Title: Price effects of financial futures trading
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Title: Price effects of financial futures trading
Physical Description: v, 135 leaves : ill. ; 28 cm.
Language: English
Creator: Cohen, David, 1953-
Publisher: s.n.
Place of Publication: Gainesville FL
Copyright Date: 1982
 Subjects
Subject: Commodity exchanges   ( lcsh )
Foreign exchange futures   ( lcsh )
Treasury bills   ( lcsh )
Genre: bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by David Cohen.
Thesis: Thesis (Ph. D.)--University of Florida, 1982.
Bibliography: Includes bibliographical references (leaves 129-134).
General Note: Typescript.
General Note: Vita.
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Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: alephbibnum - 000334774
notis - ABW4417
oclc - 09522523

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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
Non-Storable 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 90-day 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 occurrence--trading 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

90-day and one year Treasury Bonds, 30-day 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 90-day TBill contract range

between 3,000 and 4,000 contracts per day.1 The CBOT's

long-term 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 ill-effects, 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 90-day

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 85-839 (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, 90-day TBills. This futures contract

is the most important (volume-wise) 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 non-profit 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 two-way

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 85-839
(1958) which prohibits futures trading in onions.








securities. Very shortly thereafter, in January 1976, the

IMM opened trading in 90-day TBills. The CBOT followed

with 90-day 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 transactions--the 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 non-performance. 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 4-year Treasury

Notes (on the IMM) for 90-12 (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 91-12. 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 customer-broker 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
interest-bearing 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 up-coming 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 month-long

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 95-08

($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 99-08

($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. 95-08 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% 20-year
bonds is 8.42%
(96-00, or
$9,600,000 for
$10,000,000 face
value)

Cash market yield
declined to 8%
(100-00, or
$10,000,000 face
value). Buy
$10,000,000
worth of TBonds


Futures Market

Futures price is
95-08 ($9,525,000
for $10,000,000
face value), or a
yield of 8.5%.Buy
100 contracts


Futures price rose
to 99-08
($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*

0-24 or
$75,000


0-24 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 short-hand 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 short-term 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 90-day 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 90-day

TBill contract on the IMM at the current futures price of

88-00. 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 hedger--the cash price declined relative

to the futures price--and 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

operations--part 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

90-day 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 short-term pressures of large orders, keeping

bid-ask 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

non-callable 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 94-16



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 speculators--persons 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 counter-argument 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 counter-argument, 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 short-term 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 end-of-storage 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 the-constellation 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 two-way 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 counter-argument 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 risk-neutral 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

risk-neutral, 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, risk-neutral firms differing only in their infor-

mation set. As Grossman shows, if the two classes of firms

have different risk-aversion 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 risk-aversion 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 risk-transfer markets. All agents

are risk-averse and seek to maximize their expected (strictly

concave Von-Neuman-Morgenstein) 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((q-f)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

(q-f) 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 Von-Neuman-Morgenstern

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 2-c p + 1/c r p )bi.
2cTI1








Let U(y) = -e20y and W(z) = -e-2z be the farmers' and

speculators' utility functions. Then 20 and 20 are the

respective Pratt-Arrow measures of (constant) risk-aversion,

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(n|p 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 two-way 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 -W-j
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

group-determined and the stochastic nature of the model

is as postulated. If there are differences in speculators'

risk-aversion 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 market--only 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

information-seeking and risk-bearing 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

ill-informed 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.








Non-Storable Commodities

The theoretical arguments presented above did not

expressly consider futures trading in a non-storable commod-

ity. The question arises: What are the effects of futures

trading on non-storable commodities?

Again, futures trading is unique because it is so

inexpensive to trade, particularly for pure speculators,

vis-a-vis 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 decision-making 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 non-storable 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 non-storable good such as Treasury Bills.









Hedgers in this market are long hedgers--those 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 cross-hedgers 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 non-storable 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,

non-storable 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 85-839, 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, non-storable 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 no-futures 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 intra-seasonal variability

of prices. Working separates the period 1930/31 1957/58

into three subperiods: 1930/31-1940/41, a period of no-

futures trading, 1946/47-1948/49 and 1958/59, a period of

little hedging, and 1949/50-1957/58, 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 no-futures 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 15-20 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 month-by-month 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 1958-1962 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 1949-1958 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 1962-1968.

He finds that this no-futures 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 (1959-1968) as in the period of significant hedging
4
(1949-1957). 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 1930-1968 has been
strikingly similar year by year.








on the seasonal variation in onion prices agrees with

Working and Gray--the period of highest futures activity

had the lowest seasonal price variation. Other results in

his paper from regression equations modeling short-term

price movements, show also that futures trading does not

increase cash market volatility in onions.


Non-Storable 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 pre-futures

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

producer-response mechanism described by Danthine (1978) and

through the information-generating 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

pre-futures 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 non-storable commodity.

Cox (1976) focuses on the information-generating

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, Pt-j is the j-periods

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 no-futures 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 no-futures 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 no-futures 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 ten-year U.S.

Government bond prices. The rationale for this regression







equation is that the ten-year 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 spot-price determination, and an explicit

relationship of GNMA and ten-year 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 one-factor returns

generating model (e.g., the CAPM).5


5The same result would hold for a multi-factor returns-
generating mechanism.








TYGB- S-a
TYGB = a + XYG+ E or X T


GNMA = a + X GNMA+


= TYGB (l GNMA) + (n G )
8TYGB +TYGB TYGB

where TYGB = ten-year 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 zero-beta 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 vis-a-vis the

earlier period of no-futures 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 pre-futures 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 ten-year government bonds and ten-year 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 vis-a-vis no-futures 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 R-squared'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 pre-futures 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, no-futures 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 pre-futures 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 no-futures 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

one-day-previous 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 two-day-previous coefficients were

not different from zero in the later periods, but it was

significantly negative in the pre-futures 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 pre-futures

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. Cross-hedging 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 10-4

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 10-5 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 10-year 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 ten-year 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 non-futures 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" no-futures 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 auction-day 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 non-existence 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 (non-systematic) 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 well-functioning

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 3-6 contain
the monthly TBill rates and summary statistics, by sub-period
Figures 2-5 plot the TBill rate series by sub-period.








The Sargent-type 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 Pt-i 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 90-day 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 pt-1 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, semi-annual, 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 1946-1959.








where

rt = 90-day 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 components--less 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 90-day TBill rate is the dependent

variable, the 90-day inflation rate is the inflation rate

of matching horizon. However, it was not possible to form

a series Ht from equation (10) for the 90-day 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 30-day inflation

rates (annualized to match the annualized TBill rate

series). The set t included lagged values of the one-

month inflation rate (t-1 and t-2), lagged values of growth

in the money supply MlA(t-1 and t-2), lagged TBill rates

(t-1) and lagged growth rates of real personal disposable

income (t-1). 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: 1/65-7/71, 8/71-4/74, 5/74-11/80.

These three periods were used to separate out the wage/

price controls period, 8/71-4/74. 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 first-order 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
t-statistics.








coefficient of (yct mt + Pt-i) 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 R-squared'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, 11/75-10/78 was shortened to 1/75-10/78,

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 non-futures 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 F-tests 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




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