar value of short-term assets exceeds the dollar value of short
term liabilities, the b a n k has a positive maturity gap.5 This m e a n s that at
the long-term end of the maturity spectrum, the value of its liabilities is
greater than its assets. A b a n k with a negative gap has a maturity structure
which is the mirror image of a b a n k with a positive gap. A ba n k with a
positive maturity gap is exposed to an unanticipated decline in market in
terest rates, while a b a n k with a negative maturity gap is exposed to an
unanticipated rise in market interest rates. L o w e r than anticipated interest
rates m e a n s lower profits for a b a n k with a positive maturity gap because
the b a n k will be repricing its assets at lower interest rates without paying
a lower cost for its funds.6’ A bank with a positive gap will experience a
7
decline in profits w h e n there is an unanticipated decline in interest rates,
while a b a n k with a negative gap (short-term assets less than short-term l
i
abilities) will experience a decline in profits w h e n there is an unanticipated
rise in interest rates.
While the effect of unanticipated interest rate changes on the profitability
of both positively and negatively gapped banks is theoretically clear, the
effect of unanticipated interest rate changes o n the equity values of banks
with positive maturity gaps is ambiguous.
T h e ambiguity exists because
interest rate changes affect share prices via the capitalization rate investors
use in calculating the present value associated with expected dividend
streams.8 Fo r banks with positive gaps, lower than anticipated interest rates
m e a n s lower profits and dividends, but since the lower income stream will
be discounted at a lower rate, the net effect on share prices can only be
determined empirically.9 A n unanticipated increase in interest rates should
cause the share prices of banks with negative maturity gaps to decline be
cause it w o u l d result in a reduced level of expected dividends, an d the
stockholders would discount the expected dividends at a higher discount
rate. In contrast, Boo t h and Officer (1985) hypothesized that b a n k equity
values m a y decrease because of higher than anticipated interest rates re
gardless of the b a n k gap position, since they ignored the effects of u n a n
ticipated changes in interest rates o n investors’ capitalization rates.
T o assess the relation between b a n k stock returns and market, industry and
interest rate risks, the following equation is estimated
r
u
FRB C H IC A G O Staff Memoranda
= a/+
P \ jr u
+
P ij ru
+
P y ry t
+
£ j
j
()
3
4
where r t is the rate of return on the market index; r t is the rate of return
l
2
o n the banking industry stock index; r t is a measure of unanticipated
X
changes in interest rates; e is an error term in the linear regression
jt
equation. ay, Px p2 and p3 are parameters to be estimated. T h e value of
p j
j
Py indicates the relative riskiness of stock j in comparison with the market
as a whole. p2 can be interpreted to represent the industry sensitivity of
j
b a n k j stock. p3j measures the effect of unanticipated changes in interest
rates on the stock returns of b a n k j given its relation to both the market
and banking indices.
II. Data and M ethodology
T h e estimates of the parameters in equation (3) were obtained by pooling
1,642 daily time series observations for a sample of 44 b a n k holding c o m
panies between January 1, 1978 and June 30, 1984, producing a total
cross-sectional time-series sample of 72,248 observations. Equation (3) was
also estimated separately for each of the 44 bank holding companies in our
sample.
Estimation of equation (3) with pooled cross-sectional time-series data and
ordinary least-squares (OLS) is potentially inefficient due to the possibility
of firm specific differences in unsystematic risk and time varying unsys
tematic risk for all firms in the industry. Rather than m a k i n g the normal
homoskedasticity assumptions about the error term, e;„ w e exploit the n a
ture of the model. A s s u m e that the error term structure is as follows
£U
=
j=
vj
+
ut
+
wj , t
(4)
1.....44
/= 1 . . 1 4
,.,62
where v is an error c o m p o n e n t unique to each bank; utis an error c o m p o
y
nent unique to each time observation; and wj t is a term unique to the par
ticular b a n k in the particular time period.
T h e error components are
assumed to be independently distributed with m e a n zero a nd variance
c j <j, a n d a 2 > 0. T o estimate the parameters in equation (3), a version
r , x“
w
of G L S as developed by Fuller and Battese (1974) is used.1 This estimation
0
technique is designed to analyze a class of linear econometric models that
have heteroskedastic error terms which exhibit both contemporaneous cor
y.
relation (via ut ) and serial correlation (via v ) These linear econometric
models are k n o w n as error c o m p o n e n t models, wherein the regression error
is assumed to be c o m p o s e d of three components— a bank-specific c o m p o
nent, a time-specific component, and an observation-specific component.
In applying Fuller-Battese’ version of G L S rather than O L S , the existence
s
of other time- or bank-specific effects can be determined by the sample
rather than assumed, and relative weights given to between and within-bank
FRB CH ICAG O Staff Memoranda
a n d time-period variations for estimation of the parameters are determined
by the data. In O L S , it is assumed that the between a nd within-variations
are just added up.
T h e data consist of daily returns (dividends an d capital gains) for 44 b a n k
holding companies with assets over $1 billion as of year-end 1983. Seven
teen of these b a n k holding companies h a d assets over $10 billion, 12 ha d
assets between $5-10 billion an d 15 ha d assets between $1-5 billion. Daily
return data c a m e from Automatic D a t a Processing, Inc. (ADP). Techni
cally, the b a n k return data are for b a n k holding companies. F o r each of
the holding companies included, commercial banking w a s by far the major
activity of the holding c o m p a n y in terms of assets. Assets at the c o m m e r
cial banks accounted for between 81 a nd 100 percent of the parent b a n k
holding c o m p a n y assets for the 44 firms in the sample. O n the average,
commercial b a n k assets accounted for 96 percent of holding c o m p a n y as
sets, but only 63 percent of holding c o m p a n y income.1 Other b a n k holding
1
c o m p a n y activities included ownership of savings and loan associations,
mortgage banking, consumer an d commercial finance, investment advising,
various types of leasing concerns, insurance brokerage a n d underwriting,
an d data processing.
Although s o m e of the b a n k holding companies in the A D P b a n k o w n e d
m o r e than one bank, only those firms with an identifiable lead b a n k were
used in estimating equation (3), under the assumption that the lead b a n k ’
s
risk sensitivities wou l d be reflective of that for the b a n k holding company.
Only 44 of the 71 b a n k holding companies o n the A D P data tape h a d an
identifiable lead bank. Fo r the ba n k holding companies in the sample, the
lead b a n k accounted for, o n average, at least 60 percent of the total b a n k
ing assets of the holding company. However, for 39 of the 44 firms in the
sample, assets at the lead b a n k accounted for over 90 percent of the total
banking assets of the holding company.
T h e market index employed in this study w a s the value-weighted portfolio
( N Y S E a nd A M E X ) obtained from the Center for Research in Security
Prices ( C R S P ) data base.
T h e A D P data tape w a s used to construct a b a n k industry stock market
index. All 71 firms were picked to give the broadest possible sample of
b a n k holding companies. O f the 71 b a n k holding companies included in
the industry stock market index, 28 traded on the N e w Y o r k Stock E x
change a n d 43 traded o n the over-the-counter market. A list of t h e m is
provided in the appendix of this article. F or each b a n k holding company,
the aggregate market value of the stock wa s c o m p u t e d each day by multi
plying the share price by the n u m b e r of c o m m o n stock shares outstanding.
F o r days on which dividends were paid, the price was adjusted u p w a r d by
the a m o u n t of the dividend for that day.1 T h e b a n k industry stock index
2
FRB C H IC A G O Staff Memoranda
6
is c o m p u t e d by s u m m i n g the individual b a n k holding c o m p a n y market
values a n d then dividing by the value of that s u m in 1981.
Interest rates o n U.S. Treasury obligations are used to ensure that the esti
mation of the relation between b a n k stock returns and unanticipated
changes in interest rates is free from “contamination” resulting from
changes in default premia. Three-month Treasury bills are used as the
representative Treasury debt instrument because they are also pure discount
instruments (that i , they bear n o coupons).
s
T w o alternative measures of unanticipated changes in interest rates were
used in estimating equation (3). T h e first approach measures unanticipated
changes in interest rates, as in B ooth an d Officer (1985) an d Mishkin
(1982), by the difference between the actual 3-month Treasury bill rate in
time t an d the forward 3-month Treasury bill rate e m b e d d e d in the yield
curve at time t-1, ((R 3 —tF 3^ x
).tR 3 is the actual yield in time t o n a 3-month
Treasury bill a n d tF Xt_x is the forward 3-month Treasury bill rate calculated
in time t-1.1
3
T h e forward rate incorporates expectations and, in equilibrium, with no
liquidity or term premium, this rate is the market forecast of the expected
rate for period t.1 If interest rates are lower than anticipated in time period
4
0), b a n k equity values m a y increase or decrease, depending
o n whether the b a n k has a positive or negative gap, and o n h o w m u c h the
capitalization effect offset the profits effect.
A n alternative measure of unanticipated changes in interest rates w as co n
structed by computing the change in the 3-month Treasury bill rate from
the previous period, ( jR3 — ,_1 . B o o t h a n d Officer (1985) have s h o w n that
,
/^3)
experiments using this measure of unanticipated changes in interest rates
led to marginally worse fits for their regression equations, smaller interest
rate sensitivity estimates and n o appreciable differences as to the statistical
significance of any of the other coefficients in the equations. A set of esti
mates under each regression technique is presented using the change in the
3-month Treasury bill rate from the previous period as a measure of unex
pected changes in interest rates.
III. Empirical Results
T h e result of estimating equation (3) using both O L S a n d the Fuller-Battese
technique designed for cross-section time-series data for all 44 b a n k holding
companies are s h o w n in Table l.1 T h e estimated values of the parameters
5
represent their cross-sectional average values. Equation (A) under each
regression technique presents estimates using (,R3 - /F^.j) as a measure of
unexpected changes in interest rates. Equation (B) presents estimates using
FRB CH ICAG O Staff Memoranda
7
Table 1
Estimates of Bank Risk Sensitivities
3
ri.t = a + ^ i j '. + '.
J
Vf yt
/1
=
OLS
(A)
Fuller-Battese
(B )
(A)
(B )
a
0.0002
(2.718)*
0.0002
(3.897)*
h
0.5311
(80.834)*
0.5321
(80.034)*
0.5311
(66.513)*
0.5321
(65.369)*
h
0.6168
(63.707)*
0.6173
(63.745)*
0.6168
(52.420)*
0.6173
(51.966)*
h
-0.0148
(6.708)*
-0.0723
(2.942)*
-0.0148
(5.520)*
-0.0723
(2.402)**
fl2
0.1280
0.1276
S.E.E
0.0150
0.0150
N
72248
72248
72248
72248
0.0002
(2.216)**
0.0002
(3.154)*
R ^ is the coefficient of determination corrected for degrees of freedom, S.E.E. is the
standard error of estimates, N is the number of observations, and the numbers in paren
theses below the regression coefficients are the absolute values of the corresponding tratios. One star indicates that the regression coefficient is significantly different from zero
at the 1 percent level. Two stars indicate significance at the 5 percent level.
(,R3 - t_x R 3) as a measure of unexpected changes in interest rates. T h e re
sults using both regression techniques indicate that both the market index
and the banking industry index are important in explaining b a n k holding
c o m p a n y stock returns. Using the Fuller-Battese m e t h o d and equation (A),
the average b a n k holding c o m p a n y market risk and industry risk sensitiv
ities are 0.53 an d 0.62, respectively. That i , for every one percent change
s
in the market returns, b a n k returns will change 0.53 percent, while for every
one percent change in the banking industry returns, b a n k returns will
change by 0.62 percent.1
6
T h e influence of unanticipated changes in interest rates is also seen in Table
1 A n examination of the estimates in equation (A) under each regression
.
technique indicates that the coefficient of r} [ is significantly different from
FRB CH ICAGO Staff Memoranda
8
zero at the .01 level of significance. This result indicates that higher than
anticipated interest rates tends to lower ba n k holding c o m p a n y equity val
ues, while lower than anticipated interest rates tends to raise b a n k holding
c o m p a n y equity values. T h e coefficient estimates using the change in the
3-month Treasury bill rate from the previous period as a measure of u n a n
ticipated changes in interest rates are presented in equation (B) under each
regression technique. These results indicate a significant relationship be
tween this measure of unanticipated changes in interest rates and bank
stock returns. T h e similarity between the interest rate factors as well as
other coefficients in going from equation (A) to equation (B) is encouraging
for it gives us confidence that the results found here are robust to changes
in the measure describing unanticipated changes in interest rates. N o t e that
the t-ratio for unanticipated changes in interest rates in equation (A) tends
to be higher than that in equation (B), thus yielding s o m e w h a t stronger
results.
Equation (3) was estimated separately for each of the three bank holding
c o m p a n y asset classes. T h e results in Table 2 indicate that bank holding
c o m p a n y stock returns are sensitive to unanticipated changes in interest
rates, but this sensitivity varies by asset classes and interest rate measure
employed. W h e n the interest rate measure in equation (A) is employed, the
two smallest groups of bank holding companies are m o r e sensitive to u n
anticipated changes in interest rates than ban k holding companies with as
sets greater than $10 billion. O n the other hand, w h e n the interest rate
measure in equation (B) is employed, ba n k holding companies with assets
greater than $10 billion are m o r e sensitive to unanticipated changes in in
terest rates.
T w o important implications follow from the results. First, measures of
unanticipated changes in interest rates are important in explaining bank
holding c o m p a n y stock returns. Second, measures of unanticipated change
in interest rates m a y well imply different things for different asset classes
of b a n k holding companies. In particular, the stock returns of ba n k hold
ing companies with assets greater than $10 billion respond significantly
m o r e to the change in the 3-month Treasury bill rate from the previous
period than smaller bank holding companies, while the stock return of
smaller b a n k holding companies respond significantly m o r e to the differ
ence between the actual 3-month Treasury bill rate in time t and the for
wa r d 3-month Treasury bill rate e m b e d d e d in the yield curve at time t-1.
Fo r the seventeen ban k holding companies with assets greater than $10
billion, an analysis of the individual bank holding c o m p a n y regressions
from equation (B) of the three-factor model shows that six institutions
(Banker’ Trust N e w Y o r k Corporation, B a n k America Corporation,
s
Chemical N e w Y o r k Corporation, Citicorp, Manufacturers H a n o v e r C o r
poration, and J.P. M o r g a n and C o m p a n y Incorporated) appear to account
for the significant association between interest rate changes and stock re-
FRB CH ICAGO Staff Memoranda
9
Table 2
Risk Sensitivities of Bank Stocks
3
rj,t ~ ay "L
ri,t "F E
j,t
i=1
January 1978 - June 1984
a
h
R 2
h
S.E.E.
$10+ billion (17)
OLS
0.0001
(1.089)
0.7978
(81.333)*
1.0344
(71.801)*
-0.0040
(1.211)
0.2932
0.0140
(B )
0.0001
(1.395)
0.7893
(79.592)*
1.0343
(71.593)*
-0.1971
(5.374)*
0.2939
0.0140
(A)
0.0001
(1.089)
0.7978
(81.333)*
1.0344
(71.561)*
-0.0040
(1.211)
(B )
0.0001
(1.390)
0.7893
(79.593)*
1.0343
(71.593)*
-0.1971
(5.374)*
(A)
0.0000
(0.455)
0.4059
(31.931)*
0.4219
(22.525)*
-0.0207
(4.841)*
0.0734
0.0152
(B )
0.0001
(1.256)
0.4113
(31.969)*
0.4227
(22.555)*
0.0174
(0.365)
0.0723
0.0152
(A)
0.0000
(0.387)
0.4059
(27.194)*
0.4219
(19.183)*
-0.0207
(4.123)*
(B )
0.0001
(1.065)
0.4113
(27.097)*
0.4227
(19.118)*
0.0174
(0.310)
(A)
0.0003
(3.085)*
0.3291
(28.522)*
0.2996
(17.618)*
-0.0224
(5.772)*
0.0456
0.0154
(B )
0.0004
(4.056)*
0.3371
(28.864)*
0.3005
(17.661)*
0.0252
(0.582)
0.0443
0.0154
(A)
0.0003
(2.377)**
0.3291
(22.252)*
0.2996
(13.746)*
-0.0224
(4.503)*
(B )
Fuller-Battese
(A)
0.0004
(3.107)*
0.3371
(22.394)*
0.3005
(13.702)*
0.0251
(0.452)
$5 - 10 billion (12)
OLS
Fuller-Battese
$1 - 5 billion (15)
OLS
Fuller-Battese
R 2 is the coefficient of determination corrected for degrees of freedom, S.E.E. is the standard error of estimates, and the numbers in
parentheses below the regression coefficients are the absolute values of the corresponding t-ratios. One star indicates that the re
gression coefficient is significantly different from zero at the 1 percent level. Two stars indicate significance at the 5 percent level.
FRB C H IC A G O Staff Memoranda
10
turns reported in Table 2 equation (B).1 T h e results in Table 2 indicate that
7
b a n k holding companies with assets greater than $10 billion are m o r e sen
sitive to market a nd industry sources of risk than are smaller ban k holding
companies. F or these holding companies, market and industry risks are
0.79 a nd 1.03, respectively, using the Fuller-Battese technique and equation
(A). That i , for every one percent change in the market return, b a n k re
s
turns will change 0.79 percent, while for every one percent change in the
banking industry return, b a n k returns will change by 1.03 percent. T h e
results in Table 2 indicate that the equity values of the smallest of b a n k
holding companies are also sensitive to both market and industry risks.
T h e estimates of market risk a nd industry risk are 0.34 an d 0.30, respec
tively, for the smallest ban k holding companies in the sample.
T h e isolation of the statistical significance of the difference between large,
intermediate, and small banks market, industry, and interest rate sensitiv
ities is accomplished by pooling the data for the three groups an d using
“d u m m y variables” which assume the values of zero or one for each of the
three asset-size categories. T h e use of d u m m y variables is a convenient w a y
of distinguishing the response of large, intermediate, and small b a n k hold
ing companies to market, industry, and interest rate risks. In general, with
three categories only two d u m m y variables ( D u m l a nd D u m 2 ) are needed
to distinguish the categories.1 T h e following equation wa s run to test
8
whether s o m e or all of the parameters in the three-factor mod e l of equation
(3) are the s a m e for all three asset-size categories:
3
'U '
3
:+y x ru +x x Duml
1=1
1=1
3
n ,t + X
/ y
D u m l r i,t + % t
(5 )
1=1
where D u m l is a (0,1) d u m m y variable that equals 1.0 w h e n an observation
corresponds to banks with assets greater than or equal to $10 billion, zero
otherwise; D u m 2 is a (0,1) d u m m y term that equals 1.0 w h e n an observa
tion corresponds to banks with assets between $5 and $10 billion, zero
otherwise; <, i =
5y(
1,2,3) measures the risk sensitivities of the largest group
of b a n k holding companies relative to the two smallest groups; and T,y i
(
= 1,2,3) measures the risk sensitivities of the second largest group of ban k
holding companies relative to the other two groups.
/, i = 1,2,3) n o w
?y(
measures the risk sensitivities of the smallest group of ba n k holding c o m
panies.
T h e results of estimating equation (5) for version (A) of the model are
presented in Table 3. Clearly, the largest group of b a n k holding c o m p a n y
stocks exhibited significantly m o r e market and industry sensitivities than
the other two groups. T h e results for version (A) of the m o d e l indicate that
the smallest two groups of ban k holding companies are significantly m o r e
interest sensitive than are the largest group. This suggests that interest rate
FRB CH ICAG O Staff Memoranda
77
Tab le 3
T e sts of th e R e la tive Risk S e n s itiv itie s of Bank S to c k s
(O L S )
3
rj,t ~ a/'
3
3
fiij ri,t + P 'fiij ^um\ rj,t +
/1
=
/1
=
Dum2 r, t + £j t
/1
=
rjt = 0.0002 + 0.3294 ^ , + 0.2983 r2 t -0.0233 r3 t +0.4683 x Dum'i x r, t
(2.760)* (29.727)*
(1 8 .2 8 4 )*' (6.323)* ' (30.808)*
+0.7365 x Dum1 x r2 i + 0.0197 x Dum1 x rg ^+0.0763 x Dum2 x
(32.918)*
' (3.915)*
' (4.593)*
t
+0.1245 x Dum2 x r2 t + 0.0033 x Dum2 x r 3 t
(5.088)*
' (0.602)
R 2 = 0.1546
N = 72248
S.E.E. = 0.0148
Dum1 = 1 if bank has assets greater than or equal to $10 billion
= 0 Otherwise
Dum2 = 1 if bank has assets between $5 and $10 billion
= 0 Otherwise
R 2 is the coefficient of determination corrected for degrees of freedom, S.E.E. is the
standard error of estimates, N is the number of observations, and the numbers in paren
theses below the regression coefficients are the absolute values of the corresponding tratios. One star indicates that the regression coefficient is significantly different from zero
at the 1 percent level.
exposure of the two smallest groups of b a n k holding companies m a y have
affected their stock prices significantly over this period of time.
The bank
holding companies with greater than $10 billion in total assets appear to
be positioned in such a w a y that their equity values are relatively insulated
from interest rate risk.
T h e negative coefficient attached to the interest rate variable suggests that
higher than anticipated interest rates will cause bank holding c o m p a n y eq
uity values to decline.
This implies that over the estimation period the
dollar value of short-term assets was, o n average, less than the dollar value
of short-term liabilities for the bank holding companies in the sample or
FRB C H IC A G O Staff Memoranda
12
that these firms financed their long-term assets with relatively shorter-term
funds.
IV. Evaluating Cross-Sectional Variation in Interest Sensitivities
A s discussed above the statistically significant coefficients reported here for
the two smallest groups suggest that unanticipated changes in market in
terest rates will affect the market value of bank equity, depending u p o n a
bank's " maturity gap" or asset/liability maturity mismatch. It is possible
‘
to test whether changes in b a n k market value associated with unanticipated
changes in market interest rates are related to maturity mismatch informa
tion contained in balance sheet data. T h e following regression was run on
a cross-section of the 26 bank holding companies in the smallest grouping:
(6)
A
where j 3 is the value of the interest sensitivity coefficient of bank j esti
S/
mated from version (A) of equation (3); N E T is the dollar difference be
tween rate-sensitive assets and rate-sensitive liabilities as of M a r c h 31, 1984;
T A is total assets as of M a r c h 31, 1984: and ef is an error term in the linear
regression equation.1 T h e terms b0 and b x are parameters to be estimated.
9
Rate-sensitive assets include all assets repricing or maturing within one
year. Rate-sensitive liabilities are all liabilities scheduled to reprice or m a
ture within one year and include domestic time certificates of deposits of
$100,000 or more, all other large domestic time deposits, total deposits in
foreign offices, d e m a n d deposits, Super N O W s , and d e m a n d notes issued
to the U.S. Treasury.20 T h e value of b { measures the extent to which ba n k
gap position affects the interest sensitivity of its equity value. T h e coeffi
cient could be positive or negative.
T h e following results were obtained from estimating equation (6)
R 2 = 0.1365
where R 2 is the coefficient of determination corrected for degrees of free
dom . T h e n u m b e r of observations is 26. N u m b e r s in parentheses beneath
the regression coefficients are the absolute values of the corresponding tstatistics. O n e asterisk indicates that the regression coefficient is significant
at the 5 percent level. T h e coefficient o n the gap variable has a positive sign
and is significantly different from zero. This suggests that market-based
measures of interest rate sensitivity is related to interest rate risk exposure
implied by b a n k balance sheets. T h e results also indicate that maturity
f RB CH ICAGO Staff Memoranda
73
matching asset a nd liability maturities ( N E T = 0) will not, in general,
immunize b a n k holding c o m p a n y equity values against unanticipated
changes in market interest rates. Immunization of b a n k holding c o m p a n y
equity values against unanticipated changes in market interest rates can be
achieved by having m o r e rate-sensitive assets than rate-sensitive liabilities.
V . Conclusions
Since the early 1970s, economic risk— as reflected in uncertainty regarding
earnings, inflation, and interest rates— has been a major concern to bank
m a n a g e m e n t a nd regulators.
In their role as intermediaries, bankers con
tinually have ha d to monitor and m a n a g e
risks due to unanticipated
changes in inflation and interest rates, default, and liquidity. B a n k risk has
also been of particular importance to insuring agencies and bank regula
tors.
B a n k regulators b e c o m e concerned w h e n bank risk is increasing be
cause the adverse consequences of bank failure m a y extend well beyond the
losses to ban k capital investors. A t a m i n i m u m , noninsured depositors and
insuring agencies bear s o m e of the risk. T h e results of this article suggest
that b a n k equity values, and thus their sensitivity to risk are affected by at
least three factors.
T h e bank holding companies with assets greater than
$10 billion are m o r e sensitive to market and industry sources of risks than
smaller banking organizations. Smaller b a n k holding companies equities
exhibited the greatest interest rate sensitivity.
Evaluating
the cross-
sectional variation in these interest rate coefficients a m o n g the smaller bank
holding companies, w e found that changes in bank equity values associated
with unanticipated changes in market interest rates are significantly related
to balance sheet gap measures. This information might help b a n k regula
tors a nd managers to monitor and control interest rate risk exposure.
1 In theory, the market bundle of risky assets should include bonds, real estate,
and other forms of wealth. However, empirical tests of CAPM almost always use
a broad stock market index such as the CRSP value-weighted index because reli
able market-value indices of other risky assets are not available.
2 Inclusion of interest rates as a separate factor can be justified by specifying an
intertemporal capital asset pricing model, where the investment opportunity set
is permitted to vary and the level of interest rate describes changes in the oppor
tunity set (see Merton (1973)).
3 The risk-free rate is for a security that is free of default and interest rate risks.
4 The market-line theory is a by-product of Harry Markowitz’s (1959) pioneering
work in portfolio theory and James Tobin's (1958) subsequent extension of the
pricing of capital assets under uncertainty. See Sharpe (1964) and Lintner (1965a,
1965b).
FRB CH ICAGO Staff Memoranda
14
5 Ideally, an interest rate exposure measure should reflect the relative duration
of assets and liabilities. Duration is a measure of the average life of a security.
In its simplest form, duration is computed by (1) multiplying the length of time
to each scheduled payment of a default and option-free security by the present
value of that payment, (2) summing over all payments, and (3) dividing by the
total present value (or price) of the security. For a discussion of duration see
Bierwag and Kaufman (1985), Kaufman (1984) and Bierwag, Kaufman, and
Toevs (1983). In general, duration gap provides a more accurate and useful
measure of a financial institution's interest sensitivity than the maturity gap.
However, the lack of sufficiently detailed data requires the use of a relative ma
turity measure.
6 For fixed-rate loans, maturity and repricing period are the same thing. How
ever, for variable rate loans, the repricing period is the appropriate concept to
determine the wealth transfers associated with unanticipated changes in market
interest rates.
7 The term structure may contain a liquidity premium. Toevs (1983) has noted
that if such a liquidity premium exists and is positive, one would wish to be
somewhat shorter in the times to liability repricing than otherwise would be the
case. Nevertheless, conditional on the current value of the liquidity premium, the
bank asset and liability position is still one that depends on the bank's interest rate
forecast.
8 This occurs because of the use of maturity gap. On the other hand, the impact
of interest rate changes on the equity values of both positive and negative gap
banks is unequivocal using duration analysis. If the duration of a bank's assets
exceeds that of its liabilities, the bank's net worth and stock value will be affected
unfavorably by an increase in interest rates that reduces the market value of the
assets by more than that of the liabilities, and favorably by a decrease in interest
rates. Conversely, if the duration of its assets falls below that of its liabilities, the
bank’s net worth and stock value will be affected favorably by an increase in in
terest rates that reduces the market value of the assets by less than that of the li
abilities, and unfavorably by a decrease in interest rates.
9 Lower than anticipated interest rates will benefit banks with negative gap posi
tions.
assets
imply
banks
The profits of banks in this category will increase since they have long-term
and short-term liabilities. This, combined with lower discount rates will
higher stock prices. The effect of lower interest rates on positive gapped
is again ambiguous.
1 See Drummond and Gallant (1983) for a discussion of cross-sectional time0
series models.
1 The riskiness of a bank holding company common stock should be affected by
1
the diversification among bank and nonbank activity. Diversification with non
banking activities is gauged by the ratios of bank to bank holding company con
solidated assets and of bank to bank holding company consolidated income. The
more diverse the activities of the bank holding company, the lower should be the
risk assumed. Diversification reduces risk only if the earnings of the separate af
filiates are not positively correlated. In addition, bank holding companies are
restricted in the types of activities in which they are permitted to engage to those
“so closely related to banking as to be a proper incident thereto." This limits the
FRB C H IC A G O Staff M e m o r a n d a
degree of risk-reducing diversification possible. Therefore the implications of the
1/3 of other income for bank stock returns are complex.
1 This procedure is similar to that used to construct the CRSP value-weighted
2
market index. Dividends are included in the CRSP value-weigh ted market index.
1 The forward three-month Treasury bill rate embedded in the current term
3
structure of interest rates can be calculated as follows:
/ + 1*3,/ =
u
( +r*3)
1
where /+,F3 is the forward three-month Treasury bill rate embedded in the yield
^
curve at time t; ,7^ is the current yield on a six-month Treasury bill in time t; and
tRj, is the current yield in time t on a three-month Treasury bill.
14 See Hicks (1946) for a discussion of this point, pp. 135-140; pp. 146-147. Fama
(1976), in a more recent study, also makes this point.
1 The simple correlation coefficients for the three factors are (January 1978
5
through June 1984)
MM
n
r\
r1
Mr?
r2
1.0
0.74
1.0
-0.10 (0.18)
-0.08 (0.18)
1.0 (1.0)
where r, is the market index, r2 is the bank industry index, r3 is the difference be
tween the actual 3-month Treasury bill rate in time t and the forward 3-month
Treasury bill rate embedded in the yield curve at the time t-1, r3 is the change in
the 3-month Treasury bill rate from the previous period, and the numbers in pa
rentheses refer to the simple correlation coefficients when r3 is used as a measure
of unexpected changes in interest rates.
Because these factors exhibit a significant degree of multicollinearity, several
studies (see Lloyd and Shick (1977); Lynge and Zumwalt (1980); Flannery and
James (1984a); Booth and Officer (1985)) have used orthogonalizing procedures
to remove this multicollinearity. The procedures used were equivalent to using
only the residuals from a regression of the return on the second factor against the
other explanatory variable or variables. Such orthogonalization procedures are
equivalent to a transformation which extracts away the common dependence be
tween the variables, assigning such dependence to the explanatory variables in
each orthogonalizing regression equation. This procedure will change the OLS
estimators and their standard errors on the variables which are orthogonalized,
but it does not add any additional explanatory power. For example, if the true
equation is
rji ~ <*j + P \ f \ j + Pljr2J + s
jJ
but
rj j - °y + k \f \ t + 1*2/2j + E j
j
is estimated. Where
FRB C H IC A G O Staff M e m o r a n d a
76
r2.i = r2,i -
iC ov(ru ),r2<t)IVar(rUt)2rij
It can be shown that /?ly # b{J but p2j = b2j. It also can be shown that the standard
errors will change for all but the second factor, r2 ( (see Giliberto (1985)). In all
cases reported in this article, r2 t is used as the return on the bank industry index
uncorrelated with the market index.
1 This differs from one because (1) the sample includes only 44 bank holding
6
companies and (2) the cross-sectional time-series approach is equivalent to re
gressing each bank holding company stock as though it was part of an equallyweighted portfolio containing all 44 bank holding company stocks during the
sample period. The industry portfolio includes 71 bank holding companies and
is value-weighted.
17 However, these interest rate sensitivity estimates for the seventeen $10+ billion
bank holding companies appear to be not significantly related to the balance sheet
gap measure employed in this paper. This could imply that (1) the balance sheet
measure of maturity mismatch constructed from FDIC Report of Condition data
is not appropriate in detecting bank holding company exposure to unanticipated
changes in interest rates and/or (2) changes in the 3-month Treasury bill rate from
the previous period do not provide information on the effects of unanticipated
changes in interest rates on bank holding company stock returns. Because of these
reasons and the fact Table 1 indicates that (,R3
seems to be more signif
icantly related to bank stock returns than (,R3 —,_jR3 only the former measure
),
is discussed in the remaining sections of the paper.
1 See Rao and Miller (1971), pp. 88-93, 148-152.
8
1 This procedure of estimating interest rate sensitivity for each bank holding
9
company using equation (3) and then analyzing the cross-sectional relation beA
tween /?3 and the firm’s maturity gap position introduces measurement error in
/
the dependent variable of equation (6). In addition, the errors in equation (6)
may be contemporaneously correlated and heteroskedastic. An alternative ap
proach to the one used in the text to test the maturity mismatch hypothesis would
be to utilize a one-step estimation procedure of including the NET measure in
equation (3) and estimating the system of cross-section time-series equations using
the Fuller-Battese (1974) technique.
2 Flannery and James (1984b) investigate whether or not to include demand de
0
posits, passbook accounts, cash assets and retail deposits in their maturity gap
measure. They conclude that these items are not truly short-term in nature and
thus should not be included. Demand deposits were included in the equation re
ported in this paper because they appear to be related to bank interest sensitivity.
The results that included money market deposit accounts (MMDAs) were not as
encouraging, suggesting that bank interest sensitivity is not affected by MMDAs.
FRB C H IC A G O Staff M e m o r a n d a
17
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Perspectives,
Federal
Reserve
Bank
of Chicago,
8
(January/February 1984), 16-29.
FRB C H IC A G O Staff M e m o r a n d a
18
King, Benjamin F., “Market and Industry Factors in Stock Price Behavior/'
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from
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R a te s,
C., “An Intertemporal Capital
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FRB C H IC A G O Staff M e m o r a n d a
79
Table A-1
Bank Holding Companies Used in the Bank Index
B
arnett Banks of Florida, In
c.
Trust Com
pany of G
eorgia
Baybanks In
c.
Shaw ut Corporation
m
First B
ank System In
c.
N est B
orw
ancorporation
M
arine M
idland B
anks In
c.
First Security Corporation
Old N
ational Bancorporation
First W
isconsin Corporation
U
nited Virginia B
ankshares Incorporated
United Banks of Colorado, Incorporated
Society Corporation
B
ankers Trust New York Corporation
Lincoln First Banks In
c.
D inion B
om
ankshares Corporation
Southeast Banking Corporation
Com erce Bancshares In .
m
c
Bank New York In
c.
M
idlantic Banks In
c.
M
ercantile B
ankshares Corporation
United Jersey Banks of H
ackensack
Centerre B
ancorporation
First N
ational State Bancorporation
Landm Banking Corporation of Florida
ark
B
oatm
en's Bancshares In
c.
N
orthern Trust Corporation
C
entral Bancshares South In
c.
K B
ey anks In
c.
M
erchants N
ational Corporation
H
arris Bankcorp, In
c.
Suburban Bancorporation
Union Trust Bancorp
Security Pacific Corporation
Sovran Financial Corporation
Union P
lanters Corporation
M
ichigan N
ational Corporation
N
ortheast Bancorp In
c.
State Street Boston Corporation
H
artford N
ational Corporation
CBT Corporation
N
ational B
ank of D
etroit Bancorp In
c.
First Jersey N
ational Corporation
M
anufacturers H
anover Corporation
First Em
pire State Corporation
J. P M
. organ 8 Com
pany Incorporated
Chem
ical New York Corporation
Citytrust Bancorp In
c.
Chase M
anhattan Corporation
Citicorp
Fidelcor
First Pennsylvania Corporation
N
ational City Corporation
Equim Corporation
ark
Pittsburgh N
ational Corporation
FRB C H IC A G O Staff M e m o r a n d a
20
Table A-1
Bank Holding Companies Used in the Bank Index
(continued)
M
aryland N
ational Corporation
N
orth Carolina N
ational Bank Corporation
W
achovia Corporation
Am
erican Fletcher Corporation
Continental Illin Corporation
ois
First Chicago Corporation
M
anufacturers N
ational Corporation
In ian N
d a ational Corporation
F O
irst klahom Bancorporation, In .
a
c
U Bancorp
.S.
B
ankAm
erica Corporation
W
ells Fargo & Com
pany
Crocker N
ational Corporation
City N
ational Corporation
U Trust Corporation
.S.
C
entral Bancorporation In
c.
FRB C H IC A G O Staff M e m o r a n d a
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