PRICE EFFECTS OF FINANCIAL FUTURES TRADING
BY
DAVID COHEN
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1982
ACKNOWLEDGMENTS
I wish to thank my supervisory committee, Professors
A.A. Heggestad, G.S. Maddala and R. Chiang for their guid
ance and support. I wish to thank Professor F.D. Arditti
for providing the research idea which led to this disser
tation. I especially wish to thank Leslie Hill for typing
and editorial assistance above and beyond the call of duty.
TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENTS ........................................ ii
ABSTRACT ............................................... iv
CHAPTER
1 INTRODUCTION ...................................... 1
Background ...................................... 1
History and Development of Futures Trading...... 5
Introduction to Trading ........................ 10
Market Mechanics ............................... 25
2 THEORETICAL ASPECTS OF THE PRICE EFFECTS
OF FUTURES MARKETS ............................... 30
The Case for Stabilizing Futures Trading....... 31
Destabilizing Futures Markets .................. 49
Special Features of Treasury
Instrument Futures ............................ 54
3 REVIEW OF THE EMPIRICAL INVESTIGATIONS OF THE
PRICE EFFECTS OF FUTURES TRADING................. 59
Storable Commodities ............................ 60
NonStorable Commodities ....................... 64
Interest Rate Futures.......................... 68
4 METHODOLOGY AND RESULTS .......................... 78
Total Variance Analysis ........................81
Multiple Regression Analysis ................... 83
5 SUMMARY AND CONCLUSIONS .........................122
REFERENCES ............................................ 129
BIOGRAPHICAL SKETCH...................................... 135
iii
Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
PRICE EFFECTS OF FINANCIAL FUTURES TRADING
By
David Cohen
August, 1982
Chairman: Arnold A. Heggestad
Major Department: Finance
There has been much concern voiced over the possible
spot market volatility effects of the new financial futures
markets, particularly in a study by the Federal Reserve
Board and the Treasury Department regarding Treasury instru
ment futures markets. This study is designed to provide
evidence on the spot price volatility effects of futures
trading in 90day Treasury Bills. The method of analysis
is to first identify periods of time that are roughly sim
ilar in their overall capital market volatility, but
differ in that one period is before TBill futures trading
began and its comparable period is after TBill futures
trading began. Next several econometric techniques are
used to estimate models of interest rate determination.
The estimation produces measures of spot TBill rate
volatility for each of the comparable periods which are
then used in a pairwise fashion to ascertain the spot price
volatility effects of futures trading.
The interest rate models come from the rather large
body of macroeconomics literature dealing with the formation
of interest rates. The econometric techniques span dif
ferent assumptions imposed on the models and each technique
provides consistent estimates of the model parameters under
the stated conditions. Further, simple analysis of daily
and weekly TBill rates is performed to provide continuity
with studies of futures market spot price effects in other
commodities.
The results of all the statistical tests suggest that
Treasury Bill futures trading does not increase spot market
volatility during relatively stable periods of capital
market activity, but is associated with increased spot
Treasury Bill market volatility during times when overall
capital market conditions are volatile. These results
indicate that Treasury Bill futures trading alone does not
increase spot market volatility, contrary to the hypothesis
that simply the existence of financial futures trading
destabilizes the underlying spot market.
CHAPTER 1
INTRODUCTION
Background
Futures trading in financial instruments is a fairly
new occurrencetrading began in October 1975 at the Chicago
Board of Trade in Government National Mortgage Association
(GNMA) futures contracts. Since then, financial futures
trading has grown very quickly, both in volume of trading
and in types of instruments traded. At least five futures
exchanges now offer trading in some type of financial
futures contract (Chicago Board of Trade (CBOT), Interna
tional Monetary Market (IMM) of the Chicago Mercantile
Exchange (CME), Amex Commodities Exchange, Commodity
Exchange, Inc., and New York Futures Exchange), such as
90day and one year Treasury Bonds, 30day Commercial Paper,
and two types of GNMA certificates. Various futures ex
changes in the U.S. also have requests before the Commodity
Futures Trading Commission (CFTC) to open trading in more
financial futures. Volume figures for one of the most
successful contracts, the IMM's 90day TBill contract range
between 3,000 and 4,000 contracts per day.1 The CBOT's
longterm TBond futures traded over 2 million contracts in
1979. The range of contracts offered and trading volumes
1CME Statistic. Note that each contract is for $1 million
face value of TBills.
indicate that financial futures have a place in the current
economic environment.
The rapid growth of trading and proliferation of con
tracts across exchanges has not been well received in all
quarters. Particularly, the Treasury Department and the
Federal Reserve System are alarmed at the potential impacts
of financial futures trading on their activities. A
lengthy report, the Treasury/Federal Reserve Study of
Treasury Futures Market, cited the following concerns with
the Treasury Bill (TBill), Treasury Note, and Treasury
Bond (TBond) futures contracts:
1. Will there be an increase in spot interest rate
volatility from futures trading? Such an increase
in volatility could increase the cost of govern
ment debt financing.
2. Will the Treasury feel compelled to issue
securities simply to avoid "squeezes" or "corners"
in the corresponding futures market?
3. Can the exchanges and the CFTC effectively police
these markets to avoid attempts at manipulation?
(Treasury/Fed, 1979).2
The present study addresses the first of these issues.
Particularly, an empirical investigation of the impact of
2The second and third issues are the subjects of a paper by
Phillip Cagan (1981).
financial futures on the underlying spot markets in TBills
will be conducted. This is intended as a response to the
Treasury/Fed concern:
that futures trading in Government securities will
have a destabilizing effect on prices in spot markets
for these securities and that investors on whom the
Treasury normally relies to finance its debt may be
dissuaded from bidding in Treasury auctions if prices
become less stable, thus leading to higher yields
or costs to the Treasury. (Treasury/Fed, 1979, pg. 11)
The Treasury/Fed position is of great interest to
all potential and current users of financial futures mar
kets (as well as the exchanges themselves) since the CFTC
is withholding approval for some new contracts until the
Treasury/Fed are assured of no illeffects, and could with
draw approval for existing contracts if these agencies
present arguments against such futures contracts. Given
the apparent market acceptance of financial futures trading,
careful analysis of the impact of these markets on the
spot markets is important to many economic agents. Thus
the empirical investigation carried out in this study is
of interest to the regulatory agency for futures trading,
the Fed, the Treasury Department, futures exchanges, and
financial futures traders and potential traders.
This study is designed to provide evidence on the
spot price volatility effects of futures trading in 90day
Treasury Bills. The method of analysis is to first identify
periods of time that are roughly similar in their overall
capital market volatility, but differ in that one period
is before TBill futures trading began and its comparable
period is after TBill futures trading began. Next several
econometric techniques are used to estimate models of
interest rate determination. The estimation produces
measures of spot TBill rate volatility for each of the
comparable periods which are then used in a pairwise
fashion to ascertain the spot price volatility effects
of futures trading.
The interest rate models come from the rather large
body of macroeconomics literature dealing with the forma
tion of interest rates. The econometric techniques span
different assumptions imposed on the models and each tech
nique provides consistent estimates of the model parameters
under the stated conditions. Further, simple analysis of
daily and weekly TBill rates is performed to provide con
tinuity with studies of futures market spot price effects
in other commodities.
The question of spot price volatility effects from
futures trading has been raised in other futures markets,
particularly onion and potato futures. Extensive Congres
sional hearings led to Public Law 85839 (1958), which
prohibits futures trading in onions, and although the po
tato futures has not been closed by Congress, it has three
times been subjected to Congressional scrutiny (85th, 88th,
and 89th Congresses). It is clear that adverse opinion
can close futures markets and it is important that such
5
opinion be founded on carefully collected empirical fact,
not on heresay or inappropriate statistics. See Working
(1960) on the evidence presented to Congress regarding
onion futures.
This study focuses on one of the new Treasury instru
ment futures markets, 90day TBills. This futures contract
is the most important (volumewise) of the Treasury futures
and one of the most successful contracts ever traded on a
futures exchange. Its success makes it the obvious choice
for the type of analysis presented here. An interesting
extension of this study would be to apply the methodology,
with appropriate modifications, to the other Treasury
instrument futures.
In the remainder of this first chapter the fundamentals
of futures markets and futures trading will be presented.
Chapter 2 will review the theoretical arguments regarding
spot price volatility effects of futures trading. In
Chapter 3 the previous empirical work on this question is
presented. Chapter 4 explains the methodology used in this
study and presents the results. Chapter 5 contains the
summary and conclusions from the results.
History and Development
of Futures Trading
Futures trading is a very old form of commerce. In
the United States, organized trading in futures contracts
dates back over one hundred years, but in other countries
futures trading existed over three hundred years ago.
Futures trading developed in Europe during the seventeenth
century medieval fairs, and probably earlier than this in
Japan and Holland. The Chicago Board of Trade (CBOT) is
the oldest commodity exchange in this country to have
supported futures trading. The CBOT, originally established
as a market place for grading, weighing and trading physical
commodities (grains), sanctioned trading in standardized
contracts for forward delivery in 1865, along with rules
governing margins, terms of payment and terms of delivery.
Today there are at least twelve exchanges on which
futures trading takes place in the U.S. alone. In some
years the volume of trading on the CBOT, the largest ex
change, exceeds the dollar volume of trading in stocks on
the New York Stock Exchange. Most modern exchanges are
organized as nonprofit membership corporations, ruled by
committees of trading members, and assisted by paid pro
fessional staff. The exchanges do not participate in
trading or in the influencing of prices in any way. The
exchanges are meeting places for the trading conducted by
these members for their own account and the accounts of
others. The exchanges are financed by fees and dues, as
well as other business enterprises such as renting space
and investments in portfolios of assets.
According to Working, futures markets developed where
a strong demand for hedging existed (Working, 1953b). This
is evidenced by data showing that the volume of open inter
est in grains moved with the volume of grain held commer
cially, and likely to be hedged. Further, across commod
ities, the open interest varies with the amount of the
commodity that is hedged. Successful introduction of a
contract therefore, may depend on the amount of hedging
interest that is attracted. But there is a twoway
connection: the liquidity of a market is improved by a
large volume of speculation, so to the extent that hedging
costs are lower the more liquid is the market, hedging
and speculating should be viewed as jointly supporting
the success of a particular contract.
In Chicago in the middle 1800's the demand for
hedging by merchants, warehousemen and processors of grain
was strong enough to make futures trading viable. Farmers
in the fertile areas around Chicago were producing crops
far in excess of local need. But without good transporta
tion facilities and storage facilities, grain rotted after
harvest and was scarce before the next harvest. Forward
contracts soon developed to stagger the arrival of grain
at the Chicago markets. With the opening of rail and barge
3Open interest is defined as the number of futures contracts
entered into and not liquidated by delivery or an offsetting
futures market transaction.
transportation, Chicago's prominence in the grain trade
increased. Those persons dealing in forward contracts
found them to be less than perfect instruments for trading
due to several factors:
a. The contracts were not for standardized qualities
and hence not very liquid.
b. Deliveries were unreliable.
c. Payment methods varied.
All of these factors caused the eventual development of
the standardized, guaranteed contracts that are today
traded on the organized futures exchanges. These contracts
are highly liquid and traded in an open, competitive
bidding atmosphere, which makes them more suitable for
the role they play in the marketing activities of most
hedgers as well as for most speculators.
Today active trading in futures contracts for over
fifty commodities exists; examples are interest rate futures
(Treasury Bills, commercial paper, Treasury Bonds, GNMA's),
foreign currencies, lumber and plywood, grains, porkbellies,
metals, beef, and frozen concentrated orange juice (Commod
ities, 1979). Some of these commodities have nine dif
ferent contracts for delivery in nine different months
(e.g., gold), while some have fewer (e.g., oats on the CBOT
are traded in only four contracts, May, July, September
and December). Organized exchanges are located in New York,
Chicago, Kansas City, London, Paris, Singapore, and
several other cities. Primary credit for the growth in
number of exchanges and number of commodities, as well as
the growth in volume, must go to the technological develop
ments in communications. The virtually instantaneous and
low cost transmission of trading data has reduced the costs
of trading dramatically since the origin of futures markets,
thus broadening the scope of useful participation in this
marketing institution. Futures exchanges today are large,
efficient, growing institutions with emphasis on safety and
innovations in trading.
Since the inception of futures trading, public dis
trust and misunderstanding has been evidenced by repeated
attempts at government intervention. In 1916 the Cotton
Futures Act was passed and in 1922 the Grain Futures Act
was passed, bringing futures trading under government regu
lation. In 1930 the Grain Futures Act was amended to become
the Commodity Exchange Act, which established the Commodity
Exchange Authority (now called the Commodity Futures Trading
Commission) to be the government's agent in the regulation
of all aspects of futures trading. This agency may provide
a valuable service to the futures trading industry by reas
suring the public of the government's interest in the safety
of their commitments and transactions in futures markets.
The financial futures markets began in October 1975
when the CBOT opened trading in GNMA pass through
4Another important piece of legislation is Public Law 85839
(1958) which prohibits futures trading in onions.
securities. Very shortly thereafter, in January 1976, the
IMM opened trading in 90day TBills. The CBOT followed
with 90day commercial paper and long term TBond contracts
in 1977. Later other exchanges opened trading in various
financial instruments, sometimes in direct competition with
existing contracts (Commodity Trading Manual, 1980).
Generally, these financial futures contracts follow
the same pattern of trading rules as other futures con
tracts. However, some contracts specify a delivery date,
a single day, rather than a delivery month, for the delivery
and settlement of contracts positions not closed out by
reversing transactions.6
Introduction to Trading
In this section a brief discussion of trading mechanics
will be presented, along with descriptions and examples of
hedging, speculating and spreading.
It is best to introduce futures trading by describing
what futures trading is and why futures contracts are
different from other forms of forward delivery contracts.
Futures trading is "trading conducted under special regu
lations and conventions, more restrictive than those applied
to any other class of commodity transactions, which serves
5Actually trading is in Collaterized Depository Receipts
for GNMA's.
6
See Powers (1973), Hieronymus (1971), Venkataramanan
(1965), and Goss and Yamey (1976) for more detail on
the history and development of futures trading.
primarily to facilitate hedging and speculating by promoting
exceptional convenience and economy of transactions"
(Working, 1953b). This definition requires elaboration.
Futures trading is trading in commodities for future deliv
ery, to be made at the maturity date, with payment to be
made upon delivery of the commodity, the price of such
futures commodity transaction determined at the date of
contract for delivery is entered, with no exchange of money
occurring at the time of agreement.7
Futures contracts are the vehicles for such agreements.
They are standardized, legal contracts between two parties
(one of whom is always the commodity exchange clearinghouse).
A person who wishes to own the commodity later is called
the buyer, while the person who wishes to make delivery
later is called the seller. Thus the buyer profits from
a price increase, the seller from a price decline.8' 9
7For most futures contracts this "date" is the entire month
that the contract matures in. For example, delivery of
wheat on a December contract can occur at any time in
December, the exact date being the seller's option. For
many interest rate futures (TBills on the CBOT for example)
the maturity date is a particular day.
8In reality, very few contracts are settled by delivery;
rather the parties typically reverse their positions be
fore the close of trading on their contracts. The last
sentence above is a better description of "buyers" and
"sellers."
9In commercial paper futures contracts, the short, or
seller, is obligated to deliver a cash loan while the long,
or buyer, is obligated to deliver contract grade commer
cial paper. In this market, the seller benefits from a
The buyer is said to be "long" and the seller is said to
be "short" in the futures market, just as an owner of physi
cal goods is "long" the goods while a person who has forward
contracted to deliver goods he currently does not own is
said to be "short" the goods.
While the definition by Working given above did little
to illuminate the nature of futures trading, it serves well
for distinguishing futures trading from other types of for
ward purchases and sales. Many people are familiar with
forward transactionsthe purchase of a home or car for
example, typically is not consummated in a day. Possession
of the home or car does not immediately follow the trans
action. Perhaps full or partial payment is made before
delivery, or perhaps the purchase is C.O.D. In business,
formal forward contracting is usual, wherein two parties
negotiate for the delivery of a certain item at a certain
time, place and price, with the posting of some performance
bond and agreement as to remedies for nonperformance. Such
agreements are formal forward contracts, but they are not
futures contracts, nor are they instances of futures trading.
As the definition states, futures trading takes place on
organized exchanges, during certain hours, by open outcry,
subject to government regulation. This trading takes place
fall in interest rates (a rise in price). This maintains
the usual cash market relationship of discount rate
changes to long and short positions.
only for the quantity, quality and type of commodity stated
in the highly standardized futures contract that the ex
change deals in. Contracts are further standardized with
respect to delivery location, method of payment and time
of delivery. Thus futures trading and futures contracts
are distinguished by the rigid standardization and regula
tion of the commodity involved and the method of trading.
By contrast, forward contracts are "personalized" to the
needs of the contracting parties, and negotiated privately
(Working, 1960).
Speculating
Speculation in futures markets means the assumption
of risk of price movements in a commodity, for which the
speculator has no physical use. The speculator takes a
long position (is said to "buy a contract") when he be
lieves that the futures price will rise. If it does rise,
when he reverses his long position by "selling a contract"
at the higher price, he profits. The difference in price
times the number of units traded is the speculator's pro
fit, less the trading commission. Algebraically, for a
long position,
p[Pff tf j. number of units pFnumber of]
Pr long t+n,h t,h per contract J contracts]
where P is the price of a futures contract at time t for
t,h
delivery at time h (the price paid) and Pt+n,h is the price
"c'n i
of the same contract n periods later (the price received).
For an opening short position, the profit is the negative
of the long position:
profit f Pf n umber of unit number of
short jt,h t+n,hj _per contract '"contract_
Some examples of speculation follow:
(1) A speculator takes a long position in two soybean
contracts at a price of $5.15 per bushel. Two
weeks later he 'closes' his position by selling
two contracts for $5.18 per bushel. Since a soy
bean contract is for 5,000 bushels (on the CBOT),
he has earned a profit before commissions of
three cents per bushel or ($.03) (10,000) = $300.
(2) A speculator sells one contract in 4year Treasury
Notes (on the IMM) for 9012 (price is in per
centage of par, denominated in 64th's). Some
weeks later, but before the maturity date, she
closes per position by purchasing one contract
for 9112. Since the contract size is $100,000
face value, her profit is (1%)($100,000)
= $1,000, a loss of $1,000.
In the definition of futures trading given above, it
was stated that no money is exchanged at the time the
agreement is entered. However, a performance bond must
be deposited with the member through whom the individual's
trading is conducted. This deposit has the misleading
name 'margin.' Both the long and the short must post margin.
Each day the individual's margin account is credited or
debited by the amount of profit or loss for that day in
his position. This is called "marking to market." Should
the margin account fall too low (below the maintenance mar
gin level), the individual receives a margin call. Con
versely, the individual may withdraw excess margin. Minimum
margins are set by the exchange offering the contract;
typically margins are five to fifteen percent of the con
tract value. Margins are set so low due to the daily
resettlement procedure and the fact that exchanges set
limits on the amount of price change that will be tolerated
each trading day. If a contract's price "moves the limit,"
further trading is suspended for that day. Daily reset
tlement and limits on daily price changes mean that a low
margin, or rather a low performance bond, will serve to
remove the private incentive of traders to default on
contract obligations.12
Hedging
In its textbook sense, hedging involves the initiation
of simultaneously offsetting positions in the actual
10Individual brokers set their own margins for their cus
tomers. Typically these are significantly higher than
the required margin set by the exchange, and they vary
depending on the customerbroker relationship.
""Variable limits" go into effect if a commodity's price
moves the limit on three consecutive days. These limits
are generally 150% of the original limits.
1iargin requirements may often be satisfied by depositing
interestbearing securities (e.g., U.S. Treasury Bonds)
with the trader's broker, rather than cash. See Sandor
(1976) for more details on speculative activity.
commodity and the futures contract for that commodity. The
goal of such a strategy is to eliminate any price risk
associated with inventory held (short hedging), or with
input needs (long hedging). This section will discuss the
mechanics of this textbook approach to hedging in financial
futures. For a broader and more complete description of
hedging behavior see Working (1962).
Short hedgers in financial futures are those whose
actuals position would be adversely affected by a rise in
interest rates (a fall in bond prices). If interest
rates rise, prices of financial futures contracts
fall, so a short position in futures profits. This off
sets the loss in the hedger's commercial business due to
the rise in rates. Banks, insurance companies and cor
porations with current holdings of bonds, corporations with
future borrowing needs, banks that will be selling Certifi
cates of Deposit (CD's), builders with upcoming mortgage
needs are all examples of firms with short hedging possi
bilities.
Long hedgers are those whose profits would be reduced
if there was a fall in interest rates (a rise in bond
prices). If interest rates fall, futures prices of finan
cial instruments will rise, so a long position would gain
if interest rates fall. This gain on a long futures pos
ition would offset the adverse impact of a fall in rates
13Note that the definitions of long and short positions are
reversed for commercial paper futures contracts.
on the long hedger's commercial business. Insurance com
panies and pension funds with regular futures inflows of
cash to be invested in financial investments could hedge
the risk of declining yields with a long futures position.
Securities dealers with forward commitments to deliver
bonds or bills at fixed prices could also hedge the risk
in their short actuals position with a long futures position.
As an example of a long hedge in interest rate futures,
consider an insurance company executive that expects a cash
14
inflow of about $100,000,000 in one month. This money
will be invested in long term U.S. Treasury Bonds, currently
yielding 8.42% on 20 year, 8% bonds. This is a current
market price of $9,600,000 for $10,000,000 face value of
the bonds. Fearing a decline in yields over the monthlong
period until he can purchase the bonds, he takes a long
position of 100 contracts in long term TBond futures on
the Amex Commodities Exchange at a price of 9508
($9,525,000 for $10,000,000 face value) or a yield of
8.57%.15 By month end, yields have declined to 8% on the
cash market for 20 year, 8% TBonds (selling now at par
= $10 million), while the future price has risen to 9908
($9,925,000). The gain in the futures position offsets
exactly the increased cost (lowered yield) of the actual
14This example is drawn upon a nearly identical one present
ed by F.D. Arditti in a set of notes on futures contracts.
15Prices are stated in percentages of par. 9508 is 95
and 8/32% of par = $9,500,000 plus 8/32 of 1% = $9,525,000.
TABLE I
LONG HEDGING EXAMPLE
Cash Market
Current
Time
One Month
Hence
Cash market yield
of 8% 20year
bonds is 8.42%
(9600, or
$9,600,000 for
$10,000,000 face
value)
Cash market yield
declined to 8%
(10000, or
$10,000,000 face
value). Buy
$10,000,000
worth of TBonds
Futures Market
Futures price is
9508 ($9,525,000
for $10,000,000
face value), or a
yield of 8.5%.Buy
100 contracts
Futures price rose
to 9908
($9,925,000); yield
declined to 8.09%.
Sell 100 contracts
Opportunity loss = $40,000
by waiting one month
Basis change = 0
Gain = $9,925,000 $9,525,000
= $40,000
Net cost of bonds = $10,000,000 price
paid less $40,000 gain in futures =
$9,600,000.
Net yield to maturity is 8.42%.
Basis is defined as cash price minus futures price.
Basis*
024 or
$75,000
024 or
$75,000
bonds, as detailed in Table 1. The net cost of bonds is
$9,600,000, or a net yield to maturity of 8.42 %.
The example details a highly simplified hedging oper
ation. The hedge worked 'perfectly' in that futures price
movements exactly offset cash market price movements. Thus
the cash price and yield at the time the hedge was placed
were the same as the net price and yield at the time the
hedge was lifted. Such an outcome is rarely observed,
and a shorthand method of describing and predicting hedging
outcomes is used to handle more realistic (complicated)
hedging opportunities. The basis is defined as the differ
ence between the cash price and a particular contract's
futures price, at some point in time. The basis column in
Table 1 shows the basis at the two trading times in the
long hedging example. In that example, the zero change
in the basis resulted in a realized price equal to the in
itial price. The basis change then shows the difference
between the realized price and the initial price.
Another example, this one for a short hedging opera
tion, will further illustrate the basis and its importance.
Suppose a firm expects to have need for about
$1,000,000 in shortterm capital in one month, and so is
planning to borrow on a discount basis at a commercial bank.
The bank charges the firm 1% above the prime rate current
at the time of the loan. The prime rate now is 11%, so
the firm would receive $970,000 for a 90day note promising
to pay $1,000,000.16 The firm fears a rise in rates and
so hedges its future need for funds by selling a 90day
TBill contract on the IMM at the current futures price of
8800. This price is the IMM Index, which is the differ
ence between 100 and the annual discount on TBills. The
market value of this contract is then
($1,000,000) (1.00 .12(90/360)) = $970,000
One month later, the firm borrows $1,000,000 at a dis
count rate of 13%, for a loan proceed of $967,500. The
firm buys back its futures contract at the current IMM Index
of 87.6 (or a market value of $969,000). As Table 2 de
tails, the firm's net cost of borrowing is 12.6%, or a loan
proceed of $968,500. The basis changed from zero at the
start of the hedge, and declined to 0.4 (or $1,000) when
the hedge was lifted.
If the basis had remained at its initial value, (zero
in this case), the hedge would have worked perfectly, as
in the example in Table"1. However, the basis here moved
against the short hedgerthe cash price declined relative
to the futures priceand so the short hedger "lost." Of
course, his gain in the futures market partially offset
his opportunity loss in the cash market, so the hedge had
some success. If the hedger was actively and accurately
16The bank charges 12% to the firm, which is a 3% quarterly
rate, or a discount of $30,000 on 1,000,000 principal.
~~1
C:
ci
TABLE 2.
SHORT HEDGING EXAMPLE
The firm recog
nizes a future
need for about
$1,000,000 in one
month. Could
borrow at 12%
(discount) today.
$970,000 proceeds,
IMM index= 88.0.
Firm borrows
from bank at 13%.
Proceeds =
$967,500. IMM
Index = 87.00.
Futures Market
Firm sells, ane
futures contract
at 88.00. iMhrket
value = $970,000,
implies rate is
12%.
U_fl (?
Basis*
0.00 or
$0
Firm buys back its 0.4 or
futures conr actat $1,000
87.00, or a'market
value of $969,000
Opportunity Loss = $2,500
Gain = $1,0001
Net proceeds = $967,500 plus $1,000 gain = $968,500.
Net cost of borrowing (annualized discount) = 12.6%.
Basis is defined as cash price minus futures price.
Cash Market
Currently
One Month
Hence
forecasting the basis at the initiation date of the hedge,
a net 12.6% borrowing cost might well have been what he was
trying to achieve.
If the basis would have improved, that is if the fu
tures price would have fallen by more than the cash price
(say to 86.40) the short hedger would have "profited" (by
$1,500 = futures gain ($4,000) opportunity loss ($2,500)).
His cost of borrowing would have been less than the original
4
12%; 11.4% = [$1,000,000 971,500 net proceeds] x 1,000,000
x 100%].
Algebraically, the net proceeds received (net price
received) by a person engaged in a short hedge is
inii futu re final
final cash + initial futures future
net proceeds proceeds value value
By adding and subtracting the initial cash price,
initial cash initial
net proceeds = pric + final basis basis
The formula gives the net price paid by a long hedger, since
the price he pays must be the price received by the short
hedger, who takes the opposite side of the transactions
(this assumes no trading costs).
This formula makes clear that a narrowing basis hurts
the'short hedger, while a widening basis improves his
position. Prediction of basis changes, rather than interest
rate (price) changes, becomes important as the hedger trades
in price risk for basis risk. Hedging operations which
take the anticipated basis changes into account, called
"anticipatory hedging" by Working (1962), are really hybrid
operationspart hedging on price level and part speculation
on basis (Working, 1962). Note that a hedger may "unwind"
his hedge whenever the basis change is anticipated to be
unfavorable and bear the costs of storage until time for
the actual transaction.
Spreading
A third type of market participant is the spreader.
This person trades on the difference between futures prices
at two different points in time, between related futures
contracts, or between similar contracts on different ex
changes. For example, if in July the futures price for
90day TBills contract maturing in September is perceived
as too low relative to the same contract due in December,
a spreader would sell the December "expensive" contract
and buy the September "cheap" contract. If, as he expects,
the September price rises relative to the December price,
he gains as his long position has larger profits (smaller
losses) than his short position has losses (gains) if the
prices move up (down).
To add some numbers, on July 1 let the September TBill
price be 88.00 and the December price be 92.00, implying
market values of $970,000 and $980,000 respectively. The
spreader sells the December, buys the September, or he
buys the spread at 4.00. If at the end of July the
September contract is at 90.00 and the December is at 93.00,
he has profited because the spread has risen to 3.00. The
gain from reversing the spread is 1.00, or $2,500, calcu
lated as follows:
gain on September = 90.00 88.00 = 2.00 or
975,000 970,000 = $5,000.
loss on December = 92.00 93.00 = 1.00 or
980,000 982,000 = $2,500.
net gain = $5,000 2,500 = $2,500.
As with hedging, the spreader trades on price relations,
not on price levels. The key to a spreader's success is
in predicting relative price changes. His trading strategy
in interest rate trades such as the example.above may be
based on implied forward rates from term structure curves,
knowledge of trends in economic factors or knowledge of
the forward rates in the forward market. Spreaders are
thought to bear less risk than speculators, and achieve
smaller potential gains per spread. Note too that they pay
more commissions since each simple spread involves four
17,18
transactions.
17"Butterflies" or spreads of spreads require eight trans
actions in total and generally this type of trade is made
only by traders on the exchange floor who pay low trans
actions costs.
18There are other types of spreads, such as between two
contracts for different goods (e.g., a short in commercial
paper against a short in TBills) undertaken when the spreader
feels the price relation is out of line.
Market Mechanics
As noted above, futures trading is conducted only by
members of the exchange and all trading is by public outcry
during specified trading times. As trades are made, an
observer makes the prices known by posting them on a quo
tation board. Instantaneously these prices are wired across
this country and to several foreign cities.
When a person wishes to trade, he calls his broker
who in turn relays the order to his firm's floor broker.
The floor broker tries to execute the trade as it is stated
in the order. Orders may be simple such as "sell two
December TBills at market" meaning sell two contracts for
December delivery of TBills quickly, at the best price the
market will offer, or more complicated, stipulating the
time of executive, or a combination of trades to be executed
at certain price relations. The quality of the floor broker
depends on his ability to execute orders at favorable
prices. Trading is facilitated by a type of speculator
called a scalper. The scalper seeks to buy on price dips
caused by selling pressure and sell on price bulges caused
by buying pressure. Typically a scalper holds an open
position (long or short) in a contract for only a short time,
and performs no analysis of underlying economic factors to
guide his trading. A scalper engages in many transactions
per day, trading on the smallest of price moves. The
liquidity of the market is dependent on scalpers; hedging
costs are much lower in markets with active scalping which
absorbs the shortterm pressures of large orders, keeping
bidask spreads low. Once the order is executed it is
communicated verbally to the trader, and later in writing
from his broker. Sometimes execution can be so rapid that
a trader learns of execution within a minute of placing
the order.
At the end of the trading session, member firms trans
mit all executed orders to the clearinghouse, the usually
separate corporation that performs services much like the
banking system's clearing operations. Each exchange has
its own associated clearinghouse, and the members of the
exchange are all either clearinghouse members or are affil
iated with a clearing member. The clearinghouse becomes
the "seller's buyer" and the "buyer's seller" for each
transaction in the exchange, thereby facilitating reversal
of positions.
When a buyer buys, a seller must sell. These two
traders are acting for themselves or their clients. At the
end of the day, however, the clearinghouse interposes itself
between the traders, taking the long side of the seller's
trade and the short side of the'buyer's trade. Then to
close a position, either the buyer or the seller merely
reverses his original transaction in the market. That
afternoon, the clearinghouse finds that it has offsetting
positions for all traders who have closed out and merely
needs to settle their accounts for that day's price moves
(all previous days' price moves having been settled as they
occurred). For example, X buys 1 corn contract for $2.75.
Y is the seller. The next day X closes his position, not
by locating Y and negotiating, but merely by entering a
sell order in the market. Another trader takes up X's
offsetting order to sell. Say the price is $2.80. The
clearinghouse was short to X's original long and long to
Y's short. Now X closes out and the clearinghouse goes
long to X, in the process losing $.05 to X. But Y's pos
ition has declined $.05, so the clearinghouse is even on
X's and Y's trades (as well as everyone else's), has paid
X off, and will continue carrying Y's position until he
closes out.
At the maturity date of the contract, some traders
will still have long or short open positions. The clear
inghouse facilitates the delivery process by notifying
shorts that they must deliver and assigning delivery to the
oldest outstanding long positions on record. If disputes
arise between shorts and longs over delivery, the clearing
members for each side meet and resolve the dispute. Very
few disputes are not settled in this way.
A final function served by the clearinghouse corpora
tion is to guarantee performance of its members. All the
financial assets of the members are pledged in the per
formance of any of its members. The clearinghouse is
clearly central to the safe, efficient functioning of the
futures market, and the chief instrument by which the fu
tures market provides the secondary market liquidity that
makes it a valuable financial institution.19
Special Features of Financial Futures
Treasury bonds and certain other financial futures
have special delivery mechanics which should be noted. The
contract grade on the CBOT is $100,000 face value of a
noncallable 8% coupon TBond with at least 15 years to
maturity, or a callable 8% bond with at least 15 years
to the call date. If a bond of better than contract grade
is delivered, the deliverer receives a price premium, and
if a lower grade is delivered,the buyer receives a discount
from the futures price on settlement day. Premium and dis
counts are based on years to maturity and coupon rates.
The TBill contract is simply $1,000,000 face value of
90, 91, or 92 day TBills, with discounts for the two longer
maturities.
Referring to the CBOT TBond contract, a short deliver
ing a 10% TBond with 18 years to maturity would receive a
premium. This premium is computed as a factor which re
flects the price per dollar of the delivered bond at the
8% contract yield to maturity. For this bond the factor is
1.187. Thus if the futures price on settlement day is 9416
19See Powers (1973) and Sharpe (1978) for more detailed
discussions of market mechanics.
(94 and 16/32%), the short invoices the long $94,500 (1.187)
= $112,171.50 for $100,000 face value of the 10%, 18 year
TBonds.20
Another feature of financial futures, which is opposite
to some of the agricultural futures, is the changing char
acter of the actual commodity relative to the futures con
tract over the life of a hedge operation. The underlying
interest rate instrument gains value as time passes, ceteris
paribus, while some agricultural commodities decay (lose
value) as time passes, ceteris paribus.
This chapter has presented the fundamentals of future
trading and futures markets, with special reference to
financial futures. Chapters 2 and 3 describe the impor
tant theoretical and existing empirical investigations of
the spot price effects of futures trading, respectively.
These first three chapters provide sufficient background
for the presentation of the original work in this disserta
tion. The methodology and results are presented in
Chapter 4. Chapter 5 contains the summary and conclusions
of this study.
20
It should be noted first that this premium/discount
feature is the same concept as in the agricultural futures
contracts, and as in those contracts, the futures price
will track the (possibly changing) cheapest delivery
instrument contract as maturity draws near.
CHAPTER 2
THEORETICAL ASPECTS OF THE PRICE
EFFECTS OF FUTURES MARKETS
For futures trading to have any price effects on the
related cash market it must impact on the decisions of
demanders and suppliers of the cash good, since the cash
price is the outcome of supply and demand decisions by
handlers, producers and consumers of the good. Suppose
that futures market participants were "merely speculators,"
whose activities consisted only of betting with one another
on the outcome of a spot price at some future date. Suppose
that the economic agents involved in one way or another with
the actual commodity took no notice of the speculators'
activities. Clearly, while someone may object to such
futures markets as promoting gambling, there could be no
objection based on ill effects in the actual commodity
market, since there would be no effects.
Of course futures markets are not as described above.
There are real effects associated with futures market
trading because handlers, producers and users of commodities
frequently use futures markets in at least two ways:
1. They take positions in futures contracts to hedge
their actuals1 positions based on the futures price. Of
1Actual here means physical interaction with the good,
either current or contemplated.
30
course they may also take speculative positions, but this
part of their use of futures markets may be lumped in with
pure speculatorspersons with futures positions but no
current or contemplated actuals positions.
2. They observe futures prices and hence these enter
the information set that they use in making their decisions
about their actuals positions. These two channels are not
mutually exclusive; both may be operating in a given market
at the same time.
This chapter will describe the theoretical arguments
presented in the literature concerning price effects of
futures trading in light of the above channels through which
futures markets may operate. It will be convenient to
discuss first the theories concerning futures trading in
which there are beneficial effects on spot price volatility,
and then the counterargument showing potential negative
effects.
The Case for Stabilizing Futures Trading
The classical economic argument regarding the benefits
of speculation may be traced back (at least) to J.S. Mill:
These dealers [speculators] naturally buying things
when they are cheapest, and storing them up to be
brought again into the market when the price has become
unusually high; the tendency of their operations is
to equalize price, or at least moderate its inequal
ities. The price of things are neither so much de
pressed at one time, nor so much raised at another,
as they would be if speculators did not exist.
(Mill, 1848, sections 4 and 5)
This beneficial impact of speculation on price sta
bility rests on the assumption that speculators can foresee
price movements well enough on average to move supplies into
a more efficient intertemporal configuration. Before con
sidering the counterargument, it is necessary to find the
implications of this theory for our discussion of futures
trading.
Futures markets are distinguishable markets in several
respects, all of which contribute to the facilitation of
speculative activity by lowering transactions costs. First
futures markets are highly public and competitive in organ
ization. In fact these markets may approximate the ideal
of being "perfectly competitive" as well as any market.
Futures prices, volume of trade, and other important statis
tics are published often, and futures and spot price quotes
are immediately available. Futures prices are determined
by sellers and buyers of futures contracts in an open outcry
forum in a centralized location. There are typically numer
ous traders on both sides of each contract, the largest
group being speculators called scalpers and day traders,
who with equal ease take either side of a contract depending
on their forecast of very shortterm price movements.2
These traders provide a degree of "liquidity" to partici
pants in futures markets that is not found in other
2Note that one reason given for the demise of certain
futures markets has been the lack of a large body of such
traders.
marketing structures (Working, 1977). This allows buy and
sell orders to be executed at very nearly the last recorded
transaction price. Secondly, the standardization of the
traded commodity contract relieves participants of the
necessity of examining goods for differences in quality,
quantity and location, and is of course fundamental to the
difference between forward and futures trading. Third,
actual brokerage fees are low ($60 on a round trip TBill
transaction at the CME). Fourth, speculators may trade on
the futures market in accordance with their price predic
tions without the need to handle the physical commodity.
The economies that are obtained by the separation of the
handling function from the price prediction function offer
definitely lower costs of speculation than if speculators
had to store the good themselves, as in Mill's description
of speculation. Lastly, transactions costs are low because
capital requirements are smaller than in other forms of
speculation, chiefly due to the clearinghouse procedure.
The clearinghouse eliminates the possibility of default by
a futures contract holder who is losing money. The clearing
house is able to offer a guarantee of performance by forcing
daily resettlement of gains or losses on participants' mar
gin accounts, and because allowed daily price fluctuations
are limited to prevent large negative margin account bal
ances from developing. By these devices, only a small
performance bond, called margin, is required for traders to
take positions, as opposed to the much larger capital which
would be required to speculate by storing the physical
good.
Hence, futures markets contribute to speculative
activity by lowering the cost of speculation. But specula
tion in the sense described by Mill is not the same as the
term speculation referring to futures markets. It is clear
that in Mill's useage of the term, speculation "works" by
the physical handling of the good, while in a futures
market, pure speculators do not touch the good, nor would
some of them be able to even recognize it. Mill's concept
applied to a futures market requires that speculators
affect the temporal allocation of supplies of storable
commodities by providing actuals traders with the hedging
opportunities described in the introductory chapter, and/or
providing information about future spot prices.
Futures prices provide the handlers with the "price
of storage" in Working's terminology, and so influence
spot prices indirectly by influencing the storage decisions
of handlers (Working, 1948). Assuming speculators' informa
tion is correct, the futures price will guide the stockhold
ing that must be done over a crop year such that the harvest
time price is higher and subsequent spot prices are lower
than would be the case without futures markets. Hence the
seasonal spot price fluctuations are mitigated by the activ
ities of speculators. Note that there is a feedback from
handlers' storage decisions to the futures price. As crops
are moved into storage, speculators lower their estimate of
the future spot price and this provides a signal to handlers
as to the storage decision of others.3
For commodities which are not carried over from one
crop year to another, e.g. onions, futures markets can
reduce the seasonal price fluctuation by providing more
efficient regulation of flow from stocks by the establish
ment of an "equilibrium" spot price early in the storage
season. This reduces the endofstorage season spot price
changes necessary to exhaust supplies prior to the next
harvest. For commodity contracts that span the time period
between planting season and harvest, futures prices also
provide a guide to profits from production and thus influ
ence future supplies through producer response, in a manner
analagous to the storage response outlined above. The
accuracy and efficiency of the futures price in these allo
cative roles is the central empirical question in the
studies to be reviewed in the next chapter.
In summary, in order for futures market speculators
to affect spot prices of storable goods, the handlers of
the actual commodity must adjust their temporal allocation
of supplies to theconstellation of spot and futures prices.
3This is not intended as a dynamic analysis of the feedback
mechanism; speculators base their futures positions on
their estimate of the future course of prices which takes
the induced response of actuals handlers into account.
This aspect of futures trading, the separation of handling
and production from price speculation, is one of the primary
differences between futures market speculation and forward
market speculation or the speculation described by Mill.
As discussed above, it allows economies of specialization
and may lead to better temporal allocation of supplies.
However, there are elements of "speculation" in nearly all
forms of hedging, and there is a twoway link between the
futures price formation process of pure speculators and the
inventory decisions of hedgers in futures markets for
4
storable commodities. It is not possible to distinguish
hedgers, as the term is commonly used in futures markets,
from speculators, as that term is commonly used in futures
markets, in the concept of speculation which Mill described.
Ultimately, hedgers perform the intertemporal allocation of
supplies that is required to smooth prices over time, basing
their decision on the constellation of spot and futures
prices which are affected by speculators' futures positions.
This describes the mechanism by which futures trading
works to reduce the spot price volatility over a storage
season for storable commodities. Several studies have been
conducted to test whether this in fact is the case. These
studies are reviewed in the next chapter.
4Note that inventory is a broad concept here, referring
to both storage of produced goods in final form, and storage
of producable goods in the form of inputs to the production
process.
5If storage continues to the next crop year, this mechanism
is purported to stabilize year to year spot commodity prices
by guiding the crop carryover from year to year.
Two key links in the mechanism described above have
been left undiscussed. One of these links is the manner
and the degree to which the information gathered by specu
lators is reflected in the futures price. The second link
involves the quality of the information reflected in the
futures price. The first question, the informational con
tent of futures prices, has been investigated in several
papers, notably Grossman (1970), Cox (1976) and Danthine
(1978). Black (1971) has suggested that the major bene
fit of futures markets is in the price information they
provide. We leave the discussion of the second link until
later in the chapter when the case for destabilizing futures
trading is presented and concentrate here on the papers by
Grossmand and Danthine. The paper by Grossman, an impor
tant work in several respects, is not as directly relevant
or illuminating for the present study as is the paper by
Danthine, which builds upon Grossman's work. Hence, a
brief description of the Grossman paper is given first,
followed by a more detailed review of Danthine (1978) which
will highlight the potential for futures markets to be
stabilizing or destabilizing, exactly paralleling the
earlier work by Mill (1848) and Kaldor (1939).
6Kaldor presents the counterargument to Mill's view
of stabilizing speculation and his paper will be dis
cussed later in this chapter.
Grossman examines several models with differing char
acteristics as to the nature of the uncertainty about future
demand and supply and as to marketing institutions. His
interest is in deriving the conditions under which infor
mation collected by some firms is disseminated by obser
vable market prices in equilibrium. All firms fall into
one of two groups, informed or uninformed firms. There
are no speculators as such; all firms are producers of the
good in period one and stores of the good in period two.
Their single actuals decision involves how much of the
period one output to store. In a model with only spot
markets and uncertainty in both demand and output, a com
petitive equilibrium results where firms have different
expectations as to the futures spot price, depending on
whether the firm is knowledgable or not about some existing
information. Informed firms have exact knowledge of the
random component of output and some unbiased information
about the distribution of the random parameter in period two
demand. Uninformed firms have some subjective probability
distributions over the possible values of the two parameters.
Firms that become knowledgable have a better prediction of
the futures spot price, and hence have higher expected
profits from their storage decision.7 The current spot
price does not reveal all of the knowledgable firms' in
formation so these firms earn a return from their knowledge.
In Grossman's model all firms are riskneutral and hence
seek to maximize expected profits.
This result follows basically from the inability of one
statistic, the current spot price, to reveal to the unin
formed firms the two separate pieces of knowledge possessed
by the informed firms.
The introduction of a futures market into the model
changes this result. Grossman shows that with all firms
riskneutral, Pf = E[P2 I 0] where 0 is the information
possessed by knowledgeable firms, Pf if the current futures
price for delivery at time two, and E[P2 I 0] is the know
ledgeable firms' conditional expectation of the period two
spot price, at time one. That is, in this scenario all
information is revealed in the equilibrium spot price and
futures price, and uninformed firms make the same storage
decisions and have the same expected profits as do informed
firms.
This result depends critically on the assumption of
identical, riskneutral firms differing only in their infor
mation set. As Grossman shows, if the two classes of firms
have different riskaversion parameters which are known only
by the firms possessing them, the introduction of a futures
market will not eliminate the information asymmetry.
Intuitively this occurs because the futures price will no
longer reflect only the informed firms' information, but
also their unknown riskaversion parameter (Grossman, 1970,
8
Theorem 7). As in the situation with only spot
8Note also that differing storage cost functions would cloud
the information revealed by the futures price.
markets, there are too few statistics to reveal too many
unknowns.
In this model, the volume of futures trading reflects
the differences in information as well as the differences
in risk attitudes. Futures trading takes place only between
informed producers and uninformed producers. There are no
pure speculators and, ignoring differences in risk attitudes,
someone loses every time someone else gains on the futures
market. This is in contrast to a situation with pure
speculators where differences in initial positions can
cause trading that is mutually beneficial, even when risk
attitudes and expectations are identical.
Danthine presents a model with both pure speculators
and producer/hedgers, where pure speculators have some
information regarding the value of the uncertain parameter
n in next period's demand function,
Sd =D(p,n) < 0, 9D(p,>) > 0,
and g(n) is the probability density function. The output
of each identical firm is q = q(x) where x is the quantity
of input with unit price. This production function is
shared by the N producers with 2 > 0,  < 0. Danthine's
interest is in examining the role of futures markets as
information markets and risktransfer markets. All agents
are riskaverse and seek to maximize their expected (strictly
concave VonNeumanMorgenstein) utility function.
Let p represent the start of period 1 futures price
for delivery at the start of period 2, f represent the
number of unit futures contracts the producer sells, and
p represent the (random) spot price at the start of period 2
when the crop is harvested. Then the producer's problem at
period 1 is
(0) Max E[U((qf)p + p f x) I pf], s.t. q=q(x), x > 0
x,f
where locational and quality differences between the
farmer's output and the futures contract specification are
ignored. The expectation E is conditional on the only
(relevant) information the farmer possesses at the start
9
of period 1, the futures price. It is clear that the
futures price can impact on p by affecting input usage x
and hence forthcoming output and by influencing the farmer's
time 1 expectation of the forthcoming period 2 spot price.
Solving this problem requires consideration of first
order conditions only since the utility function and pro
duction function are both concave. Letting
(qf) p + p f x = y the first order conditions are
In this model there is no discussion of storage, but it
is clear that the producer could be called a storer, and
the storage cost function could be substituted for the
production function, giving the model broader interpre
tation with no change in the results of interest.
C6e ignore the possibility that x = 0 for a producer since
that would make him a pure speculator, a group to be con
sidered next.
(1) 0 = E[UI(y)p p] q1(x) E[U (y) I pf.
(2) 0 = E[U (y) I pf pf E[U (y) p p .
Substitute for E[U (y) I p ] from equation (2) into (1)
to yield
(3) pfql(x) = 1.
This equation (3) gives x as a function of p ,
(4) x = x(p f).
f)
with x l(p ) > 0. Examining y reveals it to be a function
only of p, f, and p by (4) and hence the expression in
(2) defines an implicit function in only f and p which
can be solved for f
(5) f = f(p ).
As Danthine notes, the expression x = x(p ) tells us
that the producer takes only the futures price into account
in his production decision and then acts as a speculator
if there is divergence between q* = q(x(p )) and
f* = f(p ), q* and f* the optimal output and futures posi
tion. 11 If q* > f* then the producer speculates in his
actuals position and if q* < f* he is speculating in his
futures position. Total supply is given by
See Feder, Just, Schmitz (1980) for a similar model
with this result.
(6) QS = Nq* = Nq(x(pf )).
Consider the optimization problem of each of n
identical speculators. Suppose speculator i has some
information v. regarding the value of T such that
1
I = V. + w. with w. N(0, w ) and the w. are i.i.d. That
1 1 1 W 1
is, speculators are assumed to collect unbiased infor
mation regarding the future demand and trade futures con
tracts on the basis of this information to
(7) max / W[(p(p T) p )b.] g(n I v., p ) dn
bi 
where b. is the number of unit futures contracts bought
by speculator i and g(n I v., p ) is the conditional density
for n. W is the strictly concave VonNeumanMorgenstern
utility function shared by all speculators.
f 'J
We are justified in writing p = p(p T) in (7) by
f
(6) above, and writing g(n v .i, p ) reflects a tatonnment
process wherein all traders make their final decisions based
on the market clearing p Again, any divergence that could
occur between producers' output and the contract specifica
tion is ignored in (8) so the closing futures price equals
the period 2 spot price.
The first order condition yields
(8) / W1[(p(Pf 'n) pf)b i][p(pf n) pf ] *
g( I Vi, p )dn = 0.
This integration yields an implicit function in bi, v. and
p f; hence,
(9) b. = b(pf, vi),
where by the assumption of identical speculators b(p vi)
is the common demand function for futures contracts.
Requiring the futures market to clear at price p we have
from (5) and (9):
f n f
(10) Nf(p ) Z b(p v.) = 0.
i=l
Assume that both the supply and demand for contracts are
monotonic in p (fl > 0, b1 < 0) to obtain:
(11) p = h(v J, 2 ...v' n) = h(V),
where V is the row vector (l, 2",..., n) of speculators'
individual information.
Equation (11) gives the futures price as a function of
the {vi} or of the expectation of the parameter n. The role
of the futures price in information dissemination is clear.
Some reflection of all individual pieces of information v.
are in p and producers and speculators both condition
their expectation of the future spot price on the statistic
f
p The futures price thus affects production and specula
tion decisions. The final equilibrium consists of p and
the functions h(V), b(p v.), f(p ) such that producers
and speculators have maximized their expected utilities
in equations (0) and (7) and the futures market clears
equation (10).
The futures price p = h(V) shows the potential for
information to be transmitted from speculators (information
specialists) to hedgers, who in turn base their production
(and/or storage) decisions on this price, q = q(x(p )).
The hedging function f = f(p ) shows the potential for risk
allocation through futures markets. This is a complete
model of the futures market/spot market interaction.
Although the equilibrium functions define and close
the model, Danthine provides a simple example which is
useful for understanding further the role of futures markets
and the potential for stabilizing or destabilizing effects
on spot price. Let q(x) = aX with a> 0, be the produc
tion function and D(p, n) = a cp+ with a, c > 0,
rnN(0, a2) be the demand function at time 2. Then (3)
implies p fa/2"X = 1 or since q(x) = aX q = f. ()
Solve Nq = D(p, n) to yield the equilibrium spot price at
time 2:
(12) p = a/c N c2 p + i/c f.
Now we can write the profit for a producer as
(13) y = (2 p f)(a/c N 2L p + 1/c?)
+ p f (p ,
and the profits for a speculator as
(14) z = (a/c N 2c p + 1/c r p )bi.
2cTI1
Let U(y) = e20y and W(z) = e2z be the farmers' and
speculators' utility functions. Then 20 and 20 are the
respective PrattArrow measures of (constant) riskaversion,
and each type of agent seeks to maximize2
U (y) = E(y) 0 var(y)
W (z) = E(z) .J var(z).
By the first order conditions for maximization and
the definition of y in equation (13) and z in equation (14)
above,
t2 f c2
(15) f = p pI p ) p ] and
2 26var (np )
(16) bi C2= [E (p. f) p .
20var (n li,p )
The market clearing condition (10) can be imposed on
(15) and (16) to yield the equilibrium futures price:13
(17) pf = 1 N N[a/c + 1/c E(%Ip )]
29var (np )
2 n P
+ arc % f (na/c + 1/c E E(nIvi,p )] ]
20var (nip, v) i=l
12
This requires that y and z are normally distributed, which
they are since both are linear in p which is normally dis
tributed.
13Recall that vi and v are identically and independently
distributed with G2 constant across speculators, so
w f f
var(Ip v) ar(np v.) for all i, j. Let
var(lp Vi) = var(nIpf, v)
2 2
Nc2 (l + N) N2 nc2l + N )
where M = + + .
20var (np ) 2 20var (nIp v)
As (17) shows, some information passes from speculators
to producers, and among speculators, by way of the futures
% f
price quotation through the terms var (nip v) and
n
1/c E E(iv.i, p ). In a twoway process discussed above
i=l
(page 14), this information feeds back on the production
decision of farmers, q = q(x(p )), then back again into the
expected futures spot price, etc. The question is how well
the speculators' information is disseminated by the futures
price. If the futures price reveals some of the relevant
information, and given the assumption that speculators'
information is unbiased, then the futures market is a
stabilizing force in the spot market.
Suppose that the futures price reveals all the specu
lators' information (i.e., is a sufficient statistic for
{vi}), then E(nIp ) = E(ijvi, p f). Farmers and speculators
have the same expected value of n. By the assumption of
normally distributed, independent v.i's with a common mean
and variance, a sufficient statistic for {vi} is E i.
i
Hence (DeGroot, 1970, Theorem 1):
2
E(nlp ) = E(iEv.) = and
naO + 02 E.
1 w 1
2 2
var (nip ) = var (liv., p ) = var (nlTI ) = w 2
1 1 2 2
no + 0
n w
Substituting these expressions into (17) yields the follow
ing expression for p f
f
(18) p = A + BZv. where
A = (No + nO) a/c
2 2
(N0 + nO)(N a + 1) + Na22 OJw Wj
2c c 2 2
no + o
2
nA w
B = 1/c T1 Ac
no2 2 a
n w
This is equation (11) for the example problem chosen.
Note that here, as in Grossman's paper, the futures
price is invertible in the information set of the informed
group only if the preferences of all individuals are
groupdetermined and the stochastic nature of the model
is as postulated. If there are differences in speculators'
riskaversion or their information quality (so that
owi wj) the futures price alone will not reflect all of
the information. For example, if'o 2 < o,2 it is desirable
wi wji
to be able to separate v. from vj, but one statistic, the
futures price, cannot reveal these separate pieces of
information.
In this parametric example it is interesting to note
that the variance of the spot price with futures trading
is less than without futures trading if 02 Uc> /n, that is
if the variance of the spot price given Ev. is less than
the unconditional variance (Danthine, 1978).14 This some
what obvious result highlights two facts of importance:
1. If speculators are not collecting valuable infor
mation,they do not reduce the spot price variance, although
they still serve an economic function by providing for risk
transferring.
2. More speculators with (unbiased) information are
generally helpful; although as noted above, if there are
differences in their reliability such that ew. i cwjthis
may not be true.
Destabilizing Futures Markets
This detailed review of Danthine's work highlights
the nature of the disagreement over the stabilizing effect
of futures trading. In the papers by both Grossman and
Danthine (as in Mill's and Working's models), speculators
are presumed to have accurate information of some content
and producers storesr) use the futures price as a statistic
revealing that information as well as a means of hedging
against adverse movements in the spot price.
To quote from one of Working's papers,
In the absence of futures trading the potential
holders of stocks are, in the main, only growers
and dealers who have storage facilities. In the pres
ence of futures trading, a dealer with stocks in
storage may hedge them, and when he does so, the
buyer of the hedging contracts becomes, from the
standpoint of price effect, the holder of those
14Note that this condition requires the futures price to
reveal all the speculators' information (Evi), which
it does in the example.
stocks. Hedging thus causes holders of futures
contracts to exert influence on the spot price.
[This view of futures trading shows] that the influ
ence of futures trading on spot prices must depend
roughly on the proportion of total stocks that is
hedged. . (Working, 1960, pg. 6)15
There is in this statement the clear possibility that
futures trading may be destabilizing or stabilizing, depend
ing upon the accuracy of the signal provided by the futures
price as to desirability of storage. Suppose there is
optimism among speculators with respect to spot prices in
the future. There would be increased demand for futures
contracts at the current futures price, which would then
rise. Actuals handlers would see an increased return from
storage and so increase their stockholdings. (Depending
on their risk preferences and other information, they may
choose to hedge all or part of their increased stocks.) If
speculators turn out to have been correct, the increased
stockholding will help stabilize the spot price by bringing
supplies back onto the market at the later (higher price)
period. This would then have been exactly the type of
speculation Mill envisioned. If, however, speculators were
wrong, the increased stocks would come back onto the mar
ket at a time of depressed spot price, having been shifted
from the earlier period. Spot price would then be destab
ilized and the inefficient temporal allocation in stocks
15Of course this statement needs to be broader, including
any unhedged stockholding that is encouraged by the
futures price quotation. Working recognized this;
see Working (1953b).
would have resulted in a social loss. The key is the accur
acy or inaccuracy of the information contained in the
futures price.
The standard argument in favor of accurate information
coming from speculators is simple: speculators who trade
on inaccurate information will lose money and be forced out
of the marketonly successful speculators will remain and
they do so only by being correctly informed as to future
spot market conditions (Kaldor, 1939). Hence futures mar
kets tend to stabilize spot prices.
However, this argument may not hold.16 There are two
important and related elements that need examining:
1. Losses by poor speculators lead to the survival
at any time of only successful (informed) speculators.
2. Speculation that generates profits is only related
to future spot markets conditions and so stabilizes spot
prices.
These two elements may both be false. As Kaldor sug
gested:
. the losses of a floating population of unsuc
cessful speculators will be sufficient to maintain
permanently a small body of successful speculators;
and the existence of this body of successful spec
ulators will be sufficient attraction to secure a
permanent supply of this floating population. (Kaldor,
1939, pg. 2).
Hence at any and every time there may be a large population
16
Some writers seem to claim that it does hold. See
Friedman (1953) pg. 175, and his note further down
the same page.
of uninformed or misinformed speculators, and speculators
as a group may continue to show losses indefinitely.
Further, it may be possible for successful speculation
to involve forecasting the expectations of other speculators
(the uninformed), and not the fundamental economic conditions
in the future spot market. Kaldor states: "So long as
they are numerous, they need not prove successful in fore
casting events outside; they can live on each other" (Kaldor,
1939, pg. 2). Farrell has attempted to derive the condi
tions under which profitable speculation necessarily re
duces spot price variability. He was unsuccessful at finding
a set of robust conditions, concluding that the propos
ition "is too strong to hold with any generality" (Farrell,
1966, pg. 192). It is possible then for futures markets
to destabilize spot prices by providing inaccurate signals
as to future spot market conditions. There appears no
logical grounds on which to reject this possibility so the
question must be examined by an empirical investigation.
It is useful to summarize the arguments presented thus
far as to the price effects of futures trading. Futures
trading encourages speculation (and hedging) because it
allows traders to take positions with very low transactions
costs. These low costs are due to (1) the public and
competitive nature of the markets' organization, (2) the
standardization of the contract, (3) the clearinghouse
mechanism which reduces capital requirements and the risk
of default. The low transactions costs allow trading to
take place on the basis of small differences in traders'
information sets and so encourages the gathering of infor
mation. The separation of the handling of goods from
informationseeking and riskbearing in futures markets
allows specialization in each area and hence could improve
the performance of both handlers and speculators. The
wide dissemination of direct market information by exchanges
and brokerage houses, and most importantly the information
contained in the futures price itself, could have a stab
ilizing effect on the spot price by improving the inter
temporal stockholding decisions of handlers of the good.
The possibility exists that futures trading may desta
bilize spot prices. Essentially this would occur if the
futures market provided the "wrong" price signal to handlers.
That is, if futures trading encourages speculation by
illinformed traders Cwho would show losses), the inter
temporal constellation of prices could encourage handlers
to make spot market decisions which destabilized spot
prices. It may be that such a situation could not persist
indefinitely. Studies have been conducted on the profits
of speculators but since these studies do not provide direct
evidence on the question at hand they are not discussed.17
17See Rockwell (1967) and Houthakker (1959). Basically,
there is no necessary connection between speculative
profits and stabilizing futures trading so these studies
do not provide the evidence sought here.
NonStorable Commodities
The theoretical arguments presented above did not
expressly consider futures trading in a nonstorable commod
ity. The question arises: What are the effects of futures
trading on nonstorable commodities?
Again, futures trading is unique because it is so
inexpensive to trade, particularly for pure speculators,
visavis other forms of speculation. By encouraging spec
ulation futures trading can increase the amount of informa
tion coming into the market, and the information is widely
disseminated by the exchanges and brokerage houses. This
information may lead to more efficient decisionmaking by
participants in the actuals markets by providing better
forecasts of future spot market conditions. There is then
the potential for reduction in the variance of the random
component of spot price changes with more of the price
change becoming "predictable" from the broader information
set. On the other hand, incorrect information can increase
the volatility of the spot price. For nonstorable com
modities the information aspect of futures trading is most
important.
Special Features of Treasury Instrument Futures
All of the arguments presented so far have concen
trated on the supply side of the spot market. However,
some markets may be more strongly influenced on the demand
side by a futures market. Consider the effects of a futures
market in a nonstorable good such as Treasury Bills.
Hedgers in this market are long hedgersthose persons with
an expected future demand for TBills who would be hurt by
18
a rise in price (decline in yield). For these hedgers,
the effects of a futures market hedge is to compensate them
for changes in the spot prices of TBills that may occur.
The term "compensate" here is used exactly as in demand
theory. If a person hedges his future desire for TBills
by purchasing TBill futures, gains (losses) in the actuals
position are, to some extent, offset by losses (gains) in
the futures position. But of course the future spot market
transaction may be of any size, depending on the spot
price at the time, hence only part of the loss or gain on
the futures transaction applies to the subsequent spot
market transaction and the rest is spread over the trader's
other purchases. Spot price increases are compensated by
an increase in income from the futures position gain and
spot price decreases are compensated at a decrease in
income from the futures position loss.
Assume that the spot market demand 'curves with and
without a futures market hedge can be described as linear
in quantity. As in standard demand theory the compensated
demand curve is steeper than the Marshallian demand curve.
If the two spot demand curves cross at the expected spot
price and the supply curve is taken as vertical with a
random shift parameter, Qs = S + E, then the situation is
18Ignoring crosshedgers who may use the TBill market to
hedge future planned borrowing in other markets.
19
described in Figure 1. As can be seen, any given random
shock e will result in a larger random shock to the spot
price along the demand curve with hedging in the futures
market. Let the equation of this demand curve be
P1 = a 1 blQ and let the equation of the demand curve
without futures market be P2 = a2 b2Q. Then V(P1) > V(P2)
since b1 > b2 and V(Q s) is presumed invariant to the
existence of a futures market.
P
sspot
E spot]
DEMANDwith futures trading
DEMAND
\,< v no futures trading
FIGURE 1
SPOT PRICE VOLATILITY WITH AND
WITHOUT TBILL FUTURES
19
Since the good is nonstorable this is a reasonable
formulation for a supply function if the production
decision must be made before the price is revealed. For
TBills we may further suppose very little "producer
response" to the information contained in the future
price, at least as a first approximation.
i
Of course, this effect operates only to the extent
that hedging is conducted on uncommitted forward demand for
the spot good. If long hedging only occurs when the hedger
has a commitment to purchase (for resale perhaps) a certain
amount of the good, and will purchase only that amount, the
offsetting gain or loss is totally reflected in the net
price paid for the predetermined amount of the good pur
chased. Note further that this does not negate the earlier
comments about the potential benefits of futures trading
due to information. The increased information may still
lower the variance of the unpredictable changes in spot
price by reducing the conditional variance of the random
shock E.
One last note on the theoretical papers concerning
the price effects of futures trading. Telser and
Higinbotham (1977) described futures trading as a sorting
of trades with respect to time. That is, futures markets
reduce the heterogeneity of the group of traders in each
time dimensioned market. They state that this effect may
reduce the dispersion of the distribution of spot market
price, but provide no compelling reasons as to why this will
occur. It seems as reasonable to expect just the opposite
result since a homogeneous group of traders might generate
a price that is less resilient to changes in underlying
market conditions than would a more heterogeneous group.
This concludes the review of the theoretical inves
tigations into the spot price effects of futures trading.
58
The next chapter provides a review of the more noteworthy
empirical studies on this question. These two chapters
provide the necessary background against which to present
the original work performed in this dissertation.
CHAPTER 3
REVIEW OF THE EMPIRICAL INVESTIGATIONS OF THE
PRICE EFFECTS OF FUTURES TRADING
In addition to the theoretical research into the price
effects of futures trading, several empirical studies have
been conducted to test for the influence of futures trading
on cash prices. Several of these studies, for example,
Working (1960), Gray (1963), Johnson (1973), Emerson and
Tomek (1969) and Hieronymus (1960) reviewed here, have
been concerned with the onion and potato futures markets.
These markets have come under attack for causing price
fluctuations so severe as to warrant their congressional
prohibition. Onion futures trading was outlawed in 1958,
and the potato futures market has been investigated several
times. Both of these goods are seasonally produced, stor
able commodities.
Other studies such as Powers (1970) and Taylor and
Leuthold (1974) are concerned with continuously produced,
nonstorable commodities. A third group of empirical
studies is from the interest rate futures markets. The
three reviewed here, Froeweiss (1978), Gardner (1980) and
1Onion futures are prohibited by Public Law 85839, August28,
1958, 72 Stat. 1013. The 85th, 89th and 92nd Congresses
convened hearings on potato futures.
59
Figlewski (1981), represent the existing empirical research
into the effects of futures trading on spot prices in the
interest rate futures area. For the most part these inter
est rate futures studies suffer from failure to account for
their incomplete specification of the determinants of cash
prices. Failure to "hold other things constant" lessens
the confidence one can have in the results of the studies.
The empirical studies discussed in this chapter are
representative of the work that has been done in this area
and provide a sufficiently complete background for appre
ciating the original work to be performed in this disser
tation. They will be presented in three groups: storable
commodities, nonstorable commodities, and interest rate
futures markets.
Storable Commodities
Onion futures trading was banned in 1958, after a per
iod of twelve years during which futures trading occurred
on the CME. Onion futures trading is important to study
because there are data from nofutures periods surrounding
a period with futures. This allows a better possibility
of controlling for other variables in analyzing the price
effects of futures trading. Holbrook Working (1960) con
ducted an extensive study of this market and concluded,
contrary to the Congressional findings, that futures trading
in onions did not increase the variation in spot onion prices.
Working looked at two measures of spot price volatility,
the average seasonal variability over the storage season,
about September to March, and the intraseasonal variability
of prices. Working separates the period 1930/31 1957/58
into three subperiods: 1930/311940/41, a period of no
futures trading, 1946/471948/49 and 1958/59, a period of
little hedging, and 1949/501957/58, a period of significant
hedging of stocks.2 This separation reflects the theoretical
consideration that futures market speculation affects spot
prices through the hedging behavior of holders of stocks.
The data reveal that the average seasonal price range
from September to March is smallest during the period of
significant hedging use of the futures market, while the
two other periods of nofutures market and of little
hedging show larger average cash price variation.3 The
Michigan prices show this pattern more strikingly as the
Michigan market is the most likely hedging market on the
CME due to Michigan's central location in the onion produc
ing geography. Comparing yearly total price ranges, the
data show that the years of significant hedging have con
sistently smaller price variation.
2"Significant" hedging is approximately 1520 percent of
estimated onion stocks held at the peak of the storage
season.
3Working used two different price series: U.S. average
prices to growers and prices to Western Michigan growers.
The two series show similar characteristics over the three
periods.
The end of storage price changes occur in February to
March and have historically been of relatively great magni
tude. This is because new crop onions are superior to old
crop onions so there is no carryover from one storage season
to the next harvest. Again the data show that years with
substantial hedging tended to have smaller price ranges
February to March than years of little or no hedging.
Comparison of monthbymonth cash price ranges in the three
periods shows that the end of storage price adjustment,
necessary to exhaust old crop supplies prior to the new
harvest, moved back in time to January in the period of
hedging from February or March during periods of no hedging.
Since the end of storage price adjustment regulates the
demand flow out of the stock of stored onions, the early
adjustment during the periods of hedging use of futures
markets allowed a smaller price adjustment to exhaust stored
onions before the harvest.
In summary, this study suggests that volatility of
the cash onion market did not increase due to the introduc
tion of futures trading. Rather, when futures markets were
used for hedging purposes, cash price variations, measured
several ways, seemed to be lower, contrary to the findings
of Congress which passed the law banning futures trading
in onions.
Gray (1963) and Johnson (1973) provided updates of
part of the analysis performed by Working on the cash onion
market. Gray found that the period 19581962 showed a
return to the type of average seasonal price variation
experienced before futures trading in onions became estab
lished. Since futures trading was abolished in 1958, this
evidence indicates that the decreased cash price variation
from 19491958 was all the more likely to have been a result
of futures trading, and not due to other factors that may
have been ignored.
Johnson updates Gray's paper with data from 19621968.
He finds that this nofutures period has an even smaller
seasonal price range than Working's period of substantial
hedging. Other analysis of weekly and monthly price ranges
show that, except for the year 1958, price variations have
been about the same in the period since the ban on futures
trading (19591968) as in the period of significant hedging
4
(19491957). His conclusion is that futures trading had
no effect on cash price variations.
In an early paper concerned with the price effects of
futures trading, Hieronymus (1960) found that futures
trading in onions did not increase the fluctuations in
the cash prices of onions. As did other researchers, e.g.
Working (1960) and Gray (1963), Hieronymus separated spot
price series on onions into periods of time during which
there were different amounts of futures trading. His result
4If the year 1931 is also omitted, weekly cash price varia
tion over the storage season from 19301968 has been
strikingly similar year by year.
on the seasonal variation in onion prices agrees with
Working and Graythe period of highest futures activity
had the lowest seasonal price variation. Other results in
his paper from regression equations modeling shortterm
price movements, show also that futures trading does not
increase cash market volatility in onions.
NonStorable Commodities
Much of the empirical work done on the question of
price effects of futures trading relates to seasonally
produced, storable commodities. Powers (1970) suggests
that the results of these studies may not be valid for non
storable, continuously produced goods and seeks to test this
on cash price data for live cattle and pork bellies for four
years prior to and four years during futures trading in each
commodity. He views variations in cash prices as composed
of systematic and random components, which are uncorrelated
by definition. Stating that futures trading in these types
of goods may affect the random but not the systematic com
ponents of variations in cash price, he employs Tintner's
"Variate Difference Method" (1940) to separate the two
components. His tests then require comparing the estimated
variance of the random element in price for the two four
year periods.
Note that Powers' separation of the components of
variations in cash price allows us to assign positive or
negative social value to the price effects of futures
trading. The systematic component arises from variations
in the underlying fundamental determinants of supply and
demand for the good. The random component is noise or a
random disturbance of price away from its equilibrium value.
Thus a decrease in the variance of the random element is
socially beneficial, while an increase is socially harmful,
leading to resource misallocation.
Power's results show that for both live cattle and
pork bellies the estimated variances of the random compon
ent were significantly lower in the period with futures
trading. These results hold when each of the four year
periods was split into two year subperiods. All of the
estimated variances from the futures trading periods were
significantly lower than from the corresponding prefutures
periods.
Powers argues that prices are more reflective of
systematic (fundamental economic) factors in the futures
trading period because of the improved information flow
to market participants in this period. He claims that the
only significant changes in market conditions between the
two time periods for these goods was the opening of futures
trading and hence futures trading is responsible for the
reduction in the random variation of cash prices he observed.
Taylor and Leuthold (1974) analyze annual, monthly,
and weekly variability in cash cattle prices for an eight
year period before and an eight year period after the in
itiation of futures trading in live cattle. This commodity
is not stored, in the usual sense, for any significant
time, and is continuously produced. Hence futures trading
does not impact through the hedging of stored commodity in
this market, but may affect the cash market through the
producerresponse mechanism described by Danthine (1978) and
through the informationgenerating aspect of futures trading.
The authors argue that the initiation of futures
trading was the most dramatic change in livestock marketing
over the sixteen year test period. The results of their
tests will then be directly attributed to futures trading.
Calculation of the annual average cash price variance
around the eight year average price revealed no difference
in annual variability between the two periods. Calculation
of monthly variability in cash prices showed the futures
trading period to be significantly less variable than the
prefutures trading period and a similar result appears
from calculation of the average monthly coefficient of var
iation for the two periods. The data for weekly variance
and coefficient of variation also showed this pattern.
They conclude that the cash live cattle market has
been less volatile since the initiation of futures trading.
Their explanation for this phenomenon runs (loosely) in
terms of the increased information, reduced transaction
costs, and reduced marketing costs that they feel are the
results of futures trading in a nonstorable commodity.
Cox (1976) focuses on the informationgenerating
aspect of futures trading. He develops a model based on
the Efficient Markets Hypothesis which leads him to
investigate theautoregressive structure of spot commodity
prices in periods with and without futures trading. His
hypothesis is that futures trading, by providing more infor
mation to more traders, will reduce the absolute size of
the coefficients b. in the regression equation:
n
Pt = b0 + Z b.P + ut
j=l1
where Pt is the current spot price, Ptj is the jperiods
past spot price, and ut is the random disturbance term. A
reduction in the absolute value of the b.'s is indicative
of more efficient spot price formation, with more of the
available information being reflected in the spot price at
each time t. Further, if this in fact is true, mechanical
trading rules based on past price behavior will be less
profitable as the b.'s approach zero.
The commodities Cox tests are onions, potatoes, pork
bellies, hogs, cattle and frozen concentrated orange juice.
Generally, the results are as hypothesized: for onions,
orange juice, hogs, pork'bellies the test b2 = b3 = ... bn
= 0 is rejected for the nofutures periods and not rejected
for the futures trading period, while one coefficient, b2,
remains significantly different from zero for cattle and
potatoes with futures trading.
Cox also tests for changes in the estimated standard
error of the regressions period. For all the tested com
modities only the onion market fails to show a decrease in
the estimated standard error, divided by the average spot
price to help control for overall price level changes,
when futures trading occurs versus the nofutures period.
Cox also tests a simple trading rule based on price pre
diction from past price behavior. Ignoring transactions
costs, the period with futures trading shows lower average
returns to the rule across the commodities and higher var
iances of returns than the nofutures period. Cox concludes
that futures trading has not destabilized spot price in
these commodities and has provided "more accurate signals
for resource allocation" than when there is no futures
market (Cox, 1976, pg. 1235).
Interest Rate Futures
GNMA futures began trading on October 20, 1975 on the
Chicago Board of Trade. Two papers have been written con
cerning the effects of this market on spot GNMA prices.
The first paper to appear was by Kenneth Froeweiss (1978)
in which he argued that futures trading had not destabilized
the spot GNMA market. The second paper, by Stephen
Figlewski, concluded the opposite.
Froeweiss used weekly GNMA prices from two time per
iods, May 30, 1973 October 15, 1975 and October 22, 1975 
December 28, 1977, to test the hypothesis that futures
trading increased spot price volatility. He estimated a
regression equation of weekly percentage changes in GNMA
spot prices on weekly percentage changes in tenyear U.S.
Government bond prices. The rationale for this regression
equation is that the tenyear government bond price changes
proxy changes in general bond market conditions, excepting
the influence of the new futures market. Hence any changes
in the regression relationship in the two periods is attri
butable to the futures market. The results show no dif
ference in the estimated coefficients of government bond
price changes in the two periods. Moreover, the estimated
standard error of the regression was smaller in the fu
tures trading period than in the earlier period. Froeweiss
uses this evidence to argue that futures trading has not
made the GNMA's spot market more volatile.
There are some statistical difficulties with the
method used to obtain these results. First, it is not at
all clear that a change in the slope coefficient has any
thing to do with the spot price volatility effects of
futures trading. No conclusion could be drawn from a rise
or a fall in this coefficient about the destabilizing
effects of futures trading without a considerably more com
plete model of GNMA spotprice determination, and an explicit
relationship of GNMA and tenyear government bond prices.
Secondly, and more importantly, the simple regression model
used has biased (and likely inconsistent) estimated standard
error of the regression, and it is not obvious what the
estimated slope coefficient and its standard error represent.
This may be seen by considering a simple onefactor returns
generating model (e.g., the CAPM).5
5The same result would hold for a multifactor returns
generating mechanism.
TYGB Sa
TYGB = a + XYG+ E or X T
GNMA = a + X GNMA+
= TYGB (l GNMA) + (n G )
8TYGB +TYGB TYGB
where TYGB = tenyear government bond return over the
week interval.
GNMA = GNMA return over the week interval.
X = the factor return premium (e.g., the market return
premium).
c, r = random disturbance terms, necessarily uncor
related.
a = return on the zerobeta asset.
8TYGB' ,GNMA = the response coefficients of the two
instruments to the single factor.
Froeweiss' regression equation is then interpreted
as a proxy variable approach, with X proxied by TYGB:
GNMA = TYGBy + p. An OLS estimation procedure applied to
this equation will yield yOLS as a biased estimator of
8GNMA 1
TGB5, and 2 u'u as a biased estimator of 02 where
TYGB n
u = GNMA TYGBYOLS. That is, the statistical analysis
on which Froeweiss bases his conclusions is not sound and
the results he gets are likely to be due entirely to overall
reduced bond market volatility which happened to coincide
with the futures trading period he chose visavis the
earlier period of nofutures trading that he examined.
Froeweiss conducted another set of tests using time
series methods. In one test, he regressed current GNMA
prices on the prices from the previous two weeks. Again
the slope coefficient show no significant changes, while
the estimated standard error is lower in the later period.
This too, is most likely a result of coincident lower over
all capital market volatility in the futures trading period
he used. The last test performed was a regression of the
current week's percentage change in spot prices on the
previous week's percentage change. This test showed that
the prefutures period sequence of percent changes were
correlated, while the later period showed no significant
serial correlation in the percentage spot price changes.
This result is interpreted as reflecting an increased
"efficiency" of the GNMA market in a capital market theory
sense.
Figlewski's study (1981) of the price affects of the
GNMA market focuses on a constructed series of monthly
spot price volatility, computed as
V [t (P p 1)2/N t
s=l /
where Ps is the spot price of GNMA's on day s in month
t and Nt is the number of observations in month t.
Figlewski computes this series for GNMA 8% and GNMA 9%
coupon bonds from January and February 1975 respectively,
to February 1979. He looks at these two instruments
because technical factors in the futures market resulted
in sometimes one and sometimes the other bond being the
delivery instrument.
He uses four types of factors to explain the Vt series:
(1) volatility in related markets, measured as Vt con
structed for tenyear government bonds and tenyear federal
agency bonds; (2) breadth and liquidity of the cash GNMA
market, measured as the volume of new issues of GNMA's
for the current month plus the volume of the secondary
market and the volume of new series for the future four
months; (3) the level of GNMA prices; (4) futures market
variables, such as average open interest for the month,
total trading volume for the month, and price volatility
of some GNMA futures contracts.
OLS regressions were run with Vt for GNMA 8's and
GNMA 9's as dependent variables. The volatility of govern
ment bonds was not useful in explaining GNMA volatility,
while the variables measuring the size of the GNMA market
had generally significant negative coefficients. That is,
volatility decreases as the size of the cash market in
6
creases. Average GNMA spot price was positively related
to volatility of the GNMA 8's, and was not a significant
variable for the GNMA 9's.
The variables of interest are the futures market var
iables. The open interest was significantly positive for
6The results show that for GNMA 9's the coefficient of
secondary market volume is significantly positive in some
regressions.
the 8's and the volume of trading was significantly positive
for the 9's. Futures price volatility was positively re
lated to spot price volatility.
Figlewski interprets this set of results as indicating
that futures trading causes increased volatility in the
spot GNMA market. Clearly, regressions such as this do
not allow one to draw conclusions with respect to causation,
and in this case most theoretical arguments would suggest
that the increased volatility of the cash prices would
cause the observed increase in trading activity. Figlewski
attempts to infer the direction of causality by two argu
ments. First,he claims that since the positive coefficients
on futures market activity occur in regressions with other
"explanatory" variables, the futures market activity is not
simply mirroring general bond market conditions. However,
as Figlewski states earlier, the low (near zero) explana
tory power of the related market volatility measure causes
him to drop it in the regressions which include futures
market variables. The only other variables that he includes
are size variables and average price. One might easily
argue that this is not a particularly complete set of var
iables from which to conclude that the futures market var
iables do not reflect other underlying causes of spot
price volatility.
Secondly, he argues that futures price volatility
should respond to the same factors as cash price volatility,
if the causality is from cash price volatility to futures
market activity. In other regressions performed he finds
that this is not so. However, there is no reason to expect
prices for future delivery to measurably respond to the
same factors as spot prices in his regression unless (1) the
spot prices are for instruments that are deliverable on the
futures contract. Figlewski does not indicate if his spot
prices are for deliverable instruments or not, and he
notes that only one instrument will generally be delivered,
that one not being determined until the delivery date,
(2) the costs of storage are reasonably stable, and of
course they become less stable as the spot and futures
prices become less stable, (3) his regression is fairly
well specified. Overall, Figlewski's statistical analysis
does not appear sensitive enough to tell us much about the
price effects of futures trading in GNMA's and his causality
arguments do little to justify his conclusion that futures
trading increased the volatility of spot prices. Further,
the real issue is the volatility effect of the introduction
of futures trading visavis nofutures trading, and on
this question Figlewski's results shed no light.
Gardner (1980) performed a set of tests on the TBill
market identical to those performed by Froeweiss for the
GNMA market. Gardner was somewhat more careful in his
choice of time periods, breaking down the data into several
time periods differing in their degree of average absolute
7Figlewski's regressions have adjusted Rsquared's between
0.3 and 0.57.
deviation of daily TBill rates. He thus tried to control
for other factors that might cause changes in spot price
volatility by comparing results from time periods of similar
volatility with and without futures trading. The period
January 6, 1978 to December 31, 1978 had about as large an
average absolute deviation as the January 1, 1973 to
January 5, 1976 prefutures period. (Futures trading in
TBills began on January 6, 1976 on the International
Monetary Market of the CME.) The period January 6, 1976
to December 31, 1977 had about half as much daily spot
rate deviation as the later period, and a third as much as
the earlier, nofutures period. Gardner suggests compar
isons of the earliest and latest periods will show the
effects of futures trading most clearly. Of course, there
is an obvious difficulty in choosing comparison periods by
their cash price volatility, and then testing for differ
ences in cash price volatility. It is likely that as much
evidence is covered up by this procedure as is uncovered.
Gardner's regression analysis consisted of running
percentage changes in spot TBill rates on the same measure
for spot CD (certificate of deposit) rates. The results
of this test show that the slope coefficient was nearly
the same in the prefutures period and the later futures
trading period (January December 1978), while it was
somewhat smaller in the (January 1976 December 1977)
earlier futures trading period. As noted in the discussion
of the Froeweiss paper, it is not clear what changes in
this coefficient measure. The estimated standard error of
the regression was lower in both futures trading periods
than in the nofutures period, but the later futures trading
period was higher than the earlier period. Note that this
regression is subject to the same criticism as the parallel
one in the Froeweiss paper.
We might note that the information on page 3 of
Gardner's paper reports the fact that the TBill market is
more than one and a half times as large as the CD markets
in terms of outstanding face value. This indicates that
the lower standard error of regression in the futures
trading period may reflect the increased information flowing
from the TBill futures market to the CD market, rather than
reflecting a stabilizing impact of futures trading on the
TBill spot market.
Gardner also performed a regression of daily TBill
rates on the previous two days' rates and found that the
onedayprevious coefficients were not larger (however they
do not appear smaller, contrary to Gardner's statement on
page 8) in the two futures trading periods than in the pre
futures period, while the twodayprevious coefficients were
not different from zero in the later periods, but it was
significantly negative in the prefutures period. Also,
the estimated standard errors are lowest for the lowest
volatility period (1976 and 1977), higher for the more
volatile 1978 period, and highest for the most volatile
1973 to 1976 period, exactly as one would expect, futures
trading or not.
The last set of regressions related daily percentage
changes in spot TBill rates on the previous day's percentage
change. The coefficient is significant for the prefutures
trading period, but not significantly different from zero
in the two periods with futures trading. The implication
is that the TBill spot market became more efficient in
a capital market theory sense after the start of futures
trading.
Overall, this study suffers from the same two problems
as does the Froeweiss study. First, how to control for
other factors besides the introduction of futures trading.
However, in this paper the cure may be as dangerous as the
disease. Secondly, a single proxy for market conditions is
not a satisfactory approach. Further, in this study there
is likely another problem more serious than in the Froeweiss
paper. Crosshedging opportunities may make the CD rate
respond to the introduction of futures trading in the same
way it can affect the TBill rate. Hence the first regres
sion analysis is even more suspect than the parallel
regression in the Froeweiss study.
CHAPTER 4
METHODOLOGY AND RESULTS
The review of theoretical arguments concerning the
spot price effects of futures trading, presented in Chap
ter 2, highlighted some key points:
1. Futures trading may affect spot 'price volatility
through its role as an information market.
2. Futures trading may affect spot price volatility
by affecting the responses of spot market participants to
spot market conditions, through its role as a hedging
market.
3. The overall effect of futures trading on the vol
atility of spot price must be resolved empirically.
This chapter presents the methodology used to investi
gate empirically the impact of futures trading in TBills.
The investigation is based on multiple regression analysis
of the determination of spot TBill rates drawn from the
macroeconomic literature on interest rates. Additionally,
simple analysis of the raw TBill rate series is performed,
paralleling earlier work on spot price effects of futures
trading in commodities (see Chapter 3).
The general approach taken is to recognize theory and
data limitations by specifying time periods of homogenous
capital market volatility and to perform statistical analyses
78
in reference to these time periods. This procedure pro
tects the results from the difficulties involved in failing
to "hold other things constant" in econometric work. As
noted in the discussion of the paper by Gardner (1980),
one must be careful in choosing a criterion for identifying
subperiods of homogeneous capital market volatility to
use in testing for futures trading effects. The ideal
criterion would be one that holds everything constant
except for the effects of futures trading itself and those
explanatory variables that are suggested by macroeconomic
theory and are available.
The best available criterion is a series of a measure
of volatility from some sector of the capital market that
is likely to be essentially unaffected by the presence or
absence of TBill futures trading. Two such series were
constructed for this purpose. For the first criterion
data from the Center for Research on Security Prices (CRSP)
data base was used to construct estimates of the variance of
daily stock market returns(New York Stock Exchange and Amer
ican Stock Exchange returns, dividend adjusted) for each
month from January 1970 to November 1980. From this series
four recognizable subperiods were distinguished. The period
September 1970 to April 1973 was a period of relative calm,
5
with an average estimated daily variance of 3.6 x 10
Only four observations fell outside a range of 1.3 x 10
to 5.9 x 10 which is a sample range one estimated
standard error of the mean value of 3.6 x 10. The period
May 1973 to October 1975 was one of relative instability
4
with an average estimated daily variance of 1.33 x 104
Only five observations are small enough to fit into the
pattern of relative calm in the first period.
The period November 1975 to September 1978 was a
period of relative calm in the stock market with an average
5
estimated daily variance of 3.76 x 10 Only six obser
5 5
vations fell outside the range 2.0 x 10 to 5.2 x 10
The final period, from October 1978 to November 1980 was
one of mixed volatility. The average estimated daily var
iance is 8.0 x 105 and ten observations would fit the
pattern of the preceding period of calm. There are 31
monthly observations in the first period, 30 in the
second period, 35 in the third period, and 27 in the last
period.
Data from the Federal Reserve System Board of Governors
on daily 10year government bond yields was used in the
same manner as the stock returns. Since there was no dis
cernible difference in the breakdown using this data series
instead of the stock market series, the four periods
described above were used in the subsequent research. The
data on TBond yields supported an extension of the fourth
period through April 1981.
TBill futures trading began in January 1976. The
"calm" periods September 1970 April 1973 and November
1975 September 1978 are on opposite sides of the date,
as are the more volatile periods May 1978 October 1975
and October 1978 April 1981. Thus, statistical
comparisons may be made for both relatively "calm" periods
and relatively "volatile" periods before and after the
introduction of futures trading in TBills.
The data series used in this chapter came from three
sources: daily TBill and tenyear government bond rates
are from the Board of Governors of the Federal Reserve
System, January 1970 through April 1981; auction day TBill
rates from Data Resources, Inc. (DRI), October 1972 Decem
ber 1980; monthly TBill rates (average of daily rates and
all other monthly observations from Citibank Database,
January 1980 to April 1981. The TBill rates are all cal
culated on a discount basis. The monthly series on TBill
rates is presented in Table 5 by subperiod, along with some
summary statistics. These rates are plotted, by period,
in Figures 2 through 5.
Total Variance Analysis
Testing for the effects of futures trading on the
volatility of the underlying spot price requires,of course,
a definition of volatility. As a first definition, con
sider the magnitude of raw fluctuations in price series
day by day. Such a concept of volatility implies two
things (1) there is some cost, social or private, that
increases with the magnitude of price fluctuations, and
(2) any activity that increases such fluctuations should
be evaluated for possible prohibition. Statistically,
there is a third implication changes in the magnitude of
these spot price fluctuations are due to the activity in
question, e.g., the existence of futures trading.
A test of the price effects of futures trading, given
that these three conditions are satsified, is based on the
estimated coefficients of variation of daily and weekly
TBill rates. The coefficient of variation is the ratio of
the sample standard deviation to the sample mean. This
measure of volatility allows comparison of volatility
between samples with different means to be made on a per
unit of mean basis. Use of the coefficient of variation
rather than the sample variance eliminates the bias that
could result from one period having a lower mean than
another and a lower absolute variance, while being rela
tively more volatile.
The results are presented in Tables 7 10. Tables 7.
and 8. show results from auction day TBill rates and their
first differences.1 Tables 9 and 10 present results from
daily TBill rates and their first differences.
Comparison of the coefficients of variation (c. v.) for
comparable ("calm") periods 1 and 3 in Table 7 and com
parable ("volatile") periods 2 and 4 indicate that the
futures trading periods had greater auction day TBill rate
volatility than the nonfutures trading periods. The daily
TBill rate data in Table 9 show the same pattern for per
iods 2 versus 4, but lower volatility in "calm" futures
trading period 3 than "calm" nofutures period 1.
Note that the auction day rates are from October 1972
through December 1980 only.
Tables 8 and 10 are based on the first differences of
the series in Tables 7 and 9 respectively. First differ
encing the data on TBill rates is another means of con
trolling for differences in the sample means of the raw
data in the form periods, as well as trends or nonstationar
ity in the TBill rate series. The Table 8 results indicate
that the variance of the change in auctionday rates is
lower in period 3 versus period 1, and higher in period 4
versus period 2. The results in Table 10 on first differ
ences of the daily TBill rates are similar.
Overall, this simple analysis presents mixed conclu
sions. When capital markets are relatively calm (periods
1 and 3), the presence of futures trading does not appear
to increase spot TBill rate volatility. When capital
markets are relatively volatile (periods 2 and 4), futures
trading appears to increase spot TBill rate volatility.
Of course, the confidence one can have in these conclusions
depends on both the faith one can have in the ceteris
paribus assumption and on the appeal of the definition of
volatility as the relative size of the fluctuations in the
spot TBill rate.
Multiple Regression Analysis
Consideration of these last two points leads to a
different test and a different notion of volatility.
Certainly the selection of similar time periods is only
a rough means of holding other things constant. A much
more fundamental means is through multiple regression
analysis which controls specifically for changes in impor
tant factors other than the existence or nonexistence of
futures trading. Application of a regression model of
interest rate determination to the separate time periods
allows one to attribute changes in the character of the
unexplained (nonsystematic) portion of interest rates
to the introduction of futures trading. Thus, the rele
vant concept of volatility is the volatility of the random
disturbance term in a macroeconometric model on interest
rates.
This concept is a particularly attractive one. Interest
rates are prices for the services of capital, and behave
much like other prices. That is, they are determined by
the aggregation of individual economic agents' decisions,
based on various information they may have about relevant
economic variables and relationships. When information
suggests changes in these variables, a wellfunctioning
capital market should experience changes in interest rates.
Lack of responsiveness in interest rates to changing con
ditions may be a sign of a severely inefficient capital
market. Controlling for such changes through multiple
regression analysis, coupled with the careful selection of
comparable test periods, gives one much more confidence in
attributing possible changes in the volatility of the
error term to the introduction of futures trading. If
futures trading increases the magnitude of the unexplained
spot rate fluctuations, it may be said to increase the
volatility of spot rates.
The variance and the coefficient of variation will be
used to measure the volatility of the random disturbance
term. The coefficient of variation is defined as the
ratio of estimated standard error of the regression to the
mean of the TBill rate for each period. As discussed above,
the coefficient of variation is a relative measure of
volatility and controls for differences in sample means
across time periods.
The macroeconomics literature contains several models
of the determination of interest rates which could be used
to test the hypothesis that futures trading increases the
volatility of spot TBill rates. These models fall generally
into two classes: those which are based on simultaneous
equation macroeconomic models of the entire (simplified)
economy, and those which are based on partial equilibrium
approaches to interest rate changes. Two models are used
2
in this study, one of each type. The first model is similar
to the one found in Sargent (1973), Levi and Makin (1978,
1980) and Bomberger and Frazer (1981), and is of the com
plete system type. The second model is similar to the one
in Okun (1963) and to several other models in the literature.
2Both models will be estimated using monthly data. The data
sources are as noted above (page 81 ); Tables 36 contain
the monthly TBill rates and summary statistics, by subperiod
Figures 25 plot the TBill rate series by subperiod.
The Sargenttype model will be discussed first.
Define:
yt as the log of real output
Yct as the log of real capacity output
Pt as the log of the price level for time t
t = t Pti as the inflation rate for time t
He as the expectation of H .
t t
mt as the log of nominal money balances
rt as the nominal interest rate on 90day TBills
zt as other exogenous macro variables
and consider the following three equation system
(1) Yt = YctY t t+ ult
(2) y = yt + a0 + al(rt + a2zt + u2t
(3) mt 0 + Yt + rt + u3t
Equation (1) is an expectations augmented Phillips Curve,
or an aggregate supply curve. This is the Lucas type supply
curve where deviations of real output from capacity output
are positively related to the error in the inflation fore
case so that y> 0. For a complete discussion see Lucas
and Rapping (1969) and Lucas (1973).
Equation (2) is an aggregate demand curve (IS curve),
where the deviations of real demand from capacity output are
related to the expected real rate of interest (al < 0). The
variables zt include fiscal policy variables.3
3The available monthly series for such variables are federal
debt outstanding and the federal surplus or deficit. Since
Equation (3) is a simple Keynesian portfolio balance
equation. The terms ult, u2t, and u3t are mutually uncorre
lated, mean zero disturbance terms. The endogenous vari
ables are yt, rt, Ht He and the exogenous variables are
mt, zt,' ct'
Solve the equations to get rt in terms of H the exo
genous variables, and the disturbances
(4) rt = [E0(l+y) + + YYct + a2(l+Y)zt
+ Y(Pt mt) (al Y+ Yal) t ult
+ (l+y)u2t + YU3t]
where 6 = al yf1 aly and pt1 was subtracted from both
sides of equation (3) before solving.
Equation (4) may be rewritten as
(.5) r = A + Ay m + ) + A2z + A3H +
0 1 ct t t 2 t 3 t t
1 y a2(l+Y)
where A 1 (a0(l+y) + yB0), A = , A2 
(a y + yal)
A 2 = uit + (l+y)u2t + u3t. t is
a random disturbance, presumed to be normally distributed
with mean zero.
Equation (5) is not a reduced form equation due to
e
the presence of the endogenous variable Ht, the expected
3the surplus/deficit variable had no effect on any results,
zt contains only debt outstanding. The variable Yct was
measured as the log of the trend in real personal dispos
able income from 1/65 to 4/81.
inflation rate at time t. Now impose the rational expecta
tions hypothesis
(6) H = E[H t
where 4t is the information set available to agents when
t
they form their expectations. Equation (6) says that et
is the mathematical conditional expectation of the inflation
rate, and in particular, forecast errors
(7) vt = Ht te
are uncorrelated with all elements of the set t". Equa
tions (5) and (6) comprise one of the interest rate models
used to examine the effect of futures trading on spot
price volatility.
The second interest rate model is taken from Okun
(1963) and Feldstein and Chamberlain (1973) although it
is representative of models in several other papers. (See
Pesando (1976), Levi and Makin (1978), Yohe and Karnosky
(1969), Feldstein and Eckstein (1970).4 The estimating
equation is
(8) rt = B0 + BILRMBt + B2 e + B3LFDt + B4LPDI
+ B5LPt + t
4All of these papers employ quarterly, semiannual, or
annual observations, generally ending prior to 1975. Note
that Okun's models do not contain inflation variables. His
data set contained quarterly observations from 19461959.
where
rt = 90day TBill rate
LRMBt = log of real monetary base
e
Ht = expected inflation rate
LFDt = log of federal debt outstanding
LPDIt = log of real personal disposable income
LPt = log of potential real personal disposable income
5
nt = normally distributed, mean zero random error.
Equation (8) is representative of several other interest
rate equations that have been estimated in the literature.
In general these models are based on partial equilibrium
analyses of the determinants of the interest rate, rather
than being based on a complete, if restrictive, macro
economic model as in equations (5) and (6).
The motivation for the inclusion of income and money
variables is essentially the Keynesian liquidity preference
function. The use of the money base variable rather than
money supply is due to the more direct control the Fed has
over the money base as a means of implementing policy
changes. The two income variables are designed to cover
two separate effects. The variable LPt is used to reflect
secular growth in output potential, while the variable
LPDIt recovers cyclical factors in interest rates.
5Okun defines potential output as actual GNP (1+ .032(actual
unemployment 4%)). This same computation is applied to
real personal disposable income to generate LP.
Okun argues that there are strong a priori grounds
for including both the level and maturity composition of
federal debt outstanding (Okun, 1963). Monthly obser
vations on the composition of federal debt are not avail
able, and the coefficients on the two components of federal
debt in Okun's paper are very close to each other. Each
coefficient is easily within one standard error of the other,
and it seems no harm is done by grouping the two components
into total federal debt outstanding.7
The expected inflation variable in equation (8) is
unobservable, as in equation (5). This model is completed
by attaching equation (6), and both models (5) and (6) and
(8) and (6) are estimated by identical methods.
Ordinary Least Squares Estimation
Two approaches are taken in estimating the systems
(5) and (6) and (8) and (6), ordinary least squares (OLS)
and instrumental variables (I.V.) estimation. The least
squares procedure is described first for both models. The
instrumental variables technique is described later as a
more general method of estimation.
6To measure the effect of the maturity structure he uses
two total debt componentsless than 5 years and more than
five years to maturity, and a measure of the average
maturity of the federal debt.
7Note that Okun did not find the average maturity of the
federal debt to be a significant determinant of TBill
rates.
Both approaches involve two stages of estimation.
For the first stage, rewrite (7) as
(9) lt = E[lt I Ut] + vt.
Consider that the expectation in (9) is taken to minimize
the mean square error of prediction. Then He is found as
the least squares projection of Ht on t". To implement
this idea empirically, regress Ht on a subset of t using
OLS
(10) f1t = t + ut".
e ^e
From (10) obtain an estimate of Ht' = Y
a subset of elements of t". Note that
^e
(11) Ht = et
where et is the regression residual from (10) and
cov(et,'t) = 0.
^
The requirements for 1e are that the residual error
^e
term et be serially uncorrelated and HI must be highly
correlated with Ht. In the present case, where the monthly
observation of the 90day TBill rate is the dependent
variable, the 90day inflation rate is the inflation rate
of matching horizon. However, it was not possible to form
a series Ht from equation (10) for the 90day inflation
rate with serially uncorrelated residuals. The procedure
8This is a result of overlapping horizons for the monthly
series of three month inflation.
used was to estimate equation (10) for 30day inflation
rates (annualized to match the annualized TBill rate
series). The set t included lagged values of the one
month inflation rate (t1 and t2), lagged values of growth
in the money supply MlA(t1 and t2), lagged TBill rates
(t1) and lagged growth rates of real personal disposable
income (t1). The data are all monthly observations ob
tained from the Citibank data base.
This procedure essentially assumes that the current
expectation of the inflation rate over the next three
months is the same as the expected inflation rate over
the next month. This assumption appears reasonable.
Table 11 presents the results of the regressions (10)
Ae
with t as described above. The series Ht was formed
for three periods: 1/657/71, 8/714/74, 5/7411/80.
These three periods were used to separate out the wage/
price controls period, 8/714/74. Note that over the
entire sample period the correlation of H with the actual
three month rate of inflation is over 0.80.
In the ordinary least squares approach, the series
^e
it is used directly in the estimation of equations (5)
and (8). The equations are estimated by the Cochrane
Orcutt procedure for the presence of firstorder autocor
relation. This procedure requires the strong assumption
^e e
that lt equals Ht ; otherwise the procedure suffers from
the errors in variable problem. The estimates from this
9Note that many researchers fail to mention this
procedure for equation (5) are presented in Table 12. The
estimates for equation (8) are presented in Table 14.10
Note in Table 12 that the coefficients display con
siderable variation across the four time periods. In par
ticular, the estimate of A while significantly positive
when estimated over the entire sample, changes sign in
period four and is not significantly different from zero
in any subperiod. The coefficient A2 behaves much the same
way. While the theory would suggest Al > 0, the expected
sign for A2 is not so clear. If increases or decreases
in federal debt reflect expansive and restrictive fiscal
policies, respectively, the expected sign is positive.
If changes in debt outstanding reflect tax revenue short
talls during downturns, the sign may be negative. Overall,
it appears that the latter effect is stronger, though the
former effect seems to be stronger of late. The coefficient
estimate on Hte is uniformly positive, as expected.
Several slight modifications of the two interest rate
equations were tried. The model (5) and (6) was reestimated
without the federal debt variable. The results are shown
in Table 13. The coefficient of expected inflation, A3,
is essentially unchanged in the four subperiods. The
9
problem. They construct an "expected inflation" and use
it directly in an interest rate equation with no reference
to the bias in their results due to the measurement error.
See, for example, Pesando (1976), and Feldstein and
Chamberlain (1973). For an example where the problem is
recognized, see Lahiri (1976).
1(he numbers in parenthesis in all tables are the calculated
tstatistics.
coefficient of (yct mt + Pti) is changed, however. It
is now positive in periods 3 and 4 (and significantly
greater than zero) and negative in period 2. Also, the
variance of the weekly money supply was calculated for
each month and this uncertainty variable was included as
a regressor for both models (5) and (8). There was very
little change in any of the coefficients, the Rsquared's
(unadjusted) were slightly higher, and there was no change
in the pattern of volatility behavior across the four per
iods when this variable was included. Lastly, the third
time period, 11/7510/78 was shortened to 1/7510/78,
reflecting the fact that futures trading actually began in
January 1976. As expected, the estimates from this shorter
time period had no effect on the measurements of volatility
for the third time period.
These results for both models can be used to test
the hypothesis that futures trading in TBills has affected
the volatility of spot TBill rates under the assumption
e e
that He = t The estimated coefficients of variation will
provide the evidence on the volatility effects of future
trading. As noted above, these coefficients are standard
ized measures of volatility that allow comparison across
samples with different mean values for the monthly TBill
rate. They are calculated as the ratio of the standard
error of the regression divided by the mean TBill rate for
each period. The results are presented in the table below
for the three regression models in Tables 12, 13, and 14.
Model
as in Table 12
as in Table 13
as in Table 14
C. V.
period 3
0.055
0.055
0.068
c. V.
period 1
0.130
0.127
0.108
c.v.
period 4
0.110
0.113
0.098
c.v.
period 2
0.091
0.091
0.071
The evidence in the table shows that for the rela
tively calm periods with and without futures trading, per
iod 3 versus period 1, the coefficient of variation is
uniformly higher for the nonfutures trading period, across
all three regression models. The reverse is true for the
comparable periods 4 and 2. The futures trading period has
uniformly larger coefficients of variation across the three
regression equations. Exactly the same result is obtained
from Ftests on the error variance estimates from the three
equations.
^2 ^2
Model ', 3/01
as in Table 12 0.26
as in Table 13 0.27
as in Table 14 0.59
*Values are presented as F
critical 2 ^2 critical
cii al 2 4/a2C 2 F*
F* e' e' *
1.84/2.39 3.51 1.92/2.53
1.84/2.39 3.64 1.92/2.53
1.92/2.53 4.59 1.96/2.62
.05/F .01 and are approximate.
It is important to note that these results are from
e
regression models that are based on the assumption that Ie
equals the unobserved series Het The econometric technique
described in the next section gives consistent estimates
e e e
even if 1t does not equal H t.
tt
