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Forecasting
Reduced

the Effects of

Defense

Spending

Peter Irel’
and and Chtitopher Omk ’

I.

INTRODUCTION

The end of the Cold War provides the United
States with an opportunity
to cut its defense
spending significantly. Indeed, the Bush Administration’ 1992-1997 Future Years Defense Program
s
(presented in 1991 and therefore referred to as the
“1991 plan”) calls for a 20 percent reduction in real
defense spending by 1997. Although expenditures
related to Operation Desert Storm have delayed the
implementation of the 199 1 plan, policymakers continue to call for defense cutbacks. In fact, since Bush’
s
plan was drafted prior to the collapse of the Soviet
Union, it seems likely that the Clinton Administration will propose cuts in defense spending that are
even deeper than those specified by the 1991 plan.
This paper draws on both theoretical and empirical
economic models to forecast the effects that these
cuts will have on the U.S. economy.
A. Economic Theory
Economic theory suggests that in the short run,
cuts in defense spending are likely to have disruptive effects on the U.S. economy.
Productive
resources-both
labor and capital-must
shift out of
defense-related industries and into nondefense industries. The adjustment costs that this shift entails
are likely to restrain economic growth as the defense
cuts are implemented.
Economic theory is less clear, however, about the
likely long-run consequences
of reduced defense
spending. The neoclassical macroeconomic model
(a simple version of which is presented by Barro,
1984) assumes that all goods and services are produced by the private sector. Rather than hiring labor,
accumulating capital, and producing defense services
itself, the government simply purchases these services from the private sector. Thus, according to the
neoclassical model, the direct effect of a permanent
The authors would like to thank Mike Dotsey, Mary Finn,
Marvin Goodfriend, Tom Humphrey, Jeff Lacker, Max Reid,
Stephen Stanley, and Roy Webb for helpful comments and
suggestions.
l

FEDERAL

RESERVE

$1 cut in defense spending acts to decrease the total
demand for goods and services in each period by $1.
Of course, so long as the government has access to
the same production technologies that are available
of the
to the private sector, this prediction
neoclassical model does not change if instead the
government produces the defense services itself.’
A permanent $1 cut in defense spending also
reduces the government’ need for tax revenue; it
s
implies that taxes can be cut by $1 in each period.
Households, therefore, are wealthier following the
cut in defense spending; their permanent income increases by $b According to the permanent income
1.
hypothesis, this $1 increase in permanent income
induces households to increase their consumption by
$1 in every period, provided that their labor supply
does not change.
However, the wealth effect of reduced defense
spending may also induce households to increase the
amount of leisure that they choose to enjoy. If
households respond to the increase in wealth by
taking more leisure, then the increase in consumption from the wealth effect only amounts to $( 1 -a)
per period, where cy is a number between zero and
one: That is, the increase in wealth is split between
an increase in consumption and an increase in leisure.
In general, therefore, the wealth effect of a cut in
defense spending acts to increase private consumption, and hence total demand, by $( 1 -a) per period.
The increase in leisure from the wealth effect,
meanwhile, translates into a decrease in labor
supply. This decrease in labor supply, in turn,
translates into a decrease in the total supply of goods
and services. In fact, the increase in leisure acts to
decrease the total supply of goods by $a per period
(Barro, 1984, Ch. 13). Thus, the number o! measures
r See Wynne (1992), however, for a more general version of
the neoclassical model in which the government may have
access to different technologies from those used by the private
sector. Wynne’ model also distinguishes between the goods and
s
services that the government produces itself and those that it
purchases from the private sector.
BANK

OF RICHMOND

3

.

the magnitude of the wealth effect’ impact on leisure
s
and the supply of goods relative to itsimpact on consumption and the demand for goods. The higher a
is, the larger the decrease in supply and the smaller
\ _
the increase in demand.
Combining the direct effect of the permanent
$1 cut in defense spending, which decreases total
demand by $1 per period, with the wealth effect,
which increases total demand by $( 1 - 4 per ‘
period,
shows that the permanent cut in defense spending
decreases the total demand for goods by $a per
period. Likewise, the direct effect implies no change
in supply, while the wealth effect implies a decrease
in supply of $cr per period; when combined, the two
effects imply a decrease in supply of $(Yper period.
Altogether, both total demand and total supply
decrease by $cy in each period, so that the permanent cut in defense spending reduces realoutput by
$a in each period.
Before moving on, it is important to emphasize that
although the neoclassical model predicts that total
output (GNP) will fall in response to a permanent
cut. in defense spending, this result does not imply
that households would be better. off without the
spending cut. While the permanent $1 cut in defense
spending reduces total GNP by $a per period,,it also
makes available to households $1 per period that
would otherwise be allocated to defense. Private
GNP, defined as total GNP less all government
spending, therefore increases by $( 1 - ~4 per period.
Since private GNP.accounts for the goods and services that are available to the private sector, it is a
better measure of welfare than total GNP; the rise
in private GNP indicates that households are better
off after the defense cuts, even though total GNP
is lower. In fact, the increase in private GNP
underestimates the welfare gain from reduced defense
spending since it does not ,take into account the increase in leisure resulting from the wealth effect of
the spending cut.
So far, the ana 1
ysis has assumed that the cut in
defense spending will be used to reduce taxes.
Provided that the Ricardian equivalence theorem
applies, however, the results do not change if instead
the cuts are used to reduce the government debt.
Suppose that, in fact, the permanent $1 cut in
defense spending is initially used to reduce the
government
debt. According to the Ricardian
equivalence theorem, households recognize that by
reducing its debt, the government is reducing its need
for future tax revenues by an equal amount. Thus,
using the cut in defense spending to reduce the
4

ECONOMIC

REVIEW.

government debt today simply means that tax’
cuts
of more than $1 per period will come in the future.
Under Ricardian equivalence, household wealth does
not depend on the precise timing of the tax cuts. The
magnitude of the wealth effect, and hence the
changes in aggregate supply and demand, are the.
same whether the cut in defense spending is used
to reduce the federal debt or to reduce taxes.
Central to the Ricardian equivalence theorem is
the assumption that households experience the same
change in wealth from a reduction in government
debt as they do from a cut in taxes. If this assumption is incorrect, then a cut in defense spending can
have very different long-run effects from those
predicted by the neoclassical model under Ricardian
equivalence.
Most frequently, the relevance of the Ricardian
equivalence theorem is questioned based upon the
observation that households have lifetimes of finite
length (Bernheim, 1987). Suppose, for instance, that
while individuals recognize that a reduction in government debt today implies that taxes will be lower in
the future, they also expect that the future tax cuts
will occur after they have died. In this extreme case,
individuals who are alive today experience no change
in wealth if,the cuts in defense spending are used
to reduce the government debt. Only the direct
effect of the defense cut is present; the wealth
effect is missing. Since households do not experience
an increase in permanent income, neither their consumption nor their labor supply changes. The
decrease in total demand resulting from the direct
effect of the spending cut leads to a condition of
excess supply.
In response to excess supply, output falls in the
short run, and the real interest rate falls as well. In
the long run, however, the lower real interest rate
leads to increases in both investment and output.
Thus, a departure from Ricardian equivalence can
explain why cuts in defense spending might increase,
rather than decrease, total GNP in the long run,
provided that the cuts are used to reduce the government debt.
Whether or not the Ricardian equivalence theorem
applies to the U.S. economy is a controversial issue.
There are many theoretical models in which household wealth is affected by a decrease in government
debt in exactly the same way that wealth is affected
by a decrease in taxes, so that Ricardian equivalence
applies (see Barre, 1989, for a survey of these
models). On the other hand, there are many other

NOVEMBER/DECEMBER

1992

models in which the wealth effect from a cut in
government debt differs from the wealth effect from
a cut in taxes, so that Ricardian equivalence does not
hold (see Bernheim, 1987, for a survey of these
models). Overall, economic theory provides no clear
answer as to the relevance of the Ricardian equivalence theorem. Consequently, economic theory does
not provide a clear answer as to the long-run effects
of cuts in defense spending either. Instead, empirical
models must be used to forecast the effects of reduced defense spending.
B. Previous Empirical Estimates
A detailed study by the Congressional Budget
Office (CBO, 1992) forecasts the effects of the 199 1
plan for the U.S. economy. The CBO’ conclusions
s
are based on results from two large-scale macroeconomic forecasting models: the Data Resources,
Inc. (DRI) Quarterly Macroeconomic Model and the
McKibbin-Sachs Global (MSG) Model. Both of these
econometric models incorporate short-run djustment
costs of changes in defense spending and long-run
non-Ricardian effects of changes in the government
debt into their forecasts for real economic activity.
The models predict, therefore, that the cuts proposed
by the 1991 plan will reduce growth in the U.S.
economy in the short run. The models also predict
that if the cuts in defense spending are used to reduce
the federal debt, then the real interest rate will fall
and investment and output will increase in the long
run as the non-Ricardian effects kick in. Thus, while
the CBO predicts that the 199 1 plan will reduce total
GNP by approximately 0.6 percent throughout the
mid-1990s their forecasts also show positive effects
on total GNP by the end of the decade, leading to
a long-run increase in total GNP of almost 1 percent.
The Congressional Budget Office’ econometric
s
models draw heavily on economic theory to obtain
their conclusions. As noted above, however, there
is considerable debate in the theoretical literature
concerning the possible channels through which
defense spending influences aggregate activity in the
long run. Models that assume that the Ricardian
equivalence theorem holds indicate that cuts in
defense spending will reduce output in the long run.
On the other hand, models in which Ricardian
equivalence does not apply predict that defense cuts
may increase output in the long run, provided that
the proceeds from the cuts are used to reduce the
government debt. The CBO’ models both assume
s
that Ricardian equivalence does not hold in the U.S.
economy. Hence, their forecasts show significant
long-run gains in total GNP from the 199 1 plan. But
FEDERAL

RESERVE

these forecasts will be on target only to the extent
that their underlying-and
controversial-assumption
about Ricardian equivalence is correct.
C. An Alternative Forecasting Strategy
This paper takes an approach to forecasting the
effects of reduced defense spending that differs
significantly from the approach taken by the CBO.
Rather than using a large-scale econometric model,
it uses a much smaller vector autoregressive (VAR)
model like those developed by Sims (Jan. 1980, May
1980). As emphasized by Sims (Jan. 1980), VAR
models require none of the strong theoretical
assumptions that the DRI and MSG models rely on
so heavily. The approach taken here, therefore,
recognizes that economic theory provides no clear
answer as to the likely long-run effects of reduced
defense spending. Moreover, as documented by
Lupoletti and Webb (1986), VAR models typically
perform as well as the larger models when used as
forecasting tools, especially over long horizons. Thus,
there are both theoretical and practical reasons to
prefer the VAR approach to the CBO’
s.
Forecasts from the VAR model, like those from
the CBO’ models, show that the 199 1 plan will lead
s
to weakness in aggregate output in the short run.
Unlike the CBO’ models, however, the VAR does
s
not predict that there will be a long-run increase in
total GNP resulting from the cuts in defense spending, even if the cuts are used to reduce the federal
debt. This result, which is consistent with the neoclassical model under Ricardian equivalence, suggests
that the larger models rely on the incorrect assumption that there are strong non-Ricardian effects of
changes in the government
debt in the U.S.
economy.
Although the VAR forecasts for total GNP are
considerably more pessimistic than the CBO’ fores
casts, they do not imply that the defense cuts called
for by the 199 1 plan are undesirable. Private GNP,
in contrast to total GNP, is forecast by the VAR to
increase in the long run as a result of the 199 1 plan.
This result, which is again consistent with the neoclassical model under Ricardian equivalence, indicates
that the 199 1 plan will make more resources available
to the private sector in the long run. As noted by
Garfinkel (1990) and Wynne (1991), this gain in
resources can be used to increase private consumption and investment, making American households
better off in the long run.
The VAR is introduced in the next section. Section III presents the forecasts generated by the VAR
BANK OF RICHMOND

5

and compares them to the forecasts given by the
CBO. Section IV summarizes and concludes.
II.

DESCRIPTION OF THE MODEL

The basic model is an extension of the four-variable
VAR developed by Sims (May 1980) and is designed specifically to capture the effects of defense
spending on aggregate economic activity. There are
six variables in the model: the growth rate of real
defense spending (RDEF), the growth rate of real
U.S. government debt.(RDEBT),
the nominal sixmonth commercial paper rate (R), the growth rate
of the broad monetary aggregate (MZ), the growth
rate of the implicit price deflator for total GNP (P),
and the growth rate of real total GNP (Y). All of the
variables except for the interest rate are expressed
as growth rates so that all may be represented as stationary stochastic processes. Using growth rates for
these variables avoids the problems, discussed by
Stock and Watson (1989), associated with including
nonstationary variables in the VAR.
Using vector notation, the model can be written as
Xt = ;: B,Xt-, +ut,

(1)

s=l

where the 6x1 vector Xt is given by
Xt = [RDEFt,RDEBT,,R,,MZ,,Pt,Ytj

’

(2)

and where the B, are each 6x6 matrices of regression coefficients. In order to obtain information about
the long-run effects of changes in defense spending,
the system (1) is estimated using a long data set
that extends from 193 1 through 199 1. All data are
annual (quarterly data are unavailable for dates prior
to World War II); their sources are given in the
appendix. The lag length k = 4 is chosen on the basis
of the specification test recommended
by Doan
(1989).

Once the system (1) is estimated, impulse response
functions can be used to trace out the effects of
changes in defense spending and the government
debt on total GNP and, in particular, to forecast the
effects of the 199 1 plan. For the purpose of generating impulse response functions, the ordering of
variables shown in equation (2) reflects the assumption that policy decisions that change defense
spending are made before the contemporaneous
values of the other variables are observed. Monetary
policy actions, which are best captured as changes
in Rt (McCallum, 1986), are made after decisions
6

ECONOMIC

REVIEW.

that affect defense spending and the government
debt, but before money, prices, or output are observed. Money, prices, and output are then determined in succession, given that fiscal policy has
determined RDEF and RDEBT and monetary policy
has determined R.2

III.FORECASTSFROMTHE

VAR

The VAR results are foreshadowed in Figure 1,
which plots the series Y, RDEF, and RDEBT over
the 60-year sample period. Panel B reveals that there
were significant cuts in defense spending following
World War II, the Korean War, and the Vietnam War.
In each case, the defense cuts were accompanied by
slow growth in total GNP (panel A). In light of this
past relationship, it seems likely that the VAR will
associate the defense cuts called for by the 199 1 plan
with slower total GNP growth, at least in the short
run.
By comparing the behavior of RDEBT (panel C)
to that of Y (panel A), however, it is difficult to see
the negative long-run relationship between output and
government debt predicted by models in which the
Ricardian equivalence theorem does not apply.
Growth in the real value of U.S. government debt
was negative for much of the 1950s and 1960s and
positive for much of the 1970s and all of the 1980s.
2 More formally, the variables in equation (2) are organized as
a Wold causal chain to produce the impulse response functions.
See Sims (1986) for a detailed discussion of the Wold causal
chain approach as well as other strategies for identifying impulse
response functions in VAR models.

Figure

GROWTH
20
16

1A

RATE OF REAL GNP

- n4

-8

-1i
-16
-20
1931

NOVEMBER/DECEMBER

1940
1992

1950

1960

1970

‘980
I

Ll
1990

Figure 1B

GROWTH

RATE OF REAL DEFENSE

SPENDING

500

400

300
F
8
2 200
-20

,,,,1,11,'111,,1111'1,1,,,,,,',11,1,,1,'
1952
1960

1990

1980

1970

100

0

-100
1931

1940

1960

1950

1980

1970

1990

Figure 1C

GROWTH

RATE OF REAL GOVERNMENT

DEBT

90 I

I

80 -

20'

I

I
15 -

70 10 60 550 -

1948

FEDERAL

1958

RESERVE

1968

BANK OF RICHMOND

1978

1988

7

Figure 2, panel A, shows the cumulative impulse
response function of Y to a one-time one-standard
deviation (20 percent) decrease in RDEF, computed
using the VAR described by equations (1) and (‘
Z).3
The graph shows the cumulative change in the level
of total GNP through the end of each year that results
from a decrease in RDEF in the first year. It indicates
that the decrease in RDEF yields a contemporaneous
decrease in total GNP of approximately 1.5 percent.
The effect of the shock to RDEF peaks at 5.5 percent after four years before settling down to a longrun decrease of about 2.5 percent. The confidence
interval reveals that the initial decrease in total GNP
due to the decrease in defense spending is statistically
significant. In fact, the hypothesis that changes in
RDEF do not influence Y (more formally, the hypothesis that changes in RDEF do not Granger-cause
changes in Y) can be rejected at the 99 percent
confidence level.4 Thus, the model indicates that
in response to a decrease in defense spending, total
GNP will fall in both the short run and the long run.
Figure 2, panel B, plots the cumulative impulse
response function of Y to a one-time one-standard
deviation (3 percent) decrease in RDEBT. Consistent with the non-Ricardian assumptions that are
embedded in the DRI and MSG models, this impulse response function indicates that a decrease in
RDEBT will increase total GNP in the long run. In
addition, the hypothesis that changes in RDEBT do
not influence changes in Y can be rejected at the
98 percent confidence level. However, at no time
are the effects of RDEBT on Y very large; except
in period 2, the confidence interval always includes
zero. Overall, therefore, Figure 2 is consistent with
the neoclassical model under Ricardian equivalence,
which predicts that a reduction in the size of the
federal debt will not have a large effect on output
and that a reduction in defense spending will permanently reduce total GNP.
3 Note that each of the impulse response functions in Figure 2
traces out the effects of a decrease in one of the variables on
GNP. Impulse response functions more typically examine the
effects of an increase in one of the model’ variables. Here,
s
however, it is the effects of decreases in defense spending and
government debt that are of interest, so the direction of the
shock is reversed.
4 Here and below, the likelihood ratio test for block exogeneity
described by Doan (1989) is used to test for the absence of
Granger causality.

8

ECONOMIC

REVIEW.

2A

Figure

Yet it does not appear that the growth rate of output
was substantially different before and after 1970, as
these models predict. Thus, it seems likely that the
VAR will not find strong non-Ricardian effects of
changes in government debt in the U.S. economy.

CUMULATIVE
RESPONSE OF GROWTH
RATE OF
REAL GNP TO GROWTH
RATE OF
REAL DEFENSE SPENDING
(with 95 percent
4,
2

confidence

c
\

-8

-

-10

.-

/

,--1

interval)

\

-

LJ

\
\

-12

/

/

i-

’ ’ ’ ’ ’
1 2 3.4.5.6

’

’
7

’
8

’ ’ ’
9101112

’

.

.
’ ’ ’
131415

Forecasts from the VAR are generated by constraining future values of RDEF and RDEBT as
called for by the 199 1 plan. The constrained values
of RDEF and RDEBT translate into constrained
values of the shocks to these two variables. Hence,
the VAR forecasts are essentially linear combinations
of the impulse response functions shown in Figure
‘ The impulse response functions suggest that the
2.
short-run forecasts from the VAR will be similar to
those given by the CBO’ models, but the long-run
s
forecasts will be quite different. All of the models

Figure 2B

CUMULATIVE
RESPONSE OF GROWTH
RATE OF
REAL GNP TO GROWTH
RATE OF
REAL GOVERNMENT
DEBT
(with 95 percent

confidence

interval)

5
4
31

-2

/

-

-3

I---

-

.-

--

\
\

-4

\
’
i

NOVEMBER/DECEMBER

’
2

’ ’
3 4
1992

-/------’
5

’
6

’ ’
7 8

’ ’ ’ ’ ’ ’ ’
9 10 11 12 13 14’
15

predict that cuts in defense spending will reduce total
GNP in the short run. But the VAR forecasts none
of the long-run gains in total GNP that the large-scale
models do.

Forecasts of the Effects of the 1991 Plan on GNP

The table (right) compares the forecasts of the
effects of the 199 1 plan on total GNP generated by
the VAR model to those generated by the DRI and
MSG models. All three sets of forecasts compare the
predicted behavior of total GNP under a base case,
in which real defense spending is essentially held constant as a fraction of total GNP (except for the small
decreases called for by the Budget Enforcement Act),
to the behavior of total GNP when defense spending is cut as called for by the 1991 plan and the
proceeds are used to reduce the federal debt. The
figures in the table represent the predicted differences, in percentages, between the level of total GNP
under the 1991 plan and the level of total GNP in
the base case. Details about these two alternative
paths for defense spending are provided in the CBO’
s
report (1992, Table 3, p. lo), as are the forecasts
from the DRI and MSG models (Figure 3, p. 14 and
Table 4, p. 15).

1992
1993

-0.2

-0.3

-0.4

-0.2

-0.7

-0.6

- 1.0

-0.3

1994

-0.6
-0.6

-0.5
-0.5

-1.4

1995

-0.5
-0.4

1996
1997

-0.6
-0.6

Model
Year

DRI
(total GNP)

MSG
(total GNP)

VAR
(total GNP)

-0.3

-1.8
-2.2

-0.4

-0.2

-2.4

-0.3

-0.1

2000

0.0

0.5

-2.0

2010

N/A

0.8

2015

N/A

0.9

- 1.9
- 1.9

Notes:

VAR
(private GNP)

0.3
0.3

The effects are expressed as percentage differences between GNP
under the 1991 plan for reductions
in defense spending and
GNP under the base case of no change in real defense spending.
DRI is the Data Resouces Model, MSG is the McKibbin-Sachs
Model, and VAR is the vector autoregressive model. Details about
the two alternative
paths for defense spending, as well as the
forecasts from the DRI and MSG models, are taken from CBO
(1992). N/A indicates that the forecast is not available.

The table shows that the VAR model is consistently more pessimistic than the CBO’ models about
s
both the short-run and long-run effects of the 1991
plan. While the DRI and MSG models predict that
the short-run costs of reduced defense spending will
be 0.5 to 0.7 percent of total GNP, the VAR
estimates these costs at 1 to 1.8 percent of total
GNP. While the DRI and MSG models expect longrun benefits from the debt reduction to begin offsetting the short-run costs in the mid-1990s the VAR
predicts that the costs of the 1991 plan will peak at
2.4 percent of total GNP in the late 1990s. Finally,
while both the DRI and MSG models predict gains
in total GNP by the year 2000, the VAR model
predicts that there will be a permanent loss of 1.9
percent of total GNP from the 1991 plan.

results change if nondefense government spending
or Barro and Sahasakul’ (1986) marginal tax rate
s
series is added as a seventh variable. Since Figure
1 reveals that the behavior of the model’ variables
s
was most dramatic during and shortly after World
War II, it is useful to know the extent to which the
results depend on the data from these years. When
the six-variable VAR is reestimated with quarterly
data from 1947 through 199 1, the 1991 plan is predicted to reduce total GNP in the long run by 2.7
percent, a figure that is even larger than that
generated by the original model. Finally, the forecasts
are insensitive to changes in the lag length from k = 4
to k = 3, 5, or 6. The VAR forecasts, therefore, are
quite robust to changes in model specification; in all
cases, cuts in defense spending are predicted to
reduce total GNP substantially in the long run, even
when cuts are used to reduce the federal debt.

In order to check the robustness of the VAR
forecasts, several kinds of alternative model specifications can be considered. Although the causal ordering used in equation (2) is to be preferred based on
economic theory, it would be troublesome if other
orderings yielded vastly different results. Similar
forecasts are obtained, however, when RDEF and
RDEBT are placed last, rather than first, in the ordering. The model does not include some variables that
may nonetheless be useful in forecasting GNP
growth. Following the suggestion of Dotsey and Reid
(1992), an oil price series can be added to the model,
but again the results do not change. Nor do the

To emphasize the point that the VAR forecasts,
although considerably more pessimistic than the
CBO’ forecasts, do not imply that the defense cuts
s
called for by the 199 1 plan are undesirable, the table
also presents forecasts from a VAR model that is
identical to model (l), except that the growth rate
of total GNP is replaced by the growth rate of private
GNP. Private GNP, like total GNP, is predicted to
fall in the short run as the 199 1 plan is implemented.
In the long run, however, private GNP is expected
to increase by 0.3 percent. The 1991 plan reduces
total GNP, but it also makes available to the private
sector resources that would otherwise be allocated

FEDERAL

RESERVE

BANK OF RICHMOND

9

to defense. The VAR forecasts show that on net,
private GNP increases, making American households
better off from the 1991 plan in the long run.

IV.

SUMMARYANDCONCLUSIONS

The Bush Administration’
s
1992-1997 Future
Years Defense Program (the “1991 plan”) calls for
the first significant cuts in defense spending in the
United States since the end of the Vietnam War.
Economic theory indicates that these defense cuts
are likely to restrain economic growth in the short
run as productive resources shift out of defenserelated activities and into nondefense industries.
Economic theory is less clear, however, about the
long-run consequences of reduced defense spending.
Models that assume that the Ricardian equivalence
theorem holds find that a permanent decrease in
defense spending decreases aggregate output in the
long run. On the other hand, models that assume
that Ricardian equivalence does not apply predict that
a permanent decrease in defense spending increases
output in the long run, provided that the proceeds
from the spending cut are used to reduce the federal
debt.
The large-scale econometric models employed by
the Congressional Budget Office (1992) rely on the
theoretical assumption that Ricardian equivalence
does not hold in the U.S. economy. Thus, the CBO’
s
models predict that while the 1991 plan will reduce
total GNP in the short run as the economy adjusts
to a lower level of defense spending, they also predict
that the non-Ricardian effects of reducing the government debt will generate an increase in total GNP in
the long run.

10

ECONOMIC

REVIEW,

As an alternative to the CBO’ large-scale models,
s
this paper uses a much smaller VAR model to forecast
the macroeconomic effects of the 199 1 plan. Unlike
the larger models, the VAR requires no strong
theoretical assumption about whether or not Ricardian equivalence holds in the U.S. economy. The
VAR, therefore, recognizes that economic theory
provides no clear answer as to the likely long-run
effects of reduced defense spending.
In fact, results from the VAR suggest that the
Ricardian equivalence theorem does apply to the
U.S. economy. Changes in government debt are
found to have only small effects on aggregate
output. Forecasts from the VAR, which show that
the 1991 plan is likely to reduce total GNP in both
the short run and long run, are more consistent with
the neoclassical model presented by Barro (1984),
in which Ricardian equivalence holds, than with those
of competing models in which Ricardian equivalence
does not apply.
Although the VAR forecasts are considerably more
pessimistic than the CBO’ forecasts, they do not
s
imply that the defense cuts called for by the 1991
plan are undesirable. In fact, both the neoclassical
model and the VAR forecasts suggest that as the cuts
in defense spending are implemented, growth in total
GNP is likely to be a misleading measure of household welfare. Although the 1991 plan reduces total
GNP, it also makes available to the private sector
resources that. would otherwise be allocated to
defense. The VAR forecasts show that on net, private
GNP increases. As noted by Garfinkel (1990) and
Wynne (199 l), this net gain can be used to increase
private consumption or private investment, making
American households better off in the long run.

NOVEMBER/DECEMBER

1992

REFERENCES

APPENDIX
DATASOURCES

Barro, Robert J. Macmeconomics. New York: John Wiley and
Sons, 1984.

Defense

Data for 1930 through 1938
Spending:
are national security outlays reported in Table A-I
of Kendrick (1961). Data for 1939 to 1991 are
government purchases of goods and services, national
defense, from Table 3.7a of the &rwey of Carrent
Business, Department
of Commerce,
Bureau of
Economic Analysis. The nominal data are deflated
using the implicit price deflator for GNP reported
in Table 7.4 of the same publication.
Debt before 1941 is total gross
Government Debt:
debt at the end of the fiscal year reported in the
Bzdl’ of the Treasury. Debt for 1941-1991 is total
etin
outstanding debt, also at the end of the fiscal year,
reported in the same publication. Nominal debt was
deflated to real terms using the implicit price deflator
for GNP.
Interest

Rate:
The six-month commercial paper
rate is taken from Table H 1.5of the Statkticai Reha.w,
Board of Governors of the Federal Reserve System.

Moneta y

Aggregate:

The money supply series
before 1959 is the M4 aggregate reported in Table
1 of Friedman and Schwartz (1970). The money
series for 19.59 to 1991 is the M’ series reported
Z
in Table 1.2 1 of the Federal Reserve BaDetin, Board
of Governors of the Federal Reserve System.

The implicit price deflator for GNP
Price Deflutor:
is from Table 7.4 of the Sur~q of &rent Business,
Department of Commerce, Bureau of Economic
Analysis.

“The Ricardian Approach to Budget Deficits,”
if Economic Perspectives, vol. 3 (Spring 1989),
pp. 37-54.

Journal

Barro, Robert J. and Chaipat Sahasakul. “Average Marginal
Tax Rates from Social Security and the Individual Income
Tax,” Journal of Business, vol. 59 (October 1986), pp.
555-66.
Bernheim, B. Douglas. “Ricardian Equivalence: An Evaluation
of Theory and Evidence,” NBER Macmeconomics Annual
1987. Cambridge: MIT Press, 1987.
Congressional Budget Office, the Congress of the United
States. Th Economic Effects of Reduced Defense Spending.
February 1992.
Doan, Thomas A. User’ ManuaL: RATS V,ion
s
VAR Econometrics, 1989.

3.02. Evanston:

Dotsey, Michael and Max Reid. “Oil Shocks, Monetary Policy,
and Economic Activity,” Federal Reserve Bank of Richmond Economic Review, vol. 78 (July/August 1992), pp.
14-27.
Friedman, ‘
Milton and Anna J. Schwartz. Monetary StarisEis of
the United States. New York: National Bureau of Economic
Research, 1970.
Garfinkel; Michelle R. “The Economic Consequences
of
Reducing Military Spending,” Federal Reserve Bank of
2
1990),
St. Louis Revho, vol. 7’ (November/December
pp. 47-58.
Kendrick, John W. Productivity Trends in the United States.
New York: National Bureau of Economic Research, 1961.
Lupoletti, William M. and Roy H. Webb. “Defining and Improving the Accuracy of Macroeconomic Forecasts: Contributions from a VAR Model,” JoumaL ofBusiness, vol. 59
(April 1986), pp. 263-85.
McCallum, Bennett T. “A Reconsideration of Sims’ Evidence
Concerning Monetarism,” Economics Letters, vol. 13 (1986),
pp. 167-71.

Nominal figures for GNP
Gross National Product:
Sims, Christopher A. “Macroeconomics and Reality,” Econoare taken from Table 1.1 of the Su~ey of Current
metrica, vol. 48 (January 1980), pp. l-48.
Business, Department
of Commerce,
Bureau of
. “Comparison of Interwar and Postwar Business
Economic Analysis. Nominal GNP was deflated to
Cycles: Monetarism Reconsidered,”
American Economic
real terms using the implicit price deflator for GNP.
Review, vol. 70 (May 1980), pp. 250-57.
Nondefense

Government

Spending:

. “Are Forecasting Models Usable for Policy
Analysis?” Federal Reserve Bank of Minneapolis Quar&&y
Review, vol. 10 (Winter 1986), pp. 2-16.

Nondefense
of goods and

spending is government purchases
services from Table 1.1 of The Nationa/ Income and
Pmduct Accounts (Department of Commerce, Bureau
of Economic Analysis), less the defense spending
series described above.

Stock, James H. and Mark W. Watson. “Interpreting the
Evidence on Money-Income Causality,” Journal of Econometiks, vol. 40 (January 1989), pp. 161-81.
Wynne, Mark A. “The Long-Run Effects of a Permanent
Change in Defense Purchases,” Federal Reserve Bank of
Dallas Economic Rewiew, January 1991, pp. 1-16.
. “The Analysis of Fiscal Policy in Neoclassical
Models.” Research Paper No. 9212. Dallas: Federal Reserve
Bank of Dallas, Research Department, August 1992.

FEDERAL

RESERVE

BANK

OF RICHMOND

11

A Simple Model of Irving Fisher’
s
Price-Level

Stabilization

Rule

Thomas M. Hump/lrey

It is now well understood that a price-level stabihzation policy is more ambitious than a zero-inflation
policy. Targeting zero inflation means that the cen‘ bank brings inflation to a halt but leaves the price
tral
level where it is at the end of the inflation. By contrast, targeting stable prices means that the central
bank ends inflation and also rolls back prices to
some fixed target level. By reversing inflated prices
and restoring them to their preexisting level, a pricestabilization policy eradicates the upward drift of
prices that can occur under a zero-inflation policy.
It follows that a stable-price policy is more stringent
than a zero-inflation policy.
The history of monetary thought abounds with
price-level (as opposed to inflation-rate) stabilization
rules. Not all of these policy rules. were sound;
some would have destabilized prices rather than
stabilizing them. Notoriously flawed was John Law’
s
1705 proposal to back the quantity of money dollar
for dollar with theLnominal value of land. His rule
guaranteed that changes in the price of land would
induce equiproportional changes in the money stock.
Equally flawed was the celebrated feat bills doimine
advanced by the antibullionist writers during the Bank
Restriction period of the Napoleonic’ Wars. It tied
money’ issue to the “needs of trade” as represented
s
by the nominal quantity of commercial bills presented
to banks as loan collateral. It failed to note that since
the nominal volume of bills supplied (or loans
demanded) varies directly with general prices, accommodating the former with money creation meant
accommodating prices as well. Seen by their proponents as price-stabilizing, both rules in fact would
have expanded or contracted the money supply in
response to shock-induced price-level changes, thus
underwriting or validating those changes (see Mints,
1945, pp. 30, 47-48).
Ruling out such inherently fallacious schemes
leaves the remaining valid ones. These fall into two
categories. The first consists of non-activist policy
rules that fix the money stock or its rate of change
at a constant level. Milton Friedman’ k-percent rule,
s
12

ECONOMIC

REVIEW,

which would establish .the money stock at a fixed
level when output’ growth rate is zero, is perhaps-.
s
the best known example of this type of rule. The
second includes activist feedback rules which dictate predetermined
corrective responses of themoney supply and/or central-bank interest rates to
price deviations from target. The proposals of David
Ricardo, Knut Wicksell, and Irving Fisher exemplify
this type of rule. Given England’ 18 10 regime of
s
inconvertible paper currency and floating exchange
rates, Ricardo (18 10) advocated lock-step moneystock contraction in proportion to price-level’ increases as proxied by exchangerate depreciation and:
the premium (excess of market price over mint price)
on gold. Wicksell (1898, p. 198) proposed an
interest-rate feedback rule: raise the bank interestrate when prices are rising, lower it when prices are.
falling, and keep it steady when prices are neither
rising nor falling. Fisher suggested not one rule but
two. His 1920 compensated dolcOrplan called for the
policymakers to adjust the gold weight of the dollar
equiproportionally
to changes in the preceding
month’ ‘
s general price index. In essence, he posited’
the relationship: dollar price of goods = dollar price
of gold x gold price of goods. Official adjustments.
in the dollar price of gold, he thought, would offset
fluctuations in the world gold price of goods (as
proxied by the preceding month’ general price
s
index), thus stabilizing the dollar price of goods.
His second rule (1935) was more conventional. Much
like stabilization rules proposed today, it dictated
automatic variations in the money stock to correct
price-level deviations from target.
This article examines Fisher’ second policy rule,
s
particularly its dynamic properties. Fisher himself
failed to investigate these properties. He provided
no analytical model in support of his rule. Such a
model is needed to show (1) that the rule would
indeed force prices to converge to target, (2) how
fast they would converge, and (3) whether the
resulting path is oscillatory or monotonic. Lastly, only
the model can demonstrate
rigorously whether
Fisher’ rule is capable of outperforming rival rules
s
such as the constant money-stock rule.

NOVEMBER/DECEMBER

1992

The following paragraphs attempt to provide the
missing model underlying Fisher’ scheme. In so
s
doing, they contribute three innovations to the
stabilization literature. First, they express Fisher’
s,
scheme in equations, something not done before.
They represent his proposal in the form of pricechange equations and policy-reaction functions suggested by A. W. Phillips’ (1954, 1957) classic work
on closed-loop feedback control mechanisms.
Second, they thus extend Phillips’ analysis to
encompass monetary models of price-level stabilization. Heretofore, Phillips’ work has been applied
exclusively to the design of output-stabilizing fiscal
rules in Keynesian multiplier-accelerator
models.
(See the texts of Allen, 1959, 1967; Meade, 1972;
Nagatani, 1981; and Turnovsky,
1977, for examples.) In finding a new use for Phillips’ work,
the article incorporates his notions of proportional,
derivative, and integral control into Fisher’ policys
response functions. The result is to show how
the money stock in Fisher’ scheme can be pros
grammed to respond’ automatically (1) to the discrepancy between actual and target prices, (2) to
the speed with which that discrepancy is rising or
falling, and (3) to the cumulative value of the
discrepancy over time beginning with the inauguration of his scheme.
Last but not least, the article compares within a
single model the relative performance of Fisher’
s
activist feedback rule with that of a non-activist
constant money-stock rule. Policymakers of course
must be convinced that Fisher’ rule dominates rival
s
candidate rules before they would consider adopting
it. A related issue concerns the doctrinal accuracy
of the model. To ensure that the model faithfully
captures Fisher’ thinking, one must outline his
s
scheme to determine the appropriate variables and
equations to use.

FISHER'S
SCHEME
Fisher presented his proposal in his 1935 book
200% Money. He argued that the monetary authorities
could stabilize prices at a fixed target level via open
market operations.
If money became scarce, as shown by a tendency of the
price level to fall, more could be supplied instantly; and if
superabundant,
some could be withdrawn with equal
promptness.
. . . The money management would’ thus
consist . . of buying [government securities] whenever
the price level threatened to fall below the stipulated par
and selling whenever it threatened to rise above that par.
(P. 97)
FEDERAL

RESERVE

He reasoned that price movements stem from
excess money supplies or demands. Since money is
employed for spending, these excess supplies spill
over into the commodity market in the form of
excess aggregate demand for goods, thus putting
upward pressure on prices. Prices continue to rise
until the surplus money is absorbed by higher cash
balances needed to purchase the same real output
at elevated prices. Likewise, excess money demands,
manifested in increased hoarding and decreased
spending, cause aggregate demand contractions and
downward pressure on prices in the goods market.
Prices and the associated need for transaction
balances continue to fall until money demand equals
money supply. In either case, appropriate variations
of the money stock could, Fisher thought, correct
the resulting price-level deviations from target. In
other words, the Federal Reserve expands the money
stock when prices fall below target and contracts the
money stock when prices rise above target. Clearly,
money constitutes the policy instrument and the price
level the goal variable in Fisher’ scheme.
s
A policy instrument of course is only as good as
the Fed’ ability to’control it. In Fisher’ view this
s
s
ability was absolute-or
at least it could be ,made so
by the 100 percent reserve regime advocated in his
book. As he saw it, the Fed exercises direct control
over the high-powered monetary.base. And since a
100 percent reserve regime renders the base and the
money stock one and the same aggregate, it follows
that tight command of the one constitutes perfect
regulation of the other. In sum, when deposit money
is backed dollar for dollar with bank reserves as
prescribed in his book, there can be no slippage in
money-stock control to disqualify money as the policy
instrument. For that matter, little slippage would
occur in a fractional reserve system or even a system
of no reserve requirements as long as deposit money
bore a stable relationship to high-powered money.
Nor did Fisher see policy lags as a problem.
He knew that his rule to be effective required two
things: prompt direct response of prices to money
and equally prompt feedback response of money to
prices. He was sanguine about both, although less
so about the former. In Stabilizing the Dolfar (1920),
he stated that prices seem to follow money with “a
lag of one to three months” (p. 29). As for money’
s
corrective response to price misbehavior, he found
virtually no lag at all. Money, he insisted, can be “supplied instantly” or “withdrawn with equal promptness”
in reaction to price deviations from target. His
scheme admits of no significant delays to retard the
Fed from achieving its desired target setting of the
BANK

OF RICHMOND

13

money stock. Such setting occurs immediately.
Accordingly, the model below omits all policy lags.
On this point he was quite clear.
He was not so clear on other matters, however.
For example, he did not specify the exact price
indicator to which the Fed should react. Should it
adjust the money stock in response to the differential between actual and target prices? To changes in
that differential? To both? Suppose it has missed the
target in every period since it initiated its policy.
Should it forgive these past misses? Or should it allow
them to influence current policy by linking the money
stock to the cumulative sum of the past price errors?
Which price indicator and associated policy response
yields the smoothest and quickest path to price
stability? Fisher did not say. Moreover, as noted
above, he offered no proof that his feedback rule
could in fact deliver price stability or that it would
outperform other candidate rules.

MODELINGFISHER'SSCHEME
Addressing these issues requires an explicit
analytical framework. The one supplied here employs
the four-step technique pioneered by A. W. Phillips
(1954, 1957) in his celebrated analysis of stabilization policy.
Step one models how the price level would behave
if uncorrected by policy. Consistent with Fisher’
s
exposition, the model treats prices as moving in
response to excess money supplies and demands.
Step two incorporates policy-response functions
embodying elements of pmpotiional, derivative, and
integralcorm& A proportional feedback control rule
adjusts the money stock in response to current price
deviations from target. Derivative control adjusts
money in response to the deviation’ rate of change.
s
Integral control adjusts money in response to the
cumulative sum of deviations over time. It seeks to
correct the time integral of all past misses from target.
For example, suppose prices since the inauguration
of corrective policy have fluctuated about target. Or,
what is the same thing, the discrepancy between
actual and target prices p -p, has fluctuated about
zero, as shown in the figure. The application of proportional policy at time t, requires money-stock
contraction in proportion to the price gap t,a.
Derivative’
policy
contracts the money stock by a
fixed proportion of the rate of price rise indicated
by the slope of the tangent to the curve at time t,.
Finally, integral policy aimed at correcting cumulative
deviations from target contracts the money stock in
14

ECONOMIC

REVIEW.

PROPORTIONAL,
DERIVATIVE, AND
INTEGRAL POLICY
Price Gap
(P-P4
/

+
ime

Proportional
policy contracts the money stock in proportion
to the
price gap t,a. Derivative
policy contracts the money stock in proportion to the rate of price rise as indicated by the slope of the tangent
to the curve at point a. Integral policy contracts the money stock in
proportion
to the cumulative
value of the price gap over time as
indicated
by the shaded area under the curve.

propoftion to the shaded area under the curve up to
time t,. In short, proportional policy focuses on
current price gaps, derivative policy on the direction
of movement of such gaps, and integral policy on the
sum of all gaps, past and present. Once applied, each
policy produces a different policy-corrected path for
prices;Step three solves the model for these alternative
policy;corrected paths. Step four uses a loss function to measure the cost (in terms of reputational
damage suffered by the Fed when prices deviate from
target) of adhering to each path. This procedure
allows, one to rank the alternative policy rules according to how smoothly and quickly they stabilize
prices. As shown below, at least one of the feedback
rules dominates the fixed money-stock rule.

PRICE-CHANGE EQUATION
The first step is to model the non-policy determinants of price-level behavior. To Fisher, price
changes emanated from excess money supplies and
demands caused, say, by policy mistakes and/or
shifts in the amount of money people want to hold
at existing prices and real incomes. In his words,
prices fall when money is “scarce” relative to the
demand for it and rise when money is “superabundant” relative to demand. Accordingly, one seeks the
simplest equation that captures his hypothesis.
That equation is fi =cr(m -kpq), where the time
derivativei
denotes a change in prices, m denotes
the money supply, the product kpq denotes money
demand consisting of velocity’ inverse or the Cams
bridge R times the price levelp times real output q,

NOVEMBER/DECEMBER

1992

and CY a positive goods-market reaction coefficient
is
expressing the speed of response of prices to excess
money supply. ’ Let the model’ time unit be a
s
calendar quarter. Define T=Z/CY as the number of
quarters required for prices to adjust to clear the
market for money balances. Then Fisher’ 1920
s
finding that prices follow money with a lag of close
to three months implies that both Q and T are
approximately equal to unity in magnitude. As for
the other items in the equation, output q and the
Cambridge k are taken as given constants at their
long-run equilibrium values. In his 1935 book, Fisher
mentioned no other money-demand determinants
such as interest rates or price-change expectations.
For that reason they are omitted here.2

POLICYRULES
The next step is to specify the alternative policyresponse functions the Fed might use to bring prices
to target in the model. These functions are absolutely
essential. Without them, prices p would adjust in
response to an excess money supply until they
reached an equilibrium level p =m/kq different from
the target levelp=. Permanent price gaps would result.
Under a constant money-stock G&J the Fed merely
sets the money stock at the level mT=kGT that
equilibrates money supply and demand at the target
price level pT and then leaves it there. Other than
setting mT consistent with &-, the Fed does nothing
I This equation admits of a straightforward derivation. Define
an excess supply of money x as the surplus of money m over
the demand for it Rpq,or x=m -Rpq. Assume this excess money
supply spills over into the commodity market to underwrite an
excess demand for goods g. In short, x =g. The excess demand
for goods in turn puts upward pressure on prices, which rise in
proportion to the excess demand, or b=czg, where CYis the
factor of proportionality. Substitution of x for g and m -Rpq for
x yields the equation of the text.
* It is tempting to write Fisher’ equation in expectationss
augmented form as d = c&z - (kpq- @)I where the term - rb
captures the effect of price-change expectations B’ on money
demand. This term says that people expecting money tb
deoreciate in value will hold smaller cash balances than thev
w&Id if they expected no such depreciation. One could furthe;
assume that people form their expectations rationally such that
expected price changes equal actual ones @=@ in this nonstochastic model and the equation reduces to D =/ol/ff -UT)/
(m-&q). But such an equation would be inionsistent with
Fisher’ own views on the subject. True, in his The Pudzasing
s
PowerofMorzq (191 l), he recognized that inflation perceptions
affect money demand. When money “is depreciating,” he wrote,
“holders will eet rid of it as fast as oossible” (D. 63). But he did
not spell out Low such perceptions are formgd or how they get
incorporated into money demand functions. Nor did he believe
in rational expectations. He held that people are subject to money
illusion and so revise their expectations slowly in the face of
actual price changes such that when those changes occur expectations lag behind. Indeed, he coined the phrase “money illusion” and used it as the title of his 1928 book.
FEDERAL

RESERVE

else. Thus the money-stock equation is simply
m, =mT, where m, denotes constant money-stock
policy.
Activist feedback rules attempt to improve upon
the constant money-stock rule. Thus under a pmportiona/jedback rub the Fed adjusts the money stock
above or below the desired long-run equilibrium level
mT as prices are below or above their target level.
In other words, the money stock is set to counter
price gaps or deviations from target. The resulting
policy-response equation is m, =mT -fl@ -PT), where
m, denotes proportional policy and /3 is the proportional correction coefficient.
With a derivative feedback nde the Fed adjusts the
money stock in response to the speed with which
the price gapp -pT is increasing or decreasing in size.
Or, what is the same thing (since the target price
levelp, is fixed), it adjusts the money stock above
or below money’ long-run equilibrium level to
s
counter falls or rises in the price level d. The
resulting policy-response equation is ?&=mT-+,
where m, denotes derivative policy and y is the
derivative correction coefficient.
With an integralfeedback mle the Fed adjusts the
money stock to correct cumulative price gaps or the
sum of all past policy misses over time. The Fed
learns from these price errors. It uses the information given by their integral to determine the current
setting of the money stock. Accordingly, the policy
??Zi
=mT - 6 i (p -pT)dt, where mi denotes
0
t
integral policy, 5 ( )dt denotes the integral oper-

equation

iS

0

ator, and 6 is the integral correction coefficient.
This rule can be given an alternative expression.
When differentiated to get rid of the integral, it
becomes 7iz -6(p -pT), stating that the Fed sets
=
the money stock’ rate of c/zange opposite to the
s
direction that prices are currently deviating from
target.
Finally, the Fed may employ a mixedfeedback nde
involving various combinations of the foregoing equations. For example, a mixed proportional-derivative
rule would yield the policy-response
function
111,=mT - p(p -PT) -rb embodying gap and gapchange terms together with their policy correction
coefficients.

PRICETIMEPATHSANDLOSSFUNCTTIONS
The third step is to substitute each of the foregoing policy rules into the Fisherian price-change
BANK

OF RICHMOND

1.5

equationb =cr(m -kpq). Doing so produces expressions whose solutions are the policy-corrected time
paths of prices.
Thus substitution of the constant money-stock rule
into the price-change equation yields d = c&q@, -p).
Solving this first-order expression for the time path
of prices gives p =pT + @jO ,
-p#‘
where p, denotes
the (perturbed) price level at time t=O, t denotes
time, e is the base of the natural logarithm system,
and the parameter a =akq denotes speed of convergence to target. This expression says that prices
converge to target at a rate of a = c&q per unit of time.
In short, as time passes and t gets large, the last term
on the right-hand side of the equation goes to zero
so that only the first term pT remains. In this way
the path to price stability terminates when p =pT.
Associated with the path are certain costs to the
Fed. The Fed’ objective is to keep prices as close
s
to target as possible over time. Society penalizes
it for failing to do so. It suffers losses in reputation,
credibility, and prestige that vary directly and disproportionally with the duration and size of its
policy errors. These losses can be measured by
the quadratic cost function expressing the Fed’
s
reputational loss L as the cumulative squared deviation of prices from their desired target level, or
L = r(p -p#dt.

Substituting the price path into this

loss Function and integrating yields the cost of adhering to the non-activist constant money-stock rule,
or L, = (p,-p#/Za.
As a hypothetical numerical example, let pT = I, p, = 2, c~= I, k = Z/Z, .q = ZOO, and
a = 50. Then the quantitative measure of the loss is
L, = z/zoo.

EFFECTIVENESSOFTHEACTIVIST
PROPORTIONALRULE
To compare the foregoing loss with those of the
activist feedback policy rules, one must derive the
price paths and loss measures associated with the
latter rules. Thus the proportional feedback rule
yields the price path p =pT + (pO-pT)emb’ with associated loss measure L,= (p,-p#/Zb.
Here b=
cy(kq + fi) is the speed-of-convergence
parameter.
Since parameter b is larger than parameter a computed above, prices under the proportional rule
converge to target faster than they do under the
constant money-stock rule. It follows that prices
deviate from target for a shorter time under the
proportional rule. Consequently that rule yields the
smallest loss of the two and thus dominates the constant money-stock rule. Numerically, L, = Z/202,
16

ECONOMIC

REVIEW,

assuming the proportional correction coefficient fl= 2
and the constants CY, q, pO, and pT possess their
k,
values as assigned above. This loss compares
favorably with the corresponding
loss of l/100
associated with the constant money-stock rule. Given
a choice between the two rules, the Fed will select
the proportional rule.
A word of warning is in order here. The proportional rule’ superiority rests heavily on Fisher’
s
s
assumption of no policy lags. By slowing convergence
to target, policy lags could reverse the ranking of the
two rules. Such lags would delay the Fed’ adjusts
ment m of the money stock m to its desired proportional setting m,. A new equation ~~==X(VZ*-m),
where the positive coefficient X represents the policy
lag, would have to be added to the model. The
resulting reduced-form expression for 5 would be a
second-order differential equation whose solutionthe time path of prices-would be more,complicated
than before. Overshooting and oscillations would
be a distinct possibility; slower convergence a certainty. These considerations highlight the importance
of Fisher’ assumption of zero policy lags. Embodied
s
in the model, his assumption ensures the superiority of the proportional rule such that the Fed will
select it.

OPTIMALVALUEOFTHE~~

COEFFICIENT

Given the proportional rule’ capability of outs
performing the constant money-stock rule, a natural
question to ask next is whether the proportional
correction coefficient /3 has been assigned its optimal
value. The preceding numerical example assumed
p = 2. But a glance at the proportional rule’ loss
s
measure L,, = (p,-p#/Zcx(kq+@)
suggests that the
Fed should make /3 as large as possible (@- 00) and
Lp negligibly small. That is, optimality considerations
would seem to compel instantaneous monetary contraction in amounts sufficient to force prices to target
immediately.
Fisher, however, would have rejected this implication of the mathematical formulation of his scheme.
He would have condemned the violent monetary
contraction implied by high values of 0. To him such
contraction spelled devastating losses to output and
employment. In his The Purchasing Power tf Money
(1911) and his 1926 paper on price changes and
unemployment, he ascribed these losses to the failure
of sticky nominal wage and interest rates to respond
as fast as product prices to monetary shocks. He
attributed nominal wage rigidities to fixed contracts
and the inertia of custom; nominal interest rate

NOVEMBER/DECEMBER

1992

rigidities to price misperceptions
and sluggishly
adjusting inflation expectations. Because of these
inhibiting forces, a sharp fall in money and prices
would transform sticky nominal wage and interest
rates into rising real rates, thus depressing economic
activity. In his 1933 debt-deflation theory of great
depressions, he cited still another reason to fear
violent monetary contraction. He argued that price
deflation could, by raising the real burden of nominal
debt, precipitate a wave of business bankruptcies with
all its adverse repercussions for the real economy.
To avoid these consequences, Fisher would have
recommended relatively gradual monetary contraction implied by moderate values of /3 (such as fl= 2).
Consistent with his views, p’ value here is restricted
s
to unity.

RELATIVEEFFECHVENESSOFTHE
DERIVATIVERULE
As for the other candidate rules, the Fed will
reject as inferior to proportional policy the derivative
rule. That rule calls for money-stock adjustments
opposite to the direction prices are moving. It
exerts stabilizing pressure when prices are moving
away from target; less so when they are moving
toward target. When prices fall toward target, the
derivative rule interferes perversely by expanding
the money stock. In so doing, it retards convergence
and becomes a relatively unattractive option. In symbols, derivative policy results in the price path p =
p, + (pO
-pT)emCr and loss function L, = (Pa-p#/Zc,
with speed of convergence denoted by the parameter
c=cxkql(Z +cry). This parameter is smaller than its
counterparts a and b, signifying slower convergence
and larger reputation loss with a derivative rule than
with a constant or proportional rule. Numerically, the
derivative rule’ loss is L,, =2/50, assuming the
s
derivative correction coefficient y is assigned a value
of one and the other constants possess the same
magnitudes as defined above. This loss is twice that
of the constant money-stock rule and more than twice
that of the proportional rule. The Fed, therefore,
would hardly opt for a derivative rule.

RELATIVEEFFECIWENESSOFTHE
INTEGRALRULE
Nor would the Fed opt for an integral rule that
seeks to correct the sum of all past and present misses
of target. The past misses would continue to influence
policy even when the current price level was close
to target. Too strong a response to them would cause
overshooting. Conversely, too weak a response would
cause prices to move too slowly to target. Suppose
past misses totaled 5 when the current miss was 0.
FEDERAL

RESERVE

Integral policy in this case would push the price
level below target. And if the same past misses were
exactly counterbalanced by a current miss of -5,
integral policy would fail at that moment to put
corrective pressure on prices. Of course continuation of the current miss would eventually activate
corrective pressure. But this pressure would be slow
in coming. Thus while stabilizing prices in the long
run, integral policy might do so sluggishly and via
damped oscillatory paths.
Integral policy yields the time path p =pT +A, 8’
+A,@‘ Here A,, A, are constants of integration
.
determined by initial conditions. And r,, r, =
(- crkq/Z) f J(cxkq)‘ 4&/Z are the characteristic
roots of the left-hand or homogeneous part of the
second-order expression 5 + (c&q)j + crhp = c&5pT,obtained by differentiating the Fed’ policy-reaction
s
function to eliminate the integral and substituting the
result into the Fisherian price-change equation. The
roots r,, r, possess negative real parts (-c&/Z) thus
ensuring convergence. Damped oscillations about target
occur if (cxkqf<4c& or, in other words, if the integral correction coefficient 6 is larger than olR*q*/4.
Monotonic convergence results from smaller values
of that coefficient. But convergence, whether cyclical
or monotonic, is slower under the integral rule than
under the proportional and constant money-stock
rules. The above-mentioned characteristic roots reveal as much. Dwarfed by the speed-of-convergence
parameters of the other rules, their relatively small
size renders the integral rule inferior to its rivals.
Confirmation comes from the loss function, which
shows a large reputational loss associated with the
integral rule. One computes the integral policy’ loss
s
function
as Li = - /A,Z/ZrJ - /ZA, A, l(r, + rJ/
$,
- lA,zIZrJ, where A, = /‘ - r&, -pT) jl(rl -r-J and
A,=lr,(p,-pT)
-fiJl(r,
-rJ.
Although hard to
evaluate analytically, this function yields to numerical computation. Let cr = 6 =pT = I, j, = - I, p. = 2,
k = Z/Z, and q = ZOOas before. Then the function in
this hypothetical illustrative example produces a
numerical value of 26, several hundred times the
losses under the other rules.

RELATIVEEFFECTIVENESSOFA
MIXEDRULE
Finally, the Fed might try a mixed rule embodying proportional and derivative elements. The
mixed rule yields the price path p =p, + (p, -pT)emdt
and associated loss function L, = (PO /Zd,
-pJ’
where the speed-of-convergence
parameter d=
cx(fl+kq)l(Z +cry). With the coefficient values as
BANK OF RICHMOND

17

assigned above, the loss L, is 21102, ranking the
mixed rule inferior to the proportional and constant
money-stock rules, but superior to the derivative and
integral rules. This ranking, however, depends on
the values assigned to the coefficients. Giving y a
value of l/52 instead of 1 would reverse the order
of the mixed and constant money-stock rules. In
general, the mixed rule ranks below the constant
money-stock rule if y >/3/&q
and above it if that
inequality is reversed.

CONCLUSION
Fisher’ feedback policy rule delivers price stability
s
in the simple money-demand-and-supply
model
presented here. And it does so whether the rule is
expressed in terms of proportional,
derivative,
integral, or mixed control. All the rules yield paths

that converge to target, albeit at different speeds.
Proportional policy yields the quickest and smoothest
path, followed by mixed, derivative, and integral
policies in that order. Of these four activist feedback
rules, only the proportional always outperforms the
nonactivist constant money-stock rule. For this
reason, proportional policy’ loss measure is the
s
smallest of the lot. Indeed, one can rank the loss
measures to show that the proportional feedback rule
dominates the constant money-stock rule, which in
turn dominates the derivative and integral rules.
While the mixed rule may, at certain values of the
y coefficient, outrank the constant money-stock
rule, it can never dominate the proportional rule.
Provided policy lags are short or nonexistent, these
results create a presumption in favor of a proportional
feedback rule.

REFERENCES
Alien, R. G. D. Mathematical Economics. London: Macmillan,
1959.

Meade, J. E. The ContmIed Economy. Albany: State University
of New York Press, 1972.

Macmeconomic Theory: A Mathematics/ Treatment.

London:‘
Macmillan,

1967.

Fisher, Irving. The Pa~hasing Power of Money. New York:
Macmillan, 1911. New and revised edition, 1913. Reprinted New York: Augustus M. Kelley, 1963.
Stabiking

1920.

the Dolar.

.

“A Statistical Relation between Unemployment
and Price Changes,” International Loboar Review, vol. 13
(June 1926), pp. 78592. Reprinted as “I Discovered the
Phillips Curve,” Journal of PoLitical Economy, vol. 81
(March/April 1973), pp. 496-502.
1928.

Pokies.

Law, John. Money and Trade Considered: With a Proposal for
Sapplying the Nation With Money, 1705. Reprinted New
York: Augustus M. Kelley, 1966.

ECONOMIC

REVIEW.

David. The High Price of BaLion, A Pmof of the
Depreciation of Banknot&, 1810. In P. Sraffa and M. Dobb,
eds . , Th Wok and Correspondence ofDa&d Ricardo, vol. II I.

Ricardo,

Turnovsky,

1935.

Friedman, Milton. A Pmgram for Monetary Stabikty. New York:
Fordham University Press, 1959.

18

Cam-

“Stabilisation Policy and the Time-Forms
of
Lagged Responses,” EconomicJoumaC, vol. 67 dune 1957),
pp. 265-77.

Cambridge:

“The Debt-Deflation Theory of Great Depressions,” Econometrica, vol. 1 (1933), pp. 337-57.
. 200% Money. New York: Adelphi,

Nagatani, Keizo. Macmeconomic Dynamics. Cambridge:
bridge University Press, 1981.

Phillips, A. W. “Stabilisation Policy in a Closed Economy,”
Economic Joamal, vol. 64 (June 1954), pp. 290-323.

New York: Macmillan,

. The Money Ik’
usion. New York: Adelphi,

Mints, Lloyd W. A History of Bank-ing Theory. Chicago:
University of Chicago Press, 1945.

Cambridge

University

Press,

195 1.

Stephen J. Macmeconomic Analysis and Stabilization
Cambridge: Cambridge University Press, 1977.

Wicksell, Knut. Znterzst and Prices, 1898. Translated by R. F.
Kahn, London: Macmillan, 1936. Reprinted New York:
A. M. Kelley, 1965.

NOVEMBER/DECEMBER

1992

Money Market

Futures

Anatoh Kuptianov ’

INTRODUCTION
Money market futures are futures contracts based
on short-term interest rates. Futures contracts for
financial instruments are a relatively recent innovation. Although futures markets have existed over 100
years in the United States, futures trading was limited
to contracts for agricultural and other commodities
before 1972. The introduction of foreign currency
futures that year by the newly formed International
Monetary Market (IMM) division of the Chicago
Mercantile Exchange (CME) marked the advent of
trading in financial futures. Three years later the first
futures contract based on interest rates, a contract
for the future delivery of mortgage certificates issued
by the Government National Mortgage Association
(GNMA), began trading on the floor of the Chicago
Board of Trade (CBT). A host of new financial futures
have appeared since then, ranging from contracts on
money market instruments to stock index futures.
Today, financial futures rank among the most actively
traded of all futures contracts.
Four different futures contracts based on money
market interest rates are actively traded at present.
To date, the IMM has been the site of the most
active trading in money market futures. The threemonth U.S. Treasury bill contract, introduced by the
IMM in 1976, was the first futures contract based
on short-term interest rates. Three-month Eurodollar
time deposit futures, now one of the most actively
traded of all futures contracts, started trading in 198 1.
More recently, both the CBT and the IMM introduced futures contracts based on one-month interest
rates. The CBT listed its 30-day interest rate futures
contract in 1989, while the Chicago Mercantile
Exchange introduced a one-month LIBOR futures
contract in 1990.
This article provides an introduction to money
market futures. It begins with a general description
of the organization of futures markets. The next
section describes currently traded money market
futures contracts in some detail. A discussion of the
relationship between futures prices and underlying
* This paper has benefited from helpful comments by Timothy
Cook, Ira Kawaller, Jeffrey Lacker, and Robert LaRoche.
FEDERAL

RESERVE

spot market prices follows. The concluding section
examines the economic function of futures markets.

Futures Contracts
Futures contracts traditionally have been characterized as exchange-traded, standardized agreements
to buy or sell some underlying item on a specified
future date. For example, the buyer of a Treasury
bill futures contract-who
is said to take on a “long”
futures position-commits
to purchase a 13-week
Treasury bill with a face value of $1 million on some
specified future date at a price negotiated at the time
of the futures transaction; the seller-who
is said to
take on a “short” position-agrees
to deliver the
specified bill in accordance with the terms of the contract. In contrast, a “cash” or “spot” market transaction simultaneously prices and transfers physical
ownership of the item being sold.
The advent of cash-settled futures contracts such
as Eurodollar futures has rendered this traditional
definition overly restrictive, however, because actual
delivery never takes place with cash-settled contracts.
Instead, the buyer and seller exchange payments
based on changes in the price of a specified underlying item or the returns to an underlying security.
For example, parties to an IMM Eurodollar contract
exchange payments based on changes in market
interest rates for three-month Eurodollar depositsthe underlying deposits are neither “bought” nor
“sold” on the contract maturity date. A more general
definition of a futures contract, therefore,
is a
standardized, transferable agreement that provides
for the exchange of cash flows based on changes in
the market price of some commodity or returns to
a specified security.
Futures contracts trade on organized exchanges
that determine standardized specifications for traded
contracts. All futures contracts for a given item specify
the same delivery requirements and one of a limited
number of designated contract maturity dates, called
settlement dates. Each futures exchange has an
affiliated clearinghouse that records all transactions
and ensures that all buy and sell trades match. The
clearing organization
also assures the financial
BANK OF RICHMOND

19

integrity of contracts traded on the exchange by
guaranteeing contract performance and supervising
the process of delivery for contracts held to maturity. A futures clearinghouse guarantees contract
performance by interposing itself between a buyer
and seller, assuming the role of counterparty to the
contract for both parties. As a result, the original
parties to the contract need never deal with one
another again-their contractual obligations are with
the clearinghouse.
Contract standardization and the clearinghouse
guarantee facilitate trading in futures contracts.
Contract standardization reduces transactions costs,
since it obviates the need to negotiate all the terms
of a contract with every transaction-the
only item
negotiated at the time of a futures transaction is the
futures price. The clearinghouse guarantee relieves
traders of the risk that the other party to the contract will fail to honor contractual commitments.
These two characteristics make all contracts for the
same item and maturity date perfect substitutes for
one another. Consequently, a party to a futures contract can always liquidate a futures commitment, or
open position, before maturity through an offsetting
transaction. For example, a long position in Treasury
bill futures can be liquidated by selling a contract for
the same maturity date. The clearinghouse assumes
responsibility for collecting funds from traders who
close out their positions at a loss and passes those
funds along to traders with opposing futures positions
who liquidate their positions at a profit. Once any
gains or losses are settled, the offsetting sale cancels
the commitment created through the earlier purchase
of the contract. Most futures contracts are liquidated
in this manner before they mature. In recent years
less than 1 percent of all futures contracts have been
held to maturity, although delivery is more common
in some markets.’
Forward agreements resemble futures contracts
in that they specify the terms of a transaction to be
undertaken at some future date. For this reason, the
terms “forward agreement” and “futures contract”
are often used synonymously. There are important
differences between the two, however. Whereas
futures contracts are standardized agreements, forward agreements tend to be custom-tailored to the
needs of users. While a good deal of contract standardization exists in forward markets, items such as
delivery dates, deliverable grades, and amounts can
all be negotiated separately with each contract.
I Based on data from the AnnualReport 1991 of the Commodity
Futures Trading Commission.

20

ECONOMIC

REVIEW,

Moreover, forward contracts are not traded on
organized exchanges as are futures contracts and
carry no independent clearinghouse guarantee. As a
result, a party to a forward contract faces the risk
of nonperformance
by the other party. For this
reason, forward contracting generally takes place
among parties that have some knowledge of each
other’ creditworthiness.
s
Unlike futures contracts,
which can be bought or sold at any time before
maturity to liquidate an open futures position, forward agreements,
as a general rule, are not
transferable and so cannot be sold to a third party.
Consequently, most forward contracts are held to
maturity.
Futures Exchanges
In addition to providing a physical facility where
trading takes place, a futures exchange determines
the specifications of traded contracts and regulates
trading practices. There are 13 futures exchanges in
the United States at present. The principal exchanges
are in Chicago and New York.
Each futures exchange is a corporate entity
owned by its members. The right to conduct transactions on the floor of a futures exchange is limited
to exchange members, although trading privileges can
be leased to nonmembers. Members have voting
rights that give them a voice in the management of
the exchange. Memberships,
or “seats,” can be
bought and sold: futures exchanges routinely make
public the most recent selling and current offer price
for a seat on the exchange.
Trading takes place in designated areas, known as
“pits,” on the floor of the futures exchange through
a system of open outcry in which traders announce
bids to buy and offers to sell contracts. Traders on
the floor of the exchange can be grouped into two
broad categories: floor brokers and floor traders.
Floor brokers, also known as commission brokers,
execute orders for off-exchange customers and other
members. Some floor brokers are employees of
commission firms, known as Futures Commission
Merchants, while others are independent operators
who contract to execute trades for brokerage firms.
Floor traders are independent operators who engage
in speculative trades for their own account. Floor
traders can be grouped into different classifications
according to their trading strategies. “Scalpers,” for
example, are floor traders who perform the function
of marketmakers in futures exchanges. They supply

NOVEMBER/DECEMBER

1992

liquidity to futures markets by standing ready to buy
or sell in an attempt to profit from small temporary
price movements.2
Futures Commission Merchants
A Futures Commission Merchant (FCM) handles
orders to buy or sell futures contracts from offexchange customers. All FCMs must be licensed by
the Commodity
Futures Trading Commission
(CFTC), which is the government agency responsible for regulating futures markets. An FCM can be
a person or a firm. Some FCMs are exchange
members employing their own floor brokers. FCMs
that are not exchange members must make arrangements with a member to execute customer orders
on their behalf.
Role of the Exchange Clearinghouse
As noted earlier, each futures exchange has an
affiliated exchange clearinghouse whose purpose is
to match and record all trades and to guarantee contract performance.
In most cases the exchange
clearinghouse
is an independently
incorporated
organization, but it can also be a department of the
exchange. The Board of Trade Clearing Corporation,
the CBT’ clearinghouse, is a separate corporation
s
affiliated with the exchange, while the CME Clearing House Division is a department of the exchange.
Clearing member firms act as intermediaries between traders on the floor of the exchange and the
clearinghouse. They assist in recording transactions
and assume responsibility for contract performance
on the part of floor traders and commission merchants
who are their customers. Although clearing member
firms are all members of the exchange, not all exchange members are clearing members. All transactions taking place on the floor of the exchange must
be settled through a clearing member. Brokers or
floor traders not directly affiliated with a clearing
member must make arrangements with one to act
as a designated clearing agent. The clearinghouse
requires each clearing member firm to guarantee
contract performance for all of its customers. If a
clearing member’ customer defaults on an outstands
ing futures commitment, the clearinghouse holds the
clearing member responsible for any resulting losses.
2 A good description of trading strategies employed by different
floor traders can be found in Hieronymus (1971). In addition,
detailed descriptions of different trading strategies can also be
found in almost any good textbook on futures markets such as
Chance (1989), Merrick (1990), or Siegel and Siegel (1990).
Silber (1984) presents a comprehensive analysis of scalper trading
behavior.
FEDERAL

RESERVE

Margin Requirements
Margin deposits on futures contracts are often
mistakenly compared to stock margins. Despite the
similarity in terminology, however, futures margins
differ fundamentally from stock margins. Stock
margin refers to a down payment on the purchase
of an equity security on credit, and so represents
funds surrendered to gain physical possession of a
security. In contrast, a margin deposit on a futures
contract is a performance bond posted to ensure that
traders honor their contractual obligations, and not
a down payment on a credit transaction. The value
of a futures contract is zero to both the buyer and
the seller at the time it is negotiated, so a futures
transaction involves no exchange of money at the
outset.
The practice of collecting margin deposits dates
back to the early days of trading in time contracts,
as the precursors of futures contracts were then
called. Before the institution of margin requirements,
traders adversely affected by price movements frequently defaulted on their contractual obligations,
often simply disappearing as the delivery date on their
contracts drew near. In response to these events,
futures exchanges instituted a system of margin
requirements, and also began requiring traders to
recognize any gains or losses on their outstanding
futures commitments at the end of each trading
session through a daily settlement procedure known
as “marking to market.”
Before being permitted to undertake a futures
transaction, a buyer or seller must first post margin
with a broker, who, in turn, must post margin with
a clearing agent. Margin may be posted either by
depositing cash with a broker or, in the case of large
institutional traders, by pledging collateral in the form
of marketable securities (typically, Treasury securities) or by presenting a letter of credit issued by a
bank. Brokers sometimes pay interest on funds
deposited in a margin account.
As noted above, clearing member firms ultimately are liable to the clearinghouse for any losses
incurred by their customers. To assure the financial
integrity of the settlement process, clearing member
firms must themselves meet margin requirements in
addition to meeting minimum capital requirements
set by the exchange clearinghouse.
Daily Settlement
The practice of marking futures contracts to market
requires all buyers and sellers to realize any gains or
losses in the value of their futures positions at the
BANK

OF RICHMOND

21

end of each trading session, just as if every position
were liquidated at the closing price. The exchange
clearinghouse collects payments, called variation
margin, from all traders incurring a loss and transfers
the proceeds to those traders whose futures positions
have increased in value during the latest trading
session. If a trader has deposited cash in a margin
account, his broker simply subtracts his losses from
the account and transfers the variation margin to the
clearinghouse, which, in turn, transfers the funds to
the account of a trader with a ‘
short position in the
contract. Most brokers require their customers to
maintain minimum balances in their margin accounts
in excess of exchange requirements.
If a trader’
s
margin account falls below a specified minimum,
called the maintenance margin, he faces a margin call
requiring the deposit of additional margin money. In
cases where collateral has been posted in the form
of securities rather than in cash, the trader must pay
the variation margin in cash. Should a trader fail to
meet a margin call, his broker has the right to
liquidate his position. The trader remains liable for
any resulting. losses.
Marking a futures contract to market has the
effect of renegotiating the futures price at the end
of each trading session. Once the contract is
marked to market, the trader begins the next trading
session with a commitment to purchase the underlying item at the previous day’ closing price. The
s
exchange clearinghouse then calculates any gains or
losses for the next trading session on the basis of this
latter price.
The following example involving the purchase of
a Treasury bill futures contract illustrates the
mechanics of the daily settlement
procedure.
Treasury bill futures prices are quoted as a price
index determined by subtracting the futures discount
yield (stated in percentage points) from 100. A 1 basis
point change in the price of the Treasury bill contract is valued at $2.5.3 Thus, if a trader buys a
futures contract at a price of 96.25 and the closing
price at the end of the trading session falls to 96.20,
he must pay $125 (5 basis points x $2.5 per basis
point) in variation margin. Conversely, the seller in
this transaction would earn $125, which would be
deposited to his margin account. The buyer would
then begin the next trading session with a commitment to buy the underlying Treasury bill at 96.20,
and any gains or losses sustained over the course of
the next trading session would be based on that price.
3 Price quotation and contiact specifications for Treasury bill
futures are discussed in more detail in the next section.

22

ECONOMIC

REVIEW.

Final Settlement
Because buying a futures contract about to mature
is equivalent to buying the underlying item in the
spot market, futures prices converge to the underlying
spot market price on the last day of trading. This
phenomenon is known as “convergence.” At the end
of a contract’ last trading session, it is marked to
s
market one final time. In the case of a cash-settled
contract, this final daily settlement retires all outstanding contractual commitments and any remaining margin money is returned to the traders. If the
contract specifies delivery of the underlying item, the
clearinghouse subsequently makes arrangements for
delivery among all traders with outstanding ‘
futures
positions. The delivery, or invoice price, is based
on the closing price of the last day of trading. Any
profit or loss resulting from the difference between
the initial futures price and the final settlement price
is realized through the transfer of variation margin.
The gross return on the futures position is reflected
in accumulated total margin payments, which must
equal the difference between the final settlement
price and the futures price determined at the time
the futures commitment was entered into.
Regulation of Futures Markets
The Commodity Futures Trading Commission is
an independent federal regulatory agency established in 1974 to enforce federal laws governing the
operation of futures exchanges and futures commission brokers. By law, the CFTC is charged with the
responsibility to ensure that futures trading serves
a valuable economic purpose and to protect the interests of users of futures contracts. The CFTC must
approve all futures contracts before they can be listed
for trading by the futures exchanges. It also enforces
laws and regulations prohibiting unfair and abusive
trading and sales practices.
The futures industry attempts to regulate itself
through a private self-regulatory organization called
the National Futures Association,
which was
formed in 1982 to establish and help enforce
standards of professional conduct. This organization
operates in cooperation with the CFTC to protect
the interests of futures traders as well as those of the
industry. As noted earlier, the futures exchanges
themselves can be viewed as private regulatory bodies
organized to set and enforce rules to facilitate the
trading of futures contracts.

NOVEMBER/DECEMBER

1992

Treasury bill futures prices are quoted as an
index determined by subtracting the discount yield
of the deliverable bill (expressed as a percentage)
from 100:

CONTRACT SPECIFICATIONS
FOR
MONEYMARKETFWTURES
Treasury Bill Futures
The Chicago Mercantile Exchange lists 13-week
Treasury bill futures contracts for delivery during the
months of March, June, September, and December.
Contracts for eight future delivery dates are listed
at any one time, making the furthest delivery date
for a new contract 24 months. A new contract begins
trading after each delivery date.
The Treasury bill contract
&live y Rec#rements
requires the seller to deliver a U.S. Treasury bill with
a $1 million face value and 13 weeks to maturity.
Delivery dates for T-bill futures always fall on the
three successive business days beginning with the
first day of the contract month on which (1) the
Treasury issues new 13-week bills and (2) previously issued 52-week bills have 13 weeks left to
maturity.4 This schedule makes it possible to satisfy
delivery requirements for a T-bill futures contract
with either a newly issued 13-week bill or an originalissue 26- or 52-week bill with 13 weeks left to maturity. Deliverable bills can have 90, 91, or 92 days
to maturity, depending on holidays and other special
circumstances. The last day of trading in a Treasury
bill futures contract falls on the day before the final
settlement date.
Treasury bills are discount instruPrice Quotation
ments that pay no explicit interest. Instead, the
interest earned on a Treasury bill is derived from the
fact that the bill is purchased at a discount relative
to its face or redemption value. Treasury bill yields
are quoted on a discount basis-that
is, as a percentage of the face value of the bill rather than as
a percentage of actual funds invested. Let S denote
the current spot market price of a bill with a face
value of $1 million. Then, the discount yield is
calculated as
Yiefd = [(l,OOO,OOO-S)/1,000,000](360/D&
where Day.r refers to the maturity of the bill. As
with other money market rates, calculation of the
discount yield on Treasury bills assumes a 360-day
year.
The Treasury auctions 13- and 26-week bills each Monday
(except for holidays and special situations) and issues them on
the followine Thursdav: X-week bills are auctioned everv four
weeks. Auczons for o&-year bills are held on a Thursdai and
the bills are issued on the following Thursday.
4

FEDERAL

RESERVE

Index = 100 -Futures

Discount Yield.

Thus, a quoted index value of 95.25 implies a
futures discount yield for the deliverable bill of
100 -95.25 = 4.75 percent. This convention was
adopted so that quoted prices would vary directly
with changes in the future delivery price of the bill.
Final Settlement Price

The final settlement price,
also known as the delivery price or invoice cost of
a bill, can be expressed as a function of the quoted
futures index price using the formulas given above.
For a bill with a face value of $1 million, the resulting
expression is
s = !$1,000,000
- $1,000,000(100-Zndex)(O.Ol)(Days/360),
where (loo-Index)(O.Ol)
is just the annualized
futures discount yield expressed as a decimal. The
CME determines the days to maturity used in this
formula by counting from the first scheduled contract delivery date, regardless of when actual delivery
takes place.‘
This means that calculation of the invoice cost is based on an assumed 9 l-day maturity,
except in special cases where holidays interrupt the
regular Treasury bill auction and delivery schedules.
To illustrate, suppose that the final index price of
a traded contract is 95.25 and the deliverable bill has
9 1 days to maturity as of the first scheduled delivery
date. Then, the final delivery price would be
$987,993.06

= $l,OOO,OOO
- $1,000,000(0.0475)(91/360).

Minimum

The minimum price
Price Fluctuation
fluctuation permitted on the trading floor is 1 basis
point, or 0.01 percent. Thus, the price of a Treasury
bill futures contract may be quoted as 95.25 or 95.26,
but not 95.255. The exchange values a 1 basis point
change in the futures price at $25. Note that this
valuation assumes a 90-day maturity for the deliverable bill.

Three-Month Eurodollar
Time Deposit Futures
Three-month Eurodollar futures are traded actively
on three exchanges at present. The IMM was first
BANK OF RICHMOND

23

to list a three-month Eurodollar time deposit futures
contract in December of 1981. Futures exchanges
in London and Singapore soon followed suit by listing
similar contracts. The London International Financial Futures Exchange (LIFFE) introduced its threemonth Eurodollar contract in September of 1982,
while the Singapore International Monetary Exchange
(SIMEX) introduced a contract identical to the IMM
contract in 1984. A special arrangement between the
IMM and SIMEX allows for mutual offset of
Eurodollar positions initiated on either exchange.
Thus, a trader who buys a Eurodollar futures contract at the IMM can undertake an offsetting sale on
SIMEX after the close of trading at the lMM.5
The Tokyo International Financial Futures Exchange
began listing a three-month Eurodollar contract in
1989, but that contract is not traded actively at present. The IMM contract remains the most actively
traded of the different Eurodollar contracts by a wide
margin.
The IMM Eurodollar contract is the first futures
contract traded in the United States to rely exclusively on a cash settlement procedure. Contract
settlement is based on a “notional” principal amount
of $1 million, which is used to determine the change
in the total interest payable on a hypothetical underlying time deposit. The notional principal amount
itself is never actually paid or received.
Expiration months for listed contracts are March,
June, September, and December. A maximum of 20
contracts are listed at any one time, making the
furthest available delivery date 60 months in the
future.
When a futures contract conContract Settlement
tains provisions for physical delivery, market forces
cause the futures price to converge to the spot market
price as the delivery date draws near. Actual delivery
of the underlying item never takes place with a cashsettled futures contract, however. Instead, the futures
exchange forces the process of convergence to take
place by setting the final settlement price equal to
the spot market price prevailing at the end of the
last day of trading. Final settlement is achieved by
marking the contract to market one last time based
on the final settlement price determined by the
exchange.
Price

Quotation

Eurodollar time deposits pay a
fixed rate of interest upon maturity. The rate of

5 See Burghardt et al. (1991) for a more detailed discussion of
the LIFFE and SIMEX contracts.

24

ECONOMIC

REVIEW.

interest paid on the face amount of such a deposit
is termed an add-on yield because the depositor
receives the face amount of the deposit plus an
explicit interest payment when the deposit matures.
Like other money market rates, the add-on yield for
Eurodollar deposits is expressed as an annualized rate
based on a 360-day year. Eurodollar futures prices
are quoted as an index determined by subtracting the
futures add-on yield from 100.
Final Settlement Price

Contract settlement is based
on the 90-day London Interbank Offered Rate
(LIBOR), which is the interest rate at which major
international banks with offices in London offer to
place Eurodollar deposits with one another. To determine the final settlement price for its Eurodollar
futures contract, the CME clearinghouse randomly
polls a sample of banks active in the London
Eurodollar market at two different times during the
last day of trading: once at a randomly selected time
during the last 90 minutes of trading, and once at
the close of trading. The four highest and lowest price
quotes from each polling are dropped and the remaining quotes are averaged to arrive at the LIBOR
used for final settlement.
To illustrate the settlement procedure, suppose
that the closing price of a Eurodollar futures contract
is 96.10 on the day before the last trading day. As
with Treasury bill futures, each 1 basis point change
in the price of a Eurodollar futures contract is valued
at $25. Thus, if the official final settlement price is
96.16, then all traders who carry open long positions
from the previous day have $150 ($25 per basis point
x 6 basis points) credited to their margin accounts
while traders with open short positions from the
previous day have $150 subtracted from their accounts. Since the contract is cash settled, traders with
open positions when the contract matures never bear
the responsibility of placing or accepting actual
deposits.
Minimum

The minimum price
Price Fluctuation
fluctuation permitted on the floor of the exchange
is 1 basis point, which, as noted above, is valued at
$25.

One-Month LIBOR Futures
One-month LIBOR futures began trading on the
IMM in 1990. The one-month LIBOR contract
resembles the three-month
Eurodollar contract
described above, except that final settlement is
based on the 30-day LIBOR.

NOVEMBER/DECEMBER

1992

Table 1

Three-Month Interest Rate Futures: Contract Specifications
Treasury

Three-Month

Bill

Eurodollar

Time

Deposit

Contract

Three-Month

Exchange

International
Monetary Market Division
of the Chicago Mercantile
Exchange

International
Monetary Market Division
of the Chicago Mercantile
Exchange

$1,000,000

Contract

Size

$1,000,000

Delivery

Requirements

U.S. Treasury
to maturity

bills with 13 weeks

Cash settlement
corporation

Delivery

Months

March,

June,

September,

December

March,

June,

Price Quotation

Index:

100 minus discount

yield

Index:

100

Minimum

$25

Price Fluctuation

$25

per basis point

Last Day of Trading

One day before first delivery

Delivery

September,
minus add-on

December
yield

per basis point

Second London business day before
the third Wednesday of the delivery
month

Three successive business days
beginning with the first day of the
contract month on which a 13-week
bill is issued and an original-issue
one-year bill has 13 weeks left to
maturity

Days

with clearing

date

Last day of trading

Table 2

One-Month Interest Rate Futures: Contract Specifications
Thirty-Day

Interest

International
Monetary Market Division
of the Chicago Mercantile Exchange

Chicago

Board of Trade

Contract

One-Month

Exchange

LIBOR

Contract

Size

$3,000,000

$5,000,000

Delivery

Requirements

Cash settlement

Cash settlement

Delivery

Months

First five consecutive
with current month

Rate

months

starting

First seven calendar months and the
next two months in the March, June,
September,
December trading cycle
following the spot month

Price Quotation

Index: 100 minus the LIBOR for
one-month
Eurodollar time deposits

Index: 100 minus the monthly
federal funds rate

Minimum

$25

$41.67

Price Fluctuation

per basis point

Last Day of Trading

The second London bank business
immediately
preceding the third
Wednesday of the contract month

Delivery

Last day of trading

Days

FEDERAL

RESERVE

day

average

per basis point

The last business
month

day of the delivery

Last day of trading
BANK OF RICHMOND

25

Contract Settlement
Like the three-month Eurodollar contract, the one-month LIBOR contract is
cash settled. Settlement is based on a notional
principal amount of $3 million.
Price

Quotation and Minimum

Price Fluctuation

Prices on one-month LIBOR futures are quoted as
an index virtually identical to that used for threemonth Eurodollar futures. The index is calculated
by subtracting the 30-day futures LIBOR from 100.
The minimum price increment is 1 basis point, which
is valued at $25.
Settlement Price
As with the three-month
Eurodollar contract, the final settlement price for onemonth LIBOR contract is based on the results of a
survey of primary market participants in the London
Eurodollar market.

100 -Index

= (20/3O)(awmage of the daily federal
finds rate for the previoz~s 20 days)
+ (10/3O)(ter~n federalbnds
rate fbr
10 days beginning April 2 1).

At the same time, the price of the May contract
would correspond approximately to the forward rate
on a 30-day term federal funds deposit beginning
May 1. The correspondence to the 30-day rate is
only approximate, however, because the settlement
price for the contract is based on a simple arithmetic average, which does not incorporate daily
compounding.

Final

Thirty-Day Interest Rate Futures
The Chicago Board of Trade’ 30-day interest rate
s
futures contract is a cash-settled contract based on
a 30-day average of the daily federal funds rate. The
CBT lists contracts for six consecutive delivery
months at any one time.
Contract Settlement
The 30-day interest rate
futures contract differs from other interest rate futures
in that the settlement price is based on an average
of past interest rates. Final settlement is based on
an arithmetic average of the daily federal funds rate
for the 30-day period immediately preceding the contract maturity date, as reported by the Federal
Reserve Bank of New York. The notional principal
amount of the contract is $5 million.
Price

Quotation
As with all other money market
futures, prices for 30-day interest rate futures are
quoted as an index equal to 100 minus the futures
rate. For deferred month contracts-that
is, contracts
maturing after the current month’ settlement dates
the futures rate corresponds approximately to a forward interest rate on one-month term federal funds.

In theory, the futures rate for the nearby contract
should reflect a weighted average of (1) the average
funds rate for the expired fraction of the current
month, plus (2) the term federal funds rate for the
unexpired fraction of the month. To illustrate,
suppose the date is April 21. Twenty days of the
month have passed, so the index value for the April
contract would reflect
26

ECONOMIC

REVIEW.

Minimum Price Fluctuation
The minimum price
fluctuation is 1 basis point, valued at $41.67.

Trading Activity in Money Market Futures
Charts 1 and 2 display a history of trading activity in the four money market futures contracts
discussed above. Chart 1 displays total annual trading
volume, which is a count of the total number of contracts (not the dollar value) traded for all delivery
months. Each transaction between a buyer and a
seller counts as a single trade. Chart 2 plots total
month-end open interest for all contract delivery
months. Month-end open interest is a count of the
number of unsettled contracts as of the end of the
last trading day of each month. Each contract included in the open interest count reflects an outstanding futures commitment on the part of both a
buyer and a seller.
Trading activity in the Treasury bill futures contract grew steadily from the time the contract was
first listed in 1976 through 1982, falling thereafter
below 20,000 contracts per day on average. The
trading history depicted in Charts 1 and 2 suggests
that the introduction of the Eurodollars futures contract attracted some trading activity away from
Treasury bill futures.
In recent years, the IMM Eurodollar futures contract has become the most actively traded futures
contract based on money market rates and is now
one of the most actively traded of all futures contracts. Three factors have contributed to the popularity of Eurodollar futures. First, most major international banks rely heavily on the Eurodollar market
for short-term funds and act as marketmakers in
Eurodollar deposits. Eurodollar futures provide a
means of hedging interest rate risk arising from these
activities. Second, the phenomenal growth of the
market for interest rate swaps during the last decade

NOVEMBER/DECEMBER

1992

Chart 1

AVERAGE MONTH-END
U.S. Money

Thousands

Market

OPEN INTEREST
Futures

1400

1200

m

Treasury

Bills

m

1000

30-Day

Interest

800
Rate

600

T

1976

78

82

80

84

86

88

90

92

Chart 2

TOTAL

ANNUAL
U.S. Money

Millions

TRADING
Market

VOLUME

Futures

60

50

m

Treasury

Bills

B

Eurodollar

@!$

30-Day

0

l-Month

40

30

Interest

Rate

LIBOR

?O

10

0
I976

78

80

82

84

86

88

90

92

has contributed to the growth of trading in Eurodollar
futures.6 Most interest rate swap contracts specify
payments contingent on three- or six-month LIBOR.
Swap market dealers sometimes use Eurodollar
futures to hedge their positions in interest rate swaps.
Evidence of the widespread use of Eurodollar futures
to hedge swap exposures can be found in the fact
that the IMM currently lists Eurodollar futures with
delivery dates stretching as far as 60 months into the
future. In contrast, virtually all other futures contracts
list delivery dates only 24 months into the future
(Burghardt et al., 1991). Third, it has become common practice for commercial banksto index interest
rates on loans to their corporate customers to
LIBOR. Such borrowers sometimes use Eurodollar
futures to hedge their borrowing costs. (In recent
years, however, it has become more common for
such borrowers to arrange interest rate swaps.)
The one-month LIBOR contract enables traders
to use futures contracts to synthesize maturities
corresponding to a wider range of standard maturities
in the Eurodollar market. Other than overnight and
one-week deposits, standard maturities in the Eurodollar market range from one to six months in onemonth increments, nine months, one year, eighteen
months, and two to five years in one-year increments.
The one-month LIBOR contract allows a trader to
synthetically duplicate the interest rate exposure
associated with a four-month Eurodollar deposit, as
an example, using a combination of a three-month
Eurodollar contract and a one-month LIBOR contract. Although trading in the contract has been
active since it was introduced in 1990, Charts 1
and. 2 show that trading activity in the one-month
LIBOR contract has yet to approach that of the more
popular three-month Eurodollar futures contract.
The CBT first listed its 30-day interest rate futures
contract in 1988. Although there are differences in
the way the one-month LIBOR and 30-day interest
contracts are priced, both are based on indexes of
one-month interbank lending rates. At present,
trading volume in the CBT contract is roughly onethird the volume of trading in the one-month LIBOR
contract. Past experience has shown that whenever
two different exchanges list futures contracts for
similar underlying instruments, only one contract
survives. Thus, the current outlook for these latter
two contracts remains uncertain as of this writing.
6 An interest rate swap is a formal agreement between two
parties to exchange cash flows based on the difference between
two different interest rates.

28

ECONOMIC

REVIEW,

PRICERELATIONSHIPSBETWEEN
FUTURE~ANDS~~TPVIARKETS
Price relationships between futures and spot
markets can be explained using arbitrage pricing
theory, which is based on the premise that two
different assets, or combinations of assets, that yield
the same return should sell for the same price.
Buying a futures contract on the final day of trading
is equivalent to buying the underlying item in the
cash market, since delivery is no longer deferred once
a futures contract matures. Thus, arbitrage pricing
theory predicts that the futures price of an item
should just equal its spot market price on the futures
contract maturity date: this is just the phenomenon
of convergence noted earlier. Buying a futures contract before the contract maturity date fixes the,cost
of future availability of the underlying item. But the
cost of future availability of an item can also be
fixed in advance by buying and holding that item.
Holding actual physical stocks of a commodity or
security entails opportunity costs in the form of
interest foregone on the funds used to purchase the
item and, in some instances, explicit storage costs.
The cost associated‘ with financing the purchase of
an asset, along with related storage costs, is known
as the cost of carry. Since physical storage can
substitute for buying a futures contract, arbitrage
pricing theory predicts that the cost of carry should
determine the relationship between futures and spot
market prices.
Basis and the Cost of Carry
The cost of carry for agricultural and other commodities includes financing costs, warehousing fees,
transportation
costs, and any transactions costs
incurred in obtaining the commodity. Storage costs
are negligible for financial’ assets such as Treasury
bills and Eurodollar deposits. Moreover, financial
assets often yield an explicit payout, such as interest
or dividend payments, that offsets at least a fraction
of any financing costs. The convention in financial
markets, therefore, is to apply the term net carrying
cost to the difference between the interest cost
associated with financing the purchase of a financial
asset and any explicit interest or dividend payments
earned on that asset.
Let S(0) denote the purchase price of an asset at
)
time 0 and r(O,7’ denote the market rate of interest
at which market participants can borrow or lend over
a period starting at date 0 and ending at some future
date T.’ Assuming, for the sake of convenience,
’ This discussion assumes perfect capital markets in which
market participants can borrow and lend at the same rate.

NOVEMBER/DECEMBER

1992

that transactions and storage costs are negligible, the
cost of purchasing an item and storing it until date
T is just the financing cost r(O,T)S(O). Let y(O,T)
denote any explicit yield earned on the asset over
the same holding period. Then, the net carrying cost
for the asset is

40,T) = b-(O,T)-y(O, TKW).
Since physical storage of an item can substitute
for buying a futures contract for that item, arbitrage
pricing theory would predict that the futures price
should just equal the price of the underlying item plus
net carrying costs. This result is known as the cost
of carry pricing relation. Let F(O,T) denote the
futures price of an item at date 0 for delivery at some
future date T. Then, the cost of carry pricing relation can be stated formally as:
F(O,T)

= S(0)

+ c(O,T).

= -c(O,T).

Positive carrying costs imply a negative basis-that
is, a futures price above the spot market price. In
such instances the buyer of a futures contract pays
a premium for deferred delivery, known as contango.
Cash-and-Carry Arbitrage
To see why futures prices should conform to the
cost of carry model, consider the arbitrage opportunities that would exist if they did not. Suppose the
futures price exceeds the cost of the underlying item
plus carrying costs; that is,
F(O,T)

> S(0)

Example 1: Pricing a Commodity Futures Contract Suppose the current spot price of a commodity is $100 and the market rate of interest is 10
percent. Assuming that transactions and storage costs
are negligible, the cost of carry for this commodity
for a period of one year is
c(O,T)

The difference between the spot price of an item
and its futures price is known as basis.* Notice
that the cost of carry pricing relationship equates basis
with the negative of the cost of carry. This relationship is easily demonstrated by rearranging terms in
the cost of carry relation to yield
S(O)-F(O,T)

futures delivery date. Ultimately, the market forces
created by arbitrageurs selling the overpriced futures
contract and buying the underlying item should force
the spread between futures and spot prices down to
a level just equal to the cost of carry, where arbitrage
is no longer profitable. In practice, arbitrageurs rarely
find it necessary to hold their positions to contract
maturity; instead, they undertake offsetting transactions when market forces bring the spot-futures price
relationship back into alignment.

+ c(O,T).

In this case, an arbitrageur could earn a positive profit
of F(0, T) -S(O) -c(O,T) dollars by selling the overpriced futures contract while buying the underlying
item, storing it until the futures delivery date, and
using it to satisfy delivery requirements.
This type of transaction is known as cash-and-carry
arbitrage because it involves buying the underlying
item in the cash market and carrying it until the

= (O.lO)($lOO)

= $10.
Thus, the fair futures price for delivery in one year
is $110.
Now consider the opportunity for arbitrage if the
futures contract in this example is overpriced. If the
futures price for delivery in one year’ time is $115,
s
an arbitrageur could earn a certain profit by selling
futures contracts at $115, borrowing $100 at 10
percent to buy the underlying commodity, and delivering the commodity in fulfillment of contract
requirements atthe futures delivery date. The total
cost of purchasing and storing the underlying commodity for one year is $1.10, while the short posi-’
tion in a futures contract fixes the sale price of the
commodity at $115. Thus, at the end of one year
the arbitrageur could close out his position by selling the underlying commodity in fulfillment of contract requirements, thereby earning a $5 profit net
of carrying costs.
Example 2: Pricing an Interest Rate Futures
Contract Suppose a long-lived asset that pays a 15
percent annual yield can be purchased for $100, and
assume that the cost of borrowing to finance the purchase of this asset for one year is 10 percent. In this
case, the $10 annual financing cost is more than offset by the annual $15 yield earned on the asset. The
net cost of carry for a one-year holding period is
(O.lO-0.15)$100

8 Some authors define basis as the difference between the futures
price and the spot price. The definition adopted above is the
more common.
FEDERAL

RESERVE

= -965.

Thus, the fair futures price for delivery in one year
is $95.
BANK OF RICHMOND

29

The net cost of carry is negative in this last example, resulting in a futures price below the spot
market price. This type of price relationship is known
as backwardation. It is common for interest rate
futures prices to exhibit a pattern of backwardation,
although this pattern can be reversed when shortterm interest rates are higher than long-term rates.
Reverse Cash-and-Carry Arbitrage
If the futures price of an item fails to reflect full
carrying costs, arbitrageurs have an incentive to
engage in an operation known as reverse cash-andcarry arbitrage. Reverse cash-and-carry arbitrage
involves selling the underlying commodity short while
buying the corresponding futures contract. A short
sale involves borrowing a commodity or asset for a
fixed time period and selling that item in the cash
market with the intent of repurchasing it when the
commodity is due to be returned to the lender.
In the case of a short sale of an interest-bearing
security, a lender typically requires the borrower to
return the security plus any interest or dividend
payments accruing to the security over the period
of the loan. Thus, the net profit resulting from a
reverse cash-and-carry operation is determined by the
proceeds from the short sale, S(O), plus the interest
earned on those proceeds over the holding period,
r(O,T)S(O), less the cost of repurchasing the security at date T, F(O,T), and less the interest or dividend that would have been earned by holding the
security, which is y(O,T)S(O). The total net profit
in this case is just
[I +r(O,T)-y(O,T)]S(O)-F(O,T).
Banks active in the Eurodollar market can effect
short sales of deposits simply by accepting such
deposits from other market participants and investing
the proceeds until the deposits mature. Dealers in
the Treasury bill market can effect short sales through
arrangements
known as repurchase agreements.
These operations are described in more detail below.
The Phenomenon of “Underpriced”
Futures Contracts
Futures prices sometimes fail to reflect full carrying costs, a phenomenon that is most pronounced
in commodity markets. At least two different explanations have been offered for this phenomenon: the
first deals with impediments to short sales; the
second with the implicit convenience yield that
accrues to physical ownership of certain assets.
30

ECONOMIC

REVIEW,

Reverse cash-and-carry arbitrage operations require
that market participants be able to effect short sales
of the item underlying the futures contract so as
to take advantage of an underpriced futures contract. Various impediments to short sales exist in
some markets, however. In the stock market, for
example, government regulations, as well as stock
exchange trading rules, limit the ability of market
participants to effect short sales.
The importance of such impediments is mitigated
by the fact that it is not always necessary to engage
in a short sale to effect a reverse cash-and-carry
arbitrage operation. Many firms are ideally situated
to take advantage of the opportunities presented by
underpriced futures contracts simply by selling any
inventories they hold while buying futures contracts
to fix the cost of buying back the underlying item.
Yet market participants often do not sell their asset
holdings to take advantage of “underpriced” futures
contracts because ready access to actual physical
stores of an item can yield certain implicit benefits.
For example, a miller might value having a ready
supply of grain on hand to ensure the uninterrupted
operation of his milling operations. A futures contract can substitute for physical holdings of the
underlying commodity in the sense that it fixes the
cost of future availability, but the miller cannot use
futures contracts to keep his mill operating in the
event that he runs out of grain. Supplies of agricultural
commodities can be scarce in periods just preceding
harvests, making market participants such as commodity processors willing to pay an implicit convenience yield in return for assured access to physical
stores of a commodity at such times. A measure of
the implicit convenience yield, call it yC(O,T), can be
obtained by calculating the difference between the
cost of storage and the futures price:
yc(O,T) = W)

+ 40,T)

-F(O,T),

where the term c(O,T) in the above expression
represents the explicit carrying cost.9
Pricing Treasury Bill Futures:
The Implied Repo Rate
A repurchase agreement, more commonly termed
a “repo” or “RP,” is a transaction involving the sale
of a security with a commitment on the part of the
seller to repurchase that security at a higher price
9 Siegel and Siegel (1990, Chap. 2) contains a good introductory discussion of these topics. See Williams (1986) for a
comprehensive
analysis of the price behavior of agricultural
futures.

NOVEMBERlDECEMBER

1992

on some future date-usually the next day, although
such agreements sometimes cover periods as long
as six months. A repurchase agreement can be viewed
as a short-term loan collateralized by the underlying
security, with the difference between the repurchase
price and the initial sale price implicitly determining
an interest rate, known as the “rep0 rate.” Repurchase agreements constitute a primary funding source
for dealers in the market for U.S. Treasury securities.
Cash-and-carry arbitrage using Treasury bill futures
involves the purchase of a bill that will have 13 weeks
to maturity on the contract delivery date. A cashand-carry arbitrage operation can be viewed as an
implicit reverse repurchase agreement, which is just
a repurchase agreement from the viewpoint of the
lender. A reverse repo entails the purchase of a
security with a commitment to sell the security back
at some future date. A party entering into a reverse
repo effectively lends money while taking the
underlying security as collateral. Like a party to a
reverse repo, a trader who buys a Treasury bill while
selling a futures contract obtains temporary possession of the bill while committing himself to sell it
back to the market at some future date. Just as the
difference between the purchase price of a bill and
the agreed-upon sale price determines the interest
rate earned by a party to a reverse repo, the difference between the futures and spot price determines
the return to a cash-and-carry arbitrage operation.
In effect, the trader “lends” money to the market,
earning the difference between the future delivery
price and the price paid for the security as implicit
interest. The rate of return earned on such an operation is known as the “implied repo rate.”
By market convention, the implied repo rate is
expressed as the annualized rate of return that could
be earned by buying a Treasury bill at a price S(O)
at date 0 and simultaneously selling a futures contract for delivery at date T for a price F(O,T). The
formula is
in- = ([F(O,T)-S(O)]/S(O))(360/T),

where irk denotes the implied repo rate. Note that
this formula follows the convention in money markets
of expressing annual interest rates in terms of a
360-day year.
The following example illustrates the calculation
of the implied repo rate. Suppose that it is exactly
60 days to the next delivery date on three-month
Treasury bill futures. A bill with 15 1 days left to
maturity will have 9 1 days left to maturity on the next
futures delivery date and can be used to satisfy
FEDERAL

RESERVE

delivery requirements for the nearby futures contract.
If the current discount yield on bills with 15 1 days
to maturity is 3.8 percent, the cash price of the
bill is
S(0) = $1,000,000
- $1,000,000(0.038)(151/360)
= $984,061.11.
Now suppose that the price of the nearby Treasury
bill futures contract is 96.25. An index price of 96.25
implies a futures discount yield for the nearby
Treasury bill contract of 100 - 96.25 = 3.75 percent. Since the deliverable bill will have 91 days to
maturity, the future delivery price implied by this
yield is
J-(0,60)= $1 ,OOO,OOO

- $1,000,000(0.0375)(91/360)
= $990,520.83.

The implied repo rate in this case is
irr = [($990,520.83
- $984,061.11)/$984,061.11](360/60)
= 0.0394,

or 3.94 percent.
The cost of carry pricing relation can be used to
show that the no-arbitrage price should equate the
implied repo rate with the actual repo rate. To see
this, note that the cost of carry pricing relation implies that the no-arbitrage price must satisfy
F(O,T)-S(0)

= c(O,T).

Although Treasury bills are interest-bearing securities, the interest earned on a bill is implicit in the
difference between the purchase and redemption
price. This means that y(O,T) =O, so that total net
carrying costs for a Treasury bill must just equal
c(O,T)

= r(O,OW),

where r(O,T) represents the cost of financing the
purchase of the bill, expressed as an unannualized
interest rate. Substituting these last two expressions
into the definition of the implied repo rate gives
irr = r(O,T)(360/T).

Because repurchase agreements constitute a primary
funding source for dealers in the Treasury bill market,
~(0, T) should reflect the cash repo rate. lo Thus, the
10Gendreau (1985) found empirical support for the assertion that
the repo rate provides the correct measure of carrying costs for
Treasury bill futures.
BANK OF RICHMOND

31

cost of carry pricing relation implies that the implied
repo rate should just equal the cash repo rate.
Comparing implied repo rates with actual rates
amounts to comparing theoretical futures prices, as
determined by the cost of carry model, with actual
futures prices. An implied repo rate above the
actual three-month repo rate would indicate that
futures contracts are relatively overpriced. In this case
arbitrage profits could be earned by borrowing money
in the cash repo market and implicitly lending the
money back out through a cash-and-carry arbitrage
to earn the higher implied repo rate.
Conversely, an implied repo rate below the actual
rate would indicate that futures contracts are underpriced. In this second case, arbitrageurs would have
an incentive to “borrow” money by means of a reverse
cash-and-carry futures hedging operation while lending into the cash market through a reverse repo. Such
an operation would entail buying an underpriced
futures contract and simultaneously entering into a
reverse repurchase agreement to lend money into the
cash repo market.
The concept of an implied repo rate can also be
applied to other types of financial futures. Merrick
(1990) and Siegel and Siegel (1990) discuss other
applications.
Pricing Eurodollar Futures
Now consider the problem of determining the
theoretically correct price of a three-month Eurodollar
futures contract maturing in exactly 90 days. Note
that a six-month deposit can be viewed as a succession of two three-month deposits. Thus, a bank can
synthesize an implicit six-month deposit by placing
a three-month deposit and buying a futures contract
to fix the rate of return earned when the proceeds
of the first deposit are reinvested into another deposit.
Arbitrage opportunities Will exist unless the return
to this synthetic six-month deposit equals the return
to the actual six-month deposit.
Let r(O,3) and r(O,6) denote the current (unannualized) three- and six-month LIBOR, respectively. Eurodollar deposits pay a fixed rate of interest
over the term of the deposit. For maturities under
one year, interest is paid at maturity. Thus, an investor placing $1 in a 180-day deposit in an account
paying an interest rate of r(0,6) receives $[ 1 +r(0,6)]
at maturity. Similarly, a 90-day deposit will return
(1 +r(O,3)] per dollar at maturity. Now let r,(3,6)
denote

32

the interest

rate on a three-month

deposit

ECONOMIC

REVIEW,

to

be placed in three months fixed by buying a
Eurodollar futures contract. The condition that a sixmonth deposit should earn as much as a succession
of two three-month deposits requires that
1 + r(O,6)

= 11 +r(0,3)][1

+r,(3,6)].

The no-arbitrage futures interest rate can thus be
calculated from the other two spot rates by rearranging terms to yield
r-(3,6) = [ 1 +r(0,6)]/[

1 +r(O,3)] - 1.

As an example, suppose the prevailing three-month
LIBOR is quoted at 4.0 percent and the six-month
LIBOR at 4.25 percent (in terms of annualized interest rates). Suppose further that the six-month rate
applies to a period of exactly 180 days and the threemonth rate applies to a period of 90 days. Finally,
assume that the nearby Eurodollar contract conveniently happens to mature in exactly 90 days.
Then, the no-arbitrage interest rate on a three-month
Eurodollar deposit to be made three months in the
future is
r,(3,6) = [ 1 + (0.0425)( 180/360)]/
[I+ (0.04)(90/360)] - 1
= 0.0111.
To express this result as an annualized interest rate
just multiply the number obtained above by (360/90).
The result is
r,(3,6)(360/90) = 0.0444,
which means that the no-arbitrage futures interest
rate in this example is 4.44 percent and the theoretically correct index price is 95.56. The same
methodology can be used to price one-month LIBOR
futures.”
If the futures rate is below the no-arbitrage rate,
the interest rate on a synthetic six-month deposit will
be less than on an actual six-month deposit. A bank
can effect a cash-and-carry arbitrage operation by
“buying” a six-month deposit now (that is, by
placing a deposit with another bank) while accepting
a three-month deposit and selling a Eurodollar futures
contract. In this case, arbitrage amounts to lending
at the higher spot market rate (by placing a six-month
deposit with another bank) while borrowing at the
I1 Readers interested in a more detailed exposition of forward
interest rate calculations and the pricing of Eurodollar futures
should see Burghardt et al. (1991).

NOVEMBER/DECEMBER

1992

lower synthetic six-month rate (obtained by accepting a three-month
deposit and selling a futures
contract).
Conversely, a futures interest rate above the
theoretically correct rate is a signal for banks to enter
into a reverse cash-and-carry arbitrage. In this case,
a bank would wish to accept a six-month deposit to
borrow at the lower spot market rate while placing
a three-month deposit and buying the nearby futures
contract to lend at the higher synthetic six-month
rate.
Daily Settlement and the Cost of Carry
As a concluding comment, it should be noted that
the pricing formulas developed in this section do not
take account of the effect of variation margin flows.
When interest rates fluctuate randomly, the fact that
a futures contract is marked to market on a daily basis
means that some of the payoff to a futures position
will need to be reinvested at different interest rates.
Thus, the cost of carry formulas derived above hold
exactly only if interest rates are constant or if there
are no variation margin payments, as typically is
the case with forward agreements (Cox, Ingersoll,
and Ross, 1981). In all other cases, the formulas
derived above yield theoretical futures prices that
only approximate true theoretical futures prices. As
an empirical matter, however, the approximation
appears to be a close one, so that the cost of carry
model is commonly used to price futures contracts
as well as forward contracts.lz

THEECONOMICFLJNCTIONOF
FUTURESMARKETS
Hedging, Speculation, and Futures Markets
It is common to categorize futures market trading
activity either as hedging or speculation. In the most
general terms, a futures hedging operation is a futures
market transaction undertaken in conjunction with
an actual or planned spot market transaction. Futures
market speculation refers to the act of buying or
selling futures contracts solely in an attempt to
profit from price changes, and not in conjunction with
an ordinary commercial pursuit. According to these
definitions, then, a dentist who buys wheat futures
in anticipation of a rise in wheat prices would be
classified as a speculator, while a grain dealer undertaking a similar transaction would be regarded as a
hedger.
12Chance (1989) reviews the results of studies dealing with the
effect of variation margin payments on futures prices.
FEDERAL

RESERVE

Speculators have been active participants in futures
markets since the earliest days of futures trading. On
several occasions, the perception that futures market
speculation exerted a destabilizing influence on commodity markets led to attempts to restrict or ban
futures trading. I3 But despite the association of
speculative activity with futures trading, it is widely
accepted that futures markets evolved primarily in
response to the needs of commodity handlers, such
as dealers in agricultural commodities and processing firms, who used futures contracts in conjunction
with their routine business transactions. The same
types of market forces appear to’
underlie the recent
growth of trading in financial futures, the heaviest
users of which are financial intermediaries such as
commercial banks, securities dealers, and investment
funds that routinely use futures contracts to hedge
cash transactions in financial markets.
While it is widely accepted that futures markets
evolved to facilitate hedging, the motivation behind
observed hedging behavior in futures markets has
been the topic of considerable debate among
economists. Risk transfer traditionally has been
viewed as the primary economic function of futures
markets. According to this view, the economic purpose of futures markets is to provide a means for
transferring the price risk associated with owning an
item to someone else. A number of economists have
come to question this traditional view in recent years,
however, arguing that the desire to transfer price risk
cannot fully explain why market participants use
futures contracts.
The discussion that follows examines the hedging
uses of money market futures and reviews three
different views of the economic function of futures
markets in an effort to provide some insight into the
reasons firms use futures markets. All three theories
are based on the premise that futures markets evolved
to facilitate hedging on the part of firms active in
underlying spot markets, but the different theories
each emphasize different characteristics of futures
contracts and futures markets to explain why hedgers
use futures contracts. This review is of more than
academic interest. Futures hedging operations are
complex and multifaceted transactions, and each
13One of the most drastic efforts to curb futures trading involved the arrest of nine prominent members of the Chicago
Board of Trade following ;he enactment of the Illinois Elevator
Bill of 1867. The act classified the sale of contracts for future
delivery as gambling except in cases where the seller actually
owned physical stocks of the commodity being sold. Those provisions were soon repealed, however, and the exchange members
never came to trial (Hieronymus, 1971, Chap. 4).
BANK

OF RICHMOND

33

theory provides important insights into different
aspects of hedging behavior.
Future Markets as Markets for
Risk Transfer
In conventional usage, the term “hedging” refers
to an attempt to avoid or lessen the risk of loss by
matching a risk exposure with a counterbalancing
risk, as in hedging a bet. A futures hedge can be
viewed as the use of futures contracts to offset the
risk of loss resulting from price changes. A short
(cash-and-carry) hedging operation, for example,
combines a short futures position with a long position in the underlying item to fix the future sale price
of that item, thereby protecting the hedger from the
risk of loss resulting from a fall in the value of his
holdings. Reverse cash-and-carry arbitrage, which
combines a short position in an item with a long
futures position, represents an example of a long
hedge. The long futures position offsets the risk that
the price of the underlying item might rise before
the hedger can buy the item back to return to the
owner. More generally, a long hedge combines a long
futures position with a planned future purchase of
an item to produce an offsetting risk that protects
the hedger from the risk of an increase in the future
purchase price of the item.
Most textbook hedging examples rely on this traditional definition of hedging to motivate descriptions
of hedging operations. Thus, a dealer in Treasury
securities might sell Treasury bill futures to offset
the risk that an unanticipated change in market
interest rates will adversely affect the value of his
securities holdings. Note that the short hedge in this
example effectively shortens the maturity of the
interest-bearing asset being hedged. In contrast, a
long hedge fixes the return on a future investment,
thereby lengthening the effective maturity of an
existing interest-earning asset.
This traditional definition of hedging accords with
the view that the primary function of futures markets
is to facilitate the transfer of price risk. The party
buying the futures contracts in the above example
might be an investor planning to buy Treasury bills
at some future date or a speculator hoping to profit
from a decline in market interest rates. In the first
case the risk exposure is transferred from one hedger
to another who faces an opposite risk. In the second,
the risk is willingly assumed by the speculator in the
hope of earning windfall gains.
Other common hedging operations involving
money market futures can also be viewed as being

34

ECONOMIC

REVIEW.

motivated by the desire to transfer price risk. For
example, commercial banks, savings and loans, and
insurance companies use interest rate futures to protect their balance sheets and future earnings from
potentially adverse effects of changes in market
interest rates.14 In addition, nonfinancial firms sometimes use interest rate futures to fix interest rates
on anticipated future investments and borrowing rates
on future loans.
The Liquidity Theory of Futures Markets
Working (1962) and Telser (198 1, 1986) contend
that the hedging behavior of firms cannot be
understood by looking at risk avoidance alone as the
primary motivation for hedging. Instead, they argue
that the hedging behavior of optimizing firms is best
understood when hedging is viewed as a temporary,
low-cost alternative to planned spot market transactions. According to this line of reasoning, futures
markets exist primarily because they provide market
participants with a means of economizing on transactions costs, and not solely because futures contracts
can be used to transfer price risk. Williams (1986)
has termed this view the liquidity theory of futures
markets.
Working’ and Telser’ arguments rest on the
s
s
observation that market participants need not use
futures contracts to insure themselves against price
risk. As noted in the earlier discussion on arbitrage
pricing, spot purchases (or short sales) of an item can
substitute for buying (selling) a futures contract to
fix the cost of future availability (future sale price)
of an item. Moreover, forward contracts can also be
used to transfer price risk. Because they can be
custom-tailored to the needs of a hedger, forward contracts would appear to offer a better means of insuring against price risk than futures contracts. Contract
standardization, while contributing to the liquidity
of futures markets, practically insures that futures contracts will not be perfectly suited to the needs of
any one hedger. is It would seem, then, that a
hedger interested solely in minimizing price risk
would have little incentive to use futures contracts,
I4 Brewer (1985) and Kaufman (1984) discuss the problem such
firms face in managing interest rate risk.
1s Since planned transaction dates rarely coincide with standardized futures delivery dates, most hedgers must unwind
their futures positions before the contracts mature. As a result,
hedging operations must rely upon the predictability of the spotfutures price relationship, or basis. Although theory predicts that
behavior of basis should be determined by the cost of carry,
changes in the spot-futures price relationship are not always
predictable in practice. Thus, a futures hedge involves “basis
risk,” which is much easier to avoid with forward contracts.

NOVEMBER/DECEMBER

1992

a conclusion which suggests that the view of futures
markets as markets for transferring price risk is
incomplete.
Although it makes futures contracts less suited to
insuring against price risk, contract standardization,
along with the clearinghouse guarantee, facilitates
trading in futures contracts and reduces transactions
costs. By focusing attention on these characteristics
of futures contracts, Working (1962) and Telser
(198 1, 1986) are able to explain why dealers and
other intermediaries who perform the function of
marketmakers in spot markets tend to be the primary
users of futures contracts. Market-making activity
requires dealers to constantly undertake transactions
that change the composition of their holdings.
Securities dealers, for example, must stand ready to
buy and sell securities in response to customer orders.
As they do, their cash positions change continually,
along with their exposure to price risk. Similarly, the
assets and liabilities of commercial banks change continually as they accept deposits and offer loans to their
customers. Thus, financial intermediaries such as
commercial and investment banks hedge using
futures contracts because the greater liquidity and
lower transactions costs in futures markets mean that
a futures hedge can be readjusted frequently with
relatively little difficulty and at minimal cost.
To illustrate these concepts, consider the situation faced by an investor who holds a three-month
Treasury bill but wishes to lengthen the effective
maturity of his holding to six months. The investor
could sell the three-month bill and buy a six-month
bill, or he could buy a futures contract for a threemonth Treasury bill deliverable in three months. A
long hedging operation of this type effectively converts the three-month bill into a synthetic six-month
bill. The preferred strategy will depend on the relative
costs of the two alternatives. Since transactions costs
in futures markets tend to be lower than those in
underlying spot markets, the futures hedge is often
the more cost-effective alternative.
Futures Markets as Implicit Loan Markets
Williams (1986) argues that futures markets are
best viewed as implicit loan markets, which exist
because they provide an efficient means of intermediating credit risk. Recall that a firm that needs
to hold physical inventories of some item for a fixed
period has two choices. First, it can make arrangements to borrow the item directly, often by pledging some form of collateral such as cash or securities
to secure the loan. Second, it can buy the item in
FEDERAL

RESERVE

the spot market and hedge by selling the appropriate
futures contract. In either case, the firm will have
temporary use of the item and will be required to
return (deliver) that item at some set future date.
Depending on one’ view, therefore, a short hedger
s
is either extending a loan of money collateralized
by the item underlying the futures contract or
borrowing the underlying commodity using cash as
collateral.
A natural question to ask at this juncture is why
a firm would choose to engage in a cash-and-carry
hedging operation to synthesize an implicit loan of
an item rather than borrowing the item outright. The
answer lies with the advantages that futures contracts
have in the event of default or bankruptcy. Consider
the consequences of a default on the part of a firm
that loans out securities while borrowing cash. Suppose firm A enters into a repurchase agreement with
firm B. If firm A defaults on its obligations, firm B
cannot always be assured that the courts will permit
it to keep the security collateralizing the loan because
the “automatic stay” provisions of the U.S. Bankruptcy Code may prevent creditors from enforcing
liens against a firm that enters into bankruptcy proceedings. Thus, when Lombard-Wall, Inc. entered
bankruptcy proceedings in 1982, its repurchase
agreement counterparties could neither use funds
obtained through a repurchase agreement or sell
underlying repo securities without first obtaining the
court’ permission (Lumpkin, 1993). In such cases,
s
creditors may be forced to settle for a fraction of the
amounts owed them.
Subsequent amendments to the U.S. Bankruptcy
Code have clarified the steps needed to perfect a collateral interest in securities lending arrangements,
making it possible for investors to avoid many of the
difficulties Lombard-Wall’ counterparties encouns
tered with the Bankruptcy Court. Nevertheless, collateralized lending agreements are never riskless. A
party to a reverse RP, for example, faces the risk
that the market value of the underlying security might
fall below the agreed-upon repurchase price. Moreover, parties to mutual lending arrangements sometimes fraudulently pledge collateral to several different
creditors. In either case, a lender is exposed to the
risk of loss in the event of a default on the part of
a borrower. Finally, the Bankruptcy Code amendments do not apply to all types of lending. For
example, Eurodollar deposits cannot be collateralized under existing banking laws.
The consequence of a default is quite different
when a firm uses futures contracts to synthesize an
BANK OF RICHMOND

35

implicit loan. Because synthesizing a loan through
the use of futures contracts involves no exchange of
principal, the risk exposure associated with a futures
contract in the event of a default is much smaller
than the exposure associated with an outright loan.
Thus, a futures hedging operation amounts to a collateralized lending arrangement in which the collateral
is never at risk in the event of a default. A position
in a futures contract does create credit-risk exposure
when changes in market prices change the value of
the contract; however, the resulting exposure is a
small fraction of the notional principal amount of
the contract, and the exchange clearinghouse risks
losing only the change in value in the futures contract resulting from price changes in the most recent
trading session. Here, daily settlement, or marking
to market, of futures contracts provides an efficient
means of enforcing contract performance. In the
event that a firm fails to meet a margin call, the
clearinghouse can order its futures position to be
liquidated and claim the firm’ margin deposit to offset
s
any losses accruing to the futures position. If the
defaulting firm subsequently enters formal bankruptcy
proceedings, the futures margin is exempt from the
automatic stay imposed by the Bankruptcy Code.i6
Thus, a futures clearinghouse is entitled to seize a
trader’ margin deposit to offset any trading losses
s
without being required to first appeal to the Bankruptcy Court.
Although forward contracts can also be used to
synthesize implicit loans in much the same way as
futures contracts, Williams (1986) argues that a
crucial difference between futures contracts and
forward agreements lies with their legal status in the
event of default and bankruptcy proceedings. While
forward agreements sometimes specify margin deposits, such deposits have not, until very recently,
been exempt from the automatic stay provisions of
the Bankruptcy Code.17

These observations led Williams to conclude that
futures markets are best viewed as markets for
intermediating short-term loans, which resemble
money markets. Although Williams’ rationale for the
existence of futures markets differs in emphasis from
that of Working and Telser, the two theories are not
inconsistent. While Williams acknowledges that
futures markets have certain advantages over other
markets stemming from greater liquidity and lower
transactions costs, he argues that Working and Telser
place too much importance on contract standardization and transactions costs as primary reasons for
the existence of futures markets. In the end, however,
both theories question the traditional view that the
primary function of futures markets is to accommodate the transfer of price risk.
Since Williams published his work, the Bankruptcy Code has been amended to exempt certain
repurchase agreements and forward agreements from
the automatic stay provisions applicable to most other
liabilities of bankrupt firms. As a result, such contracts now have a legal status similar to that of futures
contracts in the event of bankruptcy. Williams’ theory
would thus predict that repurchase agreements and
forward contracts should become more widely used,
which is what has happened in recent years. Rather
than replacing futures contracts, however, the growth
of over-the-counter derivatives such as interest rate
swaps and Forward Rate Agreements appears to be
driving an accompanying increase in trading in futures
contracts,
especially Eurodollar futures, which
derivatives dealers use to hedge their swap and forward contract exposures. Thus, even when forward
agreements and collateralized lending arrangements
carry the same legal status as futures contracts in the
event of a default, each type of contract appears to
offer certain advantages to different types of users.
Still, Williams’research highlights an important aspect
of futures contracts and futures markets not addressed
by earlier work in this area.

r6 Williams (1986) cites a precedent-setting
legal decision that
exempted margin deposits from the automatic stay provisions
of the Bankruptcy Code.
I7 Recent amendments to the Bankruptcy Code exempt margin
deposits on certain types of forward contracts from the automatic
stay. See Gooch and Pergam (1990) for a detailed description
of these amendments.

36

ECONOMIC

REVIEW.

NOVEMBER/DECEMBER

1992

REFERENCES
Brewer, Elijah. “Bank Gap Management and the Use of Financial Futures,” Federal Reserve Bank of. Chicago Economic
Perspectiwes, vol. 9 (March/April 1985), pp. 12-21.
Burghardt,

Belton,

Lane,

Lute,

and

McVey.

&rvdo&rr

Futures and Options. Chicago: Probus Publishing Company,

1991.
Chance, Don M. An Intnduction to OptionsandFutures.
The Dryden Press, 1989.
Commodity

Chicago:

Futures Trading Commission. AnnuulRepm.1991.

Cox, J. C., J. E. Ingersoll, and S. A. Ross. “The Relation
Between Forward Prices and Futures Prices,” Journal of
Financial Economics, vol. 9 (Winter. 1983), pp. 321-46.
Gendreau, Brian C. “Carrying Costs and Treasury Bill Futures,”
Journal of PortfoLio Management, Fall 1985, pp. 58-64.
Gooch, Anthony C. and Albert S.
and New York Law,” in Robert
Smith, Jr., eds., The Handbook of
Risk Manugement. New York: New
1990.
Hieronymus, Thomas
York: Commodity

Lumpkin, Stephen A. “Repurchase and Reverse Repurchase
Agreements,” in Timothy Cook and Robert LaRoche, eds.,
Instmments of the Money Market, 7th ed. Richmond, Va.:
Federal Reserve Bank of Richmond, forthcoming 1993.
Merrick, John J., Jr. Financial Futures Markets: &mctum, &icing,
and Practice. New York: Harper and Row, 1990.
Siegel, Daniel R. and Diane F. Siegel. The Futures Markets.
Chicago: Probus Publishing Company, 1990.
Silber, William L. “Marketmaker Behavior in an Auction
Market: An Analysis of Scalpers in Futures Markets,”
Jouma/of Finance, vol. 39 (September 1984) pp. 937-53.
Telser, Lester G. “Why There Are Organized Futures
Markets,” Journal of Law and Economics, vol. 24 (April
1981), pp. l-22.

Pergam. “United States
J. Schwartz and Clifford

Related,”
pp. s-20.

Currency and Intenst Rate

York Institute of Finance,

A. Economics of Futures Trading. New
Research Bureau, Inc., 1971.

Kaufman, George G. “Measuring and Managing Interest Rate
Risk: A Primer,” Federal Reserve Bank of Chicago Economic Perspectives, vol. 8 (January/February
1984) pp.
16-29.

FEDERAL

RESERVE

. “Futures and Actual Markets: How-They Are
The Journal of Business, vol. 59 (April 1986),

Williams,’ Jeffrey. Th Economic Function of Futures Markets.
Cambridge: Cambridge University Press, 1986.
Working, Holbrook. “New Concepts Concerning Futures
Markets and Prices,” Ametican Economic Rewieq vol. 52
(June 1962), pp. 432-59.

BANK

OF RICHMOND

37


Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102