View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

FEDERAL FUNDS: INSTRUMENT OF
FEDERAL RESERVE POLICY
Marvin Goodfriend and William Whelpley

Federal funds are the heart of the money market
in the sense that they are the core of the overnight
market for credit in the United States. Moreover,
current and expected future interest rates on Federal
funds are the basic rates to which all other money
market rates are anchored. Understanding the Federal funds market requires, above all, recognizing that
its general character has been shaped by Federal Reserve policy. From the beginning, Federal Reserve
regulatory rulings have encouraged the market’s
growth. Equally important, the Federal funds rate
has been a key monetary policy instrument. This
article explains Federal funds as a credit instrument,
the funds rate as an instrument of monetary policy,
and the funds market itself as an instrument of regulatory policy.
Characteristics of Federal Funds

Federal funds have three distinguishing features.
First, they are short-term borrowings of immediately
available money-funds which can be transferred
between depository institutions within a single business day. The vast majority, roughly 80 percent, of
Federal funds are overnight borrowings. The remainder are longer maturity borrowings known as
term Federal funds. Second, Federal funds are liabilities of those depository institutions required to
hold reserves with Federal Reserve Banks as defined
by the Monetary Control Act of 1980. They are:
commercial banks, savings banks, savings and loan
associations, and credit unions. Third, historically
Federal funds borrowed have been distinguished from
other depository institution liabilities because they
have been exempt from both reserve requirements

This article was prepared for Instruments of the Money
Market, 6th edition. The authors are Economist and
Vice President, and Assistant Economist, Federal Reserve Bank of Richmond, respectively.

and interest rate ceilings. 1 Depository institutions are
also the most important eligible lenders in the market.
The Federal Reserve, however, also allows depository
institutions to classify borrowings from Federal agencies and nonbank securities dealers as Federal funds.2
The supply and demand for Federal funds arises in
large part as a means of efficiently distributing reserves throughout the banking system. On any given
day, individual depository institutions may be either
above or below their desired reserve position. Reserve accounts bear no interest, so banks have an
incentive to lend reserves beyond those required plus
any desired excess. Banks in need of reserves borrow them. The borrowing and lending of reserves
takes place in the Federal funds market at a competitively determined interest rate known as the
Federal funds rate.
The Federal funds market also functions as the
core of a more extensive overnight market for credit
free of reserve requirements and interest rate controls. Nonbank depositors supply funds to the overnight market through repurchase agreements (RPs)
with their banks. The overnight repurchase agreement is a collateralized one-day loan, which requires
actual transfer of title on the loan collateral. Under
an overnight repurchase agreement, a depositor lends

This distinction has been blurred since passage of the
Depository Institutions Deregulation and Monetary Control Act of 1980. Reserve requirements have been eliminated on some personal time deposits and interest rate
controls have been removed on all liabilities except traditional demand deposits. However, interbank deposits are
still reservable and explicit interest is still prohibited on
interbank demand deposits.
In addition, our definition should be qualified because
Repurchase Agreements (RPs) at banks have not had
interest rate ceilings or reserve requirements. Strictly
speaking. RPs are not Federal funds. Yet as we explain
below, Their growth and use have had much in common
with the Federal funds market. And the point of view of
this article is that they are close functional equivalents.
1

A more complete list of eligible lenders is found in
Board of Governors of the Federal Reserve System,
Federal Reserve Bulletin 56 (January 1970), p. 38.

2

FEDERAL RESERVE BANK OF RICHMOND

3

funds to a bank by purchasing a security, which the
bank repurchases the next day at a price agreed to in
advance. Overnight RPs account for about 25 percent of overnight borrowings by large commercial
banks. Banks use RPs to acquire funds free of reserve requirements and interest controls from sources,
such as corporations and state and local governments,
not eligible to lend Federal funds directly. Total
daily average gross RP and Federal funds borrowings
by large commercial banks are roughly 200 billion
dollars, of which approximately 130 billion dollars are
Federal funds. Competition for funds among banks
ties the RP rate closely to the Federal funds rate.
Normally, the RP rate is around 25 basis points
below the Federal funds rate; the lower rate being
due to the reduced risk and additional transaction
cost of arranging an RP.
Methods of Federal Funds Exchange

Federal funds transactions can be initiated by
either the lender or borrower. An institution wishing
to sell (loan) Federal funds locates a buyer (borrower) directly through an existing banking relationship or indirectly through a Federal funds broker.
Federal funds brokers maintain frequent telephone
contact with active funds market participants and
match purchase and sale orders in return for a commission. Normally, competition among participants
ensures that a single funds rate prevails throughout
the market. However, the rate might be tiered,
higher for a bank under financial stress. Moreover,
banks believed to be particularly poor credit risks
may be unable to borrow Federal funds at all.
Two methods of Federal funds transfer are commonly used. The first involves transfers conducted
between two banks. To execute a transaction, the
lending institution authorizes the district Reserve
Bank to debit its reserve account and to credit the
reserve account of the borrowing institution. Fedwire, the Federal Reserve System’s wire transfer
network, is employed to complete a transfer.
The second method simply involves reclassifying
respondent bank demand deposits at correspondent
banks as Federal funds borrowed. Here, the entire
transaction takes place on the books of the correspondent. To initiate a Federal funds sale, the respondent bank simply notifies the correspondent of
its intentions. The correspondent purchases funds
from the respondent by reclassifying the respondent’s
demand deposits as “Federal funds purchased.” The
respondent does not have access to its deposited
money as long as it is classified as Federal funds on
4

the books of the correspondent. Upon maturity of
the loan, the respondent’s demand deposit account is
credited for the total value of the loan, plus an
interest payment for use of the funds. The interest
rate paid to the respondent is usually based on the
nationwide effective Federal funds rate for the day.
In practice, the correspondent frequently resells the
reclassified funds in the Federal funds market itself,
earning the Federal funds rate in the process.
Types of Federal Funds Instruments

The most common type of Federal funds instrument is an overnight, unsecured loan between two
financial institutions. Overnight loans are, for the
most part, booked without a formal, written contract.
Banks exchange verbal agreements based on any
number of considerations, including how well the
corresponding officers know each other and how long
the banks have mutually done business. Brokers
play an important role evaluating the quality of a loan
when no previous arrangement exists. Formal contracting would slow the process and increase transaction costs. The verbal agreement as security is
virtually unique to Federal funds.
In some cases Federal funds transactions are explicitly secured. In a secured transaction the purchaser places government securities in a custody
account for the seller as collateral to support the loan.
The purchaser, however, retains title to the securities.
Upon termination of the contract, custody of the
securities is returned to the owner. Secured Federal
funds transactions are sometimes requested by the
lending institution.
Continuing contract Federal funds are overnight
Federal funds loans which are automatically renewed
unless terminated by either the lender or borrower.
This type of arrangement is typically employed by
correspondents who purchase overnight Federal
funds from a respondent bank. Unless notified by
the respondent to the contrary, the correspondent will
continually roll the interbank deposit into Federal
funds, creating a longer term instrument of open
maturity. The interest payments on continuing contract Federal funds loans are computed from a
formula based on each day’s effective Federal funds
rate. When a continuing contract arrangement is
made, the transactions costs (primarily brokers fees
and funds transfer charges) of doing business are
minimized because the entire transaction is completed
on the books of the correspondent bank. In fact,
additional costs are incurred only when the agreement is terminated by either party.

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

Determination of the Federal Funds Rate

To explain the determinants of the Federal funds
rate, we present a simple model of the bank reserve
market which incorporates the actions of both private
banks and the Federal Reserve.3 In this model, the
funds rate is competitively determined as that value
which equilibrates the aggregate supply and demand
for banking system reserves.
The aggregate demand for bank reserves arises
primarily from the public’s demand for checkable
deposits against which banks hold reserves. The
aggregate quantity of checkable deposits demanded
by the public falls as money market interest rates
rise, raising the opportunity cost of holding checkable
deposits. Hence, the derived demand for bank reserves is negatively related to market interest rates.
The aggregate demand schedule for bank reserves is
shown in Figure 1, where f is the funds rate and R
is aggregate bank reserves.
The aggregate stock of reserves available to the
banking system is determined by the Federal Reserve.
In principle, the Federal Reserve could choose to
provide the banking system with a fixed stock of
reserves. If the Federal Reserve chose this strategy, a fixed stock of reserves, R, would be provided
through Federal Reserve purchases of government
securities. The resulting funds rate would be f* in
Figure 1, or the rate which equilibrates the aggregate
supply and demand for bank reserves.
Such a Federal Reserve operating procedure,
known as total reserve targeting, is the focus of
hypothetical textbook discussions of monetary policy.
The hallmark of total reserve targeting is that shifts
in the market’s demand for reserves are allowed to
directly affect the funds rate. In practice, however,

the Federal Reserve has never targeted total reserves.
Instead, it has adopted operating procedures designed
to smooth funds rate movements against unexpected
reserve demand shifts. 4 The simplest smoothing
procedure is Federal funds rate targeting, which involves selecting a narrow band, often fifty basis
points or less, within which the funds rate is allowed

to fluctuate. Explicit Federal funds rate targeting
was employed by the Federal Reserve during the
1970s.

3

Goodfriend [1982], pp. 3-16.

Goodfriend [1986]. contains a theoretical rational expectations model of interest rate smoothing and discusses
its implications for money stock and price level trendstationarity.
4

Figure 1

The funds rate can be targeted directly by supplying, through open market purchases of U. S. Treasury securities, whatever aggregate reserves are de-

manded at the targeted rate. For example, if the
Federal Reserve chose to peg the funds rate at f* in
Figure 1, it would have to accommodate a market
demand for reserves of R In principle, either total
reserve or funds rate targeting could yield the ex ante
desired funds rate, f*, so long as the Federal Reserve
had precise knowledge of the position of the reserve
demand locus. There is, however, an important
difference between these procedures. With a total
reserve target, market forces directly influence the
funds rate. They have no direct effect under a funds
rate target. Instead, they affect the volume of total
reserves.
Federal Reserve operating procedures become
more complicated when reserves are provided by
bank borrowing at the Federal Reserve discount
window. Figure 2 shows the relationship between
reserve provision and the Federal funds rate when

there is discount window borrowing. The locus has a
vertical and a nonvertical segment because reserves
are provided to the banking system in two forms, as
nonborrowed and as borrowed reserves. Nonborrowed reserves (NBR) are supplied by the Federal
Reserve through open market purchases, while borrowed reserves (BR) are provided by discount window borrowing.

FEDERAL RESERVE BANK OF RICHMOND

5

Figure 2

The distance between the vertical segment of the
reserve provision locus and the vertical axis is determined by the volume of nonborrowed reserves. The
reserve provision locus is vertical up to the point
where the funds rate (f) equals the discount rate ( d )
because when the funds rate is below the discount
rate, banks have no incentive to borrow at the discount window. Conversely, when the funds rate is
above the discount rate borrowers obtain a net saving
on the explicit interest cost of reserves. This net
saving consists of the differential (f-d) between the
funds rate and the discount rate. In administering
the discount window the Federal Reserve imposes a
noninterest cost of borrowing which rises with volume. In practice, higher borrowing increases the
likelihood of triggering costly Federal Reserve consultations with bank officials, Banks tend to borrow
up to the point where the marginal expected noninterest cost of borrowing just offsets the net interest
saving. Consequently, borrowing tends to be greater
the larger the spread between the funds rate and the
discount rate. Hence, the reserve provision locus is
positively sloped for funds rates above the discount
rate.
Discount window borrowing plays a role in determining the funds rate whenever the Federal Reserve
restricts the supply of nonborrowed reserves so that
the funds rate exceeds the discount rate. In that
case, the banking system’s demand for reserves is
6

partially satisfied by borrowing at the discount window. If the Federal Reserve chooses to keep nonborrowed reserves fixed in response to an unexpected
shift in either reserve demand or the demand for discount window borrowing, then the procedure is called
nonborrowed reserve targeting. Nonborrowed reserve targeting is a kind of cross between funds rate
and total reserve targeting in the sense that the
reserve provision locus is diagonal, rather than horizontal or vertical, thereby partially smoothing the
funds rate against aggregate reserve demand shifts.
The Federal Reserve employed nonborrowed reserve
targeting between October 1979 and the fall of 1952.
By contrast, the Federal Reserve may choose to
respond to a shift in reserve demand or the demand
for discount window borrowing by adjusting the
provision of nonborrowed reserves to keep aggregate
discount window borrowing unchanged. The latter
procedure, known as borrowed reserve targeting, is
closely related to funds rate targeting. This is because, for a given level of the discount rate, targeting
borrowed reserves determines the funds rate except
for unpredictable instability due to shifts in the demand for discount window borrowing. Borrowed
reserve targeting has been the predominant operating
procedure since late 1982. An analytically similar
procedure, known as free reserve targeting, was employed throughout the 1920s and in the 1950s and
’ 6 0 s .5
As can be seen in Figure 2, Federal Reserve discount rate policy plays an important role in determining the funds rate when f is greater than d under
either nonborrowed or borrowed reserve targeting.
As is easily verified diagrammatically, with a borrowed reserve target a discount rate adjustment
changes the funds rate one-for-one. The effect is
smaller with nonborrowed reserve targeting. Keep
in mind, however, that the discount rate would be
irrelevant for determination of the funds rate if the
Federal Reserve were to supply a stock of nonborrowed reserves sufficiently large so that the funds rate
fell below the discount rate, and banks had no incentive to borrow at the discount window. It is also
irrelevant when the Federal Reserve targets the funds
rate directly. Discount rate adjustments have played
an important role since October 1979 in both the
nonborrowed and borrowed reserve targeting periods,
as they did in the 1920s, ’50s and ’60s under free
5
Free reserves are defined as excess reserves minus
borrowed reserves, or equivalently nonborrowed reserves
Net borrowed reserves are
minus required reserves.
negative free reserves.

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

reserve targeting. In contrast, discount rate adjustments had no direct impact on the funds rate when
the funds rate itself was targeted during the 1970s.
In that period, however, the announcement effect
associated with discount rate changes sometimes
signaled Federal Reserve intentions to change the
funds rate target in the future.

funds rates. In practice, because Federal Reserve
monetary policy smooths funds rate movements, such
views depend heavily on anticipated Federal Reserve
policy intentions. As an example, consider bank
certificates of deposit (CDs), which are generally
arranged for a few months. CD rates, adjusted for
reserve requirements, are roughly aligned with an
average of expected future funds rates over the term
of the CD. Banks can raise funds either through
CDs or Federal funds and therefore choose whichever
option is expected to be cheaper. Likewise, corporations considering a Treasury bill purchase have the
option of lending their funds daily over the term of
the bill at the overnight repurchase rate, which is
closely tied to the Federal funds rate. As shown in
Chart 1, arbitrage such as described above among
alternative money market instruments generally keeps
their yields in line, abstracting from differences due
to interest rate spreads resulting from transaction
costs and risk differentials.
Such considerations on the part of market participants make current and expected future Federal

The Federal Reserve, the Federal Funds
Rate, and Money Market Rates

The Federal Reserve’s operating procedures in the
reserve market have varied greatly over the years.
As we have seen, however, the Federal Reserve has
always exercised a dominant influence on the determination of the Federal funds rate through setting the
terms upon which it makes nonborrowed and borrowed reserves available to the banking system.
The funds rate is the base rate to which other
money market rates are anchored. Market participants determine money market rates according to
their view of current and expected future Federal

Chart 1

SHORT-TERM INTEREST RATES
(Monthly Data)

Percent

1961

63

65

67

69

71

73

75

77

Source: Federal Reserve Bulletin.

FEDERAL RESERVE BANK OF RICHMOND

79

81

83

85

Reserve policy toward the Federal funds rate the key
determinant of money market rates in general.
Having made this point, we must realize that it provides only a partial explanation of money market
rates. A full explanation requires an understanding
of Federal Reserve monetary policy. In particular,
economy-wide variables such as unemployment and
inflation do ultimately play an important role in the
evolution of the funds rate through their effect on
the Federal Reserve’s monetary policy actions over
time.
History of the Federal Funds Market

The birth of widespread trading in Federal funds
is roughly pinpointed by a New York Herald Tribune
article appearing in April 1928. 6 That article described the growing importance of Federal funds
trading in the money market, reporting a typical daily
volume of $100 million. 7 The primary purpose of
the article was to announce the inclusion of the Federal funds rate in the Tribune’s daily table of money
market conditions.
As the Tribune described it, Federal funds transactions involved the exchange of a check drawn on
the clearing house account of the borrowing bank
for a check drawn on the reserve account of the
lending bank. The reserve check cleared immediately
upon presentation at the Reserve Bank, while the
clearinghouse check took at least one day to clear.
The practice thereby yielded a self-reversing, overnight loan of funds at a Reserve Bank; hence the
name, Federal funds. By 1930, the means of trading
Federal funds had expanded to include book-entry
and wire transfer methods.8
The emergence of Federal funds trading constituted a financial innovation allowing banks to minimize transactions costs associated with overnight
loans. By their very nature, Federal funds could be
lent by member banks only, since only member banks
held reserves at Reserve Banks. The beneficiaries on
the borrowing side were also member banks, which
could receive funds immediately through their Reserve Bank accounts. Federal funds offered member
banks a means of avoiding reserve requirements on
interbank deposits if they could be classified as
“money borrowed” rather than deposits.
6

9

New York Herald Tribune [1928].

Willis [1970], p. 12, contains evidence of market activity as far back as 1922.
7

Board of Governors of the Federal Reserve System,
Federal Reserve Bulletin 16 (February 1930), p. 81.
8

8

In September 1928 the Federal Reserve Board
ruled that Federal funds should be classified as nonreservable money borrowed. 9 A further decision in
1930 found that Federal funds created by book-entry
and wire transfer methods should also be nonreservable. These decisions provided the initial regulatory
underpinnings for the Federal funds market of today.
In both the 1925 and 1930 rulings, the Board indicated that it viewed Federal funds as a substitute for
member bank borrowing at the Federal Reserve discount window. It argued that because discount window borrowing was not reservable, Federal funds
borrowing should not be either. This view seemed
appropriate because the mechanics of a Federal funds
transaction restricted participation in the Federal
funds market to member banks alone.
The Federal Reserve Board’s decision to make
Federal funds nonreservable is best understood as a
means of encouraging the Federal funds market as an
alternative to the two conventional means of reserve
adjustment then in use : the discount window and the
call loan market. Following World War I, aggregate
Federal Reserve discount window borrowing generally exceeded member bank reserves. There was
relatively little Federal Reserve discouragement of
continuous borrowing at the window. Member banks
could adjust their reserve positions directly with the
Federal Reserve by running discount window borrowing up or down. In addition, banks had a highly
effective means of reserve adjustment in the call loan
market. Since the middle of the nineteenth century,
banks had made a significant fraction of their loans
to stockbrokers, secured by stock or bond collateral
on a continuing contract, overnight basis.10 A bank
could obtain reserves on demand by calling in its
broker loans, and it could readily lend excess
reserves by increasing its supply of call loans. The
call loan market was the functional equivalent of the
Federal funds market for reserve adjustment purposes.
By 1928, however, the Federal Reserve had begun
discouraging both the discount window and the call
loan market as a means of reserve adjustment. Since
1922, substantial open market purchases had reduced
borrowed reserves to less than one-third of total reserves. 11 Moreover, in an apparent effort to further
Board of Governors of the Federal Reserve System,
Federal Reserve Bulletin 14 (September 1928), p. 656.
10

See chapters 7 and 13 in Myers [1931].

Board of Governors of the Federal Reserve System,
Banking and Monetary Statistics, 1914-1941, pp. 368-96.
11

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

reduce the highly visible subsidy that member banks
appeared to receive at the window, the Federal Reserve began actively discouraging continuous discount
borrowing by individual banks12 Both policy actions
tended to make discount window borrowing less
effective for routine reserve adjustment purposes.
This was particularly true for banks with undesired reserves, because with borrowing usually low
or zero, they could not dispose of reserves by running
down borrowings from the discount window. In
addition, the Federal Reserve came to see the call
loan market as an inappropriate means of financing
security speculation during the stock market boom of
the late 1920s. It went so far as to bring “direct
pressure” on individual banks to restrict call loans.13
Apart from providing a substitute for the discount
window and call loans, Federal funds helped to offset
the increased cost of membership due to the more
restrictive discount policy and the discouragement of
call lending. Membership in the Federal Reserve
System is voluntary, and throughout most of its history the Federal Reserve has been concerned about
membership attrition. One of the significant costs of
membership was the requirement that banks hold
more non-interest-bearing reserves than nonmember
banks had to hold. In making Federal funds nonreservable, the Federal Reserve reduced a cost of membership by providing member banks a means of more
effectively competing for overnight interbank deposits.
Banking legislation in the 1930s further enhanced
the attractiveness of Federal funds by enabling banks
to continue to pay market interest on overnight interbank balances even after the Banking Act of 1933
prohibited explicit interest on demand deposits. This
benefit was to prove particularly important in the
high interest rate environment of the 1960s and ’70s.
In order to prevent excessive use of stock market
credit, the Securities and Exchange Act of 1934 authorized the Federal Reserve Board to set margin
requirements for both brokers and banks, and others
if necessary, on loans collateralized by listed stocks
and bonds. Relatively high margin requirements,
coupled with other restrictions, brought about a permanent decline in the call loan market.14
Fifteenth Annual Report of the Federal Reserve Board
Covering Operations for the Year 1928 (Washington:
Government Printing Office, 1929), pp. 7-10.

Extremely low interest rates in the 1930s greatly
reduced the interest opportunity cost of holding excess reserves. Consequently, banks held a large
volume of excess reserves during this period and
Federal funds trading virtually disappeared. Federal
Reserve pegging of Treasury bill rates between 1942
and 1947 rendered the funds market superfluous for
reserve adjustment purposes. Under this policy the
Federal Reserve freely converted Treasury securities
into reserves at a fixed price. Therefore, banks could
use their inventory of Treasury bills for reserve adjustment purposes just as they had used their discount window borrowings in the early 1920s. The
Federal Reserve abandoned its Treasury bill price
peg in 1947 and Federal funds trading gradually reemerged as the most efficient means of reserve adjustment. Furthermore, higher market interest rates
prevailing in the 1950s increased the opportunity cost
of holding excess reserves, making more frequent reserve adjustment: desirable. Consequently, the volume
of trading in Federal funds grew sharply, with daily
average gross purchases of large reserve city banks
reaching about $800 million by the end of 1959.15
In the 1960s, the Federal funds market began to
take on a broader role beyond that of reserve adjustment borrowing. Banks made more extensive use of
Federal funds as a means of avoiding the reserve
requirement tax and the interest prohibition on demand deposits, both of which became more burdensome as inflation and interest rates rose throughout
the period. Although the Federal Reserve was
responsible for enforcing both of these legislative
restrictions, it had to be concerned throughout this
period with offsetting the increased burden of membership in the System, and its actions during the
period reflected this concern.16
The Board’s first significant ruling with regard to
the Federal funds market in this period was made in
1964 when it decided that a respondent bank, whether
member or not, could request a correspondent member bank to simply reclassify a deposit as Federal
funds, instead of having to transfer Federal funds
through a Reserve Bank account. 17 This ruling
probably had its major effect on smaller respondent
Board of Governors of the Federal Reserve System,
Federal Reserve Bulletin 50 (August 1964), p. 954.

l2

15

See the discussion in Friedman and Schwartz [1963],
pp. 254-66.

Goodfriend and Hargraves [1983] document in detail
how the membership problem dominated reserve requirement reform throughout this period.

14
The historical margin requirement series is reported
in Board of Governors of the Federal Reserve System,
Banking and Monetary Statistics.

17
Board of Governors of the Federal Reserve System,
Federal Reserve Bulletin 50 (August 1964), pp. 10001001.

l3

16

FEDERAL RESERVE BANK OF RICHMOND

9

banks, who had previously found use of Federal funds
too costly for the size of their transactions. Allowing
banks to simply reclassify their correspondent balances as Federal funds enabled smaller institutions
to benefit from Federal funds, as large banks had
already been doing. Moreover, it allowed Federal
Reserve member correspondent banks to compete
more effectively for interbank funds, thereby reducIn 1986, for
ing a disincentive to membership.
example, aggregate interbank reservable deposits at
large commercial banks are only 25 to 30 percent of
aggregate Federal funds borrowings.
Banks in the 1960s also had increasing incentive
to give their nonbank depositors access to nonreservable, market interest-paying overnight loans. Nonbanks had always been prohibited from participating
in the Federal funds market. But during the 1960s
widespread use of overnight repurchase agreements
(RPs) by banks became popular as a means of allowing their nonbank depositors to earn an overnight
rate only slightly below the Federal funds rate. As
mentioned earlier, the lower rate is due to the reduced
risk and additional transaction cost of arranging an
RP. RPs do not allow nonbanks to lend Federal
funds proper. Because RPs allow nonbanks to approximately earn the Federal funds rate, however, the
RP market together with the Federal funds market
constitutes a unified overnight loan market.
Obviously, nonbank depositors did not need access
to a relatively unregulated overnight rate for reserve
But the need to facilitate
adjustment purposes.
reserve adjustment had been the rationale for waiving
reserve requirements and interest rate controls on
Federal funds. Nevertheless, the Federal Reserve
chose not to make RPs at banks subject to reserve
requirements or interest rate controls, probably because doing so would have worsened the competitive
position of member banks relative to nonmembers
and increased membership attrition.
It was necessary, however, to face up to two consequences of allowing widespread use of RPs at banks.
First, RPs were not covered by deposit insurance.
Second, shifts from deposits to RPs reduced the reserve requirement tax base and consequently cost the
U. S. Treasury tax revenue. A 1969 Federal Reserve
rule restricting eligible bank RP collateral to direct
obligations of the United States or its agencies, e.g.,
Treasury bills, responded to those concerns. In
principal, requiring RPs to be collateralized with
10

liabilities of the United States made them free of
default risk.18 In addition, restricting bank RP paper
exclusively to U. S. liabilities may have enhanced the
demand for U. S. debt, offsetting somewhat the loss
of reserve requirement tax revenue.
A 1970 Board ruling formally clarified eligibility
for participation on the lending side of the Federal
funds market. Eligibility was restricted to commercial banks whether member or nonmember, savings
banks, savings and loan associations, and others.19
In effect, the ruling explicitly segmented the overnight bank loan market into two classes of institutions, those that could lend Federal funds, and those
that were required to pay somewhat more substantial
transactions costs, through RPs, to earn a rate on
overnight loans free of reserve requirements and
interest rate controls. Because RPs were uneconomical in smaller volumes, smaller firms and households were unable to obtain nonreservable market
yields on overnight money until the emergence of
money market mutual funds in the late 1970s.
Conclusion

It is interesting to note how far the Federal funds
market has come from its beginnings in the 1920s.
Initially, the regulatory rationale for making Federal
funds nonreservable was to provide member banks
with a substitute for the discount window and call
loans for reserve adjustment purposes. Participation
in the Federal funds market was limited to member
banks, i.e., banks holding required reserves at Reserve Banks. By the 1970s, however, that initial
participation principle was effectively overturned.
Nonbanks were not allowed to participate directly in
the Federal funds market, but they were allowed to
earn approximately the Federal funds rate through
RPs at banks. Reserve adjustment obviously no
longer provided a rationale for sanctioning access to
an overnight loan rate free of reserve requirements
and interest rate controls. Rather, the granting of
such access is better explained as a means by which,
in order to minimize membership attrition, the Fed-

18
Even if collateralized by U. S. government secuirties,
as a legal matter RPs might also be subject to custodial
risk due to incompletely specified contracts. See Ringsmuth [1985].
19

See footnote 2.

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

era1 Reserve allowed member banks and their customers to avoid the reserve requirement tax and
interest rate prohibition on overnight loans.
The Federal funds market today is in many ways a
functional equivalent of the call loan market of the
1920s and earlier. The most notable differences are
that the nonbank portion of the market is now a net
lender rather than a net borrower, and the collateral

used is exclusively debt of the United States government and its agencies rather than private stocks and
bonds. Like the old call loan market, the Federal
funds market of today facilitates the distribution of
reserves among banks, and has much wider participation and a more general role as the core of an overnight credit market unencumbered by reserve requirements and legal restrictions on interest rates.

References
“Interest Rate Smoothing and Price Level
Federal Reserve Bank of
Trend-Stationarity.”
Richmond, July 1986.

Board of Governors of the Federal Reserve System.
Annual Report of the Board of Governors, v a r i o u s
editions.
Banking and Monetary Statistics, 19141941. Washington: Board of Governors, 1943.
B a n k i n g a n d Monetary Statistics, 19411970. Washington: Board of Governors, 1976.
The Federal Funds Market-A Study by a
Federal Reserve System Committee. W a s h i n g t o n :
Board of Governors, 1959.
. Federal Reserve Bulletin, various issues.
“Federal Funds’ Rate Index of Credit Status.” N e w
York Herald Tribune, April 5, 1928.
Friedman, Milton, and Anna J. Schwartz. A Monetary
History of the United States, 1867-1960. Princeton,
NJ: Princeton University Press, 1963.
Goodfriend, Marvin. “A Model of Money Stock Determination with Loan Demand and a Banking System
Balance Sheet Constraint.” Federal Reserve Bank
of Richmond, Economic Review 68 (January/February 1982), pp. 3-16.

Goodfriend, Marvin, and Monica Hargarves. “A Historical Assessment of the Rationales and Functions
of Reserve Requirements.” Federal Reserve Bank
of Richmond, Economic Review 6 9 ( M a r c h / A p r i l
1983), pp. 3-21.
Myers, Margaret G. T h e N e w Y o r k M o n e y M a r k e t ,
vol. 1. New York: Columbia University Press,
1931.
Ringsmuth, Don. “Custodial Arrangements and Other
Federal Reserve
Contractual Considerations.”
Bank of Atlanta, Economic Review 70 (September
1985), pp. 40-48.
Turner, Bernice C. The Federal Fund Market. New
York: Prentice-Hall, Inc., 1931.
Willis, Parker B.
The Federal Funds Market: Its
Origin and Development. Boston : Federal Reserve
Bank of Boston, 1970.

INSTRUMENTS OF THE MONEY MARKET

Sixth Edition
The Federal Reserve Bank of Richmond is pleased to announce the publication
of the sixth edition of Instruments of the Money Market. This completely new
edition contains articles on the following subjects: Federal funds, the discount
window, large certificates of deposit, Eurodollars, repurchase and reverse repurchase
agreements, Treasury bills, short-term municipal securities, commercial paper,
bankers acceptances, the federally sponsored credit agencies, money market mutual
funds and other short-term investment pools, short-term interest rate futures, and
options on short-term interest rate futures.
Single copies are available free of charge. For additional copies, there will be a
charge of $1.00 each, except for orders from educational institutions, including
libraries. Payment, if applicable, is required in advance by check or money order in
U. S. dollars to the Federal Reserve Bank of Richmond. Copies can be obtained by
writing to the Public Services Department, Federal Reserve Bank of Richmond,
P. O. Box 27622, Richmond, Virginia 23261.

FEDERAL RESERVE BANK OF RICHMOND

11

SHORT-TERM INTEREST RATE FUTURES
Anatoli Kuprianov

Not long ago futures trading was limited to contracts for agricultural and other commodities. Trading in futures contracts for financial instruments
began in the early 1970s, after almost a decade of
accelerating inflation exposed market participants to
unprecedented levels of exchange rate and interest
rate risk. Foreign currency futures, introduced in
1972 by the Chicago Mercantile Exchange, were the
first financial futures contracts to be traded. The
first interest rate futures contract, a contract for the
future delivery of mortgage certificates issued by
the Government National Mortgage Association,
began trading on the floor of the Chicago Board of
Trade in 1975. Today financial futures are among
the most actively traded of all futures contracts.
At present there are active futures markets for
two different money market instruments: threemonth Treasury bills and three-month Eurodollar
time deposits. Treasury bill futures were introduced
by the Chicago Mercantile Exchange in 1976, while
trading in Eurodollar futures began late in 1981.
Domestic certificate of deposit futures were also
actively traded for a time but that market, while
technically still active, became dormant for all practical purposes in 1986.
AN INTRODUCTION TO FUTURES MARKETS

A futures contract is a standardized, transferable
agreement to buy or sell a given commodity or financial instrument on a specified future date at a set
price. In a futures transaction the buyer (sometimes
called the long) agrees to purchase and the seller (or
short) to deliver a specified item according to the
terms of the contract. For example, the buyer of a
Treasury bill contract commits himself to purchase
at some specified future date a thirteen-week Treasury bill paying a rate of interest negotiated at the
time the contract is purchased. In contrast, a cash
or spot market transaction simultaneously prices and
transfers physical ownership of the item being sold.
A cash commodity (cash security) refers to the actual
physical commodity (security) as distinguished from
the futures commodity.
This article was prepared for Instruments of the Money
Market, 6th edition.

12

Futures contracts are traded on organized exchanges. The basic function of a futures exchange is
to set and enforce trading rules. There are thirteen
futures exchanges in the United States at present.
The principal exchanges are found in Chicago and
New York. Short-term interest rate futures trade
on a number of exchanges; however, the most active
trading in these contracts takes place at the International Monetary Market (IMM) division of the
Chicago Mercantile Exchange (CME).
Market Participants

Futures market participants are typically divided
into two categories : hedgers and speculators. Hedging refers to a futures market transaction made as a
temporary substitute for a spot market transaction to
be made at a later date. The purpose of hedging is
to take advantage of current prices in future transactions. In the money market, hedgers use interest
rate futures to fix future borrowing and lending rates.
Futures market speculation involves assuming
either a short or long futures position solely to profit
from price changes, and not in connection with ordinary commercial pursuits. A dentist who buys wheat
futures after hearing of a nuclear disaster in the
Soviet Union is speculating that wheat prices will
rise, while a grain dealer undertaking the same transaction would be hedging unless the futures position
is out of proportion with anticipated future wheat
purchases.
Characteristics of Futures Contracts

Three distinguishing characteristics are common to
all futures contracts. First, a futures contract introduces the element of time into a transaction. Second,
futures contracts are standardized agreements. Each
futures exchange determines the specifications of the
contracts traded on the exchange so that all contracts
for a given item specify the same delivery location
and a uniform deliverable grade. Traded contracts
must also specify one of a limited number of designated delivery dates (also called contract maturity or
settlement dates). The only item negotiated at the
time of a futures transaction is price. Third, the
exchange clearinghouse interposes itself as a counter-

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

party to each contract. Once a futures transaction is
concluded, a buyer and seller need never deal with
one another again; their contractual obligations are
with the clearinghouse. The clearinghouse, in turn,
guarantees contract performance for both parties.
The first of these characteristics is not unique to
futures contracts. A forward contract, like a futures
contract, is a formal commitment between two parties
specifying the terms of a transaction to be undertaken
at a future date. Unlike futures contracts, however,
forward contracts are not standardized; rather, they
are custom-tailored agreements. As a general rule
forward contracts are not transferable and so cannot
be traded to a third party.
Trading in futures contracts is facilitated by contract standardization and the clearinghouse guarantee. Contract standardization reduces transaction
costs. The clearinghouse guarantee removes credit
risk, or risk that a 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 so
that a party to a futures contract can always liquidate a futures commitment (or open position) before
maturity by making an offsetting transaction. For
example, a trader with a long position in Treasury
bill futures maturing in March of 1987 can liquidate
his position any time before the last day of trading
by selling an equal number of March Treasury bill
futures.
In practice, most futures contracts are
liquidated in this way before they mature. By one
estimate two percent of all futures contracts are held
to maturity on average, although delivery is more
common in some markets.1
Margin Requirements

A contract for the future delivery of an item gains
value to one of the parties to the contract and imposes a liability on the other when futures prices
change. A rise in Treasury bill futures prices, for
example, gives all traders who are long in bill futures
the right to buy Treasury bills at a price below the
currently prevailing futures price; equivalently, they
have the right to invest money at an interest rate
higher than the current market rate. Traders with
short positions, on the other hand, are committed to
sell bills at a price lower than that which they would
be required to pay if they wished to buy the contract
back at the new futures price.

1

See Little [1984, p. 43].

In the early days of trading in time contracts, as
they were called in the nineteenth century, traders
adversely affected by price movements often disappeared as the delivery date drew near. In response,
futures exchanges adopted the practice of requiring a
performance bond, called a margin requirement, of all
buyers and sellers. They also began requiring all
traders to recognize any gains or losses on their outstanding futures positions at the end of each trading
session, a practice called marking to market.
All futures exchanges now require members to
maintain margin accounts. Brokers who execute
orders on behalf of customers are required to collect
margin deposits from them before undertaking any
trades. Minimum margin requirements are set by
the exchanges. Brokers can, and most do, require
their customers to maintain margins higher than the
minimum levels set by the exchange. Any gains or
losses realized when the contracts are marked to
market at the end of a trading session are added
to or subtracted from a trader’s margin account.
If the margin account balance falls below a specified
minimum, called the maintenance margin, the trader
faces a margin call requiring the deposit of additional margin money, called variation margin, to his
account.
Futures Exchanges

The right to conduct transactions on the floor of a
futures exchange is typically limited to exchange
members, although trading privileges can be leased
to another party. Members also have voting rights,
which give them a voice in management decisions.
Membership privileges can be bought and sold; the
exchanges make public the most recent selling and
current offer price for a membership.
Exchange members can be grouped into two categories. Commission brokers (also known as floor
brokers) execute orders for nonmembers and other
customers, Some floor brokers are employees of
commission firms while others are independent operators who execute trades for other firms. The second
type of exchange member is the floor trader, or local.
Locals are independent operators who trade for their
own account.2

Different types of floor traders can be distinguished
based on the trading strategies they use most often: see
Rothstein and Little [1984] for a description. Silber
[1984] presents a comprehensive analysis of marketmaker
behavior in futures markets.

2

FEDERAL RESERVE BANK OF RICHMOND

13

The Role of the Exchange Clearinghouse

Each futures exchange operates a clearing organization, or clearinghouse, that records all transactions
and insures all buy and sell trades match. The clearinghouse also assures the financial integrity of the
contracts traded on the exchange by guaranteeing
contract performance and supervising the process of
delivery for contracts held to maturity.
Clearing member firms act as intermediaries between traders on the floor of the exchange and the
clearinghouse, assisting in recording transactions and
collecting required margin deposits. Clearing member firms are all members of the exchange, but not
all exchange members are clearing members. All
transactions taking place on the exchange floor must
be cleared through a clearing member firm. Traders
who are not directly affiliated with a clearing member
must make arrangements with one to act as a designated clearing agent.
Clearing member firms are responsible for collecting margin deposits from their customers and depositing required margins with the clearinghouse.
The clearinghouse holds clearing members responsible for losses incurred by their customers. Any
time a trader fails to meet a margin call his position
is immediately liquidated, with the resulting losses
taken from his margin account. If losses exceed
funds available in a customer’s margin account the
clearing member firm is required to make up the
difference to the clearinghouse.
Futures Commission Merchants

A Futures Commission Merchant (FCM) is an
intermediary that handles orders for the sale or purchase of a futures contract from the general public.
An FCM can be a person or a firm. Some FCMs
are exchange members employing their own floor
brokers; others rely on independent brokers to handle
trades ordered by their customers. A n F C M i s
responsible for collecting the required margin deposit
from customers before acting to execute a trade. The
FCM must in turn deposit the required margin with
its clearing agent. All FCMs must be licensed by the
Commodity Futures Trading Commission (CFTC),
which is the government agency responsible for regulating futures markets.

ment. Bills with maturities of thirteen, twenty-six,
and fifty-two weeks are issued by the Treasury on a
regular basis. The secondary market for these securities is active and well-organized, making Treasury
bills (often referred to as T-bills) among the most
liquid of money market instruments,
Treasury bill futures contracts are traded in the
United States on two Chicago exchanges: the International Monetary Market (IMM) and the MidAmerica Commodity Exchange. Both contracts
specify delivery of thirteen-week (91-day) bills. The
IMM T-bill contract, which is the most actively
traded of the two by a large margin, is described
below.
Contract Specifications

Upon maturity the IMM contract requires the
seller to deliver a U. S. Treasury bill with a $1 million face value and thirteen weeks left to maturity.
Contracts for delivery during the months of March,
June, September, and December are traded on the
exchange. At any one time contracts for eight different delivery dates are traded. A new contract begins
trading after each delivery date, making the furthest
delivery date for a new contract twenty-four months
away.
Price Quotation Treasury bills do not pay explicit
interest. Instead, they are sold at a discount relative
to their redemption or face value. The difference
between the purchase price of a Treasury bill and its
face value determines the interest earned by a buyer.
Treasury bill yields are typically quoted on a discount
basis, that is, as a percentage of face value rather
than of actual funds invested.3
Price quotations for T-bill futures contracts are
based on an index devised by the IMM. The index
is calculated by subtracting the Treasury bill discount
yield from 100. For example, if the discount yield
on a traded T-bill futures contract is 9.75 percent,
then the index value is 100 - 9.75 = 90.25. Index
values move in the same direction as the future purchase price of the deliverable bill ; a rise in the index
value, for example, means that the price a buyer must
agree to pay to take future delivery of a T-bill has
risen.
3

TREASURY BILL FUTURES

The formula for calculating the discount yield is
Discount Yield = Face Value - Purchase Price
Face Value

Treasury bills are short-term securities issued by
the U. S. Treasury to help finance the federal govern14

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

X

360

Days to Maturity

.

The minimum price fluctuation permitted on the
trading floor is one basis point (.01 percent), which
comes to $25 on a contract specifying the delivery
of a 90-day Treasury bill with a $1 million face value.
Thus, the price of a T-bill futures contract may be
quoted as 94.25, or 94.26, but not 94.255. The IMM
eliminated maximum daily price limits for all its
interest rate futures contracts in December of 1985.
A sample of a newspaper clipping reporting Treasury bill futures prices is reproduced in Box 1.
Delivery Requirements The Treasury auctions

thirteen- and twenty-six-week bills each Monday
(except for holidays and special situations) and

issues them on the following Thursday. Fifty-twoweek bills are auctioned every four weeks. These
auctions are held on a Thursday and the bills are
issued on the following Thursday. To insure an adequate supply of deliverable bills, the IMM schedules
T-bill futures delivery dates for the three successive
business days beginning with the first day of the
contract month on which a thirteen-week bill is issued
and a one-year bill has thirteen weeks to maturity.
This schedule permits delivery requirements for the
T-bill futures contract to be satisfied with either a
newly issued thirteen-week bill or an original-issue
twenty-six- or fifty-two-week bill with thirteen weeks

Box 1
FOLLOWING DAILY FUTURES MARKET ACTIVITY

Many newspapers report information on
daily trading activity in futures markets. The
clipping for IMM Treasury bill futures reproduced below is taken from the October 3, 1986,
edition of the Wall Street Journal.
Each row gives price and trading volume
data for a different contract delivery month.
Delivery months for currently traded contracts
are listed in the first column.
The next four columns show the opening
price, high and low prices, and the closing or
settlement price for the previous day’s trading.
Column six gives the change in the contract
settlement price over the last two trading
sessions.
The seventh column reports the interest rate
implied by the most recent settlement price,
calculated by subtracting the settlement price
from 100.
Column eight reports the change in the interest rates implied by the two most recent settlement prices. Note that the figures in this
column are equal in magnitude but opposite in
sign to the change in settlement price displayed
in the sixth column.
The last column lists open interest for each
contract delivery month. Open interest refers
to the number of outstanding contracts. Each
unit represents both a buyer and a seller with
an outstanding futures commitment, or open
position. Notice that open interest is greatest

for the nearest delivery month and declines
steadily for successively distant delivery months.
This pattern is typical, except when delivery
for the nearby contract is impending and market
participants begin to close out their positions.
Total trading volume and open interest for all
contract delivery months are given in the last
line. Trading volume refers to the total number
of contracts for all contract delivery months
traded on a particular day. Each transaction
included in the count reflects both a purchase
and sale of a futures contract. Note that the
clipping includes data on total trading volume
for each of the previous two trading sessions.
Total open interest, reported in the last line,
is simply the sum of the open interest for each
contract month listed in the rightmost column.
The final entry on the bottom line reports the
change in open interest over the previous two
trading sessions.

Reprinted by permission of Wall Street Journal,
© Dow Jones & Company, Inc. 1986.
All Rights Reserved.

FEDERAL RESERVE RANK OF RICHMOND

15

left to maturity. The method used to determine the
final delivery price is described in Box 2.
Market History

The IMM introduced the three-month Treasury
bill futures contract in January of 1976. At the time
the contract was introduced, trading in interest rate
futures was still a relatively new development. Trading in the first interest rate futures contract, the
Board of Trade’s Government National Mortgage
Association (GNMA) certificate contract, had begun
only a few months earlier, The Treasury bill contract was the first futures contract for a money
market instrument.
Dealers in U. S. government securities were among
the first market participants to actively use Treasury
bill futures. Other money market participants entered
into futures trading more slowly. By the time the
IMM contract was two years old, however, trading
activity had begun to accelerate rapidly.
This trend can be seen in Charts 1 and 2, which
plot two different measures of market activity for the
IMM contract from the inception of trading in 1976
through the end of 1984. The first measure, plotted
in Chart 1, is total monthly trading volume, which
is a count of the total number of contracts (not the
dollar value) traded for all contract delivery months.
Each recorded trade reflects one buyer and one seller.
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 a given month.
Each contract included in the open interest count
reflects both a buyer and a seller with an outstanding
futures commitment.

bulk of the Eurodollar market. These deposits have
fixed maturities ranging from one day to five years;
most are very short-term, three months being a
common maturity. Eurodollar CDs are also most
commonly issued with maturities under a year.
Eurodollar futures contracts are actively traded on
two exchanges. In the United States, a three-month
Eurodollar time deposit contract is traded at the
IMM. A similar contract is also traded at the London
International Financial Futures Exchange (LIFFE).
The IMM contract is described below.
Contract Specifications

Technically, the buyer of a Eurodollar contract is
required to place $1,000,000 in a three-month Eurodollar time deposit paying the contracted rate of
interest on the contract maturity date. This requirement exists only in principle, however, because
the Eurodollar contract is cash. settled. Cash settlement means that actual physical delivery never takes
place; instead, any net changes in the value of the
contract at maturity are settled in cash on the basis
of spot market Eurodollar rates. Thus, cash settlement can be viewed as a final marking to market of
the contract with the settlement amount based on the
difference between the previous day’s closing price
and the final settlement price.

Eurodollars are U. S. dollar-denominated deposits
held with banks or bank branches located outside of
the United States, or with International Banking
Facilities (IBFs) inside the United States 4 T h e r e
are two types of Eurodollar deposits : nontransferable
time deposits and CDs. Time deposits make up the

Price Quotation Price quotations for Eurodollar
futures are based on a price index similar to that
used for Treasury bill futures. Unlike Treasury bills,
Eurodollar time deposits (as well as domestic and
Eurodollar CDs) pay explicit interest. The rate of
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. In the case of
Eurodollar time deposits, the add-on yield is commonly called the London Interbank Offered Rate
(LIBOR), which is the interest rate at which major
international banks offer to place Eurodollar deposits
with one another. Like other money market rates,
LIBOR is an annualized rate based on a 360-day
year. The IMM Eurodollar futures price index is
100 minus the LIBOR for Eurodollar futures.

An International Banking Facility, or IBF, is an office
of a U. S. bank, U. S. branch of a foreign bank, or Edge
Act corporation, which is domiciled in the United States
but operates under rules and regulations similar to those
applied to foreign branches of U. S. banks.
restricted to doing business with foreign residents, foreign
banks and foreign branches of U. S. banks, and foreign
operations of multinational firms.
See Key [1982] for
further details.

Determination of Settlement Price When a futures contract contains provisions for physical delivery, market forces cause the futures price to
converge to the spot market price as the delivery date
draws near. This phenomenon is called convergence.
In the case of a cash-settled contract, the futures exchange forces the process of convergence to take place

EURODOLLAR FUTURES

4

16

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

Box 2
EXAMPLE OF A TREASURY BILL FUTURES TRANSACTION

Suppose that on October 2, 1986, a trader buys one December 1986 Treasury
bill futures contract at the opening price of 94.83. Once the transaction is complete
the trader is contractually obligated to buy a $1 million dollar (face value) thirteenweek Treasury bill yielding 100 - 94.83 = 5.17 percent on a discount basis on the
contract delivery date, which is December 18, 1986. At the time of the initial transaction, however, the trader pays only a commission and deposits the required
margin with his broker.
Effects of Price Changes The Wall Street Journal entry in Box 1 shows that
futures prices fell two basis points during that day’s trading session, meaning that
the discount rate on bills for future delivery rose after the contract was purchased.
Since each one basis point change in the T-bill index is worth $25 the trader would
lose $50 if he were to sell the contract at the closing price.
The practice of marking futures contracts to market at the end of each trading
session means that the trader is forced to realize this loss even though he does not
sell the bill; thus, he has $50 subtracted from his margin account. That money is
then transferred to a seller’s margin account. After the contract is marked to market,
the trader is still obliged to buy a Treasury bill on December 18, but now at a
discount yield of 5.19 percent (the implied futures discount yield as of the close of
trading).
Final Settlement If the trader chooses to hold his contract to maturity the
contract is marked to market `one last time at the close of the last day of trading.
All longs with open positions at that time must be prepared to buy the deliverable
bill at a purchase price determined by the closing futures index price.
The final settlement or purchase price implied by the IMM index value is determined as follows. First, calculate the total discount from the face value of the bill
using the formula

Discount =

Days to Maturity x ((100 - Index) x .01) x $1,000,000
,
360

where ((100 - Index) x .01) is the futures discount yield expressed as a fraction.
Second, calculate the purchase price by subtracting the total discount from the face
value of the deliverable bill. Note that this is essentially the same procedure used to
calculate the purchase price of a bill from the quoted discount yield in the spot
market, the only difference being the use of the futures discount rate implied by the
index value in place of the spot market rate.
Suppose that the final index price is 94.81; then, the settlement price for the
first delivery day is
$986,880.83 = $1,000,000 - 91 x .0519 x $1,000,000 .
360
This calculation assumes that the deliverable bill will have exactly 91 days to
maturity, which will always be the case on the first contract delivery day except in
special cases when a bill would otherwise mature on a national holiday.
Because buying a futures contract during the last trading session is essentially
equivalent to buying a Treasury bill in the spot market, futures prices tend to
converge to the spot market price of the deliverable security on the final day of
trading in a futures contract. Thus, the final futures discount yield should differ
little, if at all, from the spot market discount yield at the end of the final trading day.

FEDERAL RESERVE BANK OF RICHMOND

17

by setting the price of outstanding futures contracts
equal to the spot market price at the end of the last
day of trading.
To determine the final settlement price for its
Eurodollar futures contract, the Mercantile Exchange
clearinghouse randomly polls twelve banks actively
participating 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 two
highest and lowest price quotes from each polling

are dropped and the remaining quotes are averaged
to arrive at the LIBOR rate used for final settlement.
The final settlement price is 100 minus the average
of the LIBOR rates for the two sample times.
As with Treasury bill futures, every change of one
basis point in the Eurodollar futures index price is
worth twenty-five dollars. Thus, if the IMM price
index rises 10 basis points during the last trading
session all shorts have $250 per contract subtracted
from their margin accounts while the longs each
receive $250 per contract. Once the contracts are

Chart 1

MONTHLY VOLUME TOTALS FOR MONEY MARKET FUTURES
Thousands of Contracts

1976

1978

1980

1982

Source: Chicago Mercantile Exchange.

18

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

1984

marked to market for the last time, buyers and sellers
are relieved of the responsibility of actually placing
or taking the deposits specified by the contract.
The IMM Eurodollar contract is the first futures
contract traded in the United States to rely exclusively on a cash settlement procedure. The LIFFE
Eurodollar contract also relies principally on cash
settlement, although it does have provisions for
physical delivery.5
Tompkins and Youngren [1983] contains a detailed
comparison of the IMM and LIFFE contracts.
6

Market History

Trading in the IMM Eurodollar contract began in
December 1981. The LIFFE introduced its Eurodollar contract a few months later in September of
1982. Both markets are currently active. Trading
activity in the IMM contract is much heavier than
in the LIFFE contract, however. 6 Charts 1 and 2
As of the end of trading on October 2, 1986, for
example, total volume and open interest for the IMM
contract were 44,378 and 217,542 contracts, while trading
volume for the LIFFE contract was 3,454 and open
interest was 23,541.

6

Chart 2

MONTH-END OPEN INTEREST TOTALS FOR
MONEY MARKET FUTURES

Thousands of Contracts

Source: Chicago Mercantile Exchange.

FEDERAL RESERVE BANK OF RICHMOND

19

THREE-MONTH TREASURY BILL AND EURODOLLAR TIME DEPOSIT FUTURES:
IMM CONTRACT SPECIFICATIONS
Eurodollar Time Deposit

Treasury Bill

Contract Sire

$1,000,000

$1,000,000

Deliverable Grade

U. S. Treasury bills with
thirteen weeks to maturity

Cash settlement with clearing
corporation

Delivery Months

March, June, September, December

March, June, September, December

Price Quotation

Index: 100 minus discount yield

Index: 100 minus add-on yield

Minimum Price
Fluctuation

.01 percent (1 basis point=$25)

.01 percent (1 basis point = $25)

Trading Hours
(Chicago Time)

7:30 a.m. - 2:00 p.m.
(last day - 10:00 a.m.)

7:30 a.m. - 2:00 p.m.
(last day - 9:30 a.m.)

Last Day of Trading

The day before the first delivery date

Second London business day before the
third Wednesday of delivery month

Delivery Days

Three successive business days
beginning with the first day of the
contract month on which a thirteenweek T-bill is issued and a one-year
bill has thirteen weeks to maturity

Last day of trading

Source:

Chicago Mercantile Exchange

display monthly time series of total trading volume
and open interest for the IMM Eurodollar contract
through the end of 1984.
Three factors have contributed to the popularity of
Eurodollar futures. First, most major international
banks rely heavily on Eurodollar market for shortterm funds. To maintain ready access to this market,
many of these banks have become active marketmakers in Eurodollar deposits. Eurodollar futures
provide a means of hedging interest rate risk arising
from these activities.
Second, major international corporations have
come to rely increasingly on Eurodollar markets for
borrowed funds. Borrowing rates for these corporations are typically based on the three- or six-month
LIBOR. When loans are priced this way, Eurodollar
futures offer a means of hedging borrowing costs.
Finally, Eurodollar and domestic CD futures display almost identical price characteristics, which
means that the two contracts are virtually perfect
substitutes as hedging instruments.7 The physical
delivery requirements for CD futures proved to be
awkward in comparison with the cash-settled Eurodollar contract, however, causing U. S. banks, once
among the heaviest users of CD futures, to rely
Faux [1984] found the correlation between Eurodollar
and CD futures prices to be .993.

7

20

instead on Eurodollar futures to hedge domestic borrowing costs. In fact, the steep rise in trading volume
in the Eurodollar contract during 1984 evident in
Chart 1 coincides with a decline in CD futures trading volume beginning at about the same time. Thus,
it appears that the success of the Eurodollar contract
has contributed to the demise of trading in CD
futures.
USES OF INTEREST RATE FUTURES:
HEDGING AND SPECULATION

Hedging Theory

In the most general terms hedging refers to the act
of matching one risk with a counterbalancing risk so
as to reduce the overall risk of loss. Futures hedging
was traditionally viewed narrowly as the use of futures contracts to offset the risk of loss resulting from
price changes. To illustrate, consider the example of
an investor with holdings of interest-bearing securities. If market interest rates rise, the value of those
securities will fall. Since futures prices tend to move
in sympathy with spot market prices, taking on a
short position in interest rate futures produces an
opposing risk. Traders with short positions in
interest rate futures profit when interest rates rise
because the contracts give them the right to sell the

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

underlying security at the old, higher price, meaning
that they can buy back the contracts at a profit.
This traditional view emphasized risk avoidancefutures hedging was seen solely as providing a form
of insurance against price risk. The contemporary
view of hedging, on the other hand, emphasizes the
relative efficiency of futures markets. Buying or
selling futures contracts is a good temporary substitute for planned spot market transactions because
futures contracts are more liquid than cash securities
and transaction costs are generally lower in futures
markets. From this perspective, the hedging transaction described above can be viewed as a temporary
substitute for selling existing holdings of interestbearing securities and buying shorter-term securities
whose value would be less affected by interest rate
changes. Either transaction would reduce the risk
faced by the investor, but the futures hedge does so
at a lower cost.
Hedging

as

Profit-Maximizing

Behavior

The
principal shortcoming of the traditional concept of
hedging is that it does not explain the hedging behavior of profit-maximizing firms. Although all
firms must bear some risk inherent to the normal
conduct of business, it is widely recognized that firms
seek to maximize profits, and not to minimize risk.
While risk minimization is not generally consistent
with profit-maximizing behavior, cost minimization
is. This is not to deny that hedging transactions are
undertaken to reduce risk ; hedging is one tool used in
implementing a broader policy of risk management.
The hedging behavior of profit-maximizing firms is
best understood, however, when hedging is viewed
as a temporary, low-cost alternative to planned spot
market transactions rather than as a form of price
insurance. 8
The emphasis that modern hedging theory places
on transaction costs is especially useful in understanding the hedging behavior of money market
participants. In the money market, investors interested only in minimizing risk need not hedge ; they
can simply hold a portfolio composed solely of T-bills
that are close to maturity. Arbitrage pricing theory
holds that two securities that can serve as perfect
substitutes should earn identical rates of return, so
that a perfectly hedged, and therefore riskless, portThe concept of hedging as profit-maximizing behavior
was developed by Working [1962]. Telser [1981, 1986]
takes a similar view, arguing that futures markets exist
primarily because they minimize transaction costs, and
not because futures contracts can be used to insure
against price risk.
8

folio would be expected to earn only the riskless rate
of return. Most investors, however, are willing to
bear some additional risk in exchange for a higher
expected rate of return. Hedgers in the money
market selectively buy and sell interest rate futures to
fix future borrowing and lending rates when they
perceive it to be to their advantage to do so, and not
to minimize risk per se.9
Portfolio hedging theory views futures contracts in
the context of a hedger’s entire portfolio of cash
holdings. With this approach, cash holdings are
treated as fixed and the expected returns of the unhedged portfolio are compared with those of a hedged
portfolio. To the extent that futures prices are correlated with the value of the unhedged portfolio, a
hedge can reduce portfolio risk. Final hedging positions are determined by the desired risk-return
trade-off, which may not be the risk-minimizing
combination. 10
Basis Risk
Basis refers to the difference between the spot
market price of the security being hedged and the
futures price. In portfolio hedging applications, basis
can also refer to the relationship between the value of
the portfolio and the price of a futures contract.
Basis risk refers to the risk hedgers face as a result
of unexpected changes in basis.
In a perfect hedge any gains or losses resulting
from a change in the price of the item being hedged
is offset by an equal and opposite change in futures
prices. Perfect futures hedges are rarely attainable
in practice because futures contracts are not customtailored agreements. Contract standardization, while
contributing to the liquidity of the futures markets,
practically insures that those contracts will not be
perfectly suited to the needs of any one hedger. As a
result, hedgers are exposed to basis risk.
At least two sources of basis risk can be identified.
First, because standardized delivery dates for futures

Although these hedging concepts have gained widespread acceptance among market participants and regulatory agencies such as the CFTC, bank regulatory
agencies define permissible hedges in terms of risk
reduction. Federally insured banks and savings and loan
associations are permitted to buy and sell futures for
their own accounts only when the transactions can be
shown to reduce overall risk; see Koppenhaver [1984] for
more details.
9

10
Powers and Vogel [1981, chapter [4] contains an
introductory discussion of portfolio hedging theory.
Figlewski [1986] contains a formal development of the
portfolio approach to hedging, including methods for
determining a risk-minimizing hedge.

FEDERAL RESERVE BANK OF RICHMOND

21

contracts rarely coincide with planned transaction
dates, most hedgers must unwind their futures positions before the contract delivery date.
Futures
prices do not always move in perfect conformity with
spot prices before the contract maturity date, however, most often for fundamental economic reasons
but sometimes for reasons that are not fully understood. Thus, any changes in the value of the futures
contracts held as a hedge may not fully reflect
changes in the spot price of the item being hedged at
the time the hedge is lifted. If the date of a planned
spot market transaction coincided exactly with the
corresponding futures contract delivery date, delivery
of the underlying cash instrument would permit a
hedger to avoid this source of basis risk.
Second, in most cases the grade of the commodity
being hedged differs from the deliverable grade specified by the futures contract. Price differentials between different commodity grades can vary, exposing
hedgers to basis risk. This problem is not limited to
commodity futures, moreover. Interest rate differentials on bank deposits, reflecting different risk
premiums, can vary even among major money-center
banks.
As long as changes in futures prices are highly
correlated with changes in underlying cash prices a
futures hedge can reduce overall risk. Hedging
cannot eliminate basis risk, however, For this reason,
it is often said that hedging replaces price risk with
basis risk.
Cross Hedging

Futures markets do not exist for all financial instruments. Cross hedging refers to the use of a
futures contract for the delivery of one security to
hedge an anticipated future transaction in a different
security. An example of a popular cross hedge in
the money market is the use of Eurodollar futures to
hedge transactions in domestic CDS .
Futures prices tend to be more highly correlated
with the price of the deliverable security than with
other securities ; as a result, a cross hedge will carry
more basis risk than a regular hedge. When choosing a futures contract for a cross-hedging application,
hedgers try to pick the futures contract for which
price changes are most highly correlated with price
changes of the security being hedged.
Examples of Interest Rate Hedging Strategies

A wide variety of interest rate hedging strategies
have been devised in the few years since interest rate
22

futures were first introduced. Interest rate futures
can be used to establish interest rates on anticipated
future investments and borrowing rates on future
loans. Financial intermediaries, such as banks, use
interest rate futures to protect their balance sheets
from adverse effects of changes in market rates.
Examples of different hedging strategies are briefly
described below.
The Long Hedge A long hedge involves buying
futures contracts, or assuming a long futures position.
Investors use long hedges to protect against falling
interest rates by fixing interest rates on future investments. One way to think of a long hedge is as a
transaction that lengthens the effective maturity of
holdings of interest-bearing securities. This is illustrated by the following example.
Suppose a corporate cash manager is instructed to
invest $10 million in Treasury bills until the firm
anticipates needing the funds again in six months.
The manager can fix the rate of return earned over
this period in advance either by buying six-month
bills or by simultaneously buying three-month bills
and bill futures. The latter strategy of putting on a
long futures hedge creates a synthetic six-month
Treasury bill.
To take a simplified example suppose the date is
September 18, 1986, exactly 91 days before the first
delivery date for December Treasury bill futures.
Six-month bills can be purchased at a discount yield
of 5.42 percent. Creating a synthetic six-month bill
would require the simultaneous purchase of a threemonth Treasury bill and a futures contract for the
delivery of a three-month bill on December 18.
Three-month bills sell at a 5.23 percent discount yield
and the discount yield for December bill futures is
5.36 percent. Buying an actual six-month bill turns
out to be the more profitable alternative in this example (all numbers used in this example, incidentally,
reflect actual closing prices for September 18, 1986);
however, putting together a synthetic Treasury bill
can sometimes produce a higher yield than buying a
longer-term bill in the spot market. 11 Another P o tential advantage to the futures hedge is that it can
easily be lifted if market rates begin to rise.
A drawback to using the futures strategy comes
from exposure to basis risk. In the above example
the date of the initial transaction was chosen so as to
fall exactly 91 days before the maturity date of December Treasury bill futures contracts. This does not
always occur in practice.
11

See Werderits [1983], for example.

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

The Short Hedge The money manager in the
above example could have used another method to
create a synthetic six-month bill. Instead of buying
three-month bills and a futures contract for delivery
in three months he could buy nine-month Treasury
bills and simultaneously sell March 1987 bill contracts. Selling the futures contracts effectively
shortens the maturity of the nine-month bills to six
months. This last strategy is an example of a short
hedge. A short hedge involves selling interest rate
futures to protect the value of cash holdings of
interest-bearing securities or to fix borrowing costs,
The following example shows how a corporation
might use Eurodollar futures to fix a borrowing rate
on a future loan.
Overseas affiliates of multinational firms frequently
take out loans with borrowing costs tied to LIBOR.
Consider a firm that expects to need such a loan in a
month. The firm faces the risk that borrowing rates
may rise before the loan is taken out. The corporate
treasurer can hedge this risk by shorting Eurodollar futures. Since taking out a loan amounts
to selling an interest-bearing security, selling interest
rate futures contracts serves as a temporary substitute for taking out the loan now and investing the
proceeds until the funds are needed. If interest rates
rise, the cost of satisfying delivery requirements for
the futures contract falls while the contracted delivery
price remains the same. The gain from the futures
position offsets increased borrowing costs.
Hedging Interest Rate Risk Financial intermediaries, such as banks and securities dealers, fund their
holdings of earning assets largely through debt.
Traditionally, financial intermediaries have used
short-term sources of funds to finance holdings of
longer-term assets. This condition is described as a
positive gap. When an institution has a positive gap,
changes in interest rates affect funding costs faster
than asset returns. This means that any rise in
interest rates will hurt future earnings, while a fall
in rates produces windfall profits. The risk to net
earnings caused by changes in interest rates is termed
interest rate risk.
Financial intermediaries have begun to use interest
rate futures to hedge interest rate risk. A positive
gap can be hedged by either shortening the effective
maturity of asset holdings or by fixing future borrowing rates. Readers interested in learning more
about gap hedging strategies are referred to Brewer
[1985], Kaufman [1984], and Kawaller [1983].

Risks Associated with Hedging
Risk of Margin Calls Hedgers, like all traders
who take on futures positions, face the risk of margin
calls. In the case of a hedging transaction, any decline in the value of a futures position is normally
offset by gains from a cash position. Gains on the
cash position are typically not realized immediately,
however, while futures contracts are marked to market at the end of each trading session. The practice
of marking futures contracts to market every day,
while helping to insure the financial integrity of
futures contracts, can place strains on a hedger’s cash
flow.
Liquidity Risk Although futures contracts are
more liquid than the underlying security as a general
rule, liquidity can be a problem in some markets. CD
futures provide a good example. As of September 4,
1986, trading volume in CD futures was zero while
total open interest was twenty-eight contracts. In
such a market, it can at times be literally impossible
to execute market orders for the purchase or sale of a
contract. Hedgers who venture into such markets
should be prepared to satisfy delivery requirements.
Liquidity can also be a problem for futures contracts with delivery dates more than a year away.
Trading activity in futures contracts is heaviest in
contracts for the nearby delivery month. Trading in
the most distant contracts is typically very thin, indicating that those markets are less liquid. Liquidity
can also be a problem for contracts a few days away
from settlement. Unless a hedger plans delivery, it is
best to either lift the hedge or roll it over (close out
the existing futures position and buy or sell another
futures contract) into the next contract delivery
month before the last week of trading in a contract.12
The Role of Speculators

Speculators have been active participants in futures
markets since the earliest days of futures trading.
Futures markets have proven attractive to speculators for at least two reasons. First, fractional
margin requirements permit speculators to effectively
leverage their positions to a greater degree than
might otherwise be possible. Second, lower transaction costs and greater liquidity make futures contracts an attractive alternative to cash transactions
for speculators as well as hedgers.
12
Ronalds [1986] discusses contract life cycles for a
number of financial futures.

FEDERAL RESERVE BANK OF RICHMOND

23

The early history of futures trading is filled with
accounts of market squeezes-attempts at price
manipulation effected by dumping or withholding
commodity supplies on futures delivery dates-and
traders who defaulted on their obligations when price
changes created losses. Most often, speculators were
blamed for these abuses. In addition, commodity
producers often held speculators responsible for declines in commodity prices. These perceived speculative abuses produced several attempts to ban futures
trading entirely. 13
In response to these events, the futures exchanges
devised ways to insure the orderly functioning of
futures markets. Delivery requirements were designed so as to minimize the danger of market
squeezes. 14 Margin requirements and the daily
marking to market of contracts were adopted to
eliminate credit risk from futures contracts. Speculators in futures markets are still sometimes blamed
for large price fluctuations; for the most part, however, they have come to be viewed as playing a useful
role in futures markets through their willingness to
assume price risk, thereby making the markets more
liquid for hedgers.
PRICE RELATIONSHIPS BETWEEN FUTURES
AND CASH MARKETS

As a general rule futures prices tend to be highly
correlated with the spot price of the deliverable
security. All futures hedging strategies rely on this
price relationship: it is because futures and spot
prices are highly correlated that futures contracts can
serve as temporary substitutes for cash transactions.
Price relationships between futures and underlying
spot markets can be explained using arbitrage pricing
theory, which is based on the premise that two
different securities that can serve as perfect substitutes should sell for the same price. To apply this
principle to the pricing of futures contracts, note that
buying a futures contract substitutes for buying and
holding the underlying security. Arbitrage pricing
Hieronymus [1971, chapter 4] tells of the arrest of
nine prominent members of the Chicago Board of Trade
following the enactment of the Illinois Elevator bill in
1867. That bill classified any contract for the sale of
grain for future delivery as gambling, except in cases
where the seller actually owned physical stocks of the
commodity being sold. The sections of the bill classifying futures contracts as gambling were repealed in the
next session of the Illinois legislature, however, and the
exchange members never came to trial.

theory would thus predict that the futures price
should just equal the price of the underlying security
plus any net carrying costs.
The Cost of Carry Pricing Relation

The cost of financing and storing a commodity or
security until delivery is called the cost of curry.
For agricultural and other commodities cost of carry
includes financing costs, storage, and any transaction
costs. The convention in financial markets is to apply
the term net carrying cost to the difference between
any interest earned on the security and the cost of
borrowing to finance its purchase.
The cost of carry pricing relation holds that the
price of a futures contract should be determined by
the spot price plus net carrying costs. Formally, the
relation is given by
F = S + c ,
where F is the market futures price, S is the current
spot price of the deliverable security, and c is the
cost of carry.
By definition, the difference between the futures
and spot price is basis. Thus, basis should theoretically be determined by the cost of carry when the
item being hedged is the same as the deliverable
security. Understanding the cost of carry model is
important in designing hedge strategies because it
allows the hedger to anticipate certain changes in
basis over the life of a hedge.
Convergence

Carrying costs fall as the futures settlement date
approaches because the time period a cash position
must be held grows shorter. This causes futures
prices to converge to underlying spot market prices
as the delivery date draws near. On the final day of
trading in a futures contract a futures transaction is
essentially equivalent to a spot transaction, so futures
prices should differ little from spot prices. Changes
in carrying costs can thus explain the phenomenon of
convergence. Because of convergence, basis tends to
decline systematically over the life of a hedge.

13

14
Paul [1985] discusses the design of contract settlement provisions.

24

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,
for example, that the price of gold futures exceeded
the current spot price of gold plus the cost of carry.
Arbitragers could earn riskless profits by buying

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986

gold in the spot market, simultaneously selling gold
futures, and subsequently delivering the gold on the
futures settlement date. This type of transaction is
known as cash and carry arbitrage because it involves
buying the cash commodity and carrying it until the
futures delivery date.
If the futures price were below the spot price, arbitragers would have the incentive to sell any cash
holdings of gold (or short gold in the cash market if
possible), buy gold futures, and then take delivery
to replenish inventories. In either case, arbitrage
activity should force futures prices to adjust to the
current spot price plus the cost of carry.
Now consider a cash and carry transaction in the
Treasury bill market. Applying the cost of carry
pricing relation to the pricing of bill futures is a
straightforward exercise because T-bills are discount
instruments that do not pay explicit interest. The
cost of carry (c) for a Treasury bill is therefore just
the interest expense associated with funding the purchase of the bill over the period it is held. For the
sake of simplicity suppose that the next delivery date
for Treasury bill futures is exactly thirteen weeks
away. If the current futures price exceeds the cost
of buying a twenty-six-week-bill plus the carrying
cost for the thirteen-week holding period, arbitragers
can earn riskless profits by simultaneously buying
twenty-six-week bills, selling nearby Treasury bill
futures, and then delivering the bills when the contracts mature. In the opposite case a profitable arbitrage would involve selling cash holdings of twentysix-week bills, buying Treasury bill futures, and
accepting delivery in thirteen weeks. A more detailed
description of how Treasury bill carrying costs are
determined follows.
The Implied Repo Rate

A repurchase agreement (more commonly called a
repo or RP) is a transaction involving the sale of a
security, usually a Treasury security, with a commitment on the part of the seller to repurchase the
security after a stated length of time. Repurchase
agreements can be viewed as short-term loans collateralized by securities holdings. The interest rate
paid by borrowers in the RP market is called the
repo rate. Because repurchase agreements are a primary funding source for dealers in government securities, the Treasury bill repo rate is typically used
to calculate net carrying costs for Treasury bill
futures.
The implied repo rate (irr) is a measure of carrying costs implicit in the futures-spot price relation-

ship. It is formally defined as the difference between
the invoice or delivery cost F implied by the futures
price and the current spot price S, converted to an
annualized rate of return. The formula for calculating the implied repo rate is
irr =

F-S 360.
S X t

The implied repo rate actually measures the rate of
return that could be earned by buying a Treasury
bill and simultaneously selling a futures contract
with a delivery date t days away. It measures implied
interest expense in the sense that it reveals the borrowing rate at which the gross return to a cash and
carry arbitrage transaction would just equal the cost
of financing that transaction.
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 because implied
interest expense would be greater than actual interest
expense. An implied repo rate below the actual rate,
on the other hand, would indicate that futures contracts are underpriced. Gendreau [1985] presents
indirect evidence suggesting that arbitrage keeps
actual and implied repo rates for Treasury bills in
alignment.
Two final observations are in order. First, the
effect that margin calls can have on anticipated financing costs has been ignored in this discussion; Stigum
[1983, chapter 14] and Kidder [1984] explain how
this affects the calculations. Second, although this
discussion has centered on applying implied repo
rate calculations to the pricing of Treasury bill
futures, the concept can also be applied to the pricing
of other types of futures contracts ; see Kidder
[1984] and Rebel1 [1984] for more examples.

References
Brewer, Elijah. “Bank Gap Management and the Use
of Financial Futures.” Federal Reserve Bank of
Chicago, Economic Perspectives 9 (March/April
1985), pp. 12-21.
Faux, Richard G., Jr. “Hedging Eurodollar Risk.” In
The Handbook of Financial Futures,. edited b y
Nancy H. Rothstein and James M. Little. New
York: McGraw-Hill Book Company, 1984, pp. 24755.
Figlewski, Stephen. Hedging with Financial Futures
for
Institutional
Investors. Cambridge, Mass.:
Ballinger Publishing Company, 1986.

FEDERAL RESERVE BANK OF RICHMOND

25

“Carrying Costs and Treasury
Gendreau, Brian C.
Bill Futures.” Journal of Portfolio Management
(Fall 1985), pp. 68-64.

Ronalds, Nicholas. “Contract Life Cycles for Selected
C M E M a r k e t s . ” Chicago Mercantile Exchange,
Market Perspectives 4 (August 1986).

H i e r o n y m u s , T h o m a s A . Economics of Futures Trading. New
York:
Commodity
Research
Bureau,
Inc., 1971.

Rothstein, Nancy H., and James M. Little. “The Market
Participants and Their Motivations.”
Handbook of Financial Futures, e d i t e d b y N a n c y
H. Rothstein and James M. Little. New York:
McGraw-Hill Book Company, 1984, pp. 115-37.

Kaufman, George G. “Measuring and Managing Interest Rate Risk: A Primer.” Federal Reserve
Bank of Chicago, Economic Perspectives 8 (January/February 1984), pp. 16-29.
Kawaller, Ira G. “Liability Side Gap Management:
Chicago Mercantile
Risks and Opportunities.”
E x c h a n g e , Market Perspectives 1 (August 1983).
“International Banking Facilities.”
Key, Sydney J.
Federal Reserve Bulletin 68 (October 1982).
“The Implied Repo Rate.” In
Kidder, William M.
The Handbook of Financial Futures,. e d i t e d b y
Nancy H. Rothstein and James M. Little. New
York: McGraw-Hill Book Company, 1984, pp.
447-66.
Koppenhaver, G. D. “Trimming the Hedges : Regulators,
Banks, and Financial Futures.” Federal Reserve
Bank of Chicago, Economic Perspectives 8 (November/December 1984), pp. 3-12.
Little, James M. “What Are Financial Futures?” In
The Handbook of Financial Futures, edited by
Nancy H. Rothstejn and James M. Little. New
York: McGraw-Hill Book Company, 1984, pp. 3566.

Silber, William L. “Marketmaker Behavior in an Auction Market: An Analysis of Scalpers in Futures
M a r k e t s . ” J o u r n a l of Finance ( S e p t e m b e r 1 9 8 4 ) ,
pp. 937-53.
Stigum, Marcia. The Money Market. R e v . e d . H o m e wood, Illinois: Dow Jones-Irving, 1983.
Rebell Arthur L. “Numerical Relationships of Cash
and Futures: Keys to Analysis of Hedge and
Speculative Strategies.” In The Handbook of
Financial Futures, edited by Nancy H. Rothstein
and James M. Little. New York : McGraw-Hill
Book Company, 1984, pp. 467-91.
Telser, Lester G. “Why There Are Organized Futures
Markets.”
Journal of Law and Economics 2 4
(April 1981), pp. l-22.
. “Futures and Actual Markets: How They
Are Related.” The Journal of Business 5 9 ( A p r i l
1986), pp. 5-20.
Tompkins, Robert G., and Steven A. Youngren. “A
Comparison of IMM and LIFFE Eurodollar Futures.” Chicago Mercantile Exchange, M a r k e t
Perspectives 1 (June/July 1983).

Paul, Allen B. “The Role of Cash Settlement in Futures Contract Specification.” In Futures Markets:
Regulatory Issues, edited by Anne E. Peck. Washington, D. C.: American Enterprise Institute for
Public Policy Research, 1985.

Werderits, John R. “Synthetic Money Market Instruments: A Short-Term Investment.” Chicago Mercantile Exchange, Market Perspectives 1 (October
1983).

Powers, Mark, and David Vogel. Inside the Financial
Futures Markets. New York: John Wiley and
Sons, 1981.

“New Concepts Concerning FuWorking, Holbrook.
tures Markets and Prices.” American Economic
Review 52 (June 1962), pp. 432-59.

FROM TRADE-OFFS TO POLICY INEFFECTIVENESS:
A HISTORY OF THE PHILLIPS CURVE

Thomas M. Humphrey
The Federal Reserve Bank of Richmond is pleased to announce the publication
of From Trade-offs to Policy Ineffectiveness: A History of the Phillips Curve.
This 36-page monograph traces the evolution, public policy implications, and
criticisms of the idea of an inflation-unemployment relationship from David Hume
to the modern new classical school. Intended for advanced undergraduate college
students, this monograph may be used in courses in macroeconomics, money and
banking, and the history of economic thought. Copies may be obtained free of
charge by writing to Public Services Department, Federal Reserve Bank of
Richmond, P. O. Box 27622, Richmond, Virginia 23261.

26

ECONOMIC REVIEW, SEPTEMBER/OCTOBER 1986