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ECONOMIC REVIEW
Federal Reserve Bank
of San Francisco
Summer 1983
Number 3
Opinions expressed in the Economic Review do not necessarily reflect the views of the management of
the Federal Reserve Bank of San Francisco, or of the Board of Governors of the Federal Reserve
System.
The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly by the Bank’s
Research and Public Information Department under the supervision of Michael W. Keran, Senior Vice
President. The publication is edited by Gregory J. Tong, with the assistance of Karen Rusk (editorial) and
Sarah Jai Waggoner (graphics).
For free copies of this and other Federal Reserve publications, write or phone the Public Information
Department, Federal Reserve Bank of San Francisco, P.O. Box 7702, San Francisco, California 94120.
Phone (415) 974-3234.
2
Risk and Interest Rates
L
II.
Introduction and Summary
4
Bank Capital Risk in the Post-1979 Monetary and
Regulatory Environment
7
Jack H. Beebe
.. .The evidence indicates that the post-1979 economic and regulatory environment did not
significantly increase the capital risk of banks with over $1 billion in assets.
III.
Pricing Debt Instruments: The Options Approach
19
Randall J. Pozdena and Ben Iben
.. .Although much work needs to be done to improve options pricing models, our exercises
with one model suggest that they are likely to have broad applications for financial
institutions managing their portfolios in a highly competitive and uncertain world.
IV.
Real Interest Rates, Money and Government Deficits
31
Brian M otley
.. .The principal conclusion is that.. .high real rates appear to have been more closely linked
to monetary policy—and to expectations of policy—than to fiscal policies that have
produced federal deficits.
V.
The Behavior o f Money and the Economy in 1982-83
46
John P. Judd and Rose McElhattan
.. .a good deal of the growth in Ml over 1982 and early 1983... represented an increase in the
quantity of money demanded, rather than an autonomous increase in the supply of money.
In other words, effective money growth.. .was lower than actual, or measured, money
growth during the period.
Editorial Committee:
John P. Judd, Jack H. Beebe, Randall J. Pozdena, and Michael Keeley
3
Accelerating inflation and volatile interest rates,
growing federal deficits and widespread deregulation have been among the primary influences on
financial markets and financial institutions through
the 1970s and early 1980s. The resulting risk and
uncertainty have been major concerns of policymakers, corporate managers and investors, some
of whose responses are explored by the authors in
this Review.
In the opening article, Jack Beebe poses the question of whether the turbulent post-1979 economic
and regulatory environment significantly increased
the market's perception of bank capital risk. In
particular, he cites the possible effects of rapidly
rising inflation and interest rates, the change in
October 1979 in the Federal Reserve's short-term
operating procedure for influencing money, the
imminent legislation to deregulate banks, credit
controls imposed in the period from March-July of
1980, and the prospect of chronic federal deficits.
To study the effects of these forces, Beebe compared changes in actual market measures of bank
capital risk-both for bank debt and bank equityfor the two periods before and after October 1979.
With regard to debt risk, Beebe found that the
risk premia for Moody's Baa bonds and for an
equally weighted index of fifteen bank debt issues,
both relative to Aaa corporate issues, were about the
same in the 1974-79 period. During the post-1979
period, however, the bank bonds were considered
less risky than the Baa's. On average, Beebe also
found that bank-debt risk premia did not become
more dispersed across banks of different sizes, and
concludes that "bank debt issues have not been
viewed as becoming more risky in the post-1979
period."
Using the standard deviation of equity returns
over each of the two periods as a measure of equity
risk, Beebe found that equity risk declined between
the two periods and that the decline was greatest
for the largest banks, even in comparison to the
S&P 500.
Finally, Beebe calculated the sensitivity of bank
stocks to the market price of risky assets (as measured by the S&P 500) in the two· periods to see
whether banks' ability to manage risk deteriorated
after 1979. His results indicate that the sensitivity of
bank equity retums to non-diversifiable, or marketrelated, risk declined in the post-1979 period compared to the earlier period and that the decline was
statistically significant for more than half of the
twenty banks in the $10 billion-plus size (large
bank) group. Beebe concludes that capital risk was
stable in the post-Iate-1979 period for banks of over
$1 billion in assets.
In the second article, Randall Pozdena and Ben
Iben examine a method for pricing options, and use
two examples to show how this methodology can
provide a useful perspective on investment analysis
and problems of financial policy.
Their theory views the demand for options as a
demand to construct riskless hedges-portfolios of
options plus the underlying securities whose combined values are immune to changes in interest
rates. The value of an option, i.e., what the investor
will pay for it, therefore, depends on riskless returns
elsewhere and the anticipated future behavior of the
price of the underlying security. Rather than derive
analytic expressions for options prices, the authors
used numerical techniques to simulate the prices
of options under different assumed scenarios for
interest rates.
The authors applied their methodology to options
on IO-year Treasury notes and to the valuation of
early withdrawal provisions in fixed rate deposit
instruments. The first application illustrates the
ability of simple options pricing models to approximate the actual prices of traded options.
The second application highlights the use of the
options pricing model to price more complex financial instruments. In particular, this application
shows that the regulation of early withdrawal penalties may have prevented financial institutions from
using the early withdrawal feature of their deposits
4
to compete for funds against comparable instruments
(such as T-bills) without withdrawal provisions.
Brian Motley, in the third article, tries to sort out
the differential effects of money, inflation and government deficits on real, i.e., inflation-adjusted,
interest rates in order to explain the post-1979 rise in
real rates. Economic theory and popular opinion
suggest that higher levels of federal borrowing
would be associated with increases in real rates both
because deficits have to be financed by the issue
of securities to the public and because the expansionary effect of deficit spending on national income raises the demand for money. Likewise, a
demand for money in excess of supply would put
upward pressure on interest rates. A rise in inflation, however, is commonly argued to lower real
interest rates.
Motley focused his study on short-term interest
rates and applied a partial equilibrium model to
explain the real interest rate in tenus of four independent variables: a lagged inflation rate, a measure
of the excess supply of money, a measure of the
impact of government deficit spending on credit
markets, and the ratio of actual to potential GNP.
His dependent variable was the average rate on
91-day T-bills issued in the first month of each
quarter from April 1958 to January 1982, adjusted
for inflation.
His regression results for the entire period from
the late 1950s to 1982 and for subperiods within led
him to conclude that the popular explanations of the
post-1979 rise in real rates do not find strong confirmation in the data. For example, while other
studies of inflation and real rates in the period immediately after World War II found a significant
inverse relationship, Motley's results duplicated
this finding only for the 1970s. Moreover, he notes
that even during that decade, "the effect was less
significant when one took account of changes in the
money supply and the federal deficit that took place
at the same time."
Similarly, he found no support for "any simple
direct causal link between the recent sharp increase
in the federal deficit and high real rates." In the
equation he estimated for the period of April 1970
to January 1982, the estimated coefficient on the
federal borrowing variable was not statistically
significant. Instead, his equation suggested that
money shocks and changes in the inflation rate have
been more closely related to real rates than has the
federal deficit.
Motley concludes that' 'high rates appear to have
been more closely linked to monetary policy-and
to expectations of policy-than to fiscal policies
thathave produced federal deficits." Nevertheless,
he claims that there is still a great deal to be learned
"before we fully understand the causes of the recent
explosion in real rates." In particular, econometric
analyses based on data from earlier periods cannot
incorporate the present situation in which an unprecedented (for peacetime) portion of government
outlays are financed by borrowing rather than
by taxation.
John Judd and Rose McElhattan explore the
recent behavior of money and the economy in the
last article, and present the idea of an " adjusted
MI" to measure the effective force of monetary
policy more accurately.
They use, as their starting point, the unexpectedly large drop in MI velocity in late 1982. Some
observers attributed the drop to an unstable money
demand function, but Judd and McElhattan believe
that the increase in the public's desire to hold MI
was a response to unexpectedly large drops in inflation and short-term interest rates. They argue,
therefore, that the increase in MI above the Federal
Reserve's original targets in 1982 and early 1983
did not have the stimulatory effect on aggregate
demand that the measured amount would suggest.
Instead, a better representation of effective MI
would be actual MI minus the increase in the public's demand for it, caused by the parallel decline in
inflation and short-tenu interest rates.
The authors used the San Francisco money
market model to estimate the increase in the public's
demand for money. They then compared simulations of the FRBSF reduced-form macroeconomic
model using actual Ml and the adjusted measure for
the period 1982:1 to 1983:2. Simulations of MI
velocity, real GNP and inflation using the adjusted
Ml proved more accurate than those using measured MI, which yielded large over-forecasts. Their
results imply that monetary policy was effectively
quite restrictive in 1982, becarne moderately expansionary in the first quarter of 1983, and was highly
expansionary in the second quarter.
The authors warn that because the public's adjustment to lower levels of interest rates should have
5
to hold the underlying rate of inflation to its present
level. They add that their simulation suggests that
"aggregate demand is likely to increase rapidly
enough to sustain a recovery" even with this slower
MI growth.
been complete by the end of the first quarter
of 1983, a sustained expansionary money policy
would lead "to hefty increases in spending and
GNP and ultimately threaten to increase the rate of
inflation." They therefore recommend a substantial
slowdown in MI growth over the next several years
6
Jack H. Beebe*
Since the early 1970s, economic risk-as ret1ected in uncertainty regarding real output, earnings,
int1ation, and interest rates-has been a major concern to corporate managers, investors, and policy
makers. The banking sector has been no exception.
In their role as intermediaries, bankers continually
have had to monitor and manage risks due to unanticipated changes in int1ation and interest rates,
defaults, and liquidity. Bank risk has also been of
particular importance to insuring agencies and bank
regulators.
In structuring their portfolios, bank managers
explicitly or implicitly, choose their risk exposure
(an ex ante choice) with the expectation of earning
a return commensurate with the expected risk. Current finance theory suggests that investors in debt
and equity markets do not impose a uniquely optimal level of capital risk on individual banks or on
the banking system because investors in capital
markets can manage the risk of their total wealth by
di versifying their portfolios. 1 Regulators also have
no way of determining what level of bank risk is
optimal. Thus, one cannot make judgmental statements about the level of risk observed.
However, bankers, investors, and regulators
have a keen interest in knowing whether bank capital is perceived to have become more or less risky.
For example, regulators become concerned when
bank risk is increasing because the adverse consequences of bank failures may extend well beyond
the losses to bank capital investors. At a minimum,
non-insured depositors and insuring agencies bear
some of the risk. But because of externalities associated with successive collapses in wealth or possible "runs" by non-insured depositors, the failure
of one institution may increase the risk of other
institutions. In the extreme, systematic failure can
even affect the macroeconomic performance of the
economy.
Beginning roughly in late 1979, a number of
major developments had the potential of changing
the perceived risk of bank capital. During 1979, the
int1ation rate accelerated sharply, putting upward
pressure on market interest rates. By October of that
year, the Federal Reserve had changed its monetary
operating procedures by placing greater emphasis
on controlling the quantity of money while allowing
the federal funds rate to t1uctuate over a wider range
in the short run. Coinciding with the new operating
procedure was a substantial increase in the volatility
of market interest rates. Upward pressure on the
level of interest rates also mounted with the prospect of chronic federal government deficits and
monetary restraint.
In the latter half of 1979, momentum was building in Washington for landmark legislation to
deregulate banks. By March 1980, Congress had
passed the Depository Institutions Deregulation and
Monetary Control Act, which, among other things,
called for the removal of deposit-rate ceilings at
banks~nd thrifts by 1986 and extended deposit
insurance from $40,000 to $100,000 per aCCOUnt.
From March through July of 1980, the Federal
Reserve also imposed the Credit Control Program,
which was directed largely at constraining the
growth of bank credit. These developments taken
together set the stage for what could have been
perceived as a significant change in bank risk.
The purpose of this paper is to compare actual
market measures of bank capital (debt and equity)
risk in the pre- and post-October 1979 periods. 2 The
paper examines whether or not there was a significant change in measured bank capital risk in the
post-late-1979 era of monetary and fiscal policy
uncertainty, interest-rate volatility and pending
*Yice President, Banking Studies, Federal Reserve
Bank of San Francisco. The author thanks
Tom Iben and Elaine Foppiano for their research
assistance.
7
odsJor most banks. (The decline was statistically
significant for the group of largest banks-over $10
billion in assets.) On the whole, the largest banks
reduced the risk exposures of their equities·(elasticity of returns with respect to general stock price
movements) far more than did the banks in the
smaller groups ($1-5 billion and $5-10 billion).4
This paper is divided into three sections. In Section I, the theoretical underpinnings of the various
measures of bank risk and the possible effects of the
post-1979 economic and regulatory environment on
bank risk are discussed. In Section II, the empirical
evidence is presented. In Section III, conclusions
are drawn.
deposit-rate volatility. But because of the many
factors affecting the market's perception of bank
capital risk, neither the individual influences nor the
extent to which a change in risk might have been
due to government protection or increased deposit
insurance can be determined. J
In summarizing the evidence comparing risk in
the pre- and post-late-1979 periods, the picture is
encouraging. For the latter period as a whole, there
is no evidence of a significant rise in capital risk of
banks with over $1 billion in assets. Measures of
total capital risk changed little between periods,
while the sensitivity of bank equity to overall stockmarket risk actually declined between the two peri-
I. Hypotheses of Bank Risk
In observing the capital risk of banks, it is important to distinguish between the sensitivity of bank
capital risk to overall capital risk in the stock and
bond markets (primarily a concept of ex ante risk
posturing) and the actual level of bank capital risk
observed (an ex post measure). For example, economic risk, as it impacts on earnings and interest
rates, will affect capital values in the overall stock
and bond markets. One question to be addressed is
whether banks have positioned their portfolios,
operations, and capital leverages to make their capital relatively sensitive or insensitive to such economic risks.
The single-index market model from the finance
literature postulates that capital risk sensitivity can
be represented by the equity "beta," or the measured sensitivity of the firm's (or portfolio's) equity
return with respect to the return on the market bundle of risky assets, usually proxied by the return on
a broad stock market index (originally, Sharpe,
1963). Precisely because it is measured in relation
to a broad index of risky assets, beta represents
sensitivity to commonly experienced, or non-diversifiable risk, and assets with a high beta should earn
a return premium in the capital markets (originally,
Sharpe, 1964).
The single-index model has since been extended
to various multi-index models. One extension uses
a two-index model in which the two indices are
returns on a broad index of common stocks (e.g.,
the S&P 500) and returns on an index of default-free
debt instruments (e.g., Treasury issues). The first
index represents "non-diversifiable risk," which
includes the risk associated with all factors that
affect the stock market, such as expected earnings,
interest rates, inflation, defaults, and so forth.
(Since interest rates comprise one factor affecting
the stock market, the two indices obviously are not
independent.)
Bank equity is sensitive to all of the factors that
affect the stock market, including interest rates. For
example, banks are sensitive to "earnings risk"
through possible defaults on their loans and investments, changes in loan demand, and potential variability in growth and profitability of their own (nonportfolio) operations. Bank portfolio returns also
are subject to (nominal) interest rate risk because
banks carry assets and liabilities that are usually
contracted in nominal dollars and which normally
differ in duration. s Bank equity values are serlsltlve
also to interest rate risk because the real interest rate
affects the discounting of future earnings. The qu~s
tion to be addressed is whether banks are positioned
in such a way that their capital is relatively exposed
to or insulated from the economy-wide sources of
risk that are reflected in overall stock and bond
market volatilities.
In this paper, risk sensitivity is measured in several ways: (I) by estimating the bank stock beta,
which measures sensitivity to all commonly experi8
enced non-diversifiable risk factors as they affect
the S&P 500; (2) by estimating the sensitivity of
bank stock returns to returns on I-year Treasury
bills (i.e., interest rate risk); and (3) by measuring
whether bank stocks are responsive to Treasury bill
returns beyond the sensitivity to interest rates already reflected in movements of the overall stock
market (S&P 500).
While a bank may attempt to posture its risk
sensitivity through discretionary a priori portfolio
and operational policies, the risk inherent in the
economic environment will determine how these
policies translate into ex post measures of actual
capital risk. For example, a bank could attempt to
insulate itself ex ante from risk, but if total risk in
the market were to rise, the bank's ex post capital
risk actually could increase. Thus, the analysis examines not only the elasticities (sensitivities) of the
prices of bank equities with respect to stock and
T-bill prices, but also direct measures of bank-debt
risk premia, bank equity returns, and the dispersion
ofthose returns. These measures represent actual ex
post bank risk as opposed to ex ante risk posturing.
Several forces in the post-1979 environment
might have affected the capital risk of banks: (I)
During 1979 and early 1980, there was a rapid
acceleration in the rate of inflation and in the level
of interest rates while the economy was operating
roughly at capacity. Such developments in the past
often have been followed by recessions. (2) In October 1979 the Federal Reserve changed its shortterm operating procedure for monetary policy. (3)
Beginning in late 1979, legislation (of unknown
specifics at the time) to deregulate banks was becoming increasingly imminent, and resulted in the
Depository Institutions Deregulation and Monetary
Control Act of March 1980. (4) Credit controls
were imposed during the March-July period in
1980, and their possible re~imposition must have
presented some continued threat to the efficient
operation of financial institutions. (5) Finally, the
monetary-fiscal policy dilemma caused by tax
changes and the prospect of chronic federal deficits
began to surface in 1980 and 1981.
It is very difficult to say a priori how these events
should have affected bank risk. For example, one
cannot say unequivocally whether the Federal Reserve's change in operating policy should have
diminished or increased either interest rate or real
earnings risk. From a monetarist point of view, the
short run variability of the federal funds rate and
perhaps even other interest rates, economic activity,
and real earnings might have increased, while the
risk of major fluctuations would have abated. From
a Keynesian point of view, variability of most interest rates, and perhaps real earnings, might have
increased even in the longer run.
It is difficult to predict how deregulating consumer deposit ceilings also might have affected
bank risk'" Ignoring the effect of deposit insurance
for the moment, it is likely that removing consumer
deposit ceilings might actually reduce bank risk in
the long run because the shift from non-interest to
interest payments on deposits presumably would
enable a bank to shift from quasi-fixed factors of
production-buildings and other convenience or
nonprice concessions-to highly flexible factorsinterest payments (Mingo, 1978 and Quick 1977).
While the deregulation of consumer deposit ceilings might have some effect in reducing bank risk
by affording banks a more efficient and flexible
means of attracting deposits, it might also increase
the desired risk exposure of banks by increasing the
likelihood that marginal liabilities would fall under
the umbrella of deposit insurance. As a consequence of consumer deposit-rate deregulation,
banks are freer to bid up the rates on insured deposits of up to $100,000 denomination. If marginal
bank liabilities shift from non-insured to insured
sources, the discipline imposed by lenders (i.e.,
depositors) is lessened. The deregulation of (insured) consumer deposits might then tend to increase the optimal ex ante risk exposure of a bank.
In part because there is no necessarily optimal
level of risk for bank capital and in part because the
several factors in the post-1979 environment might
have either increased or decreased bank risk to
varying degrees, any change in observed bank risk
is simply an empirical question. The author's a
priori expectation was that large banks probably
attempted to reduce the ex ante exposures (sensitivities) of their capital to interest-rate and economic
risk after the mid-1970s (Beebe, 1977).7 The actual
ex post risk to be observed in the post-1979 period
was an open question.
9
II. Evidence of Risk
Month-end closing prices of common equity
were obtained from Data Resources, Inc. (DR I) for
91 large bank holding companies and banks (henceforth referred to as "banks") ranging in total assets
(year-end 1981) from $1 billion to $121 billion. The
choice of institutions was based on the availability
of stock data that indicated frequent trading x: 52
banks had assets of $1-5 billion, 19 had assets of
$5-10 billion, and 20 had assets of$IO-121 billion.
Secondary-market month-end quoted yields were
obtained for 15 debt issues of 15 different bank
q
holding companies and banks. The institutions
associated with the 15 issues ranged in size from
$1.7 billion to $121 billion, with 8 in the $1-5 billion
group, 2 in the $5-10 billion group, and 5 in the
$10+ billion group.
In the following analysis, evidence on bank debt
and equity ex post capital risk is presented first
(Charts I and 2 on debt and Tables I and 2 on
equity). Then the more complex regression analysis
of ex ante risk posturing follows (Tables 3-5).
However, during the post-1979 period, the bank
bonds were considered to be less risky than Baa's.
In fact, the post-1979 period shows very little increase in the average risk premium for these 15 bank
debt issues, with the exception of the Credit Control
period (March-July, 1980) and possibly a small
increase in 1982.
Chart 2 reports the cross-sectional coefficient of
variation of yields within the 15-bank-bond index.
(The coefficient of variation is the standard deviation divided by the mean. It measures the extent to
which the risk premia differ across the fifteen
banks.) Interestingly, the cross-section dispersion
of yields increased markedly immediately after
October 1979 and through the Credit Control period
when the cross-sectional dispersion reached its high
1975 level. After the Credit Control period, however, the dispersion of bank yields (risk premia) has
remained well below that of the turbulent 1974-1976
period.
Charts I and 2 taken together indicate that, since
1979, bank-debt risk premia (for these 15 large
banks) have neither risen significantly on average
nor become more dispersed across the banks, except during the period of Credit Controls. One may
conel ude, then, that these bank debt issues have not
been viewed as becoming more risky in the post1979 period.
Debt Risk
Chart I shows the risk premia for Moody's Baa
bonds and for an equally weighted index of the
fifteen bank debt issues, both relative to Aaa corporate issues. Hi Throughout most of the 1974-79
period, the bank bonds on average were considered
by the market to be about as risky as Baa bonds.
Chart 2
Chart 1
Dispersion of Bank Debt Yields
About Their Monthly Means
Bank/ Aaa and Baa/ Aaa Debt Risk Premia
.30
.25
.20
.15
.10
nr"
.V,J
.001----------0.5 ............._ ......_ ............._ .............O&-......._..&..--I
1974 1975 1976 1977 1978 1979 1980 1981 1982
Monthly cross-section coefficient of variation (standard deviation divided by mean) of month-end yields for fifteen major bank
debt issues.
Aaa and Baa yields are end-of-month. Bank bond index is an
equally weighted end-of-month yield of fifteen major bank debt
issues.
10
Equity Returns
Table I shows. equity returns (excluding dividends) for the pre-and post-1979 periods. I I In the
1972-79 period, bank equity returns were very close
to those on the S&P 500, although the large-bank
grollp p!3rf0 !3drnoderatelybett!3r than the smallbank group. 12 In the post-I979 period, the group of
$1-5 billion banks performed considerably better
than theS&P 5pO, and the two groups of larger
banks, considerably poorer. But within the post1979 period, there was a distinct break in stock price
behavior, with a persistent decline in the. stock market beginning in December 1981 and continuing
throughout the sample period. The two groups of
large banks registered a decline in stock prices that
was much more severe than that of the S&P 500, an
indication that the market might have reassessed the
expected earnings of the largest banks beginning in
late 1981.
Equity Risk
The standard deviation of equity returns over a
period of time is commonly used as a measure
of equity (total) risk. Table 2 presents standard
deviations of monthly equity returns (excluding
dividends) for the bank groups for the pre- and
post-1979 periods. Between the two periods, the
standard deviation of equity returns declined for all
three groups of banks. The decline was greatest for
the group of largest banks; for this group, the standard deviation declined even in comparison to that
of the S&P 500. 13 The table indicates that the total
equity risk of the largest banks declined bothabsolutely and relatively in the post-1979 period. As
indicated by the regression results reported below,
this lower risk can be interpreted in part as the
consequence of discretionary policies taken by the
largest banks either prior to or during the post-I 979
period.
nn
Table 1
Bank Equity Returns
(Monthly Percentage Returns at Annual Rates. Excluding Dividends I)
1979:10-1982:07
1972:08-1979:09
All Banks
$1-5 billion
$5-10 billion
$10+ billion
S&P 500
-0.5%
-1.5
0.3
1.1
0.3
Full Period
1979:10-1981:11
1981:12-1982:07
2.1%
6.2
-3.4
-3.5
12.0%
14.5
6.1
10.9
6.9
-27.5%
-16.7
-29.0
-38.7
-22.0
~~-
I Monthly
percentage returns are calculated for each bank over the period. Equally-weighted cross-section average returns are calculated
for each group of banks. Geometric mean returns for the group indices are then calculated for the sample periods.
Table 2
Bank Equity Risk
(Standard Deviations of Monthly Percentage Returns at Monthly Rates I)
1972:08-1979:0_9~~~~
All Banks
$1-5 billion
$5-10 billion
billion
Standard
Deviation
8.05%
7.91
8.37
8.11
Relative to
S&P 500 2
1.71
1.68
1.78
1.72
1979:10-1982:07
Standard
Deviation
7.82%
7.81
8.23%
7.46
--Relative to
_~P 500 2 ~
1.75
1.75
1.85
1.67
I Standard
deviations of monthly percentage returns (at monthly rates) are calculated for each bank over the period. Period averages are
then calculated using equal weights for each bank in the group. Returns exclude dividends.
2The standard deviation of bank returns divided by the standard deviation of returns on the S&P 500 (excluding dividends).
11
where
Risk Posturing
The above measures of ex post debt and equity
risk are the combined consequence of risk posturing
by banks and total risk in the stock and bond markets. The risk sensitivity measures reported below,
although measured on an ex post basis, are interpreted ~as exposures to total risk, and hence the
result of ex ante risk posturing. (As noted later, one
could argue also that they are the consequences of
impliedregulatory protection.)
As described earlier, the single-index stock market model employs the equity beta as a measure of
non~diversifiable, or market-related, risk. Specifically, beta is a measure of the elasticity of equity
prices with respect to the price of the market basket
of risky assets, normally proxied by the stock market (here by the S&P 500, exclusive of dividends).I"
Because it is a measure of sensitivity to non-diversifiable risk factors, the magnitude of beta can be
interpreted as being the consequence of ex ante
discretionary policies employed to manage capital
risk.
For the individual bank, the single-index stock
market model for the full sample period with a shift
in beta at 1979: 10 is as follows:
BK t =a+f3SP t +f3(SP
xO)+e I
s
t
BK = monthly stock price percentage retum(ex-
,
c1uding dividends) for the individual bank
(closing prices for the last trading day of the
month)
SP, monthly percentage return (excluding dividends) on the S&P 500 (closing prices for
the last trading day of the month)
"excess return," excluding dividends for
the periodil1 question-i.e., in excess of
the return earned for taking on non-diversifiable risk, as measured through beta
the elasticity of bank-stock prices with ref3
spect to the S&P 500
f3, = shift in,13 at 1979:10
o
0, I dummy to estimate the shift in f3 (0 = I
for the second subperiod) 15
eI
standard error, interpreted as nonmarketrelated, or residual, risk
Equation (I) was estimated separately for each of
the 91 banks. lo The individual bank results were
then summarized in Table 3 by reporting the median
values of the parameter estimates, t-statistics and
regression statistics for (I) all 91 banks, (2) the 52
banks in the $1-5 billion size class, (3) the 19 banks
in the $5-10 billion size class, and (4) the 20 banks
in the $10+ billion size class. In addition, the percentages of significant t-statistics are reported along
with median- t-values.
(I)
Table 3
Bank Equity Risk Related to the S&P 500
(Median Values of Individual-Bank Regressions1972:08-1982:07. with Dummy Shifts at 1979:10)
D.W.
shift'
All Banks
$1-5 billion
$5-10 billion
$10+ billion
.09
16;3%)
.10
(.17;4%)
09
(.16;5%)
.04
.90
(611;100%)
.84
(5.46;100%)
.97
(6.64;100%)
1.16
.76
(2.94;91%)
.79
(2.91;92%)
.84
(3.28;95%)
.63
.13
(- .45 ;20°;")
.28
2.15
6.48
-.03
(-.11; 8%)
-.13
(- .48;16%)
-.48
24
217
6.67
32
2.14
680
.36
2.16
6.26
1
Subscripts rcfer to pre- and post-1979: 10. Figures in parentheses are median t-statistics (against the null hypotheses that the coefficients
are zero) and percentages of individual t-statistics that exceed the 5-percent cntlcal level usmg a one-tailed test (two-tailed tor
a)-t-critical
1.66 for one-tailed tests.
I Units are monthly percentage changes. nonannualized.
"Elasticity of bank-stock price with respect to the price of the S&P 500.
....
.
'Because the values reported are group medians. the reported shift coefficients do not necessanly equal the dltterences between the penod
coefficients.
12
The results for beta are quite striking. Beta was
higher for the largest banks than for the other banks
in the first subperiod. By the second period, beta
was actually lower for the largest banks than for the
smaller banks, and for the largest banks its decline
betweensubperiods .was statistically· significant.
(For the shift coefficient, the mediant-value was
-1.74 compared with a critical value of ---I .66, and
55% of the individual t-values were significant.)
This evidence is consistent with the hypothesis that
the largest banks (over $10 billion in assets) postured their portfolios to insulate their capital from
non-diversifiable, or market-related, risk.'7
The estimate of beta conveys the sensitivity of
bank-stock prices to real economic activity, interest
rates and all other "common factors" that impinge
on equity prices. The fact that such factors are
numerous, complex, and correlated-and that we
do not have a reliable structural model to sort them
out-means that we cannot identify the individual
factors that explain beta. However, we can examine
the sensitivity of bank equity capital to interest-rate
risk. Tables 4 and 5 present these results.
Theregression for sensitivity to interest rate risk
IS:
BK,
+ yTB, + y, (TB, x
D)
+ e,
(2)
where
BK,
TB,
=
a
=
y
=
y,
D
=
e,
=
=
monthly stock price percentage return
the individual.banks (closing prices for the
last trading day of the month)
monthly percent<\geretumon I-year Treasury bills for the holding period from the
first to. the. second month of the life of the
T-bill (calculated from closing yields on the
last trading day of the month)'x
average elasticity-adjusted return differential, excluding bank dividends, bet\\ieen
T-bills and bank stocks
elasticity of bank-equity prices with respect
to the price of I-year Treasury bills
shift in y at 1979: 10
0, I dummy to estimate the shift in y (D= 1
for the second subperiod)
standard error of the regression
Table 4
Bank Equity Risk Related 1-Year Treasury Bills
(Median Values of Individual-Bank Regrcssions1972:08-1982:07. with Dummy Shifts at 1979: 10)
a'
All Banks
$1-5 billion
$5-10 billion
$10+ billion
S&P 500 4
-1.64
( -1.62:44%)
1.38
( 1.36:290/.:)
1.91
( -1.70:58%)
-1.93
(-1.97;70%)
-1.11
I
2.95
( 1.84;58%)
2.18
(1.36:42%)
3.95
(2.18;74%)
3.61
(2.42;85%)
2.55
1.99
(2.40:88%)
1.95
(2.39;87%)
2.06
(2.63:89%)
1.92
(2.28;90%)
0.85
I
y shift J
R2
D.W.
tr '
.88
(-.60:12%)
.37
(-.25: 0%)
-1.58
(-1.17;32%)
--1.86
(.---1.18;25%)
1.70
.05
203
7.74
.04
2.()4
7.78
06
1.98
7.86
.05
2.10
7.63
.05
1.99
4.51
I
Subscripts refer to pre- and post-1979:IO. Figures in parentheses are median t-statistics (against the null hypotheses that the coefficients
are zero) and percentages of individual t-statistics that exceed the 5-percent critical level using a one-tailed test (two-tailed for
a)__ t-criticaJ = 1.66 for one-tailed tests.
'Units are monthJypercentage changes, nonannualized.
2ElastiCity of bank-stock prices with respect to the price of the S&P 500.
J Because the values reported are group medians, the reported shiti coefficients do not necessarily equal the differences between the period
coefficients.
4 Estimates reported are for a single regression on the index for the S&P 500, and thus are not median values.
13
Equation (2) postulates that bank stock prices are
affected by T-bill prices (i. e., the inverse of interest
rates) with a possible change in the elasticity at
October 1979. In equation (2), BK and TB are
monthly holding-period returns on bank stocks and
I-year Treasury bills, respectively. For debt instruments, holding-period returns are inversely correlated with interest rates (yields). Since stock prices
generally are inversely correlated with interest rates
(yields), we should expect stock prices to be positively correlated with returns on debt instruments
(i. e., the sign on y is expected to be positive.)
Treasury bills are used as the representative debt
instrument because they are default-free and are
pure discount instruments (that is, they bear no
coupons), and hence, have a constant duration regardless of the level of interest rates.!9
In Table 4, results from equation (2) are presented for the 91 individual banks and for the S&P
500. These results show that interest rates have a
significant effect on the equity prices of banks and
the S&P 500 in both periods. For the bank stocks,
interest rate sensitivities do not increase in the post1979 period, and tend to decrease for some of the
banks in the two larger size groups. (The R' is
surprisingly small for all regressions, however, indicating that interest rates explain only a small portion of stock-price variance.)
Interest rates ought to affect bank stock returns in
at least two ways. First, if banks make contracts
whose payment streams are fixed in nominal dollars
(e.g .. fixed-rate mortgages), then unexpected
changes in nominal rates should affect the market
value of the bank's portfolio depending upon the
extent to which interest rate risk is more or less
hedged. Second, unexpected changes in the real
interest rate should affect the present value of expected dividends attributable to taking on risk, generating information needed for lending, and providing operational services. The latter effect is similar
to that impacting on all equities, not just bank
stocks, and the extent to which only the real rate
affects equities depends on the extent to which real
corporate earnings are hedged against inflation.
In the bottom line of Table 4, it is apparent that
S&P 500 returns are sensitive to interest rates. The
sensitivities are significant in both periods, and
there is a significant downward shift in the relationship.'o The large downward shift in interest-rate risk
sensitivity for the S&P 500 between the two subperiods is perplexing. Since equity valuation ought
to be sensitive generally to changes in the real
interest rate, two possible explanations come to
mind. Either there was a structural shift in the way
the market evaluated the effect of real interest rate
changes on the present value of equities after 1979.
or the market attributed a larger proportion of nominal interest rate volatility after 1979 to changes in
the inflation premium. Although some research has
concluded that variability of inflation premia has
caused much of the variability in debt yields since
October 1979, other research disagrees. The downward shift in the S&P 500's sensitivity to interest
rates requires further study.'!
In light of the results for the S&P 500 in Table 4,
it is possible that much of the response of bank
stocks to interest rates is felt through a change in
the discount rate applied to the expected dividend
stream rather than through any specific effect of
interest rates on banks' portfolios. To test this hypothesis, the right-hand variables for returns on the
S&P 500 and I-year T-bills were entered simultaneously within a single regression:
BK ,
IX
+ ~SP, + ~/SP, x
D)
(3)
+ yTB, + Ys (TB, x D) + e,
where the variables are defined as before.
Equation (3) postulates a two-factor market
model in which bank stock prices are related not
only to "common factors" as reflected in the S&P
500 but also to an additional .. interest rate" factor
beyond that already reflected in the S&P 500. Although multi-index models often are estimated by
first orthogonalizing the right-hand variables relative to one another, this method causes an unjustifiable upward bias in the t-statistics and, therefore,
the method of ordinary least squares is used in this
paperY (As suggested by the low R' of .05 in
the bottom row of Table 4, multi-collinearity between SP and TB should not present an estimation
problem).
The results reported in Table 5 help to coflfitm the
implication that arises from comparing the bank
stock results of Table 4 with the S&P 500 results:
that the interest rate effect on bank stock pric~s is
not very different from the general effect of interest
rates on common stocks. Although y in Table 5 is
14
alone in Table 3. 23 The perplexing behavior of interest rates in the latter period generally makes it
difficult to speculate on the economic reasoning
behind the results in Table 5.
positive in both periods, it is significant only in the
second period. Moreover, its magnitude is reduced
from the estimates in Table 4, and it adds little
explanatory power over the regressions on beta
TableS
Bank Equity Risk Related to the S&P 500 and l-Year Treasury Bills
(Median Values of Individual-Bank Regressions1972:08-1982:07, with Dummy Shifts at 1979: 10)
al
All Banks
$1-5 billion
$5-10 billion
$10+ billion
-.60
(-.69;12%)
-.42
(-.46;10%)
-82
(-.77:21%)
-93
(-1.03;10%)
.90
(5.93;100%)
.82
(5.31;100%)
.88
(6.05;1()()%)
1.13
(7.62;100%)
-21
.64
(2.55;82%) (-.67;25%)
.65
-.13
(2.46;83%) (-.48;15%)
-.21
.80
(2.79;89%) (-'.85;16%)
.54
.58
(2.23;75%) (-2.02;60%)
Yo4
yl4
.65
(.53; 9%)
.31
(.22; 2%)
1.42
(85;21%)
1.23
(.95;15%)
1.39
(1.94;66%)
1.38
(1.91:69%)
1.43
(2.01:68%)
129
(1.84:55%)
R2
D.W.
(TI
.29
219
6.50
25 2.19
6.63
.10
34
2.17
658
(.06; 5'7c)
-.05
(-.03; 5'1< )
.39
2 15
6.21
Y s hift
3
.65
(.50; 9%)
1.13
(.88;12%)
-~--~--~_._-~,-""~--~
Subscripts refer to pre- and post-1979:IO. Figures in parentheses are median t-statistics and perccntages of individual t-statistics that
exceed the 5-percent critical level. (One-tailed tests for negative shift for f3 and positive shift ofy; two-tailed test for a)---t-critical = 1.66
for one-tailed tests.
1 Units are monthly percentage changes, nonannuaEzed.
2Elasticity of bank-stock prices with respect to the price of the S&P 500.
3 Because the values reported are group medians, the reported shift coefficients do not necessarily equal the differences between the period
coefficients.
4Elasticity of equity prices with repect to the price of I-year Treasury bills.
III. Summary and Conclusions
clined in the post-1979 period compared to the earlier period, and the decline was statistically significant for over half of the twenty banks in the $10+
billion size group. For the twenty largest banks, the
median beta declined from 1.16 to 0.63. This evidence suggests that investors perceived the capital
of these banks to be more insulated from common
risk factors (economy-wide interest-rate, earnings,
and bankruptcy risk) in the post-1979 period than in
the earlier period.
Although bank equities are sensitive to interest
rates, the sensitivity did not increase in the post1979 period, and declined significantly for some of
the banks in the two larger size groups. However,
the general stock market sensitivity to interest rates
declined significantly, and by a comparatively
greater amount. After taking account of the change
in general sensitivity of the stock market to interest
The evidence presented here indicates that the
post-1979 economic and regulatory environment
did not significantly increase the capital risk of
banks (and bank holding companies) with over $1
billion in assets. With the exception of the Credit
Control period (March-July 1980), the risk premium on debt capital of the fifteen institutions rose
very little above. its low level of 1977-79 and remained well below the high debt-risk premium period of 1975-76. Moreover, the standard deviations of
equity returns for the 91 institutions with assets of
$ I -121 billion were lower on average in the postlate- 1979 period than in the 1972-1979 comparative
period. For the largest institutions ($10+ billion),
the standard deviation of equity returns even declined in comparison to that of the S&P 500.
The sensitivity of bank equity to common risk
factors, as measured by the equity beta, also de15
rate volatility, as retlected in beta, the specific
sensitivity of bank stocks to interest rates was
reduced considerably, and was statistically significant only in the post-1979 period. Given the perplexing behavior of interest rates in the latter
period, it is difficult to draw finn conclusions regarding changes in the effect of interest rates on
bank stock prices.
The post-late-1979 period is regarded generally
as having been a turbulent period for intlation,
economic activity, interest rates, and banking deregulation. The evidence of stable capital risk for
banks of over $1 billion in assets (and declining
betas for the $10+ billion banks) is encouraging,
although not necessarily surprising in view of the
fact that banks with assets over $1 billion are re-
garded generally as being relatively well-insulated
from interest rate risk and the adverse consequences
of deregulation.
The result could be attributed to investor perceptions that regulators (particularly the insuring
agency) and legislators increasingly protected the
capital holders of large banks, or to discretionary
policies by the managements of these banks to reduce the risk of their capital by altering their portfolios, operations, and capital leverages. Although
one cannot detennine from the data whether the
relative stability of bank capital risk is due to perceived regulatory protection or discretionary policies by bankers, the author is inclined to suspect the
latter (Beebe, 1977).
FOOTNOTES
1. Because investors in capital markets can manage the
risk of their total wealth by diversifying their portfolios, the
capital markets do not dictate a unique set of preferences,
and hence an optimal level of risk, vis-a-vis any single
investment or group of investments such as bank debt or
equity.
market-equivalent yields through non-interest concessions. Deposit ceilings would lower the marginal cost of
funds for profit-maximizing banks only if the ceilings somehow also lowered the yield on all the non-bank alternatives
available to depositors (both personal and commercial)an unlikely prospect.
2. The data end in JUly 1982 simply because they were
assembled in the Fall of that year. Passage of the Garn-St
Germain Act would not have affected the data, as its passage was not anticipated piiOi to about September 1982.
Particularly in recent years, however, deposit ceilings have
pertained only to some bank liabilities, and banks clearly
have paid explicit interest at market rates in the unregulated
commercial deposit and non-deposit markets for their marginal funds. It is difficult, therefore, to argue that removing
deposit ceilings would lead banks into riskier assets, as
removing the ceilings would change only the average cost
of funds, not the marginal cost.
3. For example, it is possible that investors simply perceived banks as being more protected by government
policies in the turbulent post-1979 period and hence bank
capital values became less volatile than they otherwise
would have been.
7. In an earlier paper, the author examined the aggregate
bank portfolio over the post-WWII period in an effort to
explain how banks had employed active liability management to affect their growth and risk postures (Beebe, 1977).
A clear picture emerged that both growth and non-diversifiable risk exposure of large banks accelerated during the
1960s and early 1970s. (The average equity beta of large
banks rose from 0.5 to 1.1 between the late 1950s and early
1970s.) The author postulated that in response to the riskier
economic environment of the mid-1970s, large banks might
reduce their risk exposure. This result is borne out in the
present stUdy, as the beta for banks over $10 billion in
assets declined from 1.2 to 0.6
4. The evidence turned up what appears to have been an
increase in bank capital risk beginning in 1982. This development is not examined in the paper because the sample
period ends in July 1982. It is the subject of a subsequent
study by the author.
5. See especially Flannery (1981 and 1982) and Flannery
and James (1982 and 1983) on interest rate risk of banks.
The impetus of much of this paper comes from their work.
6. There is a longstanding, albeit unpersuasive, argument
that the removal of deposit ceilings woUld have caused
bankers to preserve earnings spreads by investing in riskier
assets. Benston (1964) calls this postUlated effect the
"profit-target" hypothesis, as opposed to the "profitmaximum," hypothesis. See Mingo (1978) for a discussion.
8. The author thanks Chris James of the University of
Oregon for providing the names of DRI banks with Wellbehaved stock price series. The list of banks in this study
differs from the samples in the various studies done by
Mark Flannery and Chris James. They restricted their sample to holding companies with identifiable lead banks. The
present study consists of holding companies and banks
It is unlikely that the profit target hypothesis had merit even
at a time when most or all of banks' liabilities were subject to
ceiling rates. Even if deposit ceilings were binding on all
bank liabilities, profit-maximizing banks would raise additional funds by bidding up the marginal cost of funds to
16
would use returns of a value-weighted index of all risky
assets, inclUding debt and real estate. Such an index does
not exist.
that are listed by Compustat and that have monthly stock
price data dating back to 1972 in the DRI database.
9. Month-end quoted yields were obtained from Moody's
Bond Record, and information on the bonds, from Moody's
Bank and Finance Manual. Reliable data were available for
only 15 bank holding companies and banks. The bonds
were issued between February 1971 and March 1974. All
had call options after 10 years at par or slightly above, and
all carried. coupons such that they initially sold approximately at par. Eleven had initial maturities of 25 years and four
had maturities of 30 years.
15. The t-statistics for {3 in the second period ({31 in Table 3)
were obtained by running the same specification, substituting (0, 1) multiplicative dummies for both of the subperiods.
This technique was used to obtain second-period t-statistics in Tables 4 and 5 also.
16. All of the regressions in the paper (Tables 3-5) were run
with and without the Credit Control period (March-July,
1980). The omission of these months made almost no
perceptible difference, and so the regressions reported in
the paper include the Credit Control period.
There is a dearth of regularly traded bank debt issues in the
secondary market. Even for these 15 issues, which
Moody's considered to be frequently traded, statistical
analysis of the monthly returns indicated that the bonds
were not always traded at month-end. Serially correlated
errors in the returns with respect to the returns on broad
bond indices implied average lags of over a week, a sign of
infrequent trading and/or data that are based on bids rather
than actual trades. For this reason, bank bond risk prernia
are reported only in graphical forrn.
17. In work reported earlier, the author argued that such a
shift might occur. (See footnote 7.)
18. TB in equation (2) is the 1-month return on anew 1-year
Treasury bill held for one month only. Month-end effective
yields (not discount yields) are from the DRI-FACS database with back data from Bank of America. The formula
used to convert yields to monthly returns at monthly rates is:
10. In Charts 1 and 2, risk premia were divided by the level
of interest rates becaUSe the change in yield (or yield differential) is directly proportional to the level of yields for any
given holding period percentage return.
1+
~~o] 11/1~1
x 100.
[ 1 + Yt+1
100
The increased variance after October 1979 in the Bank/
Aaa differential in Chart 1 maybe due to short-run discrepancies caused by infrequent trading of bank bonds during
the period of great day-to-day volatility in bond prices. Aaa
and Baa rates are for the last trading day of the rnonth.
Although reported bank bond rates are also quoted for the
last trading day of the month, statistical tests indicated
infrequent trading throughout the entire sample period, in
that yields lagged behind those of the broad indices (See
footnote 9).
19. It is known that for bonds with fixed coupons, the duration (the present-value-weighted effective maturity of all the
payments-coupons and principal) varies inversely with
the level of interest rates. This effect would alter a relationship between BK and coupon-bearing bonds, and thus
would make interpretation of y difficult. A T-bill has only a
single payment at maturity and hence its duration is always
its stated maturity, regardless of changes in the level of
rates. The duration of TB at the beginning of each monthly
holding period is a constant value of 12 months, regardless
of the level of interest rates.
11. Bank equity data are common stock prices as of closing
on the last trading day of the month. Monthly percentage
returns are calculated as percentage changes in price.
Returns exclude dividends because dividend data were not
available. Lack of dividend data seriously affects calculations of average returns (as in Table 1) but has little effect on
the measures of the variability of returns used in the regressions and reported in Tables 2-5.
20. One has to take care in interpreting the higher t-statistics and lower standard error for the S&P 500 equation
compared with the individual bank equations in Table 4.
Part of the higher significance results from the fact that the
S&P 500 index represents a diversified portfolio.
21. The perplexing behavior and interpretation of interest
rates in the post-late-1979 period has been explored by
Evans (1981) and others. His study and others do not fully
explain post-1979 interest rate behavior.
12. Differences in dividend policies are unknown to the
author. Dividend differentials could have a substantial effect relative to such a small discrepancy.
13. Because the S&P 500 is a portfolio of diversified stocks,
its standard deviation understandably is below the average
standard deviations of its component issues and of the
individual bank issues. While the absolute level of the bank
standard deviations relative to that of the S&P 500 conveys
no meaning, changes over time are meaningful.
22. There are several papers analyzing stock prices using
orthogonalization, or more generally, principal components. All are subject to the criticism of overrated significance. (For an interpretation of these methods, see Fogler,
John, and Tipton, 1981). Recently, papers by Flannery and
James (1982 and 1983) have found significant effects of
interest rates on bank stock prices. These papers use only
that portion of stock market returns orthogonal to debt
returns in an equation like that of equation (3). The measured interest rate elasticity is then the total effect (direct
and through the stock market) of the interest rate on bank
14. Given the wide variations of price returns using monthly
data, omitting dividends affects estimated betas only slightly. Returns are sometimes expressed in excess of the riskfree rate of return, a nuance that also has little effect on
empirical results. Ideally, in place of the S&P 500, one
17
stocks. Orthogonalization sidesteps the fact that SP and TB
are jointly determined in a structural model of the economy.
Besides overstating the resulting t-statistics, it ignores possible structural changes between these two important macroeconomic, endogenous variables. The significant shift
variable in the S&P 500 equation in the bottom line of Table
4 indicates structural change between interest rates and
the stock market between the two superiods.
REFERENCES
Beebe, Jack, "A Perspective on Liability Management and
Bank Risk," Federal Reserve Bank of San Francisco
Economic Review, Winter 1977, pp. 12-24.
Benston, George, "interest Payments on Demand Deposit
and Bank Investment Behavior," Journal of Political
Econorny, October 1964, pp. 431-449.
Evans, Paul, "Why Have Interest Rates Been So Volatile?,"
Federal Reserve Bank of San Francisco Economic
Review, Summer 1981, pp. 7-20.
23. The R2 values are improved very little over those reported using beta alone (Table 3). F tests on the 91 individual
bank regressions to test the significance of adding the
interest rate parameters-i.e., testing for improved regression fit for the specification in Table 5 over that in Table
3-show critical F-values (95 percent confidence) in 25 of
91 cases.
Flannery, Mark J., "Market Interest Rates and Commercial
Bank Profitability: An Empirical Investigation," Journal of Finance, December 1981, pp. 1085-1101.
~
~"Retail Bank Deposits as Quasi-Fixed Factors of Production," American Economic Review,
June 1982, pp. 527-536.
Flannery, Mark, and Christopher James, "An Analysis of
the Effect of Interest Rate Changes on Common Stock
Returns," Mimeo, 1982.
_______ ~
, "Market Evidence on the Effective Maturity
of Bank Assets and Liabilities," Mimeo, April 1983.
Fogler, H. Russell, Kose John, and James Tipton, "Three
Factors, Interest Rate Differentials, and Stock
Groups", Journal of Finance, May 1981, pp. 323-335.
Mingo, John, "The Effect of Deposit Rate Ceilings on Bank
Risk," Journal of Banking and Finance, Vol. 2, 1978,
pp.367-378.
Peltzman, Sam, "Capital Investment in Commercial Banking and Its Relationship to Portfolio Regulation," Journal of Political Economy, January/February 1970,
pp.1-26.
Quick, Perry, "Interest-Searing Demand Deposits and
Bank Portfolio Behavior: Comment," Southern Economic Journal, September 1977, pp. 399-402.
Sharpe, William, "A Simplified Model for Portfolio Analysis," Management Science, January 1963, pp.
277-293.
__________, "Capital Asset Prices: A Theory of Market
Equilibrium Under Conditions of Risk," Journal of
Finance, September 1964, pp. 425-442.
18
Randall J. Pozdena and Ben Iben*
As interest rates have become more volatile, participants in financial markets have become more
aware of the need to accommodate interest rate
uncertainty in the design of their portfolios. This
increased awareness has led to a rise in the demand
for mechanisms capable of transferring interest rate
risk between the parties to a transaction.
One of these mechanisms is the trading of options
on debt securities such as Treasury bills and Treasury notes. These instruments, traded on organized
exchanges, give the holder the option to buy or sell
a debt security at a predetennined price within a
specific time frame. As such, they help a market
participant avoid the effect of interest rate risk on
the value of his portfolio. However, the investor in
debt options must be able to determine whether the
option is "over-" or "underpriced" from his standpoint compared to the price determined by the
market.
A similar observation may be made concerning
the pricing of liability products by depository institutions. Fixed rate bank or savings and loan time
deposits, for example, traditionally offer a fixed
return over the term with significant penalties for
premature liquidation. In a period of volatile interest rates, the choice of the combination of the deposit rate and the early withdrawal penalty can
critically affect the marketability of the fixed rate
deposit instrument in comparison to a more nearly
variable rate instrument such as money market
mutual fund shares.
Thus, financial institutions, like investors in debt
securities, also face the difficulty of determining the
appropriate price of an option-in their case, the
early withdrawal option inherent in their fixed rate
deposits. There is certainly some "price" at which
a financial institution with a given set of interest rate
expectations would be willing to market a deposit
with given early withdrawal features. But many
financial institutions may not have enough confidence in their ability to translate their interest rate
forecasts into appropriate prices.
The purpose of this paper is to present the results
of some new experiments with a debt instrument
pricing methodology. The methodology is based on
options theory and recently developed pricing techniques. Its application is illustrated first by pricing
the recently approved "put" options on government securities and comparing simulated results
with market outcomes. The methodology is then
used to illustrate the applicability of options pricing
in an indirect context, namely, that of evaluating
policy regarding early withdrawal penalties on
deposit liabilities. In each case, options are invol ved and the methodology relates the" prices" of
these instruments to interest rate forecasts. The
empirical estimates presented are not intended to
apply directly to a particular options pricing problem. They are intended instead to illustrate the
sensitivity of rational debt instrument prices to
interest rate forecasts (and the features of the instruments) and the usefulness of the options perspective to both investment analysis and policy problems.
Two specific results come from our analysis.
First, in the simulation of options on Treasury
notes, the options prices obtained by the pricing
model are good approximations of the prices at
which options on Treasury notes have recently
traded. Second, our estimates of early withdrawal
option prices suggest that the combination of regulated rates and the penalty structure that existed in
the 1970s (particularly on fixed rate deposit
instruments of less than one year) may have put
depository institutions at a severe competitive disadvantage in marketing their deposit services
against other instruments in the marketplace.
*Senior Economist and Research Associate, Federal Reserve Bank of San Francisco. Our thanks
to Lloyd Dixon for research assistance early in
this project.
19
The remainder of the paper is divided into four
sections. In the first, the basic theory of options
pricing is presented. The second section expands
this discussion and focuses on the pricing of options
on debt securities. In addition, we present the methodology incorporated in our computations in this
section. The valuation methodology is tested by
pricing Treasury note options. In the third section,
the methodology is applied to the valuation of early
withdrawal penalties. The fourth section concludes
the paper with a discussion of the policy implications
and limitations of current pricing methodologies.
I. Options Theory
We often think about options in the context of
marketed options, such as those on corporate shares
traded on organized exchanges since 1973, or options on certain Treasury securities that have been
traded on selected U. S. exchanges since 1982. In its
most general foml, however, an option is simply a
contract-or stipulation within a contract-that
gives the owner of the option the right to trade in
some asset at a defined price any time on or before a
given date (the "exercise" date). From this perspective, many conventional financial agreements
contain options, and these implicit options can be
analyzed in the same fashion as explicitly traded
options.
For example, a corporate bond that is issued with
a call provision giving the corporation the right to
buy the bond back at a stipulated price, in essence,
contains an option. Specifically, it contains a call
option because it gives the owner (the corporation)
the right to acquire ("call away") an underlying
security (the bond) from the lender (who would also
be called the option writer). The price stipulated in
the bond indenture is called the exercise price.
Similarly, the ability to withdraw funds from a
deposit account gives the depositor the option to
force the borrower of the funds (the depository
institution) to buy back the deposit instrument-in
options terminology, to "put" the deposit on the
borrower. The early withdrawal feature is thus a put
option owned by the depositor.
Whether or not a particular option is traded in the
market as an independent security, it should have
value. If it is also part of a more complicated securities contract, it should influence the price of the
underlying securities contract. Indeed, options in
some sense are the fundamental building blocks of
more complex financial instruments. Thus, even a
complete instrument could be valued if it were decomposed into its constituent options, each of
which would be a simpler instrument and easier to
value.
Pricing Options
The price of an option, whether explicitly traded
as a separate security or not, depends upon expectations of future economic conditions as these affect
the value of the underlying security. In the abstract,
the prospective and contingent nature of options
would appear to make evaluation of an option extremely difficult because future conditions are
never known with certainty. Nonetheless, financial
economists have devised methods of evaluating
such contingent claims.
The analytical breakthrough in this area came in
1973 with the work of Black and Scholes. I They
reasoned that an option could be valued by inference from the value of portfolios that contained the
option. Specifically, Black and Scholes used the
idea of a riskless hedge-a portfolio consisting of
the option and its underlying security constructed to
yield the riskless return. The price that the investor
will be willing to pay for the options necessary to
construct a riskless version of such a hedge will
depend upon the riskless return available elsewhere
as well as the anticipated scenario of the stock price
movements.
Although the underlying security may take on a
wide range of values, Black and Scholes were able
to derive an analytical formula for the price of an
option on corporate stock by relying on very general
assumptions about the stochastic nature of stock
price movements, the current price of the stock, and
an assumed riskless real rate of retum." Although
the user of this formula must provide the estimates
of the variability of the stock's future price movements, the implication of the Black/Scholes work is
that the price of the option is otherwise unambiguous.
The Black/Scholes formula applies only to options on corporate stock, but the notion of inferring
options values from riskless hedges and alternative
future values of the underlying security has enabled
other researchers to apply the idea to the valuation
20
of options on debt securities as well. The application of options valuation to these instruments, however, is somewhat more complex because the value
of the underlying security is likely to move in a
complex fashion as interest rates change. In other
words, although it may be reasonable to assume that
interest rates move in a random fashion about some
trend, for example, it is not reasonable to assume
that the value of debt securities moves similarly. If
the underlying instrument is a bond, for example,
the response of the value of a new bond to movements in interest rates may be very complex depending upon the bond's features (e.g., the number
and timing of coupon payments); nevertheless, the
value of the bond is virtually known with certainty
toward the end of the bond's life.
As a result, it is difficult to derive a purely analytical debt option valuation methodology, except
for specific underlying securities.) The generalizable approaches thus tend to consist of numerical
approximation techniques.
tree of movements in interest rates can be translated
into a tree of prices for a debt instrument because its
value in any given period depends upon the path
which interest rates may take between now and
some future time period. By working backwards
from the date the instrument matures (when the
value of the bond is known with certainty), all
values of the debt corresponding to each interest
rate value on the interest rate tree can be computed.
With the tree of values of the underlying debt, the
value of the option on the debt instrument, were it to
be exercised, can be computed for each branch of
the tree as well. With this information and the basic
notion of a riskless hedge, it will be shown below
that it is possible to derive the option's appropriate
price at any branch of the tree.4 Thus, if the discrete
interest rate movement process could be shown to
approximate a continuous process in a reasonable
fashion, options on instruments with quite complex
features could be valued.
This approach to pricing options has been used by
a number of analysts,S but most notably by Rendleman and Bartter." The arithmetic of the computations is quite simple. The contribution of these
authors was in relating this simple binary interest
rate movement process to the continuous movement
that can be expected in the real world. In particular,
they showed that the "up" and "down" jump
ratios can be manipulated to incorporate various
underlying assumptions about the trends in interest
rates and the variance of their movement about that
trend.
The numerical approximation technique, therefore, yields a valuation methodology that uses inputs that are almost as simple as those required by
the original Black/Scholes formula for corporate
stocks-only forecasts of the trend and variance of
interest rates need be provided. Once the precise
features of the underlying security and its option are
imbedded in the procedure, the value of the option
under different interest rate movement scenarios
can be computed easily.7
Numerical Approximation
Numerical approximation techniques rely upon
the observation that a continuous process (such as
movements in the value of a security) can be divided
into discrete steps without losing the essential features of the process. Since there are theoretical
relationships between certain discrete statistical
processes and continuous statistical processes, the
valuation can be made to depend upon a few simple
parameters, much in the spirit ofthe original Black/
Scholes analytical approach.
An example may help to clarify this point. Let us
assume that risk-free nominal interest rates move in
equally probable discrete steps or jumps (either up
or down) and that the magnitude of the movements
up or down does not change over time. In Chart I,
for example, we show alternative paths for the interest rate over three future time periods, assuming
that a jump' 'up" always multiplies the interest rate
by a factor of 1.1 and a jump "down" by .9. This
II. Valuing Options on a Bond
other instruments. For ease of exposition, we focus
on a specific option and bond: a put option with the
same life as the underlying bond. In other words,
lives of the option and the bond are both assumed to
In this section, we will make our presentation
more specific by pricing a put option on a coupon
bond. A coupon bond is a general instrument and
procedures applicable to it are broadly applicable to
21
be T periods. Later on, we will use the methodology
to value bond options that are actually traded, in
which case the option life is shorter than the bond
maturity. We emphasize, however, that the procedure is a very general one despite the simplifying
assumption of the example. Our numerical approximation technique is a modification of the methodology of Rendleman and Bartter8 and involves a
sequence of modelling steps beginning with the
specification of the process of interest rate
movements.
To find values for Z+ and Z-, we need to make
assumptions regarding the statistical properties of
interest rate movements. If we assume that the probabilities of the two states are constant over time,
then the logarithm of Z (denoted z) can be said to
be drawn from a binomial distribution with annual
mean of
M N [Z+W + Z- (1- W) ]
and annual variance of
S2 = N[(Z+-Z')2W (I-W)]
where
N
Number of periods per year and
W = Probability of Z+
The result is important for two reasons. First of
all, for large N and for W = .5 (an assumption
employed in our work), the binomial distribution
approaches that of the lognormal. This means that
under these assumptions, the interest rate jump
process approximates a state of the world in which
the instantaneous riskless interest rate follows a
lognormal distribution. Second, if one knows M
and S one can solve for Z+ and Z-.
On a more intuitive level, M can be thought of as
a measure of the annual geometric drift9 of the mean
interest rate, while S is a measure of the dispersion
of interest rates around the mean. The drift and
dispersion parameters, a part of the option pricing
process, must be forecast by the pricer of the option.
In the empirical work that follows, we obtain simple
forecasts of the drift and dispersion of the interest
rate by econometrically estimating the historical
drift (and dispersion about that drift) of short-term
interest rates. JO We vary these parameters considerably in our analysis.
The purpose of employing an empirically derived
forecast is simply to provide a benchmark for the
various values of the mean and drift employed.
These values are by no means offered as sophisticated or definitive forecasts.
Interest Rate Pattern
We will use the following example to illustrate
the process. As in other examples discussed earlier,
we shall assume that the short term risk-free interest
rate one period in the future can take one of two
values: Z- denoting a fall in the interest rate and
Z+ denoting a rise in the interest rate. (In this paper
a plus superscript indicates an increase in a variable
and a minus superscript a decrease). The risk-free
interest rate in period t takes one of the following
values:
I = Z-I
t
t-I
1+ = Z+I
t
t-I
We assume further that the values of Z- and Z +
are constant over time, and that each year there are
only a finite number of times that interest rates can
move (N). In addition, the life of the bond is assumed to expire at the beginning of the T + I year.
In the general case, a binomial tree would generate
2TN values in the last period. However, since we
assume that the Z+ and Z- ratios remain constant
over time and that the relationship between interest
rates over time is multiplicative, we obtain the following interest rate tree which has only TN values
in the final period:
Chart 1
Interest Rate Tree
10.0"
9.0
Beginning
of Period (I)
=
2
Bond Pricing Under Uncertainty
In pricing the bond, we employ the pure expectations hypothesis under which, at any time t, the
bond should be priced so that its expected return
(over time t - I to t) is the rate earned on a defaultfree discount bond. That is, its value in period t- I
should be equal to its expected value (plus any
coupons) in period t, discounted at the risk free rate,
'9.9
,/
"'"
8.1
3
22
or
there were no possibility of variation in bond prices,
H+, would equal H~ and no options would be needed
to form a riskless hedge."
Since the joint investment is riskless, the option
should be priced to earn the riskless rate of interest.
Rendleman and Bartter have shown that this price is
where
D, is the bond price in period t
E(D\ is the expected bond price in period t
C is the annual coupon payment
N is the number of periods per year.
Since the expected bond price in the terminal
period (that is, T+l) is its face value ($100), the
bond pricing formula for period Tis:
P'··.. I
V~[(I+1,,)'iN
(H~ -
+ C/N
(l + I )I/N
As discussed earlier, the in~erest rate in period T
D = 100
can take on T possible values. Thus, there are T
possible bond prices in this period. In the preceding
periods, the expected bond price is the discounted
average of the two possible bond prices in the next
period. The bond prices can then be determined
recursively using a tree of the same form as the
interest rate tree.
Pricing the Option
Now we have all of the elements necessary for
pricing the option. As stated earlier, the basic pricing method is based upon the notion that one can
form a riskless hedge by purchasing the right combination of a bond and its option. If the price of the
bond increases or decreases, that of the option will
move in the opposite direction, offsetting the effect
of the bond price movements in the yield of the
portfolio, at least for small bond price changes. In
the case of put options, for every $1 invested in a
bond at time t - 1, the number of put options that
should be purchased is
(H~-
H7)
V~)
H~ = (D~
+ C/N)/D
+ C/N)/D
t,,~
I
t ..-
!
+It_,)'!N
Options on Treasury Notes
As a simple test of the methodology presented
above, we will use the valuation technique to price
a real world instrument. There are a number of
options on currently traded government debt securities that could be priced using this technique, but we
have chosen options on IO-year Treasury notes
being traded on the American Stock Exchange
(AMEX) because the features of these options are
most like those of the hypothetical instrument
described.
Before proceeding with the demonstration, some
differences between the Treasury note options and
our hypothetical options should be noted. First, the
options on T-notes which Amex is trading are avail-
where
H~ = (D~
H~)(l
To use this formula, we must first calculate the
value of the option (V) in each period. In doing so,
we must consider the alternatives facing the option
holder at the beginning of each period. If he exercises the option, its value is just the difference (call
it VEXER) between the exercise price and the market price of the bond. Otherwise, the option's value
is the price at which he could sell it. Since the
investor is assumed to be rational, the value of the
option to the investor will be the larger of these two
numbers.
We know that the price of the option is zero in the
last period of its life, since it cannot be exercised
after it has expired. And we know VEXER because
the price of the bond and the exercise price are
known for each period. Thus, by beginning the
option pricing process in the last period of the option's life, it is possible to use the pricing formula
above to determine the option price one period
earlier. We repeat this process until we reach period
I and obtain the initial price of the option.
T
(V7 -
=
- H~J+V;[H;- (l+I,.JiiNJ
and
V~
value of option if the price of the bond
increases,
V~ = value of option if the price of the bond
decreases,
Simply stated, this formula tells us that as the
possible variability in bond prices increases (i.e., as
D~ and D~ diverge) so does the need for a hedge. If
23
tral role, two features of these changes should each
be a major factor in determining the price of an
option: the magnitude of expected changes and
their associated uncertainty. In other words, the
higher one expects interest rates to rise during the
life of the option, and the more uncertain one is
about future interest rates, the more one would
value protection against such fluctuation and the
higher the price one would be willing to pay for the
option. Thus, one of the factors which we shall test
is the sensitivity of the price of the option on the
T-note to different interest rate scenarios. These
results will then be compared to the prices of options actually traded.
able with March, June, September, and December
exercise dates, with the option expiring the Saturday following the third Friday of the expiration
month. This differs from the hypothetical instrument discussed above in that the life of the option is
not the same as that of the bond. Second, the bond
pays interest semiannually, while the equivalent
coupon in our hypothetical model is paid continuously. Third, in the real world, costs such as brokerage and settlement fees must also be considered.
To keep the exposition as straightforward as possible, we will not attempt to incorporate all these
differences into our model. Instead, we will employ
the model as outlined in the previous section, with
the exceptions that we shall assume the life of the
option to be 3 months and, of course, give the note a
lO-year maturity instead of the arbitrary maturity
used before. Finally, there are several exercise
prices for the option offered in the AMEX instrument. These are stated as if the value of the underlying instrument were $100. For simplicity, we
employ only the exercise prices 96, 100, and 104
dollars because they are the rnajar exercise prices on
recently traded instruments.
Analysis and Results
Although we are not attempting to price particular options, the sensitivity analysis is more useful
when based on a realistic interest rate range. To
devise a forecast for interest rate movements that
simulates what the market may be using, we use a
simple time-series econometric model and extract
from it the two main parameters of the option pricing model, M and S.12 The first parameter represents the trend or drift followed by the interest rate,
while the second represents the variability ofuncertainty about the forecasted trend. The results of this
estimation process for various periods are presented
in Table I. Because T-note options were first traded
in late 1982 and we wish to value the instruments as
of December 1982, we choose the values .02 for M
and .40 for S from the table. The final parameter
needed is the initial interest rate. We use 8.53 percent because it was the interest rate on one-month
commercial paper in December 1982.
The sensitivity analysis performed uses these
parameters. We start the analysis by allowing the
forecast dispersion, S, to change while holding the
trend or drift term, M, constant. The results from
the exercise are presented in Chart 2, and are consistent with simple intuition about options pricing.
First, as expected, the option price increases as
interest-rate dispersion increases. Second, and also
as expected, the option has no value even when
there is a positive interest rate trend. The latter
indicates that even an expected rise in interest rates
would not give an option value if the rise were
known with certainty.
Next, we vary the trend term while holding the
Interest Rates and Option Prices
As we have already stated, the primary function
of an option is to protect the owner against future
interest rate fluctuations. In the case of a put option
on a T-note, for example, the owner is protected
against upward movements in interest rates. Given
that expected interest rate changes play such a cenTable 1
Estimated Interest Rate Drift and Dispersion:
Varous Periods, 1978-1983
Estimation
Period (Year. Month)
Drift (M)
Dispersion (8)
81.04 - 83.03
-10
42
81.02-83.01
80.11 - 8210
80.08 - 82.07
80.05 - 82.04
80.02 - 82,{)j
79.11 -8l.l0
79'{)8 - 81.07
79.05 - 81.04
79.02 - 81.0 I
78.11 - 80. IO
-.06
.02
.08
.41
.40
.10
16
.24
.23
.18
23
.25
34
.33
.34
29
28
.22
.20
.21
Source: see text
24
sian of such costs tends to bias th~ .
tions upward, since the net proceeus 01 e",eH':lsmg
the option would otherwise be lower by the amount
of the costs. Transactions costs are particularly
important in light of the current thinness of the
existing AMEX options market.
A second possible source of divergence is our
forecast of interest rate trend and dispersion. As the
previous section on sensitivity analysis indicates,
the option prices calculated by the model are greatly
affected by the interest rate parameters used. Thus,
if our forecast of interest rate trend and dispersion is
different from that of the market, then the option
price calculated by the model will differ from the
actual option price. In this regard, however, we
have another piece of data to corroborate the results:
the price of the underlying T-note. The simulated
note prices are within one percent of the prices of
the notes underlying the actual options traded. This
does not guarantee that our forecast parameters are
correct, but it does suggest that the model is at least
pricing the option and the note consistently.
A more subtle potential problem with the model
is that by employing the pure expectations hypothesis, it leaves no room for specifying the utility
Chart 2
Option Price/Interest Rate Dispersion with
Historic Interest Rate Trends'
Option Price ($)
10
o
0.0
0.2
0.4
0.6
Interest Rate Dispersion
0.8
*This graph assumes that the underlying instrument has a face
vaiue of $100.
dispersion tenn constant. The results, presented in
Chart 3, are again what one would expect. The price
of the option increases when the trend is toward
higher interest rates, since the likelihood of the
option being exercised profitably is higher when
interest rates are expected to rise. One should note
that even with a negative trend term, the option will
have a positive value if the dispersion term is large
enough. This means that market participants may
wish to purchase an option to protect themselves
against the possibility that interest rates may rise
when they expect rates to fall, if they were not
certain interest rates will in fact fall.
Finally, we compare the option prices estimated
by the model with those actually traded. The price
of the note and its option calculated from the model
using the forecasted interest rate parameters (i.e.,
M = .02 and S
.40) with strike prices of 96 and
100 are $2.73 and $3.88 per $100 of face value of
underlying note, respectively. The prices of options
on a similar note actually traded on AMEX on
December 21, 1982, were $.87 and $2.69, respectively. Clearly, the model produces simulations that
are within the same order of magnitude as the actual
prices of the options traded.
Some differences between actual and simulated
prices should not be surprising. For one, the model
does not incorporate transactions costs. The exclu-
Chart 3
Option Price/Interest Rate Trend
with Historic Interest Rate Dispersion*
Option Price ($)
9
8
7
6
5
4
3
2
~
Exercise Price $96
Ol.-.....I'--......_ ......._....a.._......_""-_I.-.......
-0.1
0.0
0.1
0.2
-0.2
Interest Rate Trend
25
structure of wealth. That is, the degree of riskaversion is not a parameter of the model. Although
explicit inclusion of a risk aversion parameter in
the bond pricing formulae may be desirable (and,
indeed, has been tried by other investigators), the
addition of a third parameter makes our presentation more cumbersome and is unlikely to yield
radically different results when applied to shortterm instruments. 13
In light of the imperfect means available to incorporate the factors relevant to options pricing, the
Rendleman-Bartter model, on the whole, approximates the real world reasonably well.
m. An Application to Early Withdrawal Penalties
Besides simulating the prices of traded options on
debt securities, the options pricing methodology
developed in Section II can be applied to more
general policy issues regarding debt instruments.
An example is the evaluation of early withdrawal
penalty features of fixed rate deposit instruments.
Fixed rate deposits, unlike other instruments of
the same maturity offered in the marketplace, include an early withdrawal provision that allows the
depositor to liquidate the account and obtain the par
value of the account less a pre-stipulated penalty. In
the presence of uncertainty regarding future interest
rates, the early withdrawal provision should increase the value that investors place on the underlying instrument, while the pre-payment penalty,
which exercising the provision entails, should have
a negative effect. Thus, the early withdrawal structure as well as the rate structure are important factors in pricing a deposit account in relation to other
investment opportunities.
Historically, early withdrawal penalties and deposit rates were largely determined by regulation.
Deposit rates were either regulated directly or
linked by regulation to a market rate. The latter
mechanism allowed deposit rates to reflect, at least
partly, changing market conditions. This was not
true of pre-payment penalties which were determined without any attempt to measure the effect of
the penalty structure on the marketability of fixed
rate deposit instruments. Thus, the regulation of
pre-payment penalties prevented banks from tailoring the interest rate and pre-payment features offered on their deposit accounts to investors' interest
rate risk/return preferences.
whose magnitudes are determined by the deposit
rate. The holder of such an account-one that permits early withdrawal-essentially owns the option
to "put" this "bond" on the depository institution
for an exercise price equal to the principal value of
the account less any predetermined penalty. (We
assume there is zero risk of default on the part of the
institution. )
The value of such an option derives from the
possibility of a larger than expected rise in interest
rates. That is, if the rise in interest rates makes the
yield on the fixed rate deposit less than the yields of
competing instruments, the market value of the
deposit account will fall below its par value. Since
the early withdrawal option enables the depositor to
get back the par value of his deposit, he may,
depending on the penalty associated with early
withdrawal, profit from exercising the option.
In such a context, the exercise price (X) can be
considered the deposit's principal amount (F) minus
the early withdrawal penalty (E). The value or proceeds of the exercise (VEXER) are then X D F - E - D where D is the market value of the
deposit. The price of the early withdrawal option
can then be determined using the general option
value formula described earlier.
This valuation method is applied here to hypothetical deposit accounts whose deposit rates and
early withdrawal penalties are tied to the yield on
risk-free market instruments. A comparable realworld example, of course, is the 6-month money
market certificate (MMC) introduced in 1978. Its
deposit rate is fixed for the six-month period and is
linked to the yield on newly issued Treasury bills in
the week the deposit is created. It presently has an
early withdrawal penalty of 3 months interest. We
will also include valuation of the early withdrawal
options on one-year, 2 1/2-year, and 4-year deposit
instruments in our analysis. We assume that the
Valuation Method
The option to withdraw funds from a deposit
account is a put option on a debt security. The
security is a deposit account which pays coupons
26
yields for all of these instruments are linked to
discount-type Treasury security yields of similar
maturity (an assumption that departs from reality
but makes our analysis more consistent across
instruments. )
There are three major steps involved in valuing
the early withdrawal option on such instruments.
First, since the deposit rates are linked to market
yields, it is necessary to simulate the Treasury
security yield using the (assumed) market interest
rate tree. We use the bond valuation approach described in Section II to price the relevant Treasury
security and to obtain the appropriate implicit yield.
The second step in the process is to link the
implicit yield to the deposit instrument, since we
assume that the deposit rate is linked to this yield by
regulation. We use the implicit yield to derive the
stream of "coupons" offered by the MMC account
as well as the interest penalty. In keeping with the
actual practice in the case ofMMCs, we assume that
the deposit pays simple interest only, so the
"coupon" or periodic interest payment is constant
throughout the instrument's life. Thus, the deposit
can be seen as a "bond" which pays a constant
coupon each period and returns the principal
amount at the end of its life. Finally, using this
representation of the deposit and the early withdrawal penalty, we price the early withdrawal put
option using the formulae described earlier.
Chart 4
Option Price/Interest Rate Dispersion
with Current Penalty and
Historic Interest Rate Trend*
Option Price ($)
14
12
10
8
6
4
2
Q2
OA
Q6
0.8
interest Rate Dispersion
*This graph assumes that the underlying instrument has a face
vaiue of $100.
1979 to 1981 period. We also employ a starting
interest rate of 12 percent, which is approximately
the rate that prevailed in late 1981.
Effects of Interest Rate Uncertainty
Chart 4 demonstrates the effect of interest rate
uncertainty (dispersion) on the value of the early
withdrawal option (using the assumed penalty
structure and a historic forecast of drift of .2). Only
the I-year, 2 1/2-year, and 4-year instruments are
sensitive to changes in uncertainty in a broad range
around the historic dispersion of .3. The withdrawal
feature on the 6-month instrument takes on zero
value throughout except at high uncertainty levels.
(We will see later that this is due to the very high
penalty implicit in the 6-month instrument.)
In general, however, the greater the uncertainty
about interest rate movements the greater is the
value of the early withdrawal option inherent in a
deposit-type instrument. The value of the option is
also greater, at any given level of uncertainty, for a
longer maturity deposit. Both are results that we
would expect to follow from the very nature of an
option as a hedge against an uncertain world. The
Assumed Penalty Structure
Current early withdrawal penalty policy requires,
in most cases, a sacrifice of 3 months interest on the
6-month and one-year instruments and a sacrifice of
6 months simple interest on instruments greater than
one year in maturity. Since one of the goals of the
analysis is to examine the interaction between regulated rates and early withdrawal penalties, these
penalty structures are the ones assumed in our
analysis.
Using the valuation techniques and assumptions
described above, the prices of the par-value withdrawal options inherent in our hypothetical deposit
instruments result from a variety of interest rate and
penalty environments. For reference purposes, we
employ M = .2 and S = .3. As Table I indicates,
these values are consistent with the "forecasts"
produced by our simple econometric model in the
27
of uncertainty (dispersion) at its historic level and
using the current withdrawal penalty structure, we
find that by varying the drift, the early withdrawal
option indeed increases dramatically in value as
anticipated drift increases. This is particularly true
for the instruments of longer maturity.
We can conclude that during periods of widely
anticipated (but uncertain) increases in interest rates
(such as the late 1970s), long-term deposit-type
instruments with withdrawal options should be very
attractive in comparison to their bond-market competition paying roughly comparable rates. (Recall
that the deposit rate on these instruments is linked to
the yield offered by a government debt security.)
In addition, we can surmise that if anticipated
drift is significantly negative (i.e., interest rates are
anticipated to fall sharply over the life of the instrument), the value of the early withdrawal option
rapidly approaches zero. This, too, is a common
sense consequence of the nature of the early withdrawal option. Within a declining rate scenario, the
exercise of the option prior to maturity would expose the investor to investment alternatives with
lower returns than the existing instrument. The option is thus less likely to be of value to the investor.
Even under conditions of zero anticipated drift,
the early withdrawal options on the 1-, 21/2 - and
4-year instruments have positive value in an uncertain world. For the 4-year instrument, the option's
value is approximately $2.50 for every $100 in
deposit value, representing a significant feature of
par-value deposits that should not be ignored in
pricing these instruments competitively.
more uncertain that world or the longer the investment must be in place, the more valuable the option
to liquidate becomes.
From the standpoint of the policy behavior of
financial institutions, it is obvious that, if they
could, they should pay lower rates of interest (or
find other ways of charging for the option) during
periods of high interest rate volatility, everything
else being equal. At the historic dispersion, the
2 lh-year certificate contains an option worth ap-,
proximately $1.25 per $100 of face value. The
4-year certificate contains an option worth approximately $4.75 per $100 of face value. Whether
charged" up front" or in the form of lower deposit
rates, such options represent a valuable service provided by depository institutions and should be an
important source of income and an important means
of differentiating the deposit product from other
financial instruments.
Effects of Interest Rate Drift
Chart 5 illustrates the effect of another important
interest rate forecast parameter: anticipated drift in
interest rates. The more widely held is the view that
interest rates are going to rise (i .e., the greater is the
forecast of drift), the greater is the value of an
option to liquidate (and reinvest). Holding the level
ChartS
Option Price/Interest Rate Trend
with Current Penalty and Historic Dispersion'
Option Price ($)
:: [
Effects of Early Withdrawal Penalties
Note that in all of the previous figures, the option
price of the shortest term deposit instruments reacted least (if at all) to changes in drift and dispersion. To some extent, this is to be expected. The
shorterthe intended term of the investment, the less
important the option to liquidate and reinvest in
response to changing economic conditions. However, a less obvious but major factor in the behavior
of the 6-month and I-year instruments is the prevailing penalty structure. The current penalty structure
appears to eliminate the distinction between parvalue deposit instruments and bonds for those
deposit instruments whose yields are linked to Treasury market yields. This is illustrated clearly in
10
8
6
4
2
or.:;;;...J._...L.--IL.-....L_.L...---o&_..L.--J
-0.2
0.0
0.2
0.4
0.6
Interest Rate Trend
28
withdrawal option has no value for deposits of less
than one year,
Calculations from the options model suggest that
at the conventional penalty of 3 months' interest,
the early withdrawal option has zero value for the
6-monthdeposit. In fact, the penalty must be reduced to approximately a 1/2 month's interest before
it takes on anon-zero value. This suggest that,for
our simulated interest rate uncertainty, the existing
penalty structure on the 6-month instrument prevented banks from using the pre-payment option to
differentiate their deposit account from bond-like
instruments available on the marketplace and,
therefore, to compete for funds. It also restricted the
ability ofinvestors to choose between instruments
offering a higher return and those offering prote<,>
tion against interest rate risk but with a lower return.
Obviously, our valuations depend critically upon
interest forecast assumptions and ignore transactions costs and convenience aspects of deposittype instruments and their alternatives. Nonetheless, the results do strongly suggest that under
conditions of rising interest rates and high levels of
uncertainty, the existing structure of early withdrawal penalties on short-term instruments (combined with regulated rates) has been extremely
onerous. It may have contributed to the difficulties
that depository institutions faced in the late 1970s
and early 1980s in competing effectively against
money market funds and direct investment in Treasury securities,
Chart 6
Option Pricel Penalty with
Historic Interest Rate Trend and Dispersion*
Option Price ($)
10
P **
Penalty
= -------"~~ = 0
IP
Interest Payable
-
9
8
1
4
1
2
3
4
Life of Instrument (Years)
*This graph assumes that the underlying instrument has a face
value of $100"
* *The assumption here is that the penalty for early withdrawal is
a constant fraction of the total interest payable" For example,
for a two-year instrument with a penalty of six months' interest, P/IP= IlL
Chart 6 where the valuation of the early withdrawal
option on all four instruments (at the historic drift
and dispersion) for a variety of early withdrawal
penalties expressed in terms of months of simple
interest is plotted. Even at penalties considerably
smaller than those presently enforced, the early
V. Conclusion
This paper has applied a simple option-pricing
model to two instruments: traded options on Treasury notes and fixed rate deposit instruments. The
first application illustrated the importance of interest rate forecast parameters to the valuation of
traded options. An investor (or seller) of such options can use such pricing techniques to help relate
his view of the future path of interest rates to option
prices and, thereby, to help him take positions in the
options.
The second application illustrates the usefulness
of the options perspective to setting general policies
regarding deposit-instrument pricing. Although the
option pricing exercises were based on somewhat
hypothetical instruments, they highlight the sensiti vity of proper instrument prices to the features of
the instrument and to alternative future interest rate
scenarios.
A specific implication of the simulations is that
the regulation of early withdrawal penalties prevented financial institutions from using the early
withdrawal feature of their deposits to compete for
funds. That is, they were prevented by the prohibitively high penalty structure from using the early
withdrawal option to enable them to offer a lower
return on their deposit accounts than those of comparable instruments (such as T-bills) without withdrawal provisions. Our analysis of MMC rates provided empirical evidence to support this point at
least in the case of the 6-month instrument. Despite
the fact that the regulated deposit rate was simply a
ceiling rate (that is, the institutions could offer a
29
lower rate if they desired), virtually all MMCs in
recent years have been marketed at the ceiling rate.
This suggests that under the regulated penalty structure (and the interest rate environment), the early
withdrawal option was not an attractive investment
feature.
Whatever the specific nature of financial instruments, the increased complexity of financial markets will require more sophisticated and careful
accommodation of interest rate risk. The options
perspective appears to be a useful and practical
mechanism for analyzing the effects of alternative
future interest rate paths on financial instruments
and their markets. Although much work needs to be
done to improve options pricing models, our exercises with one model suggest that they are likely to
have broad applications for financial institutions
managing their portfolios in a highly competitive
and uncertain world.
FOOTNOTES
1. Fisher Black and Myron Scholes, 'The Pricing of Options
and Corporate Liabilities," Journal of Political Economy,
May 1973, pp. 637-654.
9. It is important to emphasize the difference between arithmetic and geometric drift. Since arithmetic drift, A, is equal
to (M+S2)/2, readers must be cautious abouttheempirical
inferences drawn about the sensitivity analysis presented
in this paper. Constant arithmetic drift-the conventional
notion of "flat" interest rate evolution-is not the same as
constant geometric drift when there is some dispersion
about the drift. In this paper, the sensitivity analysis is
presented. in terms of the original parameters of the model,
namely M and S, rather than in terms of arithmetic drift to
illustrate better the sensitivity of the model to its specified
parameters.
2. More precisely, it is a function of the current price of the
underlying stock, the life of the option, the variance of the
continuously compounded annual rate of return on the
stock, the exercise price and the continuously compounded
riskless rate of return. The stochastic assumption is thatthe
continuously compounded rate of return follows a normal
distribution with constant variance. (See Black and
Scholes, op. cit.).
3. Some of the complexity of the analytical pricing approach
is revealed by the work of Michael Brennan and Eduardo
Schwartz, "Savings Bonds, Retractable Bonds and Callable Bonds," Journal of Financial Economics, August
1977, pp. 67-88.
10. The interest rate parameters are obtained from a regression of the general form
In (it/it·12) = a + u
where. it is the monthly commercial paper rate, a is a parameter, and u is an error term. The coefficient a is interpreted
as the estimated geometric drift M and the standard error of
the equation is interpreted as the dispersion parameter S.
4. This process is elaborated upon below.
5. William Sharpe appears to have been the first to suggest
the general type of numerical approximation technique presented here (albeit in the context of options on stock) in his
text Investments, (Prentice-Hall), 1978, pp. 366-371. A
useful review of numerical techniques, however, is presented in Robert Gerske. and Kuldeep Shastri, "Valuation
by Approximation: A Comparison of Alternative Option Valuation Techniques," Working Paper 13-82, University of
California, Los Angeles, August 1982.
11. This computation is conventionally referred to as the
"hedge ratio:' Instinctively, the variable H is the gain anticipated between periods t-1 and t in the holding ofthe underlying security and V is the value of the associated option.
Both V and H will depend upon the interest rate state that
actually evolves. If the difference in the gain on the underlying security. between states differs from the offsetting
movements that would occur in the option value, the proportion Of options to underlying instruments in the portfolio
must be changed accordingly.
6. Richard Rendleman, Jr. and Brit Bartter, "The Pricing of
Options on Debt Securities:' Journal of Financial and
Quantitative Analysis, March 1980, pp. 11-24.
12. See footnote 10. The values presented were estimates
using a time series dated 11/80 to 10/82.
7. See Rendleman and Bartter or Geske and Shastri, ibid.
8. The major theoretical changes are a continuous-time
discounting procedure and a slightly different time-dating
convention necessitated by the computer simulation program written by the authors. However, to assist readers in
relating this paper to the work of Rendleman and Bartter,
similar terminology and nomenclature are employed where
possible. We wish to thank Dr. Rendleman for his helpful
comments at several points in this adaptation of their work.
13. See Richard Rendleman, "Some Practical Problems in
Pricing Debt Options," Duke University, August 1982,
Mimeo.
30
Brian Motley*
In the last five years both long- and short-tenn
interest rates have reached levels not seen in U.S.
economic history since the Civil War. Yields
on long-tenn corporate bonds never exceeded 7
percent in the one hundred years before 1970 but
ratcheted steadily upward after that year, reaching
double-digit levels by 1979. Similarly, when the
yield on short-term commercial paper reached 10.9
percent in 1979, it exceeded the previous record
high which had stood since 1873.
It is generally agreed that these historically high
interest rates reflected the unusually rapid inflation
experienced during the 1970s. Economic theory and
common observation suggest that both borrowers
and lenders in loan markets are influenced by the
rate of inflation in detennining the rate of interest. If
the prices of goods and services are rising at ten
percent a year and a loan is negotiated at fifteen
percent, the true cost of the loan to the borrowerin terms of purchasing power over goods and services-and the true return received by the lender are
only five percent. Presumably, it is this inflationadjusted or real rate of interest that borrowers and
lenders negotiate. If the rate of inflation were to
decline, but all the factors detennining the real interest rate were to remain unchanged, the nominal
interest rate offered by borrowers and accepted by
lenders would also decline. For example, if the
inflation rate were to fall from ten percent to five
percent, the nominal rate of interest would decline
correspondingly from fifteen percent to ten percent.
Empirical evidence supports these theoretical
expectations. Chart I shows the nominal yield I on
9I-day Treasury bills, the rate of inflation over
three-month spans as measured by the official consumer price index, and the realized real interest rate
computed as the difference between these two
series. 2 From this chart, it is clear that in the quartercentury after 1953, variations in the nominal shortterm rate were associated closely with changes in
the rate of inflation and, thus, the real rate did not
vary much from its long-run average level of around
one percent.
However, Chart I also suggests that the close link
between inflation and short-tenn interest rates may
have broken down after 1979. Although the rate of
inflation declined in response to the Federal Reserve System's policy of slowing monetary growth
after 1979, nominal interest rates remained high.
Even after the sharp decline in rates beginning in
mid-1982, the nominal Treasury bill yield averaged
8.55 percent in December 1982. As measured by
the consumer price index, the rate of inflation during the three-month period beginning in that month
was slightly less than one-half of one percent, so
that the real yield realized by holders of these bills
was just over 8 percent. From Chart I, we can see
that a real rate of 8 percent is extremely high by
historical standards.
In this article, we consider a number of factors
which economic theory and popular opinion suggest may be important in determining short-term
real interest rates and examine whether they are
capable of explaining the recent experience of high
real rates. The principal conclusion is that, at least
over the sample period examined in this study, high
real rates appear to have been more closely linked to
monetary policy-and to expectations of policythan to fiscal policies that have produced federal
deficits.
Focus on Short-Term Rates
Throughout our study, we focus on short-term
rather than long-term interest rates for several reasons, some purely practical and others funda-
*Senior Economist, Federal Reserve Bank of San
Francisco.
31
mental. The principal practical reason arises from
the fact that in determining the nominal interest rate
on a financial asset. investors will take account of
the rate of intlation which they expect to occur over
the life of that asset. That is, the nominal rate will be
set so that the real rate which is expected to emerge
will adequately compensate investors for holding
the asset. However, because those intlation expectations are not observable, the real rate required by
investors also is not observable.
This measurement problem, in principle, affects
both short-term and long-term securities, but may
be less serious for short-term assets. Except in periods when the rate of intlation is changing rapidly,
investors should be able to predict the prices of the
goods and services they buy and sell over the next
three months quite accurately. The differences between predicted and realized rates of intlation
should therefore be quite small. By contrast, intlation forecasting over a longer time horizon is a
much more difficult undertaking. Divergences between expected and realized intlation rates in such
long-term forecasting are therefore likely to be
larger. In other words, whereas the realized, or ex
post, real rate on short-term securities should be a
reasonably good approximation of the rate which
investors required ex ante when they acquired the
securities, the same is less likely to be true for
longer-term securities. Because of this measurement problem, it is more difficult to test hypotheses
regarding the determinants of long-term real rates
than it is for those of short-term rates.
Traditionally, economists have argued that
changes in the financial side of the economy mainly
affect the real side through their effect on long-term
interest rates. The interest-sensitive components of
aggregate demand consist primarily of residential
construction and plant and equipment spending.
Since these components represent purchases of
long-lived physical assets, economists have argued
that they should respond to changes in the yield on
long-term financial assets because this return represents the appropriate opportunity cost of funds
used to purchase such assets. This argument would
imply that although hypotheses with regard to shortterm rates are easier to test, they are less important
to policy-makers than those concerned with long
rates.
In fact, however, there are good fundamental
Chart 1
Comparison of Nominal and Real Interest Rates
and Inflation (1953-1982)
A. Short Term Nominal Interest Rate
Percent
20
15
91-day Treasury Bills ~
10
5
o
1953 1955
1960
1965
1970
1975
1980 1982
B. Quarterly Inflation Rate
Percent
20
15
Consumer Price Index"
10
5
o
-5
1960
r
1965
1970
1975
1980 1982
C. Short Term Real Interest Rate
Percent
20
15
r
10
5
o
-5
- 10 .......lI..&.....................&..&...........................u..Il""L,Il..L........lI..&.&...I...............
1953 1955
1960
1965
1970
1975
1980 1982
32
reasons-in addition to the practical technical reason discussed above-justifying this article's
emphasis on short-term rates.
The first reason is that changes in short-term rates
tend to be reflected in long rates. A household or
business wishing to invest its funds for a long period
may, if it wishes, hold a sequence of short-term
securities rather than a single long-term security.
Conversely, an investor wishing to invest for a short
period may purchase a long-term security and resell
it before maturity. Hence, long-term and short-term
securities are to some extent substitutes, and as a
result, their rates of return tend to move together.'
A second reason for focusing on short-term rates
is that in recent years the share of short-term borrowing in the total of all funds raised in the nation's
capital markets has increased. Of the $85 billion
raised by private domestic non-financial borrowers
(excluding residential mortgages) in 1971, almost
70 percent represented corporate and municipal
bonds and non-residential mortgages. Ten years
later, the amount raised had risen to $225 billion but
the share of long-term financing had declined to 42
percent. Conversely, commercial paper, bankers'
acceptances and bank loans increased from 13 percent to 46 percent of the total over this ten-year
period.
A final reason for studying short-term rates is
that, in some sense, their behavior since 1979 has
been more surprising than that of long rates. The
failure of nominal long rates to decline in line with
inflation may be explained by arguing that, although the current inflation rate has declined,
investors are still worried about future inflation, so
that long-term ex ante real rates are not particularly
high by historical standards. Although this argument is difficult to test empiricalll because, as
noted earlier, long-term inflation expectations and
hence ex ante real rates are not observable, it is not
implausible. This argument cannot, however, be
applied to short-term rates because short-term inflation rates clearly have come down substantially.
When investors set an 8.55 percent rate ofreturn on
3-month Treasury bills in December 1982, it would
have required an expected inflation rate of close to 7
percent for the real rate on those bills to be at its
long-run average level. The realized inflation rate
was almost zero over the 3-month period beginning
in December 1982. It seems very unlikely that
expectations of inflation were that far off the mark.
Thus, it is virtually certain that the ex ante real rate
was exceptionally high by historical standards. This
unusual behavior requires an explanation.
What Determines the Real Interest Rate?
The real interest rate represents the return which
investors expect to earn on holdings of securities.
Each investor decides how many securities to hold
by comparing this return with that available on
alternative assets. The principal alternatives are
money, which often yields no explicit return, and
physical assets, such as business plant and equipment and residential housing, which provide a return in the form of productive services.
Although each investor chooses how to allocate
total wealth among these various assets, in the aggregate, all securities outstanding must be held.
This means that the interest rate must be such that
the entire outstanding stock of securities is willingly
held by investors. The rate of interest, therefore, is
determined by the demand to hold securities and the
available supply of securities 5
Before discussing these factors in detail, one
methodological point should be mentioned. In this
paper, the interest rate is treated as being determined by the supply of and demand for securities.
As we shall see, a variety of macroeconomic variables influence these supplies and demands. But
these variables are themselves affected by the interest rate. For example, the demand to hold securities, and hence the interest rate, is influenced by the
level of nominal GNP. But conversely, the interest
rate affects the level of nominal GNP through its
effect on the spending decisions of households and
businesses. In turn, the level of GNP influences
other macroeconomic variables, such as the government deficit, which may affect interest rates.
In a complete model of the economy, the interest
rate would be determined simultaneously with other
macroeconomic variables such as income, the government deficit, and the inflation rate. In such a
"full equilibrium" model, the level of nominal
GNP, for example, both affects and is affected by
the level of interest rates. The model used here,
however, is a "partial equilibrium" one and seeks
to explain the real interest rate in terms of other
macroeconomic variables without exploring the
33
feedback effects of changes in interest rates on those
variables.
There is ample precedent for this procedure. The
well-known IS/LM paradigm, for example, is a
complete model of the economy which determines
both the level of income and the interest rate.
Within this framework, the LM curve is essentially
a model which determines the interest rate in tem1S
of income and the IS curve describes the feedback
from the interest rate to the level of income. The
equations estimated here are analogous to the LM
eurve since the level of income is taken as one of the
determining variables. Factors influencing interest
rates via the IS curve (fiscal policy, for example) do
so through their effect on the level of income.
Within this broad framework, economists have
two ways of approaching the determination of interest rates: The liquidity-preference approach which
focuses attention on the decision between holding
securities and holding money, and the demand/or
capital approach which emphasizes the decision
between holding (or issuing) securities and holding
producti ve capital.
In the liquidity-preference approach the rate of
interest is regarded as "the reward for parting with
liquidity."" In this approach, the key characteristic
of money is that it is used to make payments so that
the demand to hold it is closely related to the level of
nominal income. But the demand for money also
depends on the opportunity cost of holding it. In
equilibrium, this opportunity cost must be such that
in the aggregate the stock of money is willingly
held. When the stock of money is willingly held,
this implies that the same is true of the stocks of
other assets.
Until recently, money was distinguished by the
fact that it yielded no explicit return, so the cost of
holding it was simply the interest rate which could
be earned on alternative non-money assets such as
securities. This meant that the interest rate on securities had to be such that the public was willing to
hold the existing stock of money. If, for example,
the level of income were to rise with no increase in
the total stock of money, individual investors would
seek to increase the level of their money-holdings
by selling securities. Since all securities must be
held in the aggregate, security prices would fall and
interest rates would rise until investors stopped try-
ing to switch out of securities into money. Conversely, if the level of income were to remain unchanged and there were an increase in the supply of
money, individual investors would tend to push
down interest rates as they sought to reduce their
money holdings and to inerease their holdings of
securities.
Although the recent deregulation of the financial
system has eroded the unique characteristic of
money as an asset which provides no explicit return,
it remains true that the yield on monetary assets
is less flexible than that on securities. As a result,
rates on securities continue to do most of the adjusting to equate the supply of money to the demand for
money.
Whereas the liquidity preference approach emphasizes the choice between holding money and
holding securities, the demandfor capital approach
emphasizes the decision between holding productive capital and holding securities, and argues that
the nominal rate of interest on securities must be
such that wealth holders are willing to hold the
existing quantities of these two types of earning
assets. If, for example, the expected return to productive capital rises, businesses and households
will wish to hold fewer (or issue more) securities in
order to hold more capital. Since all outstanding
securities must be held, this will tend to drive up
yields on securities.
Frequently, this argument is expressed in flow
rather than in stock terms, and the interest rate is
explained in terms of the supply of lendable funds
out of current saving relative to the demand for
funds to finance private capital formation and the
government's deficit. When the demand for funds
increases relative to the available supply, their
price, which is the interest rate, tends to rise.
The liquidity-preference and productive-capital
approaches to interest rates focus on different
aspects of the process of interest-rate determination. The liquidity preference approach emphasizes
substitutions between money and securities whereas the capital model stresses the ehoice between
securities and physical assets. Each approach suggests that certain variables will have predictable
effects on security prices and interest rates. The
variables most often considered by both economists
and market commentators are changes in the money
34
accept such a change. x
However, inflation also may affect the real rate
itself. In that case, a change in the rate of inflation
would result in a larger or smaller change in the
nominal rate. In fact, a number of writers on the
determinants of real interest rates have found a
significant negative relationship between the past
rate of inflation and the current real interest rate on
securities. Their finding implies that a given change
in the inflation rate leads to a smaller change in the
nominal rate.
A theoretical argument underlying this empirical
finding is that more rapid inflation leads investors to
want to hold more of their wealth in the form of
tangible capital and less in the form of financial
assets because the nominal returns on capital vary
with the price level whereas the returns on securities
and money are fixed in nominal dollars. This increased demand for capital has the effect of driving
up its price and lowering its yield. The shifting of
household savings into residences and the resulting
steep increase in house prices during the 1970s may
have been an example of this phenomenon. More
rapid inflation also lowers the real return to holding
money, because the nominal return on money is
fixed. 9 Finally, since inflation reduces the real rates
of return on both money and capital, the real interest
rate on securities must also decline if investors are
to remain willing to hold the existing stocks of
money and capital. This argument apparently was
first developed by James Tobin 'o ; hence the result
frequently is called the Tobin effect.
In the years up to 1979, inflation increased sharply; since that year, it has declined dramatically. The
Tobin effect would predict that real rates would fall
during the 1970s and rise subsequently. Thus, casual observation of the recent behavior of interest
rates would support Tobin's argument. There may,
however, be other explanations for recent interest
rate movements; and we can sort through them only
by formal econometric testing.
A prominent alternative explanation for these
interest rate movements is that increases in the federal deficit have tended to drive up real interest
rates. The sharp rise in real rates since 1980 has
coincided with the emergence of federal deficits
which are larger and apparently more long-lasting
than any in recent U.S. history. This does not, of
course, prove that the high rates have been caused
supply relative to the demand, changes in the inflation rate and changes in the govemment's deficit.
Consider first the effects of monetary changes,
better analyzed in terms of the liquidity preference
paradigm. An increase in the demand to hold money
with no change in the available supply puts upward
pressure on interest rates. To be more specific, the
amount of money investors want to hold depends
positively on recent levels of nominal income and
negatively on short-term interest rates. In a given
month, money demand may rise as a result of past or
present increases in personal income or as the delayed result of past declines in interest rates. If the
supply of money does not rise to match such an
increase in demand, the current interest rate must
rise to restore equilibrium in the money market.
Conversely, if the supply of money increases by
more than the demand, interest rates will decline.
Since the stock of money is a policy variable
determined largely by the central bank, the liquidity
preference approach implies that the central bank
can make a significant impact on the general level of
nominal interest rates. A policy-induced increase in
the stock of money will, ceteris paribus, tend to
lower interest rates.
In the short run, the stock of money also may
increase as a result of a rise in the amount of commercial bank lending. The public is willing to hold
this money for a short while with little or no change
in interest rates but will eventually seek to get rid of
these excess money holdings. 7 When they do so,
interest rates will tend to decline.
The effects of inflation and government deficits
on interest rates are better examined in terms of the
demand for capital approach since inflation affects
the nominal returns to holding productive capital
relative to those on securities, while deficits require
changes in the supply of securities.
Consider first the effect of a change in the rate of
inflation. Since wealth-owners are concerned with
the real return on their portfolios of securities, the
nominal interest rate which they require will be
equal to the real rate they demand plus the rate of
inflation they expect. Conversely, the return which
issuers of securities will pay will be equal to the real
rate they offer plus the inflation rate they expect.
Hence, if the real rate is constant, a given change in
the rate of inflation will cause an equal change in the
nominal rate since both lenders and borrowers will
35
depend on their having this effect of raising aggregate demand and hence nominal income. Because
an increase in the actual deficit must be financed by
the issue of more government securities to the public, it causes interest rates to be higher at any given
level of GNP. If income does rise, this provides a
second (logically distinct) reason for expecting interest rates to rise. 13
Conversely, the argument that only the highemployment deficit matters implies that an increase
in the actual deficit which retlects a cyclical decline
in GNP rather than a shift in fiscal policy will not
raise interest rates. This argument ignores the point
that actual deficits-however they arise-must be
financed by the issue of securities and hence cause
interest rates to be higher than they otherwise would
be. In this case, however, the upward pressure on
interest rates associated with this deficit-financing
tends to be offset by the downward pressure from
the decline in GNP. 14
The sharp increase in the federal deficit since
1979 has been widely blamed for the recent high
level of real interest rates. It is important, therefore,
for us to test rigorously the hypothesis that, if other
things remain unchanged, an increase in government borrowing causes interest rates to rise. An
obvious empirical problem in this test is that those
other things do not remain unchanged in the actual
world. In particular, the size of the deficit both
affects and is affected by the level of business activity in the economy, and this activity in turn intluences and is intluenced by interest rates.
To distinguish those effects of deficits related to
financing by the issue of securities to the public
from those due to the link between deficits and the
level of income, we include the gross national product relative to potential GNP as an additional variable in the empirical equations estimated below. In
addition, we measure government borrowing as a
proportion of potential GNP in order to adjust for
the long-run growth in the economy and, hence, in
the supply of private savings available to finance the
deficit. The coefficient on the government borrowing variable, therefore, may be interpreted as representing the effect of deficits while holding the level
of income constant.
In recent years, high interest payments on the
existing federal debt have boosted the size of the
federal deficit. In fact, the government has been
by the high deficits. Indeed, the reverse may be the
case because an important source of these deficits
has been a sharp increase in government interest
payments. 11 Nonetheless, a theoretical explanation
of why deficits will drive up interest rates is readily
available. Interest rates must rise in order to induce
the public to hold the government securities which
the Treasury issues when it runs a deficit.
Suppose, for example, the government reduces
tax rates without cutting its outlays. The Treasury
must issue securities to make up for its loss of tax
revenues. Although the tax reduction means that the
public has higher after-tax income, th~ public may
not want to loan all of these additional funds to the
Treasury. Hence, the demand for loanable funds by
the government rises by more than the supply of
funds, causing their price-the interest rate-to
rise .12 In slightly different language, the rise in the
interest rate is necessary to induce the public to hold
a larger share of its asset portfolio in the form of
government securities.
Such a tax reduction also leads to an increase in
aggregate demand for goods and services which,
through the familiar Keynesian multiplier process,
causes an increase in nominal national income. This
income effect also will tend to raise interest rates.
At higher income levels the transactions demand to
hold money is greater and if this demand for money
is not accommodated by the Federal Reserve, interest rates must rise to restore equilibrium between
the supply of and the demand for money. In addition, at higher levels of income, businesses may
become more optimistic about the likely future
return on new investment projects and hence more
willing to issue securities in order to finance such
projects. These additional claims on the nation's
capital markets drive interest rates further up. An
analogous argument may be made that an increase
in government outlays will drive up interest rates.
These last arguments frequently are summarized
by saying that interest rates are intluenced by the
high-employment deficit rather than the actual
deficit. The high-employment deficit is a measure
of the setting offiscal policy. A more expansionary
fiscal policy-represented by an increase in the
high-employment deficit-tends to raise interest
rates through its effect on current and prospective
future GNP. However, our earlier argument that
actual deficits tend to raise interest rates does not
36
borrowing in order to pay interest on its outstanding
debt. A number of economists" have argued that to
the extent that these interest payments result from
high nominal rates caused by inflation, the additional Treasury borrowing should have no effect on
real rates. Their reason is that inflation reduces the
real value of government debt outstanding and that
wealth-owners would be willing to purchase additional securities to maintain the real value of their
stocks of securities with no change in their real rate
of return.
In the empirical work reported below a crude
correction for this effect is made by simply deducting government interest payments from measured
Treasury borrowing. This deduction is too large
since not all interest payments represent inflation,
but the actual proportion of interest payments that
represent inflation-induced increases in nominal
rates cannot be measured precisely. 16
The upshot of this section is that at any given
level of GNP, there are reasons to expect real interest rates to be higher if the money supply is smaller
in comparison to demand, if the inflation rate is
lower, or if the government deficit is larger. Each of
these events has occurred since 1979. Nonetheless,
formal empirical tests are required to determine
which, if any, of these various effects we have
identified was the primary cause of high interest
rates.
matures, of course, the actual inflation rate becomes known and the investor can calculate the real
rate actually realized. The realized or ex post real
rate is written:
rep = i
P
(2)
where fP is the ex post real rate and p is the actual
rate of inflation.
The difference between the ex ante real rate demanded by investors when they set the nominal rate
and the ex post rate they actually receive is equal to
the error investors made in forecasting inflation. By
substracting equation (1) from equation (2) we find:
reP-r=pc p=u
(3)
where u is the error which investors made in their
forecast of inflation.
To test the various hypotheses advanced in the
last section concerning the determinants of the ex
ante real rate r, we must solve the problem of having
data only on the ex post rate, reP. Fortunately, the
theory of efficient markets provides a framework
for attacking this problem. IR
An efficient market is one in which participants
use all availabl.e information in determining prices.
Since the markets for short-term government securities are highly competitive, it is generally assumed
that they are efficient in this sense. Participants who
did not take advantage of all available information
would earn lower profits than, and ultimately be
driven out of business by, competitors who did.
This assumption of market efficiency implies that
when the nominal interest rate is set, investors use
all the infonnation available to them both to determine the real interest rate they demand and to form
their expectations of the future inflation rate. What
this means is that the inflation-forecast error, u, is a
random variable that is independent of all the other
variables that determine the real rate. It is independent because the other variables were necessarily
known when the market set the nominal rate while u
reflects information that was unknown at that time.
By exploiting this implication of the theory of efficient markets, we can investigate the determinants
of the ex ante real interest rate and test the hypotheses outlined in the previous section, despite the
fact that the ex ante interest rate is not directly
observable.
To illustrate the procedure, let X represent the
factors that theory suggests determine the ex ante
Measuring the Real Rate of Interest
On a given date the real rate of interest on a
security is equal to the nominal rate minus the rate
of inflation that investors expect to materialize over
the maturity of the security. Put differently, the
nominal rate which is detennined in the financial
markets is equal to the real rate which investors
require ex ante when they purchase the security plus
the rate of inflation they expect. Symbolically,
(1)
r = i-pc
where r is the real rate, i is the nominal rate and pc is
the expected inflation rate. 17 It was the detennination of this ex ante real rate which the theory of the
preceding section sought to explain.
As stressed earlier, the empirical problem with
this fonnulation is that the expected rate of inflation
is not an observable variable and hence neither is the
required or ex ante real rate. After the security
37
quarters ending in those same months. Thus, market participants would have had information on
each of these four variables when the nominal interest rate was set. For example, when the nominal
interest rate was set in January, investors would
have had information on the rate of inflation over
the three months that ended in December, and data
on the excess supply of money, the government
deficit, and the level of GNP in the fourth quarter of
the previous year. The variables, therefore, satisfy
the conditions required for the application of the
efficient markets hypothesis.
Our theoretical discussion suggested that an
increase in the expected rate of inflation will lead to
a decline in the real interest rate. As evidence of this
Tobin effect, several authors '9 have found a statistically significant inverse relation between the current real interest rate and the past rate of inflation
and have interpreted this finding as evidence of this
effect. Although, strictly speaking, the Tobin effect
implies a relationship between the real interest rate
and the expected future inflation rate, it is difficult
to test this hypothesis in the efficient market framework so that lagged inflation is used as a proxy for
expected inflation. We have tried to replicate the
results of these other authors before considering
other possible influences on the real rate suggested
by theory. The relevant equations are shown in
Table I. In an attempt to capture the possible influence of lagged variables, the error terms in these
equations were assumed to follow a fourth-order
autoregressive process.
The earlier studies generally used a relatively
long sample period that encompassed the sixties and
seventies. Hence, it is comforting to find that using
a similar long period-April 1958-0ctober 1979we were able to reproduce their conclusion. The
estimated equation shown in the first column of
Table I implies that if the quarterly rate of inflation
increases by one hundred basis points, the real rate
for the succeeding quarter declines 30 basis points,
or, to putthe same point slightly differently, if the
higher inflation rate is expected to continue in the
future, the nominal rate will rise 70 basis points.
Clearly, if this result holds up when the sample
period is extended beyond 1979 and when additional variables are added to the equation, it will
help to explain why falling inflation rates have been
associated with rising real interest rates.
real rate and assume that the relation between X and
that rate is a linear one. Then
(4)
r a + bX + v
where v is a random error which is independent of X
and essentially captures the variables that affect r
but that have been inadvertently left out of X.
Combining Equations (3) and (4) gives
{P = a + bX + v + u
(5)
The dependent variable in this equation is the ex
post real rate that is observable. The combined error
term, v + u, represents both errors in determining
the real rate, v, and errors in predicting inflation, u.
Both of these errors are independent of X so that
least-squares estimation of Equation (5) will yield
unbiased estimates of the parameters of Equation
(4). Notice that although the efficient markets hypothesis implies that u is not autocorrelated, it says
nothing about the characteristics ofv. Hence, in our
empirical work, the combined error term is assumed
to be autocorrelated.
Empirical Results
Equations have been estimated in the form of
Equation (5) for various sample periods. The nominal interest rate is the average rate on 91-day
Treasury bills, issued in January, April, July and
October, and converted to a bond equivalent basis.
The inflation rate is represented by the annualized
change in the logarithm of the consumer price index
over 3-month spans beginning in those same
months. The dependent variable in the estimated
equations is the ex post real interest rate defined as
the difference between the Treasury bill rate and the
inflation rate. Notice that both the bill rate and the
inflation rate refer to non-overlapping time periods.
The vector X was taken to include the following
independent variables: the lagged inflation rate
(PLAG), the excess supply of money (XMONEY),
a measure of the impact of government deficit
spending on credit markets (FEDDEF), and the
ratio of current to potential GNP (INCOME). These
variables are designed to capture the theoretical
considerations outlined earlier.
Lagged inflation refers to the rate of price change
over the three-month period ending in the month
preceding the interest rate observation (December,
March, June, and September). Similarly, the other
three variables are quarterly data for the calendar
38
The remaining columns of Table I show the regression results when the long sample period is
divided into two shorter periods-April 1958January. 1970 and April 1970-0ctober 1979, and
when the latter period is extended to January 1982.
The first ofthese equations shows only a small, and
not statistically significant, effect of inflation on the
real rate during the 1958-1970 period. The effect
during the 1970s is larger and highly significant,
implying that the negative relationship between inflation and the real rate found in other studies (and
apparently confirmed by the results in the first column), in fact, represents only the experience of the
seventies. Given the much lower inflation rate experienced in the sixties, the result is not surprising.
If there are transactions costs associated with rearranging asset portfolios to hold more tangible
assets and fewer financial assets, modest changes in
the inflation rate may not induce any response.
The last column of Table I shows the estimated
equation when the sample period is extended to
January 1982. Again, the estimates show a negative
relation between inflation and the real rate, sug-
gesting that the Tobin effect continued to hold up
after .the Federal Reserve changed its operating
procedures. This result suggests that the decline in
the rate of inflation after 1979 may have been at
leastpartially responsible for the upward movement
inrealrates. However, the structure of the autoregressive process on the residuals was sharply
different in this extended sample period, suggesting
that some new variable(s) began toint1uence real
rates after 1979,
The theoretical discussion argued that increases
in the supply of money relative to the demand.to
hold it tend to lower interest rates. Our excess
supply of money variable is designed to capture this
effect. We derived the variable by, first, estimating
a defil.and for money equation in which money demand in any quarter depends on current and past
values of the interest rate and of nominal personal
income and on the current quarter's increase in
outstanding bank loans. The parameters of this
equation for various sample periods are shown in
Table 2. The inclusion of the bank loans variable is
based on the work of Judd and Scadding 20 who
Table 1
Inflation and Real Rates
Periods
Independent
Variables
Apr 1958Oct 1979
April 1958Jan 1970
Apr 1970Oct 1979
Apr 1970Jan 1982
0.020
(520)
OOIS
(794)
0011
(135)
0.004
1(32)
PLAG
-0.30
(517)
-006
(079)
-02S
(119)
-·0.24
(2.06)
RHOI
-0.17
(163)
-013
1(97)
-0.21
(141)
( 101)
0.12
(121)
0.05
«39)
0.06
<03S)
030
(224)
RH03
030
(290)
O.OS
1(64)
0.29
(206)
0.62
(4.36)
RH04
0.13
( 125)
(174)
0.31
(211 )
(UO
(182)
O.OS
034
0.53
CONSTANT
RH02
R-SQUARED
-
-
0.395
-
-
- - - - - - - - - - - - - - ----
-o.n
0---_---
RHO I. RH02. RH03. RH04 are fourth order autocorrelation coefficients.
39
o 15
argue that when banks increase their lending, membyrsof the public receive additional bank deposits
(money), some of which they are willing to hold
temporarily until they rearrange their portfolios to
add to their earning assets. Thus, the demand to
holdiffioney also depends On recent increases in
banklending.
In· a given quarter, the demand to· hold money
may rise as a result of past or present increases in
personal income or as the delayed result of past
declines in interest rates. Ifsuch a rise in dernarid is
not .matched by a corresponding increase in the
supply of money, the interest rate must rise torestore equilibrium in the market. Since members of
the public do not adjust their money-holdings instantanously, this interest-rate change may be
spread over severaLmonths. Similarly, to the extent
that there is a rise inthestockofmoney as a result of
an addition to the volume of bank lending, the rise
will tendto drive down interestrates inlatermonths
because members ofthe public are only willing to
hold this additional money temporarily.
To capture these effects of money on interest
rates, the estimated coefficients ofthe money demandequation are usedto predict whatthe quantity
of money demanded in a given quarter would have
been if the interest rate had remained the same as the
preceding quarter and if there had been no change in
Table 2
Quarterly Demand for Money Equations
. . Sa.!1'ple Periods
Independent
Variables
1956:4-1969:4
-
1968:4-1979:4
1968:4-1982:4
-1.795
(1.70)
0.264
(049)
--_._--~--_._-
CONSTANT
0.689
(1165)
c
-0.00074
(0406)
-0.0014
(071)
TIME DUMMy 1
0.00013
(0.332)
0.00
(000)
TIME DUMMy4
0.00002
(0728)
0.00001
(0.37)
TIME DUMMY
LOG REAL PERSONAL
INCOME*
0.685
(7.58)
1.054
(6.79)
0.750
(8.98)
LOG CONSUMER
PRICE INDEX**
0608
(341)
0.656
(7.12)
0.721
(23.7)
-0.029
(3.24)
-0047
(2.86)
-0.033
(317)
0.224
(2.38)
0.048
(076)
o 107
(1.30)
0.943
(20.6)
0.910
( 14.6)
0.671
LOG COMMERCIAL
PAPER RATE*
LOG BANK LOANS
(QUARTERLY CHANGE)
RHO
*Coefficients are sums of four-quarter distributed lags.
**Coefficient is sum of eight-quarter distributed lag.
TIME DUMMY
O. 1956(4) - 1974(3);
1.2.3 . . .8. 1974(4)
1976(3)
= 8
1976(4)
1982(4)
=
The dummy variable is raised to the second. third and fourth powers to allow the implicit constant tem1 in the equation to vary smoothly.
RHO = First Order Auto Regression Parameter
40
the volume of bank loans. The difference between
this quantity and the actual supply of money is the
excess supply of money, XMONEy' 21 Increases in
this variable are expected to be associated with
declines in the interest rate in the sUbsequent month.
Notice that because the demand for money is made
to depend on nominal income, this variable captures
the effect of changes in income on interest rates via
the transactions demand for money.
Two alternative measures ofFEDDEF, the variable representing the impact of government borrowing on credit markets, were used: the overall federal
government deficit shown in the national income
and product accounts and the total of government
and agency securities issued to the public (exclud-
ing the Federal Reserve system). Each variable was
deflated by potential GNP and each was measured
both inclusive and exclusive of Treasury interest
payments. The second variable, which measures
more directly the impact of federal borrowing on the
credit markets, fit the data slightly betteL For this
reason, only equations using the second definition
of this variable are reported below.
The final variable in the estimated equation is the
level of GNP relative to potential. This variable
captures any effect on interest rates of cyclical variations in real income in addition to those operating
through the transactions demand for money. Also, it
enables us to interpret the coefficient on FEDDEF
as representing only the effect of financing changes
Table 3
Determinants of Real Interest Rates
Periods
Independent
Variables
Ap~1~~l!
-
Jan 1970
Apr 1970
-
Oct 1979
Apr 19!()~::: Jan 1982
CONSTANT
0.148
(181 )
0.149
( 182)
0.089
(()63)
0.092
(0.66)
0.550
( 1.(2)
0.572
( 1(9)
PLAG
0213
( 185)
0216
( 188)
-0 113
(110)
-0.101
(097)
0362
(213)
0 ..169
(2.17)
FEDDEFI
0.141
(110)
FEDDEF2
o.on
0369
(0090)
(In)
(un
0.137
( 1(9)
-(l.OII
(CUB 8 )
( 1.78)
-1006
(3.23)
-1006
(3.23)
--0 168
(0 175)
~O.147
(0.15)
1368
( 1.70)
1380
( 1.72)
·-0.134
( 158)
-O.U.1
( 157)
-0.104
(on)
-0.102
(072)
-0.576
( 1(3)
-0600
( 1(9)
RHOI
0.083
(063)
0.086
(().65)
-0.112
(0.76)
-0.105
«(UI)
O.7U
(450)
0.716
RH02
0250
(194)
0248
(193)
0005
(U9)
0.002
(()Ol)
-0.
(()80)
-0.150
(082)
RHO-'
o 178
(lAO)
0.177
( 1.39)
0.307
(2AO)
(um
(2.36)
0.387
(2.11 )
(U85
(2.09)
-0.178
(IAI)
-0.178
(141)
OA.10
(3 II)
OA26
(3.08)
-0.055
(0.33)
-0059
(0 ..16)
0.17
0.18
0 ..16
0 ..16
OA8
0.48
XMONEY
INCOME
RH04
FEDDEF! includes and FEDDEF2 excludes government interest payments.
41
levels of real interest rates after 1979 were the result
of the sharp increase in federal borrowing, the coefficients on FEDDEF in these equations are small
and insignificant. Thus, statistical analysis does not
confirm the popular view that high real interest rates
in recent years have been due to the increased volume of Treasury borrowingY
A similar lack of stability in the coefficients was
found with respect to the inflation and money
variables. As the first column of Table 3 shows,
during the 1958-1970 period, increases in the excess
supply of money had a strongly negative impact on
real interest rates: This is the result which traditional Keynesian liquidity-preference theory would
predict.
In the subsequent decade, changes in monetary
conditions had no perceptible influence on real
rates. The estimated coefficient on XMONEY in
the second column of Table 3, although negative, is
small and not statistically significant. The most
plausible explanation of this result is that it reflects
the growing recognition by the public of the role of
money in the inflation process. As investors come
to realize that increases in the money supply lead to
higher prices and, if sustained, to faster inflation,
the net effect of monetary changes on interest rates
becomes ambiguous.
Increases in the inflation rate were associated
with increases in the real rate during the first sample
period. Our analysis of the Tobin effect would lead
us to expect the contrary. Until 1965, however, the
average inflation rate was very low so that changes
in the rate may not have led the public to alter its
inflation expectations. Hence, increases in PLAG
may have captured the effect of increases in the
level of prices, which tend to raise interest rates
when the money stock is held constant, rather than
of increases in the expected inflation rate, which
tend to lower real rates via the Tobin effect. During
the 1970s, however, the estimated equation indicates that increases in the inflation rate were associated with higher nominal but lower real rates, as the
Tobin effect would predict. However, this result is
not significant at conventional probability levels
when the influences of other variables are incorporated into the equation.
When the sample period is extended beyond October 1979, the estimated coefficients both on
PLAG and on XMONEY are significantly positive.
in the deficit, holding the level of income constant.
An increase in real income tends to raise the anticipated return on real assets because businesses become more optimistic. This will tend to drive up
interest rates as businesses seek to borrow to finance
capital investment. At the same time, however, the
supply of savings typically rises during a business
cycle upswing and mitigates the upward pressure on
interest rates. Thus, the sign of the coefficient on
the. INCOME variable is not determinate on the
basis of economic theory.
Table 3 shows the results of adding these three
variables to the equations estimated in Table I.
Since the INCOME variable is defined as the ratio
of actual to potential GNP it is equal to one when the
economy is operating at potential. Hence, the estimated value of the interest rate when the economy is
at full employment and when there is no inflation,
no federal borrowing and no excess money is represented by the sum of the constant term and the
coefficient on the INCOME variable. This value
was close to Ilf2 percent in the sixties and was
negative in the seventies. Over the 1970-82 sample
period, this value was even more negativebetween - 2 1/2 and - 3 1/ 2 percent, implying that the
high real rates actually observed were associated
with changes in one or more of the independent
variables in the equation and not with a shift in the
intercept.
Both in the 1960s and in the 1970s, the coefficient on government borrowing is estimated to be
positive. Thus, as theory would suggest, increases
in federal borrowing at given levels of income were
associated with higher real interest rates. The effect
was smaller-and not statistically significant-in
the earlier sample period when government borrowing was much smaller relative to the size of the
economy. These results are hardly affected when
government interest payments are excluded from
total government borrowing. Apparently interest
rates were influenced by total government borrowing, regardless of whether the funds were used to
make interest payments on earlier borrowings. This
result casts some doubt on the argument that deficits
caused by high nominal Treasury interest payments
do not drive up the real rate.
The last two columns of Table 3 display the
results of extending the sample period to January
1982. Despite the widespread belief that the high
42
Real rates rose when either the inflation rate increased or the supply of money grew faster than the
demand. Since this extended period was one in
which the Federal Reserve was strictly limiting
money growth with a view to ending inflation, this
result__which does not accord with the predictions
of standard macroeconomic theory__suggests security markets. interpreted increases in either money
growth or inflation as signals of impending tightening of policy· by the Fed; interest rates consequently
rose. As previously indicated,the Treasury's borro\Ving had no significant impact on the real rate
during this period when the effects of inflation and
monetary policy were controlled for.
1979, this relationship-if it continued to holdwould imply that real rates should have risen. However, the empirical results of this paper suggest that
this relation only held during the seventies and that
even during this decade the effect was less significant when one took account of change in the money
supply and the federal deficit that took place at the
same time.
Higher levels of federal borrowing were associatedwith increases in real rates during thel970s.
However, the empirical results do not support the
proposition that there is any simple direct causal
link between the recent sharp increase in the federal
deficit and high real rates. In the equation estimated
for the period between April 1970 and January
1982, for example, the estimated coefficient on the
federal borrowing variable is small and not statistically significant. In fact, this equation suggests that
money shocks and changes in the inflation rate have
been more closely related to real rates than has the
federal deficit. However, in this period high rates
were. associated with high inflation and positive
monetary shocks rather than the reverse, probably
because these factors were interpreted as signals of
likely Federal Reserve policy in the near future.
Thus, the statistical analysis in this paper of the
various factors which economic theory and popular
opinion suggest as possible causes of the post-1979
rise in real rates does not strongly confirm anyone
of them. The results suggest that there is a great deal
more to be learned before we fully understand the
causes of the explosion in real rates.
A situation in which a substantial portion of government outlays are financed by borrowing rather
than by taxation is unprecedented in peacetime.
Hence, we should not be surprised that econometric
analysis of data from an earlier period fails to provide a good. guide to the current situation. This
suggests that in formulating policy, we should be
guided by the predictions of economic theory even
though that theory has yet to be confirmed by empirical evidence.
Summary and Conclusion
In recent years, real interest rates have risen
sharply. It is widely argued that the need to finance
increasing government deficits combined with a
tight monetary policy on the part of the Federal
Reserve System have been the principal reason for
this development. In this paper, the formal theory
underlying these arguments has been explained.
This theory also suggests that a reduction in the rate
of inflation will be associated with increased real
rates.
An inescapable problem in testing hypotheses
about the real· interest rate is that when the market
sets the nominal interest rate, it does Sa on the basis
of an expected rate of inflation. Wealth-holders
determine the nominal interest rate by adding their
expected inflation rate to the ex ante real rate which
they demand. However, the outside observer of the
market cannot measure this ex ante rate; he can only
measure the ex post rate that emerges. Nonetheless,
by making use of the theory of efficient markets, it
is possible to test hypotheses about the determinants
of the ex ante rate using data on the ex post rate.
A number of studies by other authors havefound
that there was a significant inverse relationship in
the post-war period between the rate of inflation and
the real rate. Since the inflation rate has fallen since
43
FOOTNOTES
1. Throughout this paper, yields are measured on a bondequivalent basis in order to make them consistent with rates
of inflation.
sumption and will be willing to invest their increased savings in securities in order to provide for those future tax
liabilities, Hence the supply of loanable funds increases by
as much as the demand so that the .interest rate is unaffected, David Ricardo was an early exponent of this view
so that economists who take this position are frequently
described as neo-Ricardians. Although there is some empirical evidence for this position, most economists believe
the argument assumes a greater degree of rationality and
farsightedness than most households possess, For an extensive discussion of this issue, see Robert J. Barro, "Are
Government Bonds Net Wealth," Journal of Political
Economy, Vol. 82, No, 6 (1974),
13. In terms of the traditionallS/LM paradigm, the increase
in the interest rate which results from the expansionary
effect of an increase in the high employment deficit on
nominal income is represented by an upward shift of the IS
curve, The increase which results from the fact that actual
deficits must be financed by the issue of securities is represented by an upward shift of the LM curve. The public will be
willing to hold a larger share of its portfolio in the form of
securities (and hence a smaller share in the form of money
or physical capital) only if interest rates on securities rise.
For an early explanation of this distinction see William L.
Silber, "Fiscal Policy in IS-LM Analysis: A Correction."
Journal of Money, Credit and Banking, Vol. II (November
1970), More extensive discussions of the role of government deficits are provided in L.H, Mayer, "The Balance
Sheet Identity, the Government Financing Constraint and
the. CrOWding-Out Effect," Journal of Monetary Economics Vol. 1 (January 1975) and Brian Motley, Money,
Income and Wealth, Lexington, Mass: D,C. Heath and
Co., 1977. Chapter 6.
2,Holders of Treasury Bills pay attention to the inflation rate
they expect to occur over the maturity of the bill. Chart 1
shows the inflation rate which actually occurred, Over long
periods, however, the rate of inflation which investors expect should not diverge too far from the actual rate. Hence
the realized real return on bills should be a good proxy for
the real rate which their holders anticipated,
3. The reader will recognize this argument as a simplified
form of the expectations theory of the term structure of
interest rates,
4, For one attempt to measure real long-term interest rates,
see Charles Pigott, "Measuring Real Interest Rates Using
the Term Structure and Exchange Rates," in a forthcoming
issue of the Economic Review.
5. Notice that both the supply and the demand refer to the
stock of securities. However, if these stock supplies and
demands are equal at two successive dates, then the new
securities issued between these dates must have been
willingly purchased by investors. Some economists, and
most market commentators, prefer to think of the interest
rate as equating the flow of new issues by borrowers with
the demand by investors to add to their holdings of securities.
6, J.M, Keynes, The General Theory of Employment,
Interest & Money, New York, Harcourt Brace & Company,
1936, (p. 167),
7, For a more detailed exposition of this argument see John
P, Judd and John L. Scadding, "Liability Management,
Bank Loans and Deposit 'Market' Disequilibrium," Economic Review, Federal Reserve Bank of San Francisco,
Summer 1981.
14. An exogenous cyclical downturn is represented by a
downward shift of the IS curve, which, by itself, tends to
10Vl/er interest rates. The upward pressure on rates caused
by the associated rise in the deficit to be financed is represented by an upward shift of the LM curve, Hence, the net
effect on interest rates cannot be predicted a priori on the
basis of economic theory.
15. Adrian W. Throop, "Changing Fiscal Policy II," Weekly
Letter, Federal Reserve Bank of San Francisco, January
16,1981. Brian Horrigan and Aris Protopapadakis, "Federal Deficits: A Faulty Gauge of Government's Impact on
Financial Markets," Business Review, Federal Reserve
Bank of Philadelphia, MarchiApril 1982,
16. For one attempt to measure the effect of inflation on the
Treasury's interest-costs, see Throop, op. cit. An alternative approach which directly measures the decline in the
real value of the government debt, is used by Horrigan and
Protopapadakis, op, cit.
8, If nominal interest incomes are taxable, nominal rates will
rise proportionately more than inflation, since investors will
demand that their after-tax real incomes be protected
against the effects of rising prices,
9. Notice that the deregulation of interest rates on monetary"
assets may weaken this effect in the future,
10. For an exposition of the argument in the context of a
complete model of asset markets, see James Tobin, "A
General Equilibrium Approach to Monetary Theory," Journal of Money, Credit and Banking, Vol 1, Number 1,
(February 1969).
11. In the 1982 fiscal year the federal government had an
overall deficit of $123.9 billion, while net interest payments
were $82.5 billion.
12, Some economists have argued that as long as government outlays have not changed, members of the public will
recognize that a cut in their current tax liabilities will have to
be offset by an increase in their (or their children's) future
tax liabilities. Thus, they will not change their level of con-
17, This formulation assumes that investors are risk neutral
and hence do not require a risk premium to cover the fact
that the inflation rate is uncertain,
44
REFERENCES
18. Fora detailed exposition of this argument, see Frederick S. Mishkin, "The Real Interest Rate: An Empirical
Investigation:' Carnegie-Rochester. Conference Series
on Public Policy, 15, (1981).
Brian Horrigan and ArisProtopapadakis, "Federal Deficits:
A Faculty Gauge of Government's Impact on Financial Markets," Business Review, Federal Reserve
Bank OfPhiladelphia, MarchIApril 1982.
19. See, for example, Frederick S. Mishkin, op. cit., John H.
Makin, "Real Interest, Money Surprises and Anticipated
Inflation:' W?rking Paper 878, National Bureau of Economic Research, (December 1981).
John P. Judd and John L. Scadding, "Liability Management, Bank Loans and Deposit 'Market' Disequilibrium:' Economic Review, Federal Reserve Bank of
San Francisco, Summer 1981.
20. John P. Judd and John L. Scadding, op. cit.
21. The stock of money in a given quarter t may be written
M St
at
J. M. Keynes, The General Theory of Employment, Interest, and Money, New York: Harcourt Brace and
Company, 1936.
+ blNCOME t +cINTEREST RATE t
+dLiBKLOANS t + et
where ilt includes the effects of all lagged variables on
money demand as well as the constant term, and e t is the
residual between the actual money stock and the fitted
money demand. Then
John H. Makin, "ReaIJnterest, Money Surprises and Anticipated Inflation:' Working Paper 878, National Bureau
of Economic Research, (December 1981).
L.H. Mayer, "The Balance Sheet Identity, the Governement
Financing Constraint and the Crowding-Out Effect:'
Journal of Monetary Economics, Vol. 1 (January
1975).
XMONEYt
MSt - (at + b INCOME t +
clNTEREST RATEt-1) = c (INTEREST RATE t
INTEREST RATE t _ 1) + dLiBKLOANS + e t
Brian Motley, Money, Income and Wealth: The Macroeconomics of a Monetary Economy, Lexington,
Mass., DC Heath and Co., 1977.
22. This result does not, however, mean that real rates
would not have been lower if fiscal policy had been less
expansionary, but only that-given the level of nominal
income which resulted from that policy-the additional impact on interest rates of the associated deficits was small.
Frederic S. Mishkin, "The Beallnterest Rate: An Empirical
Investigation" Carnegie-Rochester Conference
Series on Public Policy, 15, (1981).
Charles Pigott, "Measuring Real Interest Rates Using the
Term Structure and Exchange Rates," forthcoming,
Economic Review, Federal Reserve Bank of San
Francisco.
Adrian Throop, "Changing Fiscal Policy II," Weekly Letter,
Federal Reserve Bank of San Francisco, January 16,
1981.
William L. Silber, "Fiscal Policy in IS-LM Anillysis: A Correction," Journal of Money, Credit and Banking,
Vol II (November 1970).
James Tobin, "A General Equilibrium Approach to Monetary Theory," Journal of Money, Credit and
Banking, Vol 1, Number 1, (February 1969).
45
John P. Judd and Rose McElhattan*
sented evidence that the decline in velocity was
consistent with a stable demand for money relationship, representing an increase in the quantity of
money demanded because of lower interest rates
and inflation, rather than an unstable money demand function.
This analysis suggests that a good deal of the
growth in MI over 1982 and early 1983 did not have
a stimulatory effect on aggregate demand because it
represented an increase in the quantity of money
demanded, rather than an autonomous increase in
the supply of money. In other words, effective
money growth-effective in the sense of measuring
the thrust of monetary policy-was lower than actual, or measured, money growth during the period.
We attempted to measure this effective growth by
subtracting from measured MI an estimate of the
increase in the public's demand for MI caused by
the decline in short-term interest rates that paralleled the decline in inflation. This estimate came
from the MI demand equation in the San Francisco
money market model. The results suggest that
whereas measured MI increased at a rapid II pcrcent rate over 1982/Q3-1983/QI, adjustedMI grew
at only a I J/2 percent rate.
If the analysis behind these estimates were correct, adjusted MI should be a better indicator of
monetary policy in 1982-1983 than measured M I.
To see if this is the case, the FRBSF Research
Department's macroeconomic model (which predicts real GNP and inflation from reduced-form
equations on Ml and other variables), was simulated over the period 1982/QI-1983/Q2 using adjusted Ml and, alternatively, actual MI. The results
of this experiment confirmed the above analysis of
events in 1982-83. Simulations. of velocity, real
GNP and inflation using adjusted Ml were more
accurate than those using measured M I, which
yielded large over-forecasts of all three macroeconomic variables.
In 1982, MI velocity unexpectedly declined at a
5-percent rate in contrast to its 3-percent average
rate of increase over the previous twenty years. As a
result, the Federal Reserve de-emphasized MI in its
conduct of monetary policy, and allowed that
monetary aggregate to grow at a rapid 81/2-percent
rate for the year compared to its target range of 2 J/2
to 5 1/2 percent. But even with this change in policy,
nominal income rose only moderately and real income declined.
A paper in the Spring Economic Review assessed
what went "wrong" with velocity in 1982. 1 One
possibility it considered was that the public's demand
to hold money balances "shifted" upward in the
sense that, for given interest rates, income, and
prices, the public wanted to hold more money than
historical relationships would have predicted.
However, the article presented evidence from the
San Francisco money market model suggesting that
the demand for MI was stable, and that the decline
in velocity largely is explained by the sharp parallel
drop in short-term interest rates and inflation in
1982. In sum, the drop in interest rates raised the
quantity of money demanded by the public, and the
Federal Reserve responded by allowing money to
grow faster than originally targeted. This drop in
interest rates was roughly equal in size to the surprisingly sharp decline in inflation that occurred in
1982. Thus, the declines in nominal interest rates
and inflation meant that inflation-adjusted, or real,
short-term interest rates remained high and depressed total spending in the economy. As a result, GNP
grew very slowly or declined. The combination of
fast M I growth and slow income growth meant that
velocity actually fell. Thus the earlier article pre*Research Officer and Senior Economist, respectively, Federal Reserve Bank of San Francisco.
Research assistance was provided by Elizabeth
Christensen, Thomas Iben and David Murray.
46
velocity suggests that it would be desirable for MI
growth to slow down in the last half of 1983. Otherwise, there would be hefty increases in spending
which ultimately would threaten to increase the rate
of inflation.
The remainder of this paper is divided into four
sections. Section I briefly reviews the discussion in
the earlier paper on what went' 'wrong" with velocity in 1982-83. The estimates of adjusted Ml growth
are presented in Section II. Section III contains a
discussion of the simulations of macroeconomic
variables. Finally, conclusions and policy implications are presented in Section IV.
These results have an important policy implication. They suggest that although monetary policy
was quite restrictive in 1982, it became moderately
expansionary in 1983/QI and highly expansionary
in 1983/Q2. The money market model suggests that
the public's demand for money had fully adjusted to
the new lower levels of interest rates by the first
quarter of 1983, while money growth continued to
grow rapidly. It expanded, for example, at a fast
12 1/ 2 percent rate in the second quarter of 1983.
With the adjustments in money demand over, one
could expect the growth in velocity to revert to a
more commonly observed range. Such a rebound in
I. What Went "Wrong" with Velocity in 1982-83?
between 1982/Q2 and 1983/QI is explained by the
drop in nominal interest rates.
One possible explanation for the unexpected
change in velocity in 1982 is that there was an
upward shift in the public's demand for money, that
is, that increasing quantities of MI were demanded
by the public for given levels of prices, real GNP
and interest rates. This alleged shift has been attributed to a precautionary motive for holding money
caused by the economic uncertainty of the recession." This would be a plausible hypothesis if the
evidence showed that the demand for Ml did shift
upward in 1982. However, simulations of the MIdemand equation in the San Francisco Money Market Model' suggest that the demand for MI was
stable. The MI equation predicted annualized
growth of 10.2 percent in 1982/QI-1983/QI when
actual growth was 10.3 percent. (Ex ante forecasts
made during the year produced nearly identical
results.) Thus, the rapid Ml growth can nearly all be
"explained" by the determinants of MI demand;
these results provide no indication of a shift in the
money demand relationship.
If the demand for MI did not shift, what explains
the rapid growth of that aggregate in the period
considered? An analysis of the simulations indicates that the largest contributions were made by the
declines in the commercial paper rate in the third
and fourth quarters. These drops by themselves
caused M I to grow an annual rate of about 11.8
percent between August 1982 and February 1983,
compared to a contribution of a 0.4 percent rate of
decline in Ml over the preceding seven months.
Apparently, most of the sharp increase in Ml growth
Lower Inflation
Given that the demand for M I does not appear to
have shifted, an alternative explanation of the decline in velocity in 1982 is required. The Federal
Reserve Bank of San Francisco staff has argued that
the unexpectedly rapid decline in inflation provides
an explanation. 4 This explanation rests on the distinction between nominal, or market interest rates,
and real, or inflation-adjusted interest rates. The
level of spending on goods and services depends on
the real rate of interest. In contrast, the public's
demand for Ml depends on the nominal rate of
interest. To illustrate the significance of this dichotomy for developments in 1982-83, assume that the
rate of inflation falls and that this is reflected in an
equal decline in nominal interest rates. In this circumstance, the real rate of interest would be unchanged, implying that the decline in nominal interest rates would not stimulate additional growth
in Teal GNP. However, the public's demand for
money would grow more rapidly, for a time, in
response to the drop in nominal interest rates. As a
result, money growth would accelerate in comparison to GNP growth, implying a decline in the growth
of velocity.
This stylized scenario is a rough approximation
to the events that occurred in 1982 as whole.) The
GNP deflator rose at an 8.9 percent rate in 1981,
then fell suddenly to a 4.4 percent rate in 1982, for a
decline of 4.5 percentage points in the rate of intla-
47
tion. The commercial paper rate fell about the same
amount, dropping 4.1 percentage points from 12.9
percent in the fourth quarter of 1981 to 8.8 percent in
the fourth quarter of 1982. The very rapid growth in
M I associated with the drop in nominal interest
rates did not stimulate the economy because real
interest rates were not reduced substantially for the
year as a whole. Thus, real GNP over this period fell
on average at a 0.9 percent rate.
II. Adjusted M1 Growth
In the midst of a decline in velocity as large as
that in 1982, growth in MI obviously would not be
a good indicator of the impact of monetary policy.
A macroeconomic model that exploits the historical relationship between money and income would
likely have over-predicted nominal income and,
thus, velocity in 1982. The analysis in the preceeding section suggests a way to correct for this problem by adjusting the growth in M I downward, and
then using the adjusted MI growth rates to predict
income on the basis of historical money-to-income
relationships.
How should these MI-adjustments be calculated?
A significant part of the desired adjustment should
be calculated as the growth in M I caused by a drop
in nominal interest rates that paralleled the drop in
inflation. Since interest rates and inflation both declined by about the same amount, we calculated the
adjustment as the M I growth due to the full drop in
interest rates in the last half of 1982. We then
subtracted these adjustments from actual MI growth
to obtain what can be called adjusted M 1 growth.
The figures for adjusted MI growth are presented
in Table Ion a quarterly average basis. Two aspects
of the figures are worth emphasizing. First, the
adjustments are quite large in 1982/Q3-1983/QI,
and convert rapid measured M I growth of 11.I
percent into very slow growth in adjusted MI of 1.7
percent. Second, the decline in interest rates in the
latter part of 1982 affected MI growth only temporarily, specifically for three quarters. Because money
growth will rise relative to GNP growth only as long
as the pllblic's demand for money is stimulated by
declines in interest rates, the effects on money
growth dissipate once interest rates stabilize at new
lower levels. The exact timing depends on the lags
in the demand for money.
The M I-demand equation used suggests that
interest rates affect the public's demand for money
for about six months. According to the equation, a
one-time decline in the commercial paper rate in
any given month causes MI to accelerate relative to
GNP (that is, causes velocity growth to fall) contemporaneously and for the next five months. This
suggests that MI growth induced by the decline in
interest rates in 1982 should have played itself out
by the second quarter of 1983. In fact, the commercial paper rate fell sharply in the third and fourth
quarters of 1982. By the second quarter of 1983,
these interest rate changes should have had only
minor effects on MI growth, and should not have
required any adjustment in that growth after the first
quarter. Thus this analysis suggests that the rapid
measured MI growth in the second quarter accurately indicated the thrust of policy in that quarter.
Table 1
Growth in M1 at Annualized Rates
(Quarterly Average Basis)
1982/QI
Q2
Q3
Q4
1983/QI
Q2
Measured
Adjustments
Adjusted
M1 Growth
10.5
3.2
0.0
0.0
- 5.4
- 14.7
- 8.2
0.0
10.5
3.2
0.7
- 1.6
5.9
12.3
6.1
13.1
14.1
12.3
48
III. Using Adjusted M1 in Macroeconomic Simulations
The unusual experience with inflation and veloc
ity in 1982 and early 1983 resulted in large errors
from macroeconomic forecasting models in gen
eral. Many models, including that of the FRBSF,
were thrown off-track, and overestimated actual
velocity, real GNP and inflation during that period.
If the above explanation for the macroeconomic
developments of the past year and a half were cor
rect, adjusted Ml should be a significantly more
accurate indicator of monetary policy than actual
M l . One way to check the validity of the M1-adjust
ments, and therefore the underlying explanation of
events in 1982-83, is to use them in the FRBSF
Research Department’s macro-model to simulate
events over the 1982-83 period.
The model is a reduced form representation of the
U.S. economy and includes equations for real GNP
growth and inflation as functions of Ml and the high
employment deficit.6 Velocity is not estimated di
rectly but is obtained by subtracting (exogenous)
Ml growth from the sum of the predicted growth in
real GNP and predicted inflation.
The model was estimated over 1966-81, and then
simulated over 1982/Q1- 1983/Q2 with measured
Ml and, alternatively, with adjusted Ml to see
which yielded results closer to the actual events of
the period. As shown in the charts below, adjusted
Ml produces simulated values for inflation, real
GNP and velocity that are reasonably close to actual
developments, whereas actual Ml produces large
over-forecasts.
Chart 1shows actual velocity and dynamic model
simulations with observed and adjusted Ml. With
observed Ml, the model follows the general pattern
of velocity from mid-1966 until 1982. The 1982-83
period is unusual in that the model substantially
overestimated velocity for a sustained period of
time. Historically, when large simulation errors
occurred, they abated within one to two quarters.
Thus, the recent errors made with actual Ml are
unusual because of their size and because they per
sisted so long. In contrast, the Ml adjusted simula
tions produce errors well within the range of those
experienced in the past. The same observations hold
for the real GNP and inflation simulations (not
shown). Using adjusted Ml improved the model’s
simulation accuracy not only for nominal GNP (and
thus velocity), but also for the split between inflation
and real GNP growth.7
Charts 2 through 4 show a detailed view of actual
Chart 1
M1 Velocity
Percent Change
(Annual Rate)
1966:2-1983:2
49
Chart 2
Chart 4
GNP Implicit Price Deflator-Inflation Rates
M1 Velocity
Percent Change
(Annual Rates)
Percent Change
(Annual Rates)
8
10
6
4
9
2
8
0
-2
7
-4
-6
6
5
-8
-10
4
-12
I
II
IV
III
3
II
1983
1982
Chart 3
Percent Change
(Annual Rates)
10
8
6
4
2
ol--+..,;;;:j~----~;;""'----
-2
-4
I
II
......_ _....._ _....._ _...
III
1982
I
I
I
I
I
I
II
III
IV
I
1983
II
1982
Real GNP
-6 .....- _....._
ot
IV
I
1983
II
and model simulations of velocity, real GNP growth
and inflation from 1982/QI to 1983/Q2. The simulated values for velocity growth in Chart 2 using
observed Ml are much higher than actual values for
the entire period. In contrast, the simulation with
adjusted MI closely follows the actual course of
velocity and captures both the dramatic decline in
velocity in the second half of 1982 and the increase
during the first half of 1983. The model still makes a
larger error in 1982/Q I, but, overall, forecast errors
for the growth rate of velocity were reduced from an
average overforecast of 8.2 percentage points
between 1982/Q3 and 1983/Q2 with actual MI to
0.2 percentage points withadjusted Ml.
The model forecasts of real GNP considerably
overstated the strength in the economy in 1982 and
early 1983. In contrast, the simulations with adjusted
Ml tracked actual activity more closely, with the
exception of 1983/Q2 in which adjusted MI underestimates the strength of the economy. On average,
both simulations overforecasted real GNP growth in
the period 1982/Q3-1983/Q2. But the average forecast error was only 0.2 percentage points with adjusted MI in contrast to 5.0 percentage points with
actual Ml. Similar observations apply to inflation.
Forecast errors were reduced from an average overforecast of 3.2 percentage points in the case of
simulations with actual Ml to 0.01 percentage point
with adjusted MI during 1982/Q3-1983/Q2.
IV. Policy Implications
The conclusion that the behavior of velocity in
1982 may be attributed to the (surprisingly) sharp
drop in inflation and nominal interest rates has an
important implication for monetary policy in 1983.
With this explanation, there is good reason to believe that velocity will return to more commonly
observed rates of change in the second half of 1983.
As noted earlier, the 1982 decline in interest rates
50
should affect MI growth (and thus velocity growth)
only temporarily. Money will rise relative to GNP
only as long as the public's demand for money is
stimulated by declines in interest rates. Once interest rates stabilize at new lower levels, the effects on
money growth should dissipate according to the
lags in the demand for money. Thus, by the second
quarter of 1983, these interest rate changes should
have only minor effects on MI growth and velocity.
This implies that MI growth needs to be reduced
substantially from its 12-percent rate in the second
quarter to avoid a highly expansionary effect.
In July 1983, the Federal Reserve announced a
revision in the 1983 target range for M I. It replaced
the original 1983 range of 4 to 8 percent for the
entire year with a 5 to 9 percent range for the second
half of 1983. By establishing a second quarter base,
the Federal Reserve accommodated the rapid 12
percent growth in MI in the second quarter. If MI
were to grow at the 9 percent upper boundary of its
new range, for example, average MI growth over
the period 1983/Q 1-1983/Q4 would be ten percent.
The macroeconomic model was simulated assuming 9 percent MI growth in the second half of
1983, followed by growth of 8 percent in 1984 (the
upper boundary of the 4 to 8 percent range tentatively established for that year by the FaMe) and 7
percent in 1985. The figures represent a gradual
reduction in MI growth in 1984-85 that is consistent
with a policy of minimizing the adverse effects of
lower money growth on the economy. Our simulation suggests that the rate of inflation would be 5 1h
percent in the second half of this year, followed by
increases to 6Vz percent and 7Vz percent in 1984 and
1985 respectively. If MI growth were held to the 7
percent mid-point of the range for the second half of
this year, followed by growth of 6 percent in 1984
and 5 percent in 1985, the inflation rate would be
held to about 5 percent over the entire period.
Thus, a substantial slowdown in M I growth
appears to be required over the next several years to
hold the underlying rate of inflation at its present
level. Moreover, the simulation suggests that even
with this slower MI growth, aggregate demand is
likely to increase rapidly enough to sustain a recovery. Velocity is estimated to grow at 4 1h percent rate
in the last half of 1983 and 1984, leaving room for
real GNP to grow at a 5 1/2 percent rate
FOOTNOTES
1. John P. Judd, "The Recent Decline in Velocity: Instability
years. The reason for this is that following a permanent
in Money Demand or Inflation?, Economic Review, Federal
change in money growth, inflation initially will change more
Reserve Bank of San Francisco, Spring 1983, pp. 12-19.
slowly than the money supply. Consequently, the public's
holdings of real money balances will be disturbed leading to
2. This possibility is raised, for example, in "Record of
adjustments in the public's holdings of both real and finanPolicy Actions of the Federal Open Market Committee",
cial assets. For instance, it takes about two years before a
meeting held on August 24, 1982.
decrease in money growth is matched by a decrease in the
.
t d' J hPJ dd "A M thl
3 . Th e modeI IS presen e In on. u ,
on y
. fl .
d"
B b
.
I
Model of the Money and Bank Loan Markets", Working
In atlon rate, accor mg to the model. ut y that time, rea
Theory nd Econometrics
money balances are far below their longer-term deSired
P apers I'n Applied Econom'c
I
a
.
d ad'JUstment In
. rea I money baIances
· 'I
va ue. Th e continue
N um ber 83-01, Fed eraI Reserve Bank af San FranCISCO,
'11
.
. I
. bo h . fl'
d
I
WI sustain cyclica movement In
t In atlon an rea
M 1983
ay
.
GNP until both nominal and real quantities are at their new,
4. See Michael W. Keran, "Velocity and Monetary Policy in
longer-run values consistent with the lower monetary growth.
1982, Weekly Letter, Federal Reserve Bank of San FranR
M Elh tt
'Th R
f RIO
t d I fl
cisco, March 18, 1983.
. ose c a an, . e esponse? ea. utpu an n a.
.
.
.
tlon to Monetary Policy", Economic Review, Federal ReS. Infl~tlon fell early ~n 1982,. whe~eas Inter~st rates fell In
serve Bank of San Francisco, Summer1981, pp. 45-70, and
the thl.rd quarter. ThiS. consldera~lon complicates the ex"On Federal Deficits and their Economic Impact", EconoplanatIon of events Without altering the fundamental exmic Review Federal Reserve Bank of San Francisco,
Summer 1982 pp. 6-17.
planation given in the text. See the article cited in footnote 1
for a discussion of these points.
' "
. .
.
7. OPEC price shocks have been Important determinants of
6. A feature of the model, whIch IS not generally found In
short-term changes in the overall rate of inflation. The inflation model allows for this in 1974 and 1975 but does not
other reduced form models, IS that both real GNP and
infl~tion r~act in a cyclical manner to changes in m.onetary
include the substantial oil price increases in 1979 and 1980
policy. Ultimately only the level of prices an~ the Inflation
when the relative price of oil increased around 15 percent
rate are affected by changes I~ money. ThiS property IS
and 30 percent, respectively. This exclusion is related to the
often referred to as the ~~~trality of money. In particular,
relatively large under forecasts of inflation during that time.
~bou.t two years after an IllItlal c~ange In monetary growth,
On the other hand, real oil prices declined about 5 percent
mflatlon will overshoot ItS sustal~able, long-run value and
in 1982 and no doubt have been responsible for some of the
then slowly return to that value WithIn the next two-to-three
overforecast of inflation in that year.
51
@FedFRASER