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____________ Rev i e w ____ ____
Vol. 66, No. 8




October 1984

5 The Recent Decline in Agricultural
Exports: Is the Exchange Rate the
Culprit?
15 Hedging Interest Rate Risk with
Financial Futures: Some Rasic
Principles
26 An Early Look at the Volatility o f
Money and Interest Rates under CRR

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Federal Reserve Bank of St. Louis
Review
October 1984

In This Issue . . .




After expanding rapidly throughout the 1970s, the volume o f U.S. exports of
agricultural products has declined in recent years. Many economists have argued
that the high value o f the dollar — caused, at least in part, bv what they view to be
restrictive m onetaiy policy — is responsible for these declines. In the first article
o f this Review, Dallas S. Batten and Michael T. Belongia attempt to separate fact
from fiction in the debate over monetary policy’s role in determining the value of
the dollar and the effect o f exchange rate movements on the volume o f U.S.
agricultural exports.
Batten and Belongia first draw distinctions between nominal and real changes
in the exchange rate and conclude that monetary policy causes nominal changes
in the value o f the dollar whereas real changes — associated primarily with
nonmonetary factors — are the exchange rate movements that affect trade flows.
The authors examine data on real exchange rate changes and agricultural exports
from several perspectives and conclude that the exchange rate has been only one
factor in the recent export decline. Their analysis finds that foreign real income,
depressed by the recent w orld recession, has also been a primary reason for the
low er volume o f U.S. agricultural exports.
In the second article, “ Hedging Interest Rate Risk with Financial Futures: Some
Basic Principles,” Michael T. Belongia and G. J. Santoni discuss the problem of
interest rate risk facing depositoiy institutions in an era o f financial deregulation
and volatile interest rates. The authors use simple examples to show how changes
in interest rates affect a depository institution’s equity value. Because share
owners are interested in protecting their wealth, some institutions have initiated
efforts to hedge the value o f their equity.
Belongia and Santoni then discuss the econom ic principles o f hedging the
interest rate risk of a financial portfolio with futures contracts. They show how
interest rate risk can be measured and, based on that measurement, how futures
contracts can preserve a given equity value w hether interest rates rise or fall. The
examples also illustrate that a variety o f cash flows are consistent with a true
hedge based on insulating a firm's equity. This result is important because many
hedging strategies are designed to maintain a fixed cash flow. While this may be
important for some management purposes, such a strategy w ill often result in a
hedge that does not protect the wealth o f share owners. Therefore, focusing
attention solely on cash flows, as many hedging strategies seem to do, will often
result in a hedge that does not protect equity.
In the third article, “An Early Look at the Volatility of Money and Interest Rates
Under CRR," Daniel L. Thornton examines w hether the Federal Reserve’s adop­
tion o f a system o f contemporaneous reserve requirements (CRR) in February
1983 has had any noticeable effects on the variability o f m oney growth and
interest rates. Although CRR was adopted with the expectation that it would
reduce the variability o f money growth, Thornton points out that there are two
reasons w hy this w ould not necessarily occur. First, depositoiy institutions may
react in ways that reduce the contemporaneous link between reserves and de­
posits (and, hence, money) under CRR. Second, the October 1982 change in the
Federal Reserve's operating procedures may have weakened the contemporane-

In This Issue




ous relationship between reserves and money; the argument that CRR w ould
reduce the variability in money growth was predicated on the use o f a strong
reserve aggregate targeting procedure.
Thornton then examines the week-to-week variability o f m oney growth and.
interest rates before and after February 1984 and to see if the adoption o f CRR had
any impacts. He finds that there have been no significant changes in the variability
of m oney growth on interest rates associated with CRR.

The Recent Decline in Agricultural
Exports: Is the Exchange Rate the
Culprit?
Dallas S. Batten and Michael T. Belongia

4

J- M.FTER increasing at an annual rate o f 5.9 percent
between 1973 and 1980, the volume o f U.S. exports of
agricultural products exhibited no growth in 1981 and
declined at a 5.0 percent annual rate in 1982 and 1983.
Many analysts blame these export declines on the
appreciation of the U.S. dollar.
Chattin and Lee, for example, attribute at least half
of the export decline in 1982 and 1983 to this cause:
“Over the last two years, the real value of the dollar has
appreciated just over 25 percent (on a trade-weighted
basis) for importers of U.S. com and 16 percent for
importers o f U.S. wheat. Our analysts estimate that . . .
the United States has lost up to $6 billion in farm
export sales due to the strong dollar.” '

Similarly, Schuh, using the nominal agricultural ex­
port and exchange rate data plotted in chart 1, con­
cludes that “the export boom o f the 1970s is seen to be
closely tied to the fall in the value o f the dollar. The
decline in our export performance is closely associ­
ated with the rise in the value o f the dollar in the
1980s.”-

Dallas S. Batten is a senior economist and Michael T. Belongia is an
economist at the Federal Reserve Bank of St. Louis. Sarah R. Driver
provided research assistance.
'Chattin and Lee (1983), p. 19.
2Schuh (1984), p. 244. Other papers drawing a similar causal
relationship between exchange rates and agricultural exports in­
clude Chambers and Just (1982), Tweeten (1983) and Hathaway
(1983).



The problem with these statements is that such
simple analyses generally are inadequate in establish­
ing a cause-and-effect relationship between exchange
rates and agricultural exports. First, the comparison in
chart 1 fails to distinguish nominal changes in ex­
change rates, which reflect changes in relative rates of
inflation across countries, from real changes in ex­
change rates, which reflect structural changes. An
analysis o f the impact o f exchange rates on trade must
first separate these two types o f exchange rate
changes, because only changes in real magnitudes
influence trade flows.
Second, a simple two-variable comparison will not
correctly identify the relationship between exchange
rate movements and exports because factors other
than exchange rate fluctuations influence export
flows. This being the case, the relevant procedure is to
isolate the marginal impact o f exchange rates on trade,
holding constant the impact o f the other forces that
affect export flows.
The purpose o f this article is to explain the funda­
mental differences between nominal and real changes
in exchange rates and to show w hy only real changes
in exchange rates influence trade flows. In addition,
the effects o f real changes in exchange rates on export
volume during the 1982-83 decline are estimated by
using a simple econom etric m odel o f the determi­
nants o f w orld trade.

5

FEDERAL RESERVE BANK OF ST. LOUIS

THE SOURCES OF EXCHANGE RATE
FLUCTUATIONS
Analysts generally agree that observed changes in
exchange rates are either nominal or real in nature.'
Nominal changes occur when the rates o f inflation
differ among countries. For example, if the U.S. rate of
inflation is consistently below those o f its trading
partners, then the U.S. dollar should appreciate at
rates roughly equal to the spread between inflation
rates.4 Real changes, on the other hand, reflect chang­
ing relative prices (due to diverging structural devel­
opments among countries) that have different effects
on the exchange rate than on the relative rates of
domestic inflation. For example, some w ould argue
that the discoveiy o f North Sea oil in the United
Kingdom induced a substitution o f domestically pro­
duced for im ported oil, thereby causing the British
pound to rise in value independent o f any differences
in inflation rates.’

Money Growth and Nominal Exchange
Rate Changes

OCTOBER 1984

value o f the dollar, all other things equal. Thus, a
monetary disequilibrium, through its impact on the
rate o f aggregate spending, simultaneously induces a
change in the rate o f domestic inflation and the
foreign exchange rate.
In the long run, the change in the foreign exchange
rate will offset exactly the change in the rate of
domestic inflation, all other things equal. Therefore,
while domestic inflation changes the domestic prices
of exportable goods, it also changes the number o f
domestic currency units that a unit o f foreign cur­
rency can purchase in proportion to the difference
between the foreign and domestic inflation rates.
Consequently, changes in the rate o f m oney growth
should have no long-run effects on either the foreign
currency price o f U.S. exports or the competitive
positions o f U.S. exporters in foreign markets.

Purchasing Power Parity
This link between nominal changes in the exchange
rate and relative rates o f domestic inflation is summa­
rized bv the concept o f purchasing pow er parity (PPP),
which can be expressed as:
(1) % A e = TTF — TTlIS ,

The rate o f domestic inflation and, hence, nominal
changes in the exchange rate are determined jointly by
the rate o f domestic m oney growth relative to the
growth o f the amount o f m oney that individuals,
domestic and foreign, desire to hold. A country’s
m oney supply is determined primarily bv its m one­
tary authority; the demand for m oney (i.e., the sum
total o f individual desires to hold a portion o f their
wealth in the form o f money) is determined primarily
by income, real interest rates, prices and price expec­
tations in that country and abroad. The equilibrium
rate o f inflation is the one that maintains continuous
equality between the aggregate supply of and demand
for money. Any other inflation rate generates a “m one­
tary disequilibrium,” which motivates individuals to
alter their spending rate in order to bring their money
holdings nearer to the amount they desire to hold.
Changes in the rate o f consumer spending affect the
demand for both domestically produced goods and
services and those produced abroad. Altered de­
mands for foreign goods and services, in turn, produce
changes in the U.S. demand for foreign currencies and,
as a consequence, changes in the foreign exchange

3See, for example, Korteweg (1980) and Pigott (1981).
“For a more detailed discussion, see Batten and Ott (1983).
5For example, see Chrystal (1984) and Korteweg.

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6
Federal Reserve Bank of St. Louis

where %Ae is the rate o f change o f the foreign cur­
rency price o f a U.S. dollar, and ttiis and ttf denote the
rates of inflation in the United States and a foreign
country, respectively.6 If, for example, the rate o f in­
flation in the United States falls relative to inflation
rates abroad, the number o f units o f foreign currency
per dollar will rise; that is, the dollar w ill appreciate.
Under PPP, nominal changes in exchange rates will
offset differences in domestic inflation rates across
countries. Therefore, if PPP is maintained, the offset­
ting effects o f foreign and domestic inflation rates do
not permit a change in the value o f the dollar — over
the long run — to affect trade o f any type, including
agricultural trade. Consequently, if the appreciation of
the dollar has produced the recent decline in U.S.
agricultural exports, PPP must not have been main­
tained during this era o f flexible exchange rates.

Money Growth and Real Exchange Rate
Changes: Deviations fro m PPP
Real changes in exchange rates im ply deviations
from PPP. Even though real changes in the exchange

Equation 1 actually represents the concept of relative PPP, which
states that changes in the exchange rate will exactly offset the
inflation differential. See Frenkel (1981).

FEDERAL RESERVE BANK OF ST. LOUIS

OCTOBER 1984

Chart 1

N om in al U.S. Agricultural Exports a n d N o m in a l Exchange Rate
March 1973=100
150

Billions of d o lla rs
50

T r a d e - w e ig h t e d e x c h a n g e rate
SCALE

1967

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

1984

S o u r c e s : U.S. D e p a r t m e n t o f C o m m e r c e S u r v e y o f C u r r e n t Business a n d B o a r d o f G o v e r n o r s
o f t h e F e d e r a l Reserve System.
Q_ S e a s o n a l l y a d j u s t e d a n n u a l r a te .

rate typically are associated with structural differ­
ences in real econom ic performance across countries,
the short-run adjustment to a monetary disequilib­
rium may generate temporary deviations from PPP.
If, for example, there is an unexpected decline in
money growth, producers cannot discern im m edi­
ately whether the associated decline in aggregate
demand (spending) is permanent or merely tem po­
rary. Thus, they respond initially to a monetaryinduced reduction in demand by lowering their rate of
production, which reduces the rate o f real econom ic
activity below its normal rate. Only when producers
recognize that the decline in spending is a permanent
adjustment to slower m oney growth w ill they respond
by reducing prices and returning production to its
normal rate. Hence, the impact o f the monetary dis­



equilibrium on output eventually vanishes, leaving
only the rate o f inflation permanently lowered. These
long-run adjustments do not occur immediately, how ­
ever, because there are lags in the transmission of
information on the origin and magnitude o f the shock
to aggregate demand.
Unlike domestic com m odity prices, exchange rates
respond quickly to a monetary disequilibrium/ The
exchange rate is determ ined in highly organized,
internationally integrated markets that quickly and
efficiently assimilate new information. Consequently,
it will change before com m odity prices change suf­
ficiently to regain the domestic monetary equilibrium.

7
See Mussa (1979, 1982) and

Dornbusch (1976).
7

FEDERAL RESERVE BANK OF ST. LOUIS

OCTOBER 1984

C hart 2

Inflation D ifferen tial and N o m in a l Exchange Rate
M arc h 1 9 7 3 =1 0 0

P ercen t

6

-2

S o u r c e s : I n t e r n a t i o n a l M o n e t a r y F u n d I n t e r n a t i o n a l F i n a n c i a l S ta ti s ti c s a n d B o a r d o f G o v e r n o r s o f t h e
F e d e r a l R eserve S ystem
L I U.S. i n f l a t i o n m i n u s t r a d e - w e i g h t e d f o r e i g n i n f l a t i o n
[2 F o u r - q u a r t e r m o v i n g a v e r a g e o f n o m i n a l t r a d e - w e i g h t e d e x c h a n g e r a t e .

Between these two events, exporters w ill face a
temporarily deteriorating competitive position in for­
eign markets. The exchange value o f the dollar— and,
therefore, the prices paid by foreign importers o f U.S.
goods — will rise before the rate o f domestic inflation
and domestic com m odity prices have declined by the
full amount consistent with the reduction in the rate
of m oney growth. This monetary-induced deviation
from P P P , however, cannot persist for long.

MONEY SHOCKS AND DEVIATIONS
FROM PPP: THE EVIDENCE
The general relationship between exchange rates
and inflation differentials since 1976 is exhibited in
chart 2. This chart shows the trade-weighted foreign
currency value o f the U.S. dollar and the difference

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8
Federal Reserve Bank of St. Louis

between the U.S. rate o f inflation (as measured by the
CPI) and the trade-weighted rate o f inflation o f the
U.S.’s 10 major trading partners.8
It is apparent from the chart that the foreign cur­
rency value o f the dollar rises w hen the rate o f dom es­
tic inflation falls relative to that o f its major trading
partners, and vice versa.8 This chart should not be

“For a description of the calculation of the trade-weighted exchange
rate and the weights employed, see “ Index of the WeightedAverage Exchange Value of the U.S. Dollar" (1978). The tradeweighted inflation differential is the difference between the rate of
growth of the U.S. CPI and the rate of growth of the trade-weighted
foreign CPI for the same countries and weights as used for the
exchange rate.
9The simple correlation coefficient between the two series for the
period 1/1976-1/1984 is - 0.766; the correlation between changes in
the two series for the same period is -0.465. Each is statistically
significant at the 5 percent level. This analysis simply extends
Batten and Luttrell (1982).

FEDERAL RESERVE BANK OF ST. LOUIS

OCTOBER 1984

Chart 3

Deviations from Purchasing P o w er Parity

1976

77

78

79

80

11

81

82

83

1984

S o u r c e s : I n t e r n a t i o n a l M o n e t a r y F und I n t e r n a t i o n a l F i n a n c i a l S ta ti s ti c s a n d B o a r d o f G o v e r n o r s o f th e
F e d e r a l Rese rv e System
L i F o u r - q u a r t e r p e r c e n t c h a n g e in t h e n o m i n a l t r a d e - w e i g h t e d e x c h a n g e r a t e p l u s t h e c o r r e s p o n d i n g i n f l a t i o n d i f f e r e n t i a l

interpreted as proof o f the existence o f PPP; it does,
however, demonstrate that these series are inversely
related, which is consistent with the notion that the
rate o f inflation and nominal changes in the exchange
rate are jointly determ ined by excess m oney growth.
The issue o f PPP is examined more closely in chart 3.
Using the data in chart 2 to calculate values for
equation 1 reveals that there have been significant and
consistent positive deviations from PPP during the
past four years. In other words, the rise in the value of
the dollar has more than compensated for the decline
in U.S. inflation relative to inflation in the rest o f the
world.'" Although this indicates the existence of devia­

,0The use of a trade-weighted index of the foreign exchange value of
the U.S. dollar may bias the calculation of PPP. Its use here is
mainly for illustrative purposes.



tions from PPP, there is no w ay to tell directly whether
short-run adjustments to changes in m oney growth or
changes in real phenom ena are responsible. Attribut­
ing a cause-and-effect relationship between some
event and exchange rates is difficult because it in­
volves a complete understanding o f the dynamic pro­
cess that characterizes the adjustment to a monetary
shock. There are, however, several indirect routes to
take.

Previous Empirical Studies
One source o f evidence is the existing literature on
changes in money growth and exchange rates. Frankel
(1979), for example, has analyzed the deutsche mark/
dollar relationship over the period from July 1974 to
February 1978. He found that with a once-and-for-all 1
percent expansion o f the U.S. money supply, the DM/$

9

FEDERAL RESERVE BANK OF ST. LOUIS

OCTOBER 1984

Chart 4

Deviations from Purchasing P o w e r Parity and M o n e ta ry Shocks

1976

77

78

79

80

81

82

83

1984

S o u r c e s : I n t e r n a t i o n a l M o n e t a r y F und I n t e r n a t i o n a l F i n a n c i a l S t a t i s t i c s a n d B o a r d o f G o v e r n o r s
o f th e F e d e r a l R e s e r v e System
l_L F o u r - q u a r t e r p e r c e n t c h a n g e in t h e n o m i n a l t r a d e - w e i g h t e d e x c h a n g e r a t e p l u s t h e c o r r e s p o n d i n g i n f l a t i o n d i f f e r e n t i a l
1 2 C u r r e n t o n e - q u a r t e r m o n e y g r o w t h m i n u s p r e v i o u s 1 2 - q u a r t e r m o n e y g r o w th
_

exchange rate overshot its PPP rate by 0.23 percent, all
other things constant. After one year, approximately
44 percent o f this PPP deviation was eliminated.
Pigott also investigated the relative importance of
real and nominal sources o f monthly exchange rate
changes. Using data from May 1973 to August 1980 for
six currencies, he found that “real factors have repre­
sented a major source . . . o f exchange-rate fluctua­
tions. . . .'M Moreover, monetary influences did not
l
appear to have been substantially responsible for real
changes in the exchange rate.
Finally, using Granger causality tests, Throop (1984)
could find no statistically significant relationship be­
tween changes in the real exchange rate and current

"Pigott (1981), p. 49.

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Federal Reserve Bank of St. Louis

and past rates o f m oney growth during the period
from 1973 to 1980. Therefore, unless the w orld has
changed dramatically since 1980, it appears unlikely
that monetary shocks could have been the primary
cause o f the substantial and persistent deviations
from PPP that w e have seen in the past four years.1
2

A Comparison o f the Data
Another approach to assessing the link between
money and PPP is sim ply to compare deviations from
PPP with a measure o f m onetaiy shocks. Chart 4 does
this using deviations from PPP (from chart 3) and
m onetaiy shocks measured as deviations o f the quar­

,2M1 growth does not Granger-cause changes in the real tradeweighted exchange rate even when the sample is extended to
March 1984.

OCTOBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Table 1

Changes in Bilateral Real Exchange Rates and Real Imports of U.S. Agricultural
Products: Selected Countries
1982

1981

Country
France
United Kingdom
Germany
Venezuela
Brazil
Japan
Morocco
Saudi Arabia
Mexico
Spain
Canada
Netherlands

Exchange Rate
21.3%
3.8
27.5
-7 .2
-18.8
-1.9
26.3
8.5
-12.5
22.9
1.5
26.5

Imports

Exchange Rate

-35.6%
-19.8
-16.8
35.3
10.3
6.1
15.0
31.3
25.4
-25.0
5.1
-18.3

15.5%
16.4
10.1
-3.2
0.0
15.0
13.4
8.0
44.1
11.6
-1.9
9.4

1983

Imports
20.8%
12.7
2.8
-5.3
-20.0
-3.2
15.7
5.2
-33.6
63.8
2.9
15.6

Exchange Rate

Imports

12.3%
14.4
5.7
-3 .0
57.6
3.0
14.6
2.8
40.2
20.9
-2.9
7.4

-19.4%
-8.9
-5 .5
-15.3
-28.7
5.1
37.1
-1.1
21.0
-27.1
3.3
-12.3

NOTE: Figures are percent changes from previous fiscal year. A positive change in the real exchange rate indicates an appreciation of the
dollar against that country's currency.
SOURCES: IMF’s International Financial Statistics, Agricultural Statistics, Annual Supplement to Foreign Agricultural Trade of the U.S.
terly rate o f U.S. M l growth from the previous 12quarter moving average. If quarterly deviations o f M l
growth from its trend growth accurately measure
monetary shocks, and if monetary shocks were re­
sponsible for generating deviations from PPP, a nega­
tive relationship should be revealed between the se­
ries in chart 4. That is, faster than expected money
growth should induce negative deviations from PPP,
and vice versa. A comparison, however, reveals no
statistically significant relationship between monetary
shocks and deviations from PPP over the entire
period.,;l

FACTORS AFFECTING AGRICULTURAL
EXPORT DEMAND

this period has been blamed as the primary cause o f
the recent decline in agricultural exports. The extent
to which the real appreciation o f the exchange rate
has actually affected exports, however, remains to be
investigated.
To do so requires identifying the marginal impact of
real changes in the exchange rate on exports. A variety
of factors other than exchange rates could be im por­
tant determinants o f the w orld ’s demand for U.S.
agricultural exports. In fact, these factors could dom i­
nate the effect that exchange rates have had on the
competitive trade position o f U.S. agriculture.

Agricultural Exports and Exchange
Rates

The evidence presented above suggests that m one­
tary policy has not been responsible for deviations
from PPP during the 1980s. Thus, the real rise in the
exchange rate came from other sources. Whatever the
source, the real appreciation of the exchange rate over

As an introduction to investigating the relationship
between exchange rate changes and U.S. trade, con­
sider how the volum e o f agricultural exports to spe­
cific countries has behaved since the dollar began to
appreciate in real terms in 1981. The countries listed
in table 1 represent a broad cross-section o f developed

13The simple correlation coefficient between the two series in chart 4
is -0.137, which is not statistically different from zero at the 5
percent level. There is a subperiod, however, during which the
hypothesized relationship is supported. In particular, the correlation
between these series for the period 1/1976—IV/1979 is -0.84. The
correlation over the subsequent period (1/1980-1/1984) is only
-0.085. Thus, monetary shocks are highly correlated with devia-

tions from PPP during the former period, but not at all during the
latter one.
Furthermore, when Granger causality tests were performed be­
tween monthly changes in the real trade-weighted exchange rate
and monthly monetary shocks for the period March 1973-March
1984, Granger-causality was statistically significant at the 5 percent
level in only one of 144 different lag specifications investigated.




11

FEDERAL RESERVE BANK OF ST. LOUIS

and developing nations with a variety o f capacities for
domestic agricultural production. Moreover, because
each nation’s currency has changed in value relative
to the dollar by a different amount, these data show
individual cases for which a given movement in the
real exchange rate has been associated with a particu­
lar change in a nation's imports o f U.S. agricultural
products. The nations listed represent about half of
U.S. agricultural exports in the three years shown.
The data in the table reveal no consistent relation­
ship across countries between changes in the real
value o f their currencies relative to the dollar and
changes in their real imports o f U.S. agricultural prod­
ucts. No country’s trade pattern was com pletely con­
sistent with an exchange rate explanation o f trade
flows: imports decreasing in years when the value o f
the dollar rose and increasing when the value o f the
dollar fell. Indeed, M orocco and Saudi Arabia gener­
ally increased their imports even though their curren­
cies depreciated against the dollar in all three years.
The import patterns o f the other countries followed
no consistent pattern over this interval. For example,
the pound/dollar exchange rate increased between
about 4 percent and 16 percent over the period, but
changes in British imports ranged between 12.7 per­
cent and —19.8 percent. Similarly, the Spanish peseta
declined in both 1981 and 1982; imports in those iwo
years, however, first fell by 25 percent, then rose by 64
percent.

OCTOBER 1984

higher the level o f foreign real econom ic activity, other
things equal, the larger w ould be foreign dem and for
U.S. agricultural exports. The higher the price o f U.S.
exports relative to those abroad, other things equal,
the smaller w ould be the demand for U.S. agricultural
exports.
On the other side o f the market, the supply o f U.S.
agricultural exports was expressed as a function o f the
prices o f U.S. agricultural exports relative to the prices
o f other goods and services produced in the United
States and exogenous factors such as weather, embar­
goes, etc. Other things equal, the higher the price o f
U.S. agricultural exports relative to prices o f other
goods, the larger the production o f U.S. agricultural
products for export.
To generate an estimating equation for this model, a
market equilibrium was assumed and a reduced form
obtained. Furthermore, since adjustment to price
changes w ill not occur immediately, each relative
price variable was specified as a distributed lag to
capture the dynamics o f this adjustment process.1
5
The real exchange rate was included to measure U.S.
prices relative to those in the rest o f the w orld (ex­
pressed in dollars), net o f changes in inflation differen­
tials. Finally, a log-linear specification was employed,
yielding the following equation estimated for the p e­
riod 1/1971—
1/1984:
(2) In (AGX), = 0.73 + 1.32 In (FGNP),
(0.54)
(10.93)
2

A Simple Model o f U.S. Agricultural
Exports
Since the data in table 1 reveal no consistent rela­
tionship between real changes in the exchange rate
and the volume o f U.S. agricultural exports, other
factors must also be important determinants o f for­
eign demand for U.S. agricultural products. To isolate
the relative importance o f these other influences, as
w ell as to assess the marginal impact o f exchange rate
changes, a simple m odel o f agricultural exports was
constructed.1
4
This m odel focuses on the forces that affect the
world demand for and the supply o f U.S. agricultural
exports. The w orld dem and for U.S. agricultural ex­
ports was assumed to depend on just two factors: the
level o f foreign real econom ic activity and the price of
U.S. exports relative to those o f other countries. The

14This model is fashioned after those in Clark (1974), Goldstein and
Khan (1978), Spitaller (1980) and Stevens, et al. (1984).

12


-

-

RJ = 0.94

0.30 I b, In (USAGP/USCPI)W
(5.43) i = 1
5
0.71 2 Cj In (RTVVER)h
(4.49) j = 1

SE = 0.058

DW = 1.51

where AGX = the volume of U.S. agricultural exports (in
1972 dollars),
FGNP = the trade-weighted index of foreign real
GNP,
USAGP = the price index o f U.S. agricultural exports,
USCPI = the U.S. consumer price index,
RTWER = the real trade-weighted index o f the foreign
exchange value of the U.S. dollar, and

,5The lag lengths were chosen using procedures described in the
appendix to Batten and Thornton (1984). A search for a distributed
lag for foreign real income was also conducted, but none was found.

FEDERAL RESERVE BANK OF ST. LOUIS
In = the natural logarithm.'6

The absolute value o f the t-statistic for testing the
hypothesis that the estimated coefficient equals zero
is reported in parentheses below each estimate. The
equation fits the data well, explaining 94 percent of the
variance o f the natural logarithm o f the volume o f U.S.
agricultural exports.
Since our objective is to assess the relative impacts
o f foreign econom ic activity and real exchange rates
on export volume, the coefficients o f FGNP and
RTWER are o f particular interest. The log-linear speci­
fication generates estimated coefficients that are par­
tial elasticities. A partial elasticity measures the per­
centage change o f the dependent variable (AGX here)
resulting from a 1 percent change in one o f the
independent (right-hand-side) variables, holding all
other variables constant. For example, the estimated
coefficient o f RTWER measures the percentage change
in the volume o f U.S. agricultural exports resulting
from a 1 percent change in the real exchange rate. In
this case, a 1 percent increase in the real exchange rate
leads to a 0.71 percent decline in the volume o f U.S.
agricultural exports. The significantly negative coef­
ficient o f RTWER suggests that increases in the value of
the dollar indeed have contributed to the recent
decline in U.S. agricultural exports. At the same time,
however, the estimated equation contradicts the no­
tion that exchange rate changes are the most im por­
tant determinant o f U.S. agricultural exports.
This contradiction can be seen by calculating the
standardized regression coefficients for the explana­
tory variables in the equation. The reported coef­
ficients give no indication o f the relative explanatory
pow er o f the independent variables, because these

,6Since weather Is an important exogenous determinant of agricul­
tural production, a dummy variable (0, 1) was included initially to
reflect periods of below-normal rainfall in the United States. The
estimated coefficient of this variable is not statistically significant
and, consequently, is not reported.
The real trade-weighted exchange rate, included to capture
relative price changes, was calculated as:
RTWER = TWER x (USCPI/TWFCPI),
where TWER = nominal trade-weighted exchange rate, and
TWFCPI = trade-weighted foreign CPI (see footnote 9 for
further details).
17The sum of the estimated coefficients of (USAGP/USCPI) should be
positive. The significantly negative coefficient may represent an
example of the classical identification problem. For example, this
may denote that the supply of agricultural exports may be shifting
relatively more than the demand for agricultural exports during the
period over which the equation is estimated.



OCTOBER 1984

variables are expressed in different units. In contrast,
the standardized regression coefficient is calculated
from an equation in which the variables have been
standardized (i.e., expressed in the same units). Con­
sequently, a comparison o f these coefficients indi­
cates the relative importance o f the independent vari­
ables in explaining the dependent variable.
In this case, the estimated standardized regression
coefficient o f foreign real incom e is 0.69, w hile that of
the real trade-weighted exchange rate is —0.39. In
other words, foreign dem and for U.S. agricultural
exports has been about 75 percent more sensitive to
changes in foreign real econom ic activity (FGNP) than
to changes in the real exchange value o f the dollar.
Based on these reduced-form coefficients, changes in
foreign incom e have been primarily responsible for
the changes in foreign demand for U.S. agricultural
exports from 1/1971 to 1/1984.

The 1982— Decline
83
Though the data demonstrate that the level of
foreign real econom ic activity has been a more im por­
tant determinant o f real U.S. agricultural exports than
the real exchange rate since the early seventies, they
shed no light on the question o f w hy the volume o f
agricultural exports has declined recently. Since the
income effect and the exchange rate effect have op p o­
site signs, identifying whether the recent impact of
changes in foreign real incom e is larger or smaller
than that o f changes in the real exchange rate w ould
be straightforward if both w orld real incom e and the
real exchange rate had risen during 1982 and 1983.
During this period, however, the w orld experienced
an econom ic recession as w ell as a real appreciation of
the dollar. Consequently, both effects resulted in
low er exports o f U.S. agricultural products.
To isolate these two effects, the following experi­
ment was performed. First, the level o f foreign real
income was held at its IV/1981 level. (This date was
chosen because it marks the beginning o f the w orld
recession.) Next, the m odel’s predicted values for
exports, holding foreign incom e constant, w ere com ­
pared with predicted export values, allowing foreign
income to vary for the period 1/1982-1/1984. The differ­
ence represents the marginal impact o f changes in
foreign real incom e on the predicted level o f real
agricultural exports. The simulation was repeated
under conditions that held the real exchange rate
constant, then allowed it to vary as it did between 1
/
1982 and 1/1984.

13

FEDERAL RESERVE BANK OF ST. LOUIS

The results are striking. From 1/1982 to IV/1982, the
marginal impact o f the w orld recession was to reduce
predicted U.S. agricultural exports by almost 2 per­
cent, while the marginal impact o f the appreciation of
the U.S. dollar was negligible. As the w orld econom y
began to recover in 1/1983, the marginal impact o f
foreign income became positive, stimulating pre­
dicted U.S. agricultural exports by nearly 5 percent
from 1/1983 to 1/1984. During the latter period, how ­
ever, the continued appreciation o f the dollar de­
pressed predicted U.S. agricultural exports by almost 7
percent, outweighing the positive impact o f the w orld
recoveiy. In sum, only during the past five quarters
can the fall in U.S. agricultural exports be “blam ed” on
the appreciating dollar. Before that, the w orld reces­
sion was the culprit.

SUMMARY AND CONCLUSIONS
A number o f economists have argued that increases
in the foreign exchange value o f the dollar have been
responsible for recent declines in exports o f U.S.
agricultural commodities. These arguments, however,
generally have been based on simple comparisons o f
exchange rates and exports. Moreover, they have not
recognized essential distinctions between real and
nominal exchange rate changes.
The analysis presented in this article explained the
fundamental differences between nominal and real
movements in exchange rates and investigated the
effects o f variables other than the exchange rate on
exports. Tabular data for 1981-83 indicated no con­
sistent pattern between changes in the real value of
the dollar and imports o f U.S. agricultural com m odi­
ties by foreign countries. More detailed empirical
evidence on factors affecting the volume o f U.S. agri­
cultural exports showed that real exchange rates were
related negatively to exports, but their impact was
dominated by the level o f real GNP in importing
nations. Overall, the analysis suggests a weak link
between U.S. m oney growth and real exchange rates
and indicates that foreign incom e — not exchange
rates — has been the primary determinant o f agricul­
tural exports.

REFERENCES

Batten, Dallas S., and Clifton B. Luttrell. “ Does Tight Monetary
Policy Hurt U.S. Exports?" this Review (August/September 1982),
pp. 24-27.
Batten, Dallas S., and Mack Ott. "Five Common Myths About
Floating Exchange Rates," this Review (November 1983), pp. 515.
Batten, Dallas S., and Daniel L. Thornton. “How Robust Are the

14


OCTOBER 1984

Policy Conclusions of the St. Louis Equation?: Some Further
Evidence,” this Review (June/July 1984), pp. 26-32.
Chambers, Robert G., and Richard E. Just. “An Investigation of the
Effect of Monetary Factors on Agriculture,” Journal of Monetary
Economics (March 1982), pp. 235-47.
Chattin, Barbara, and John E. Lee, Jr. “United States Agricultural
Policy in a 'Managed Trade’ World,” in United States Farm Policy in
a World Dimension, Special Report 305, Agricultural Experiment
Station, University of Missouri-Columbia (November 1983), pp.
18-27.
Chrystal, K. Alec. “Dutch Disease or Monetarist Medicine?: The
British Economy under Mrs. Thatcher," this Review (May 1984),
pp. 27-37.
Clark, Peter B. “The Effects of Recent Exchange Rate Changes on
the U.S. Trade Balance,” in Peter B. Clark, Dennis E. Logue and
Richard James Sweeney, eds., The Effects of Exchange Rate
Adjustments, the Proceedings of a Conference sponsored by
OASIS Research (Department of the Treasury, 1974), pp. 201-36.
Dornbusch, Rudiger. “ Expectations and Exchange Rate Dy­
namics," Journalof Political Economy (December 1976), pp. 1161—
76.
Frankel, Jeffrey A. “On the Mark: A Theory of Floating Exchange
Rates Based on Real Interest Differentials,” American Economic
Review (September 1979), pp. 610-22.
Frenkel, Jacob A. “The Collapse of Purchasing Power Parities
During the 1970s,” European Economic Review (May 1981), pp.
145-65.
Goldstein, Morris, and Mehsin S. Khan. “The Supply and Demand
for Exports: A Simultaneous Approach,” Review of Economics and
Statistics (May 1978), pp. 275-86.
Hathaway, Dale E. “Agricultural Trade: 1984 and Beyond,” in
Outlook '84, Proceedings of the Agricultural Outlook Conference,
U.S. Department of Agriculture, Washington, D.C. (November
1983).
“Index of the Weighted-Average Exchange Value of the U.S. Dollar:
Revision,” Federal Reserve Bulletin (August 1978), p. 700.
Korteweg, Pieter. Exchange-Rate Policy, Monetary Policy, and Real
Exchange-Rate Variability (Princeton University Press, 1980).
Mussa, Michael. "Empirical Regularities in the Behavior of Ex­
change Rates and Theories of the Foreign Exchange Market,” in
Karl Brunner and Allan H. Meltzer, eds., Policies for Employment,
Prices, and Exchange Rates, Carnegie-Rochester Conference
Series on Public Policy (1979), pp. 9-57.
________. “A Model of Exchange Rate Dynamics,” Journal of
Political Economy (February 1982), pp. 74-104.
Pigott, Charles. “The Influence of Real Factors on Exchange
Rates,” Federal Reserve Bank of San Francisco Economic Review
(Fall 1981), pp. 37-54.
Schuh, G. Edward. “Future Directions for Food and Agricultural
Trade Policy,” American Journal of Agricultural Economics (May
1984), pp. 242-47.
Spitaller, Erich. “Short-Run Effects of Exchange Rate Changes on
Terms of Trade and Trade Balance,” IMF Staff Papers (June
1980), pp. 320-48.
Stevens, Guy V. G., et al. The U.S. Economy in an Interdependent
World: A Multicountry Model (Board of Governors of the Federal
Reserve System, 1984).
Throop, Adrian W. "Anatomy of the 1981-83 Disinflation," Federal
Reserve Bank of San Francisco Weekly Letter (March 23, 1984).
Tweeten, Luther. “Economic and Policy Outlook for U.S. Agricul­
ture,” in United States Farm Policy in a World Dimension, Special
Report 305, Agricultural Experiment Station, University of Mis­
souri-Columbia (November 1983), pp. 13-17.

Hedging Interest Rate Risk with
Financial Futures: Some Basic
Principles
Michael T. Belongia and G. J. Santoni

F

M . OR much o f the postwar period, stable rates o f
inflation — accompanied by stable levels o f interest
rates — created a comforting economic environment
for managers o f depositoiy institutions. Beginning in
the mid-1970s, however, more variable interest rates,
brought about in part by more variable inflation, caused
a substantial change in the economic conditions facing
depositoiy institutions. Offering long-term credit at
fixed rates became riskier as larger and more frequent
unexpected changes in interest rates introduced more
variation into the market value o f these assets.1
This article describes h ow variation in interest rates
affects the market value o f depositoiy institutions. The
discussion then demonstrates how financial futures
contracts might be used to hedge some o f the interest
rate risk o f a portfolio com posed o f interest-sensitive
deposit accounts and loans o f unmatched maturities.
Although some regulatoiy authorities have denied or
strictly regujated the use o f futures contracts by de-

Michael T. Belongia is an economist and G. J. Santoni is a senior
economist at the Federal Resen/e Bank of St. Louis. John G. Schulte
provided research assistance.
'For a general description of events that have introduced or in­
creased interest rate risk, see Carrington and Hertzberg (1984) and
Koch, etal. (1982).



positoiy institutions in the belief that futures trading
is risky and unduly speculative, w e argue that the
judicious use o f futures can reduce the firm ’s expo­
sure to interest rate fluctuations.’

DURATION GAP AND INTEREST RATE
RISK
In the mid-1970s, w hen large fluctuations in interest
rates began to occur, it became increasingly evident
that depository institutions needed some measure of
the relative risks associated with various portfolio
holdings. One approach to the measurement o f inter­
est rate risk is called Duration Gap analysis. "Dura­
tion” refers to the "average” life of some group of
assets or liabilities. “ Gap” refers to the difference
between the durations o f an institution 's assets and its
liabilities.3

2Legal restrictions and guidelines on the use of financial futures by
different types of financial institutions are summarized in Lower
(1982). A comparison of statutes on the use of futures by insurance
companies is made in Gottlieb (1984).
3For more detailed discussions of duration analysis and its applica­
tion to financial institution portfolios, see Kaufman (1984); Bierwag,
Kaufman andToevs (1983); Toevs (1983); Santoni (1984); Samuelson (1944); and Hicks (1939), pp. 184-88.
15

FEDERAL RESERVE BANK OF ST. LOUIS

OCTOBER 1984

Table 1

Expected Streams of Receipts and Payments
0

Panel A: No Change in Interest Rates
Asset (loan)
Receipts
Payments
Liabilities (borrowings)
Receipts
Payments
Net Receipts

90

Day
180

270

$1,000.00

$909.09
909.09
-0-

360

$926.75
926.75
-0-

$944.76
944.76
-0-

$963.11
963.11
-0-

981.82
$ 18.18

Present Value $18.18/1.10 = $16.53
Panel B: Interest Rates Rise by 200 Basis Points
Asset (loan)
Receipts
Payments
$909.09
Liabilities (borrowings)
Receipts
909.09
Payments
Net Receipts
-0-

$1,000.00
$926.75
926.75
-0-

$949.10
949.10
-0-

$971.98
971.98
-0-

995.42
$ 4.58

Present Value = $4.58/1.12 = $4.09
Panel C: Interest Rates Fall by 200 Basis Points
Asset (loan)
Receipts
Payments
$909.09
Liabilities (borrowings)
Receipts
909.09
Payments
Net Receipts
-0-

$1,000.00
$926.75
926.75
-0-

$940.35
940.35
-0-

$954.15
954.15
-0-

968.15
$ 31.85

Present Value = $31.85/1.08 = $29.49

An Example
The risk introduced into a portfolio o f assets and
liabilities o f different duration is illustrated in tables 1
and 2. In this example, for expositional simplicity, the
firm’s planned life is assumed to be only one year. It
has extended a loan with a face value o f $1,000 to be
repaid in a single payment at the end o f the year at an
interest rate o f 10 percent. The present value o f the
loan, and, thus, the amount paid out by the firm to the
borrower, is $909.09. To finance this loan, the firm
borrows $909.09 for 90 days at 8 percent interest. The
two percentage-point spread is the return earned by

16


the firm for em ploying its specialized capital in inter­
mediating between borrowers and lenders.
The amount that the firm w ill ow e in three months'
time is $926.75 ( = $909.09(1.08)“ ), which it plans to
pay by borrowing this amount for another 90 days.
Because the firm ’s proceeds from the new loan and its
payment o f the old loan cancel, its net receipts at this
time are zero. The firm anticipates being able to roll
the loan over every 90 days at the same interest rate.
Consequently, at the end o f 180 days, the firm expects
to owe $944.76 ( = $926.75(1.08)■“ ), which it plans to pay
with new borrowings. At the end o f the year, the firm

OCTOBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Table 2

Interest Rate Changes and the Present
Value of a Portfolio of Assets and
Liabilities of Different Durations
Panel A: Initial Conditions
Present Values
Asset:
Liability:
$1,000.00 „
$981.82
------------- = $909.09
----------- =
$892.56
1.10
1.10
Equity:
$909.09 - $892.56 = $16.53
Panel B: All Interest Rates Rise by 200 Basis Points
Present Values
Asset:
Liability:
$1,000.00 = $892.86
„
$995.42 =
----------------------$888.77
1.12

1.12

Equity:
$892.86 - $888.77 = $4.09
Percentage change in equity =
-75.26

anticipates having to pay $981.82 ( = $909.09 X 1.08).
This amount will be paid out o f the $1,000 proceeds
from its matured asset. The firm ’s expected net receipt
at year-end is $18.18, as shown in panel A o f table 1.
Panel A of table 2 is a balance sheet summary o f the
present value o f this investment plan. The present
value o f the expected net receipt at year-end is $16.53
and is equal to the difference between the present
value o f the asset, $909.09 ( = $1,000/1.10), and the
present value o f the expected liability, $892.56
( = $981.82/1.10). Both future values are discounted at
10 percent, the firm ’s opportunity cost.

The Effects o f Changing Interest Rates
on Equity
This package o f assets and liabilities is subject to
considerable interest rate risk because the 10 percent
interest rate on the firm's loan is fixed for one year
w hile its borrowings must be refunded every 90 days.
In this example, the gap between the durations of the



asset and liability is 270 days ( = 360 — 90).4 As a
practical matter, the asset’s longer duration implies
that a given change in interest rates w ill change the
present value o f the asset more than it w ill affect the
present value o f the liability. This difference, o f course,
w ill change the value o f the firm ’s equity.
Panel B o f table 1 shows the effect o f an unexpected
200 basis-point rise in interest rates. The increase
raises the firm ’s anticipated refunding costs. As a
result, the amount the firm expects to pay at year-end
increases to $995.42. Net receipts fall to $4.58 and the
present value o f the investment plan falls to $4.09.
Panel B o f table 2 presents a balance sheet summary
o f the effect o f the change on the present values o f the
asset, liability and ow ner equity. The increase in
interest rates reduces the present values o f both the
asset and liability, but the asset value falls by relatively
more because its life is fixed for one year, w hile the
liability must be rolled over in 90 days at a higher
interest rate. The increase in interest rates causes
ow ner equity to fall by $12.44, or about 75 percent. In
contrast, had the interest rate declined by 200 basis
points, the net present value o f the firm ’s equity w ould
have risen to $29.49 (see panel C o f table 1), an increase
of about 78 percent.
This extreme volatility in the firm ’s equity is due to
the mismatch o f the durations o f the asset and liability
that make up the firm ’s portfolio. Table 3 illustrates
this point. The only difference between this and ear­
lier examples is that, in table 3, the duration o f the
liability has been lengthened to match the duration of
the asset. W hile a 200 basis-point increase in the
interest rate still causes the present value o f the
portfolio to fall, the change, —$0.30 or —1.8 percent, is
much less than before. Clearly, matching the dura­
tions o f the asset and liability exposes the value o f the
portfolio to much low er interest rate risk.

COPING WITH THE GAP
Depository institutions, particularly savings and
loan associations, maintain portfolios o f assets and
liabilities that are similar to the one shown in the
initial example.5 That is, the duration o f their assets

4The durations of single-payment financial instruments are equal to
the maturities of the instruments. In other cases, calculation of
duration is not as straightforward. See footnote 3.
5Savings and loan associations are required to maintain a significant
share of their portfolios in long-term home mortgages in order to
obtain federal insurance of deposits. See Federal Home Loan Bank
Act of 1932, sec. 4(a).
17

FED ER A L R E S E R V E BA N K OF ST. LOUIS

O CT O B ER 1984

Futures Markets and Risk

Table 3

Interest Rate Changes and the Present
Value of a Portfolio of Assets and
Liabilities of the Same Duration
Panel A: Initial Conditions
Present Values
Asset:
Liability:
$1,000.00 = $909.09
„
$981.82 =
-------------------- -$892.56
1.10

1.10

Equity:
$909.09 - $892.56 = $16.53
Panel B: All Interest Rates Rise by 200 Basis Points
Present Values
Asset:
Liability:
$1,000.00 „
$981.82
—J--------- = $892.86
----------- =
$876.63
1.12

It may seem odd that the futures market, which is
generally thought of as being very risky, can be used to
reduce risk. Futures trading is risky for people w ho bet
on the future price movements o f particular com m od­
ities or financial instruments by taking long or short
positions in futures contracts. Such speculative bets
on future price movements, however, are not unique
to futures market trading. The nature o f most types o f
businesses requires a speculative bet about the future
course o f a particular price.

1.12

Equity:
$892.86 - $876.63 = $16.23
Percentage change in equity =
-

Growing crops, for example, gives farmers long
positions in physical comm odities during the growing
season. These long positions expose the farmer to the
risk o f price declines — declines that can reduce the
profits from efficient farming (the activity that the
farmer specializes in). Judicious use o f the futures
market allows the farmer to offset his long position in
the com m odity by selling futures contracts. Since the
sale reduces his net holdings o f the commodity, the
farmer's exposure to the risk o f future price declines is
reduced. Similarly, futures trading presents deposi­
tory institutions with the opportunity to reduce their
exposure to the risk o f interest rate changes.

1.8

Futures Contracts
typically is longer than the duration o f their liabilities.
As a result, the market values o f these institutions have
been particularly sensitive to interest rate fluctua­
tions. This, along with the recent experience o f highly
variable interest rates, has led these institutions to
seek out methods to reduce their exposure to interest
rate risk. Am ong other things, these firms have made
greater use o f floating rate loans and interest rate swap
agreements. Recent regulatory changes have allowed
them to allocate more o f their loan portfolios to short­
term consumer loans. In addition, a number o f institu­
tions are using financial futures to reduce their expo­
sure to interest rate risk.6

6See Booth, Smith and Stolz (1984). While a number of financial
firms are employing the futures market, it seems that accounting
requirements have discouraged the use of futures to hedge interest
rate risk. Until recently, regulators and accountants feared that
losses from futures transactions could be hidden in financial reports.
Therefore, they would not permit a hedge to count as one transac­
tion with spot gains or losses offsetting futures markets losses or
gains. Instead, they required futures losses to be marked to the
market while spot gains could be deferred. This asymmetric treat­
ment of gains and losses on the two sides of a hedge distorted
earnings estimates and, therefore, discouraged the use of futures.

18


A futures contract is an agreement between a seller
and a buyer to trade some w ell-defined item (wheat,
com , Treasury bills) at some specified future date at a
price agreed upon now but paid in the future at the
time o f delivery. The futures price is a prediction
about what the price o f the item w ill be at the time of
delivery.
In the case o f commodities, the price o f the good
today (the spot price), on average, w ill be equal to the
futures price minus the cost o f storage, insurance and
foregone interest associated with holding the good
over the interval o f the contract. A similar relationship
exists between the spot and futures prices o f financial
instruments. However, since the storage and insur­
ance cost of holding these instruments is very low, the
spread between the spot and futures prices is largely
determined by the interest cost.

See Morris (1984) for more detail on changes in accounting stan­
dards. Asay, et al. (1981) provide examples of how former account­
ing standards discouraged the use of futures by banks and thrift
institutions.

FED ER A L R E S E R V E BA N K OF ST. LOUIS

The Relationship Between Spot and
Futures Markets f o r Treasury Bills: An
Illustration
In January 1976, the International Monetary Market
(IMM), now part o f the Chicago Mercantile Exchange
(CME), began trading futures contracts in 13-week
Treasury bills.7The basic contract is for $1 million with
contracts maturing once each quarter in the third
week o f March, June, September and December. Since
there are eight contracts outstanding, the most distant
delivery date varies between 21 and 24 months into the
future.
Panel A o f table 4 presents quotations for Treasury
bill futures for the trading day o f August 7,1984. Panel
B o f table 4 lists spot quotations for Treasury bills for
the same trading day*
Panel A o f table 4 is interpreted as follows: Septem­
ber Treasury bill futures were trading at a discount of
10.49 percent on August 7, 1984. Any person trading
this contract obtained the right to buy (sell) a Treasury
bill the third week in September with a remaining
maturity o f 13 weeks at a discount rate o f 10.49
percent. A similar statement holds for the other con­
tracts listed in panel A.
Panel B lists spot market quotations. For example,
Treasury bills due to mature August 9,1984, traded at a
discount o f 9.91 percent (bid) to 9.79 percent (ask),
while those maturing September 20, 1984, traded at a
discount o f 9.95 (bid) to 9.91 (ask), etc.
We noted earlier that the spot and futures markets
must be closely related, and the data in panels A and B
can be used to illustrate this point. For example, on
August 7, 1984, an investor could purchase a Treasury
bill due to mature December 20, 1984 (i.e., 134 days
later). If he purchases the bill on the spot market, he
obtains the asked discount o f 10.39 percent. At this
discount rate, the price he pays for the bill is $96.41 per
$100 o f face value.3

'Futures contracts in other types of financial instruments, such as
GNMA passthrough certificate contracts, 90-day CDs, Treasury
bonds and Treasury notes, also are available at the Chicago Board
of Trade.
8The information in table 3 is taken from pages 38 and 39 of the
August 8, 1984, Wall Street Journal. The actual tables in the Wall
Street Journal contain more information than is presented here. For
our purposes, however, the additional information is extraneous.
9$96.41 = $100/(1.1039)37. The discount factor is raised to the
power of 134/360 = .37. This calculation is slightly different from the
discount calculation used in determining actual trading prices, but



O CTO BER 1984

Table 4

Market Quotations for U.S. Treasury
Bills: August 7 , 19841
Panel A: Treasury Bill Futures (IMM)
Discount
Contract
settle
1984
September
10.49
December
10.85
1985
March
11.13
11.35
June
September
11.52
December
11.66
1986
March
11.79
11.90
June
Panel B: Treasury Bill Spot
Discount
Maturity Date
August 9, 1984
September 20, 1984
December 20, 1984
March 21, 1985
June 13, 1985
July 11, 1985

Bid
9.91
9.95
10.45
10.63
10.72
10.73

Ask
9.79
9.91
10.39
10.56
10.66
10.69

'Wall Street Journal, August 8, 1984, pp. 38-9.
Alternatively, the investor could purchase a futures
contract that gives him the right to buy a Treasury bill
in September that w ill mature the third week in
December. This alternative gives him a discount rate of
10.49 percent. Buying the Treasury bill in September at
this discount w ould require a payment o f $97.54.’" This
payment w ill be made 43 days into the future, roughly,
September 20, and the present value o f the payment
on August 7 is $96.44." Notice that this is very near the
amount that the investorw ould pay ($96.41) if he were
to purchase a Treasury bill on the spot market that
matured during the third week o f December.
Of course, other alternatives are open to the investor
as well. He could, for example, buy a Treasury bill that
matured the third week in March on the spot market.

numerical differences between the two formulas are small. See
Stigum (1981) for the market’s discount formula.
,0$97.54 = $100/(1.1049)2S.
” $96.44 = $97.54/(1.0991 ) 12. The interest rate used in the calcula­
tion is the rate on August 7 for a security maturing on September 20
(43 days in the future).
19

FEDERAL RESERVE BANK OF ST. LOUIS

The present cost o f doing this should be near the
present cost o f buying a futures contract that allows
him to purchase a Treasury bill in Decem ber maturing
the third week in March. Table 5 uses the data in table
4 to compare the present costs o f this and other
alternatives. In each case, the present costs of em ploy­
ing the spot vs. the futures market are very close.1
2
Because a close relationship between these markets
exists, the Treasury bill futures market can be used
effectively to hedge interest rate risk.1
3

HEDGING THE GAP
The Streams o f Receipts and Payments
The example in table 1 can be used to illustrate how
futures contracts can be applied to hedge the interest
rate risk caused by the mismatch in the lives (dura­
tions) o f the firm’s assets and liabilities. Considerable
confusion appears to exist as to what the firm's hedg­
ing objective should be and how hedges should be
constructed. One possible hedging strategy is to pro­
tect the equity o f the firm (in the present value sense)
from interest rate fluctuations. Another often-cited
strategy is to m inim ize discrepancies between cash
flows over time. It seems clear, however, that firm
owners w ill choose a hedge that protects their net
wealth (present value o f the firm ’s equity). This focus
on net wealth is crucial because, as the examples
show, reducing cash flow mismatches to zero does
not m inim ize the exposure o f the firm ’s equity to
interest rate changes.

Hedging Met Wealth: An Example
Suppose it is September 15, 1984, and the firm
initiates the transactions summarized earlier in panel
A o f table 1. In addition, to hedge each o f its three
refunding requirements, the firm sells December,
March and June futures contracts at 10 percent dis­
counts.1 The price o f each contract is $1,000/(1.10)2 =
4
5

12Small differences are due to the existence of transaction costs. If the
differences were large, profitable arbitrage opportunities would
exist. These, of course, would vanish quickly as traders took
advantage of the situation.
,3There is, of course, the problem that the spot instrument being
hedged may not be identical to the futures market instrument. If so,
the price of one may diverge from the other because of a change in a
factor that affects the price of one but not the other. This is called
“basis risk” and is ignored in the following examples.
,4A flat yield curve is assumed for ease of exposition. The examples
become more complicated if the yield curve slopes up or down and/
or the spread between borrowing and lending rates changes.

http://fraser.stlouisfed.org/
20
Federal Reserve Bank of St. Louis

OCTOBER 1984

Table 5

The Relationship Between Treasury Bill
Spot and Futures Prices: August 7,
1984, Per $100 of Face Value
Case 1: Purchase of a Treasury bill that matures the third week
in December 1984
Present Cost
Spot Market Purchase
$96.41
September Futures Purchase
96.44
Difference
.03
Case 2: Purchase of a Treasury bill that matures the third week
in March 1985
Present Cost
Spot Market Purchase
$93.92
December Futures Purchase
93.94
Difference
.02
Case 3: Purchase of a Treasury bill that matures the third week
in June 1985
Present Cost
Spot Market Purchase
$91.45
March Futures Purchase
91.47
Difference
.02

$976.45. These contracts obligate the firm to deliver a
13-week Treasury bill with a face value o f $1,000 during
the third w eek o f December, March and June in
exchange for $976.45.
Panel A o f table 6 presents the firm ’s expected
streams o f receipts and payments given the structure
o f interest rates on September 15. It is identical to
panel A o f table 1 except that the streams o f receipts
and payments generated by the futures contract are
included. The futures contract generates a certain
stream o f receipts equal to $976.45 in December,
March and June in exchange for delivery o f the 90-day
Treasury bills. The firm must acquire these bills in
order to make delivery and, on September 15, the
expected cost o f acquiring each o f the Treasury bills is
$976.45. If interest rates remain unchanged, expected
and actual costs w ill be the same so that the actual
receipts and payments generated by the futures con­
tract net out in each period. The net flow o f receipts is
zero untilyear-end w hen the firm receives $18.18. The
present value o f this amount is $16.53.
In panel B, interest rates are assumed to rise unex­
pectedly by 200 basis points immediately following

OCTOBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Table 6

Expected Streams of Receipts and Payments
0
Panel A: No Change in Interest Rates
Asset (loan)
Receipts
Payments
Asset (futures)
Receipts
Liabilities (borrowings)
Receipts
Payments
Liabilities (futures)
Payments
Net Receipts

90

Day
180

270

360
$1,000.00

$909.09
$976.45
909.09

-0-

$976.45

$976.45

926.75
926.75

944.76
944.76

963.11
963.11

981.82

976.45
-0-

976.45
-0-

976.45
-0-

$ 18.18

Present Value = $18.18/1.10 = $16.53
Panel B: Interest Rates Rise by 200 Basis Points
Asset (loan)
Receipts
Payments
Asset (futures)
Receipts
Liabilities (borrowings)
Receipts
Payments
Liabilities (futures)
Payments
Net Receipts

$1,000.00

$909.09
$976.45
909.09

-0-

$976.45

$976.45

926.75
926.75

949.10
949.10

971.98
971.98

972.07
$ 4.38

972.07
$ 4.38

972.07
$ 4.38

995.42
$

4.58

Present Value = $4.38/(1.12)25 + $4.38/(1.12) “ + $4.38/(1.12)75 + $4.58/(1.12) = $16.50
Panel C: Interest Rates Fall by 200 Basis Points
Asset (loan)
Receipts
Payments
$909.09
Asset (futures)
Receipts
$976.45
$976.45
Liabilities (borrowings)
Receipts
909.09
926.75
940.35
Payments
926.75
940.35
Liabilities (futures)
Payments
980.94
980.94
Net Receipts
$ -4.49
-0$ -4.49
Present Value = - $4.49/(1.08)25 - $4.49/(1.08)50 - $4.49/(1.08)76 + $31.85/(1.08) = $16.52




$1,000.00
$976.45
954.15
954.15

968.15

980.94
$ -4.49

$ 31.85

21

OCTOBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

the firm’s September 15 transactions. As in panel B of
table 1, the increase in interest rates raises the firm ’s
refunding cost and reduces the net year-end receipt to
$4.58. In addition, however, the increase in interest
rates reduces the expected cost o f acquiring the Trea­
sury bill to $972.07. Since the firm will receive $976.45
upon delivery o f the Treasury bills, the futures con­
tract w ill generate a net flow o f receipts equal to $4.38
in December, March and June. The present value of
this flow added to the present value o f the net receipt
at year-end ($4.58) is $16.50, which is nearly identical
to the present value for the case in which interest rates
remained unchanged (the small difference is due to
rounding errors).
Panel C illustrates the outcom e for a 200 basis-point
decline in interest rates. In this case, the futures
contract generates negative net receipts for the firm in
December, March and June. The present value o f this
negative flow added to the present value o f the higher
positive net receipt at year-end sum to $16.52. As the
examples show, this hedge protects the net wealth of
the firm regardless o f the direction o f the change in
interest rates.
While this hedge protects net wealth from changes
in interest rates, it does so by allowing net cash
receipts to vary. Net cash receipts, both in amount and
timing, are considerably different in panels A, B and C.
In panel A, net receipts are $18.18 at year-end while in
panel B net receipts are spread out over the year and
total only $17.72. In panel C, the firm has negative net
receipts during the year and a large positive net
receipt at year-end for a total o f $18.38. However, the
present value o f the firm is the same in all three cases.

The Balance Sheet
Panel A o f table 7 presents the firm ’s balance sheet
position in terms o f present values. The futures con­
tracts are entered as both assets and liabilities, leaving
equity the same as that shown in panel A of table 2.1
5
The futures asset is the present value o f the future
receipt o f a fixed amount. The futures liability, on the
other hand, is the present value of the expected cost of
covering the futures contract given the structure o f
interest rates on September 15. Panels B and C illus­

15Strictly speaking, futures contracts entered into by member banks of
the Federal Reserve System are treated as balance sheet memo­
randa items. These are reported on Schedule L, Commitments and
Contingencies, of the Call Report. Hence, for accounting purposes,
futures contracts do not affect the assets and liabilities of the firm
until the contracts are exercised.

http://fraser.stlouisfed.org/
22
Federal Reserve Bank of St. Louis

trate the effect on the present values o f the firm ’s
assets, liabilities and equity if, immediately following
the above transactions, interest rates rise unexpect­
edly (panel B) or fall unexpectedly (panel C) by 200
basis points.
An unexpected increase in interest rates causes the
present value o f the loan to fall relative to the present'
value o f the liability. By itself, this w ould cause a
reduction in the firm ’s equity. At the same time,
however, the increase in interest rates generates a
positive expected net cash flow from the futures
contracts, which, o f course, has a positive net present
value. Other things the same, this causes equity to rise.
The net effect o f both changes is that equity remains
unchanged. The reverse occurs if interest rates de­
cline by 200 basis points.
This hedge has eliminated the firm ’s exposure to
interest rate risk. In contrast, recall that a 200 basispoint change in the interest rate causes the equity of
the unhedged firm in table 2 to change by about 75
percent.

Hedging as a “Profit Center”
The purpose o f hedging is to reduce the variance o f
a firm ow ner’s wealth. In a textbook example o f a
perfect hedge, the gain or loss from a short position in
the futures market w ill offset exactly the compensat­
ing loss or gain on the spot assets and liabilities held
by the firm. A hedge is constructed because — in the
presence o f an uncertain future — wealth is greater if
the institution foregoes a profit stream that is higher
on average (if it goes unhedged) in exchange for a
profit stream that is low er on average (by the cost of
the hedging operations) but more certain.
Some portfolio managers, however, lose sight o f this
fact and assume speculative positions in the futures
market with the objective o f earning profits from the
position if interest rates change in their favor. While
speculative positions in futures (or spot instruments)
can increase earnings, they can have the opposite
effect as well.
One potentially significant danger in the use of
futures contracts to hedge interest rate risk is that the
firm may misunderstand the nature o f the hedging
function. Trading futures for hedging is not intended
to generate profits from the trading itself. Rather, its
purpose is to establish futures positions so that the
ow ner’s wealth is held constant; this w ill occur if the
increase (decrease) in the value o f the firm's spot
holdings o f assets and liabilities is offset exactly by the
loss (gain) in the futures market.

FEDERAL RESERVE BANK OF ST. LOUIS

OCTOBER 1984

Table 7

Interest Rate Changes and the Present Value of a Hedged Firm
Panel A: Initial Conditions (9/15/84)
Present Values
Assets:
Liabilities:
Loan: $1,000.00/1.10 =
$ 909.09
90-day CD: $981.82/1.10 =
Contracted Future Receipts
Expected Cost of Covering the Futures Contract:
December Future: $976.45/(1.10)25 =
953.46
December Future: $976.45/(1.10)25 =
March Future: $976.45/(1.10)50 =
931.01
March Future: $976.45/(1.10)50 =
June Future: $976.45/(1.10)75 =
909.09
June Future: $976.45/(1.10)75 =
3,702.65
Equity:

$ 892.56
953.46
931.01
909.09
3,686.12
16.53
3,702.65

Panel B: All Interest Rates Rise by 200 Basis Points
Note: The expected cost of covering each contract falls to $1,000/(1.12)2S = $972.07 while the contracted future receipt remains
unchanged.
Present Values
Assets:
Liabilities:
$ 888.77
Loan: $1,000.00/1.12 =
$ 892.86
90-day CD: $995.42/1.12 =
Contracted Future Receipts:
Expected Cost of Covering Futures Contract:
December Future: $976.45/(1.12)26 =
949.17
December Future: $972.07/(1.12)25 =
944.92
March Future: $976.45/(1.12) 50 =
918.52
922.66
March Future: $972.07/(1.12)50 =
June Future: $976.45/(1.12)75 =
896.88
June Future: $972.07/(1.12)75 =
892.86
3,661.57
3,645.07
Equity:
16.50
3,661.57
Panel C: All Interest Rates Fall by 200 Basis Points
Note: The expected cost of covering each contract rises to $1,000/(1.08)25 = $980.94
Present Values
Assets:
Liabilities:
Loan: $1,000.00/1.08 =
$ 925.93
90-day CD: $968.15/1.08 =
Contracted Future Receipts:
Expected Cost of Covering Futures Contract:
December Future: $976.45/(1.08)25 =
957.84
December Future: $980.94/(1.08)25 =
March Future: $976.45/(1.08) 50 =
939.59
March Future: $980.94/(1.08)50 =
June Future: $976.45/(1.08)75 =
921.68
June Future: $980.94/(1.08)75 =
3,745.04
Equity:




$ 896.44
962.25
943.91
925.92
3,728.52
16.52
3,745.04

23

FEDERAL RESERVE BANK OF ST. LOUIS

OCTOBER 1984

Real World Complications in Hedging
The examples in tables 6 and 7 simplify real
w orld problems to illustrate the basic concepts of
interest rate risk and hedging. In practice, a number
o f complicating factors will make the construction
o f a hedge considerably more difficult.
The first difficulty to note is that the calculation
o f present values for a large portfolio com posed of
many different assets and liabilities will require a
great deal o f information. Moreover, resources will
be needed to estimate interest elasticities lor dura­
tions). And, unlike our examples, which are based
on single-payment loans and deposits o f known
durations, firms face the additional problem of
loans that are subject to early payment and de­
posits that are subject to early withdrawal.
Even with a good estimate o f its exposure to
interest rate risk, firms will face practical problems
in implementing a hedge. Typically, liquidity is very
thin in futures contracts dated for delivery more
than nine months in the future. Firms also are not
likely to find futures contracts for the exact dollar
amount they wish to hedge or for the specific spot

SUMMARY
Higher and m ore variable interest rates have in­
creased the risk faced by financial institutions associ­
ated with attracting deposit funds and extending
credit. This article presented some simple examples of
techniques that can isolate and quantify sources o f a
financial institution’s exposure to interest rate risk.
The discussion also described h ow financial futures
can be used to reduce this risk. A simple hedging
example indicated that relatively conservative use of
futures markets can have a potentially large impact on
reducing risk exposure. The use o f futures trading is a
threat to the long-run performance o f a financial firm
only if applied in a manner inconsistent with hedging.

REFERENCES

Asay, Michael R., Gisela A. Gonzalez, and Benjamin Wolkowitz. “ Financial Futures, Bank Portfolio Risk, and Account­
ing," Journal of Futures Markets (Winter 1981), pp. 607-18.
Bierwag, G. 0., George G. Kaufman and Alden Toevs. "Bond
Portfolio Immunization and Stochastic Process Risk,” Journal
of Bank Research (Winter 1983), pp. 282-91.

24


asset or liability being hedged. For example, m oney
market certificates (MMCs) might be hedged with
Treasury bill futures. It is possible, however, that
interest rates on MMCs and Treasury bill futures
will not move by identical amounts or in the same
direction, an event that w ill reduce the effectiveness
o f a hedge. When the futures contract does not
correspond exactly to the spot commodity, as in
this case, the firm is exposed to “basis" risk.
Firms also face the possibility o f changes in the
slope o f the yield curve; that is, unlike our exam­
ples, short- and long-term rates could change by
differing amounts. If, for example, long rates in­
creased 200 basis points but short rates increased
only 100 basis points, the change in the difference
between the present values o f spot assets and spot
liabilities w ould not be com pletely offset by a
change in the difference between the present val­
ues o f the futures asset and liability. True hedges,
however, are im plem ented under the expectation
of no change in the yield curve’s slope. It is easy to
see, therefore, that hedging does not eliminate this
source o f risk.

Booth, James R., Richard L. Smith, and Richard W. Stolz. “ Use
of Interest Rate Futures by Financial Institutions,” Journal of
Bank Research (Spring 1984), pp. 15-20.
Carrington, Tim, and Daniel Hertzberg. “ Financial Institutions
Are Showing the Strain of a Decade of Turmoil," Wall Street
Journal (September 5,1984).
Federal Home Loan Bank Act of 1932. Public No. 304, 72 Cong.,
HR 12280.
Gay, G. D., and R. W. Kolb. “The Management of Interest Rate
Risk,” Journal of Portfolio Management (Winter 1983), pp. 6570.
Gottlieb, Paul M. “New York and Connecticut Permit Insurers to
Use Futures and Options: A Comparison,” Chicago Mercantile
Exchange Market Perspectives (May/June 1984), pp. 1-6.
Hicks, J. R. Value and Capital (Oxford: Clarendon Press, 1939).
Kaufman, George G. “Measuring and Managing Interest Rate
Risk: A Primer,” Federal Reserve Bank of Chicago Economic
Perspectives (January-February 1984), pp. 16-29.
Koch, Donald L., Delores W. Steinhauser and Pamela
Whigham. “Financial Futures as a Risk Management Tool
for Banks and S&Ls,” Federal Reserve Bank of Atlanta Eco­
nomic Review (September 1982), pp. 4-14.
Kolb, R. W. Interest Rate Futures: A Comprehensive Introduction
(Robert F. Dame, Inc., 1982).
Kolb, Robert W., Stephen G. Timme and Gerald D. Gay. “Macro
Versus Micro Futures Hedges at Commercial Banks,” Journal
of Futures Markets (Spring 1984), pp. 47-54.

FEDERAL RESERVE BANK OF ST. LOUIS

Lower, Robert C. Futures Trading and Financial Institutions: The
Regulatory Environment (Chicago Mercantile Exchange,
1982).
Morris, John. “ FASB Issues Rules for Futures Accounting,”
American Banker (August 24, 1984).
Olson, Ronald L. and Donald G. Simonson. 'Gap Management
and Market Rate Sensitivity in Banks," Journal of Bank Re­
search (Spring 1982), pp. 53-58.
Samuelson, P. A. "The Effect of Interest Rate Increases on the
Banking System,” American Economic Review (March 1944),
pp. 16-27.
Santoni, G. J. “Interest Rate Risk and the Stock Prices of
Financial Institutions,” this Review (August/September 1984).

GLOSSARY

Basis

The price or yield difference be­
tween a futures contract and the
cash instrument being hedged

Basis point

OCTOBER 1984

Simonson, Donald G., and George H. Hempel. ' Improving Gap
Management for Controlling Interest Rate Risk,” Journal of
Bank Research (Summer 1982), pp. 109-15.
Stigum, Marcia. Money Market Calculations: Yields, Break-Evens
and Arbitrage (Dow Jones-lrwin, 1981).
Toevs, Alden. "Gap Management: Managing Interest Rate Risk in
Banks and Thrifts,” Federal Reserve Bank of San Francisco
Economic Review (Spring 1983), pp. 20-35.
Wardrep, Bruce N. and James F. Buch. The Efficacy of Hedg­
ing with Financial Futures: A Historical Perspective,” Journal of
Futures Markets (Fall 1982), pp. 243-54.

Hedge

An attempt to reduce risk by tak­
ing a futures position opposite to
an existing cash position

Interest rate
swap

The exchange o f two financial
assets (liabilities) which have the
same present value but which
generate different streams o f re­
ceipts (payments)

Long hedge

A hedge in which the futures
contract is bought (long position)

M acro-hedge

A hedge designed to reduce the
net portfolio risk o f an organiza­
tion

M icro-hedge

A hedge designed to reduce the
risk o f holding a particular asset
or liability

Open interest

The number o f open futures con­
tracts, that is, unliquidated pur­
chases o r sales o f futures con­
tracts

Short hedge

A hedge that involves selling a
futures contract (short position)

Spot price

The current market price o f the
actual physical com m odity

1/100 o f 1 percent

Delivery month A specified month within which
delivery may be made under the
terms o f the futures contract
Discount yield

The ratio o f the annualized dis­
count to the par value

Evening up

Buying or selling to offset or liq­
uidate an existing market posi­
tion

Futures
contract

A standardized contract, traded
on an organized exchange, to
buy or sell a fixed quantity o f a
defined com m odity at a price
agreed to now but delivered in
the future

Gap analysis




A technique to measure interest
rate sensitivity

25

An Early Look at the Volatility
of Money and Interest Rates
under CRR
Daniel L. Thornton

February 2,1984, the Federal Reserve enacted
a system o f contemporaneous reserve requirements
(CRR) to replace the system o f lagged reserve require­
ments (LRR) that had been in effect since September
1968. The Fed made this change in response to w id e­
spread criticism that, under a reserve target operating
procedure, LRR made it more difficult to control the
monetary aggregates and contributed to the volatility
of m oney and, perhaps, interest rates. Thus, critics
believed a return to CRR w ould reduce the volatility o f
m oney and might reduce the volatility o f interest rates
as well.'
The purpose o f this article is to determine whether
the return to CRR has had, so far, any significant im ­
pact on the variability o f m oney and interest rates. The
article begins with a concise review o f the arguments
bearing on the presumed effects o f the change from

Daniel L. Thornton is a senior economist at the Federal Reserve Bank of
St. Louis. John G. Schulte provided research assistance.
’See Thornton (1983b) and the references cited there.

26


LRR to CRR on the volatility of m oney or interest rates.
The actual behavior o f these variables is then exam­
ined to see w hether arguments in favor o f the return to
CRR have been supported.

WHAT CRR IS SUPPOSED TO
ACCOMPLISH: THE STANDARD
ANALYSIS
The rationale for returning to CRR rests primarily on
the argument that LRR weakens the contem porane­
ous link between reserves and deposits o f depository
institutions. For example, it was argued that deposi­
tory institutions w ould have no incentive to curtail
their lending activities under LRR because they are not
required to hold reserves against the deposits that
these activities create until the following week. Conse­
quently, an increase in loan dem and w ould be more
readily transmitted into a change in the money stock
in the short run under LRR.
At a more formal level, the case for CRR was usually
presented in terms o f the supply o f and demand for

FEDERAL RESERVE BANK OF ST. LOUIS

OCTOBER 1984

Figure l

D e m a n d - S id e V a r ia b ilit y u n d e r C R A a n d LR A

Figu re 2

S u p p l y - S id e V a r ia b il it y u n d e r C R A a n d LRA

money. Within this framework, the proponents o f CRR
argued that the m oney supply schedule is flatter un­
der LRR than under CRR. This is illustrated in figures 1
and 2. Consequently, random variation in the demand
for m oney (represented by the shaded area in figure 1)
results in more variability in the stock o f money and
less variability in the interest rate under LRR, as illus­
trated in figure 1. Also, random variation in the supply
o f money (represented by the shaded areas in figure 2)
results in more variability in m oney and interest rates
under LRR. Thus, compared with CRR, LRR produces
greater variation in the money stock. Whether interest
rates are also more variable depends on the relative
magnitude o f the variance o f the supply-side and d e­
mand-side disturbances.2

money and interest rates, at least in the short run.
Second, the suggested outcom e is predicated on the
assumption that the Federal Reserve is targeting on a
reserve aggregate. If the Federal Reserve is not target­
ing explicitly on m oney or a reserve aggregate in the
short run, the variability o f money and interest rates
will not necessarily be related to the reserve account­
ing svstem.

There are two reasons w hy the result predicted
above need not occur. First, depository institutions'
behavior may not be as sensitive to the reserve ac­
counting system in effect as this analysis suggests.
Consequently, the switch from LRR to CRR may not
significantly alter the week-to-week variability o f

The first view argues that the short-run contem po­
raneous link between depository institutions’ deci­
sions to make additional loans and investments and
their holdings of reserves need not be close even under
a system o f CRR. ' In the short run, depository institu­
tions can obtain additional reserves by borrowing
from the Federal Reserve or holding temporarily fewer
excess reserves than they w ould hold otherwise.
These factors may be sufficient to accommodate most
short-run, week-to-week supply- and demand-side
disturbances. Consequently, the slopes o f the money
supply schedules under LRR or CRR may be similar.
Unless the adoption o f CRR fundamentally changes
the way that depository institutions adjust their re­
serve positions, there may be no dramatic change in
the volatility o f money and interest rates in the short
run.

2There are other factors, not considered here, that also affect the
outcome; see Thornton (1983b) and the references cited there.

3See Thornton (1983b) for a more detailed explanation of the argu­
ments presented in this section.

An Alternative Analysis o f What to
Expect under CRR




27

FEDERAL RESERVE BANK OF ST. LOUIS

This conjecture is likely to be even more valid given
that the new CRR system lengthened the reserve set­
tlement period from one to two weeks.4 Depository
institutions may now make loans early in the account­
ing period, waiting to settle (through the discount
window, the m oney market or changes in excess re­
serves) toward the end o f the period. By accomm odat­
ing loan demand at the first part o f the period and
settling later in the period, week-to-week variability in
m oney and interest rates could be similar under the
new system o f CRR and the old system o f LRR.5

The Role o f Federal Reserve Operating
Procedures
Expectations o f differential effects in the variability
o f m oney and interest rates under CRR and LRR are
based on the assumption that the Federal Reserve is
attempting to hit a monetary target by manipulating a
reserve aggregate. If this is not the case, there is little
reason to expect differential effects associated with a
change in the reserve accounting system. For exam­
ple, week-to-week variability o f m oney and interest
rates are unaffected by the choice o f reserve account­
ing system under an interest rate targeting procedure.6
This point is important because the Federal Reserve
changed operating procedures in the fall o f 1982,
about a year and a half before the implementation of
CRR. The Federal Open Market Committee (FOMC)
follow ed a reserve aggregate targeting procedure that
placed greater emphasis on movements in M l as a
policy guide from October 6, 1979, to early October
19827 Since then, the FOMC has placed less emphasis
on the behavior o f M l in the short run, aiming instead
at longer-run monetary and credit aggregate objec­
tives. This policy has been im plemented in the short

4For a discussion of the new system, see Gilbert and Trebing (1982).
For an interesting analysis of the carryover provision of the new
system of CRR, see Spindt and Tarhan (1984).
5Some have suggested that the Federal Reserve has no choice but
to accommodate this credit expansion, since the additional reserves
needed to support the new deposits can only come into the system
via the discount window. This argument comes perilously close to
saying that the Federal Reserve must accommodate credit demand
completely under LRR. This position, however, ignores the dy­
namics of these long-run adjustments. For another view of this
process, see Thornton (1982), p. 29.
The short-run money supply schedule is completely flat (interestelastic). Thus, the variability of money would be completely deter­
mined by the random variation in the demand for money, and this
would be unaffected by the reserve accounting system.
7For a discussion of the issues surrounding the decision to deemphasize M1 as an intermediate target, see Thornton (1983a).

http://fraser.stlouisfed.org/
28
Federal Reserve Bank of St. Louis

OCTOBER 1984

run through a "flexible nonborrowed-reserves path.’’8
As a result o f this procedural change, the variability of
m oney and interest rates immediately before and after
the implementation o f CRR may reveal little change.

HAS THE VARIABILITY OF MONEY
AND INTEREST RATES CHANGED
SINCE CRR?
Before a comparison o f the weekly variability of
money and interest rates for periods before and after
the adoption o f CRR can be made, one must decide
what measure o f variability to use. The measure used
here is the average absolute percentage change
(AAPC).9 This is preferable to two more comm only
cited measures, the standard deviation and the coef­
ficient o f variation, as a measure o f the short-run,
week-to-week variability that this article is concerned
with (see the insert on page 30).
Data are presented for various subperiods to reflect
both the move from LRR to CRR and the change in
Federal Reserve operating procedures. Data for the
two weeks im m ediately before and after the im ple­
mentation o f CRR w ere excluded to guard against the
possibility that they w ere contaminated by expecta­
tions or other problems associated with the im ple­
mentation o f the new procedure.
Results for the m oney stock, M l, are presented in
table 1. The AAPC o f seasonally adjusted M l appears
to have increased significantly in the 28-week period
following the implementation o f CRR, compared with
that o f the 28-week period immediately before CRR.
The AAPC o f seasonally adjusted M l increased from
about 0.13 percent to 0.43 percent, a difference that is
significant at the 5 percent level.1 When the most re­
0
cent period is com pared with a similar period in 1983,
the increase is much smaller; nevertheless, it is statis­
tically significant."
These comparisons, however, are deceptive be­
cause revised seasonally adjusted data is “ sm oother”
than preliminary seasonally adjusted data. Thus, the
significant increase in the variability o f seasonally ad-

8Wallich (1984), p. 26. Also, see Solomon (1984).
T
9The AAPC is defined as AAPC(X) = (1/(T -1 )) X
t=1
( | X, —X,_, |/X,_,)100. It is a measure of relative variability in that
AAPC (kX) = AAPC(X), where k is an arbitrary constant.
’“The t-statistic is 5.20.
"The t-statistic is 3.15.

OCTOBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Table 1

The Variability of M1
Seasonally
Period
adjusted
2/27/84 — 9/03/84
7/13/83— 1/18/84
3/02/83 — 9/07/83

Not seasonally
adjusted

0.43%
0.13
0.24

1.61%
1.46
1.57

First-published
seasonally adjusted
0.44%
0.36
0.44

Table 2

The Variability of M1 and Selected Interest Rates
Revised
seasonally
First-published
Federal Treasury1 Commercial1
Period
adjusted seasonally adjusted funds
bill
paper
10/17/79 — 9/29/82
10/06/82 — 9/28/83

0.22%
0.24

.50%
.43

4.48%
2.52

3.91%
1.90

4.11%
1.81

'For week ending two days later than date shown.
justed M l with the implementation o f CRR may be a
statistical artifact o f the seasonal adjustment re­
vision.1
2
This is investigated by a comparison o f the AAPC
over the three periods using either not seasonally ad­
justed or first-published seasonally adjusted data. If
the increased variability is primarily the result o f the
seasonal adjustment revision rather than the change
in the reserve accounting system, then the AAPC for
the first-published or not seasonally adjusted M l
should be essentially the same over these periods.'3
Likewise, a comparison of not seasonally adjusted
data for the 28-week period since the implementation
of CRR and the corresponding period a year earlier
should reveal no change in the AAPC. The data are
consistent with both o f these conditions. Thus, there
appears to be no change in the variability o f M l be­
tween the pre- and post-CRR periods.
It is indeterminant, however, w hether this result
stems from depository institutions not changing their

12For example, see Hein and Ott (1983).
'3A comparison of these data is perhaps more relevant because these
are the figures that economic agents and policymakers use to make
their decisions.



behavior following the enactment o f CRR or from a
change in the operating procedure in the fall o f 1982.
In order to determine which explanation is more con­
sistent with the facts, the AAPC was calculated for M l
and three interest rates — the federal funds rate, the
three-month Treasury bill rate and the commercial
paper rate — for the three-year period o f reserve ag­
gregate targeting (October 17, 1979, to September 29,
1982) and for the year immediately following the
change in the Federal Reserve’s operating procedure
(October 6, 1982, to September 28, 1983). These results
are presented in table 2. The data indicate a decline in
the AAPC for both revised and first-published M l after
the fall o f 1982; however, this decline is not statistically
significant at the 5 percent level.'4 Thus, it appears
there was no significant change in the week-to-week
variability o f M l following the change in the operating
procedures.
The AAPCs for all three interest rates, however, de­
crease significantly after the fall o f 1982. Thus, it ap­
pears that the change in operating procedure had
some impact on the behavior o f interest rates. Hence,

14The relevant t-statistics for first-published and not seasonally ad­
justed data are 0.91 and 0.15, respectively.
29

The Limitations of Two Common Measures of Variability
Both the standard deviation (SD) and the coef­
ficient o f variation (CV) measure the variability of
the data relative to an average. For the SD the aver­
age is the mean of the raw data; for the CV the mean
is unity, that is, the average o f the raw data divided
by the mean. Thus, the SD is a measure o f absolute
variability and the CV is a measure o f relative varia­
bility.1
Because both o f these statistics average squared
deviations from their respective means, they may
give relatively small weight to large weekly changes
and relatively large weight to small weekly changes.

T
'The SD = ( 2 (X, - X)2/(T -1 ))'« and the
t= 1
T
CV = ( 2 (X;-X*)2/(T-1))’«,
t=1
where X is the mean of the raw series,
*T
i.e., X = 2 X/T, and X? = X/X,
t=1
T
so that X* = 2 ((X/TJ/X) = 1. Furthermore, while the SD
t=1
depends on the scale of the data, the CV does not; i.e., the
SD(kX) = kSD(X), while the CV(kX) = CV(X), where k is a
constant.
it is possible that the lack o f a significant change in the
variability o f money after the implementation o f CRR
was due to the earlier change in operating procedures.
Unfortunately, these results cannot rule out the possi­
bility that the short-run reserve management behavior
by depository institutions is simply insensitive to
changes in the reserve accounting system.1
5

The Variability o f Interest Rates
The AAPC was calculated for the federal funds, the
three-month Treasuiy bill and the 30-day commercial
paper rate for comparable 28-week periods before and
after the implementation o f CRR. The results, which
are reported in table 3, indicate a slight increase in the

,5Neither of these, however, rules out other potential gains from CRR
See Goodfriend (1984).

30


This is illustrated in the accompanying charts,
which show the level o f seasonally adjusted M l, by
itself and relative to its mean level for the 28-week
period following the implementation o f CRR.
Charts 1 and 2 show that the largest (in absolute
and relative terms) one-week change in M l oc­
curred on May 7, w hen the m oney supply increased
by $5.3 billion. Because the absolute and relative
(i.e., mean-adjusted) levels are only slightly above
their respective means for the period, their respec­
tive contributions to the SD and the CV are small.
Moreover, the smallest one-week change in M l oc­
curred on March 19. Because the levels are further
from their mean, their contribution to the SD and
the CV is larger than that o f the largest change.
The average absolute percentage change (AAPC)
is a measure o f relative variability that avoids the
problem o f inappropriate weighting. Thus, it is a
better measure o f the week-to-week variability with
which this article is concerned.2

2Of course, if the growth rate is constant across time periods, then
the AAPC will not necessarily be preferable to the SD of the
growth rate. If there is variable growth or short periods of rapid
growth preceded and followed by periods of approximately equal
growth, as in the charts above, then the AAPC is likely to be a
better measure of week-to-week variability. If the growth rates
were constant over these periods, however, the CV of the growth
rate might be a useful measure.
AAPC for the federal funds rate for periods im m edi­
ately before and after the implementation o f CRR and a
slight decrease for both the Treasury bill rate and the
commercial paper rate; however, none o f these were

Table 3

The Variability of Selected
Interest Rates
Federal1 Treasury Commercial
Period
funds
bills
paper
2/24/84 — 8/31/84
7/15/83 — 1/20/84
3/04/83 — 9/09/83

2.55%
2.33
1.99

1.13%
1.21
1.58

'For week ending two days earlier than date shown.

1.13%
1.27
1.56

OCTOBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

C hart 1

Levels of M l

FEB.

MAR.

APR.

M AY

JUNE

JULY

AUG .

JUNE

JULY

AUG.

SEPT.

1984

C hart 2

Ratio of M l to Sa m p le M e a n




FEB.

MAR.

APR.

M AY

SEPT.

1984

31

FEDERAL RESERVE BANK OF ST. LOUIS
P.O. BOX 442
ST. LOUIS, MISSOURI 63166

Subscriber: Please include address
label with subscription inquiries or
address changes.
significant at the 5 percent level."1 Thus, the results
suggest that the implementation o f CRR had little ef­
fect on the variability o f money or interest rates. The
significant reduction in interest rate variability ap­
pears to correspond with the earlier change in operat­
ing procedures, not with the implementation o f CRR.

CONCLUSIONS
The purpose o f this article was to take an early look
at the effect o f the Federal Reserve’s new system of
contemporaneous reserve accounting on the variabil­
ity o f m oney and interest rates. Although the CRR
system was adopted with the expectation that it
w ould reduce the variability o f m oney under a reserve
targeting procedure, it may not have that effect for two
reasons. First, depositoiy institutions may behave in
ways that reduce the short-run contemporaneous link
between aggregate reserves and deposits even under
CRR. Second, the change in operating procedures in
October 1982 may have preem pted any potential
benefits from the switch in accounting systems.
The data for M l indicate that there was no signifi­
cant change in week-to-week variability following ei­
ther the change in operating procedure in October
1982 or the adoption o f CRR. The variability o f shortrun interest rates declined significantly after the
change in operating procedures, but has been unaf­
fected by the im plem entation o f CRR. Thus, the
change in the reserve accounting procedure had no

,6The relevant t-statistics for a comparison of periods immediately
before and after the implementation of CRR for the federal funds
rate, the three-month Treasury bill rate and the commercial paper
rate are 0.30, 0.39 and 0.53, respectively.

http://fraser.stlouisfed.org/
32
Federal Reserve Bank of St. Louis

statistically significant impact on the variability of
m oney either because depository institutions’ lending
and investment decisions are insensitive to the reserve
accounting system, or because o f the change in oper­
ating procedures that occurred some year and a half
earlier. Consequently, CRR’s potential usefulness in
reducing the variability o f m oney can be determined
for certain only if the Federal Reserve implements a
strict reserve aggregate or monetary base target.

REFERENCES
Gilbert, R. Alton, and Michael E. Trebing. "The New System of
Contemporaneous Reserve Requirements,” this Review (Decem­
ber 1982), pp. 3-7.
Goodfriend, Marvin. “The Promises and Pitfalls of Contemporane­
ous Reserve Requirements for the Implementation of Monetary
Policy," Federal Reserve Bank of Richmond Economic Review
(May/June 1984), pp. 3-12.
Hein, Scott E., and Mack Ott. "Seasonally Adjusting Money: Proce­
dures, Problems, Proposals," this Review (November 1983), pp.
16-25.
Spindt, Paul A., and Vefa Tarhan. “Bank Reserve Adjustment Pro­
cess and the Use of Reserve Carryover as a Reserve Manage­
ment Tool: A Microeconometric Approach,” Journal of Banking and
Finance (March 1984), pp. 5-20.
Solomon, Anthony M. “Unresolved Issues in Monetary Policy,”
Federal Reserve Bank of New York Quarterly Review (Spring
1984), pp. 1-6.
Thornton, Daniel L. “Simple Analytics of the Money Supply Process
and Monetary Control,” this Review (October 1982), pp. 22-39.
_________ “The FOMCin 1982: De-emphasizing M1," this Review
(June/July 1983a), pp. 26-35.
________. “Lagged and Contemporaneous Reserve Accounting:
An Alternative View,” this Review (November 1983b), pp. 26-33.
Wallich, Henry C. “Recent Techniques of Monetary Policy,” Fed­
eral Reserve Bank of Kansas City Economic Review (May 1984),
pp. 21-30.