Title: On the performance of the GNMA hedge in volatile money markets
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ON THE PERFORMANCE OF THE
GNMA HEDGE
IN VOLATILE MONEY MARKETS





BY

JAMES WAYNE EARLE


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































Copyright 1982

By

James Wayne Earle


























To Anne, whose unselfish spirit and
extraordinary resilience give evidence
of how much there is yet to learn.
















ACKNOWLEDGMENTS


Acknowledgment and appreciation are extended to the

College of Business Administration at the University of

Florida, where this research originated, and to the

University of Alaska, Anchorage, where the project achieved

maturity and culmination.

Special thanks to Dr. Halbert C. Smith, who served as

chairman of my dissertation committee and provided guidance

throughout my doctoral effort; to Dr. Clayton C. Curtis, who

served as a member of my dissertation committee and first

suggested the subject matter of this research; and to

Dr. Stanley Su, who served as a member of my dissertation

committee and ably advised me in the area of my strong

minor.

















TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS . . . . . . . . . .. iv

LIST OF TABLES . . . . . . . ... .vii

LIST OF FIGURES . . . . . . . . ... . ix

ABSTRACT . . . . . . . . .. . ... .xii

CHAPTER I. BACKGROUND AND HISTORICAL PERSPECTIVE . 1

Basis for a Futures Market and for Futures
Trading in Financial Instruments . . . . 1
Development of an Interest Rate Futures
Market on the Chicago Board of Trade . . . 3
Advantages and Disadvantages of the New
Interest Rate Futures Market Over the
Existing Forward Market . . . . . . 7

CHAPTER II. THE CONCEPT OF HEDGING .. . . . 10

Rationale for Hedging . . . . . . .. 10
Factors Affecting the Performance of the Hedge .17
Theories of Hedging . . . . . . .. .19

CHAPTER III. THE MARKET ENVIRONMENT . . . .. .31

The Potential of the Prime Rate as a Proxy
for Uncertainty in U.S. Money Markets ... .31
The Concepts of Volatility and Stability in
U.S. Money Markets . . . . . . ... 36

CHAPTER IV. METHODOLOGY . . . . . . .. .39

Statement of Objectives . . . . . .. .39
Data Collection and Refinement . . . . .. .40
Critical Parameters . . . . . . ... 43
The Concept of a Moving Performance Parameter .47
Statistical Model . . . . . . . . 50

CHAPTER V. ANALYSIS AND INTERPRETATION . . . .. .62

The Performance of the 28-Day Hedge in the
Near-Term Contract . . . . . . .. .62









Page
The Performance of the Hedge Under Selected
Alternative Conditions . . . . . .. .84

CHAPTER VI. CONCLUSIONS AND RECOMMENDATIONS ... .95

APPENDIX A. SELECTED PLOTS DISTANT CONTRACTS . . .103

APPENDIX B. SELECTED STATISTICS DISTANT CONTRACTS . 129

REFERENCES . . . .. . . . . . . 134

SUPPLEMENTARY BIBLIOGRAPHY . . . . . . .. .136

BIOGRAPHICAL SKETCH . . . . . . . . .. .139
















LIST OF TABLES


Table Page

1. The Classic Short Hedge . . . . ... .13

2. The Classic Long Hedge . . . . ... 16

3. Summary of Current and Previous Findings
28-Day Hedge in the Near-Term Contract . 69

4. Selected Statistics for Multivariate
Regression . . . . . . . ... 75

5. Selected Statistics for Multivariate
Regression . . . . . . . . 76

6. Multiple Coefficient of Determination (r) 77

7. Selected Statistics for Multivatiate
Regression (Autocorrelation Corrected) . 82

8. Selected Statistics for Multivate Regression
(Autocorrelation Corrected) . . . .. ..83

9. Multiple Coefficient of Determination (r2) 83

10. Summary of Selected Hedge Characteristics
from the Viewpoint of the Classic Short
Hedger 28-Day Hedge, All Contracts . .. .85

11. Summary of Selected Current Findings 28-Day
Hedge in the Distant Contracts . . ... .90

12. Summary of Selected Hedge Characteristics
from the Viewpoint of the Classic Short
Hedger 126-Day Hedge, All Contracts .... .93

13. Summary of Selected Current Findings 126-Day
Hedge in the Distant Contracts . . ... .94

B.1. Selected Statistics for Multivariate
Regression 28-Day Hedge, 6-Month Contract
Dependent Variable b* . . . . ... .129


vii









B.2. Selected Statistics for Multivariate
Regression 28-Day Hedge, 6-Month Contract
Dependent Variable e . . . . . . 129

B.3. Selected Statistics for Multivariate
Regression 28-Day Hedge, 9-Month Contract
Dependent Variable b* . . . . ... 130

B.4. Selected Statistics for Multivariate
Regression 28-Day Hedge, 9-Month Contract
Dependent Variable e . . . . .. 130

B.5. Selected Statistics for Multivariate
Regression 28-Day Hedge, 12-Month Contract
Dependent Variable b* . . . . ... 131

B.6. Selected Statistics for Multivariate
Regression 28-Day Hedge, 12-Month Contract
Dependent Variable e . . . . ... 131

B.7. Selected Statistics for Multivariate
Regression 126-Day Hedge, 9-Month Contract
Dependent Variable b* . . . . ... 132

B.8. Selected Statistics for Multivariate
Regression 126-Day Hedge, 9-Month Contract
Dependent Variable e . . . . ... 132

B.9. Selected Statistics for Multivariate
Regression 126-Day Hedge, 12-Month Contract
Dependent Variable b* . . . . .. 133

B.10. Selected Statistics for Multivariate
Regression 126-Day Hedge, 12-Month Contract
Dependent Variable e . . . . ... 133


viii
















LIST OF FIGURES


Figure Page

1. Prime Rate Activity . . . . . ... 33

2. Market Period Indices . . . . ... .60

3. Weekly Average Change in Basis GNMA8/CBOT/
4 Week Hedge/3 Month Contract, 1976-1981 . 64

4. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/3 Month Contract,
1976-1981 . . . . . . . ... 71

5. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/3 Month Contract,
1976-1981 . . . . . . . ... 72

6. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/3 Month Contract
(Autocorrelation Corrected), 1976-1981 . 80

7. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/3 Month Contract
(Autocorrelation Corrected), 1976-1981 . 81

A.1. Weekly Average Change in Basis GNMA8/CBOT/
4 Week Hedge/6 Month Contract, 1976-1981 . 103

A.2. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/6 Month Contract,
1976-1981 . . . . . . . . . 104

A.3. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/6 Month Contract,
1976-1981 . . . . . . . ... 105

A.4. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/6 Month Contract
(Autocorrelation Corrected), 1976-1981 . 106

A.5. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/6 Month Contract
(Autocorrelation Corrected), 1976-1981 . 107









A.6. Weekly Average Change in Basis GNMA8/CBOT/
4 Week Hedge/9 Month Contract, 1976-1981 .108

A.7. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/9 Month Contract,
1976-1981 . . . . . . . ... 109

A.8. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/9 Month Contract,
1976-1981 . . . . . . . . . 110

A.9. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/9 Month Contract
(Autocorrelation Corrected), 1976-1981 . 111

A.10. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/9 Month Contract
(Autocorrelation Corrected), 1976-1981 . 112

A.11. Weekly Average Change in Basis GNMA8/CBOT/
4 Week Hedge/12 Month Contract, 1976-1981 113

A.12. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/12 Month Contract,
1976-1980 . . . . . . . . . 114

A.13. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/12 Month Contract,
1976-1981 . . . . . . . ... 115

A.14. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/12 Month Contract
(Autocorrelation Corrected), 1976-1981 . 116

A.15. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/12 Month Contract
(Autocorrelation Corrected), 1976-1981 . 117

A.16. Weekly Average Change in Basis GNMA8/CBOT/
18 Week Hedge/9 Month Contract, 1976-1981 118

A.17. Performance of Hedge Efficiency Index
GNMA8/CBOT/18 Week Hedge/9 Month Contract,
1976-1981 . . . . . . . ... 119

A.18. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/18 Week Hedge/9 Month Contract,
1976-1981 . . . . . . . ... 120

A.19. Performance of Hedge Efficiency Index
GNMA8/CBOT/18 Week Hedge/9 Month Contract
(Autocorrelation Corrected), 1976-1981 . 121









A.20. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/18 Week Hedge/9 Month Contract
(Autocorrelation Corrected), 1976-1981 . 122

A.21. Weekly Average Change in Basis GNMA8/CBOT/
18 Week Hedge/12 Month Contract, 1976-1981 123

A.22. Performance of Hedge Efficiency Index
GNMA8/CBOT/18 Week Hedge/12 Month Contract,
1976-1981 . . . . . . . ... 124

A.23. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/18 Week Hedge/12 Month Contract,
1976-1981 . . . . . . . . . 125

A.24. Performance of Hedge Efficiency Index
GNMA8/CBOT/18 Week Hedge/12 Month Contract
(Autocorrelation Corrected), 1976-1981 . 126

A.25. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/18 Week Hedge/12 Month Contract
(Autocorrelation Corrected), 1976-1981 . 127

















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


ON THE PERFORMANCE OF THE
GNMA HEDGE
IN VOLATILE MONEY MARKETS

By

James Wayne Earle

August 1982


Chairman: Halbert C. Smith
Major Department: Finance, Insurance and Real Estate

Since the Middle Ages, merchantmen have attempted to

insulate themselves from price change risk, a phenomenon

inherent in business transactions involving passage of time.

In no area of business endeavor has price change risk been

more acute in recent years than in the area of financial

securities.

A common means by which an investor can obtain a degree

of protection from price change risk is by "hedging" a cash

market position in financial futures. The brief existence

of the markets in financial futures has encompassed both

relatively benign and highly volatile money market

conditions. Such differing economic climates provide the

exigency for examining the performance of the hedge over

time.


xii









This research constructs hypothetical sample hedges

from the population of all possible hedges to make

inferences about the performance of the Government National

Mortgage Association (GNMA) hedge over time. Bivariate

regression is used to obtain estimates of two critical

measures of hedge performance, the risk-minimizing hedge

ratio and the hedge efficiency index. By computing each

respective measure over time in a manner similar to

computing a moving average, the long-term secular trend in

hedge performance can be observed. Multivariate regression,

utilizing as independent variables a series of descriptive

coefficients developed from the movement of the prime rate,

is employed in an attempt to link the measures of hedge

performance to uncertainty in the money market.

It appears hedge efficiency may be far more volatile

and significantly reduced in magnitude from that implied by

previous research. This is likely a result of uncorrected

positive autocorrelation in the error terms of the early

regression models. The erosion of the positive

change-in-basis characteristic of early markets has resulted

in a generally increased risk-minimizing hedge ratio over

that observed in previous research.

Efforts to bind the performance of the hedge to the

uncertainty indicators developed from the movement of the

prime rate prove largely disappointing but do reveal the

considerable masking of weakness in the performance of the

hedge due to violation of the critical nonautoregression

assumption of the regression model.
xiii
















CHAPTER I

BACKGROUND AND HISTORICAL PERSPECTIVE



Basis for a Futures Market and for Futures
Trading in Financial Instruments



Origin of a Futures Market

Modern futures trading has it origins in the ancient

trade networks and markets that developed in 12th century

Europe. At that time, merchantmen and farmers began

developing increasingly sophisticated means of reducing

their business risks by transferring those same risks to

other individuals. Advance pricing arrangements, which

would eventually evolve into the widespread use of both

forward and futures contracts that are common today, became

commonplace at the trade fairs and seasonal festivals of

medieval Europe. By 1570, the first organized futures

market in Western civilization was created with the

establishment of the Royal Exchange of London [13]. Almost

simultaneously, organized futures trading was beginning in

feudal Japan, where trading dealt exclusively with rice

contracts. Remarkably, the Imperial government supervised

trading with rules and procedures not unlike our own today.









Futures activity in America was initiated in 1851 when

the first contract was recorded with the Chicago Board of

Trade. The activity was compelled by risk considerations

not unlike those which faced medieval merchantmen in Europe

and Japan centuries before. Goaded by frequent market

crashes that could and often did wipe out their profits in

cotton and grain, merchants began selling their commodities

on a "to-arrive" basis. Importers, aided by the formation

of a trans-Atlantic cable service, began selling their

purchases while the goods were still at sea on slow-moving

surface vessels. This futures activity enabled the transfer

of price change risk to a middleman, the speculator, who

would assume that risk in hopes of commensurate profits.

By 1967 the Chicago Board of Trade had, since its

inauguration over 100 years earlier, developed primarily if

not exclusively as a grain exchange. Futures trading

activity had concentrated in wheat, soybeans, corn, and

oats. The unqualified success of the grain futures markets

understandably resulted in increased interest in the type of

price protection and speculative opportunities offered. In

1968, a new kind of diversification began with the

introduction of trading in iced broilers. Trading in silver

futures and the highly successful plywood contract was

initiated in 1969. By 1974 the Chicago Board of Trade, now

the world's oldest and largest futures market, was

experiencing record volumes. In the six years since the

initial diversification, the number of contracts traded had









increased from 4.7 million to 14.5 million [11].

Significant growth and development of activity on the

Chicago Board of Trade, essential to authentication of the

futures markets as a viable vehicle for minimizing price

change risk, were clearly being demonstrated.



Development of an Interest Rate Futures Market
on the Chicago Board of Trade


Conceptualization. The origin of an interest rate

futures market can be traced back to 1969. A market

phenomenon coined a "credit crunch" had in that year

produced significant interest rate risk for financial

institutions. Mortgage bankers, insurance companies, and

savings and loan associations found themselves faced with

the problem of having to make commitments of funds at

current interest rate levels in an era of increasingly

volatile rate structures. An association of businessmen and

economists, desirous of securing a satisfactory interest

rate on a securities transaction planned for months in the

future, noted the similarity between a businessman's

portfolio of fixed-income securities and a farmer's bins of

wheat. Both the businessman and the farmer could be

adversely affected if prices fell. The farmer could,

however, protect his holdings against price change risk by

selling futures contracts on the Chicago Board of Trade.

The businessman, at least at this point in time, had no such









comparable alternative. Since the organized futures markets

had provided a simple, proven, and popular mechanism for the

farmer or grain dealer to minimize price change risk, it

seemed reasonable to conclude that the same might be

possible for the financial manager. A financial instrument

known as the Government National Mortgage Association (GNMA)

Pass-Through Certificate was to provide the vehicle for just

that opportunity.



Method. During the middle 1960's, considerable effort

was invested in finding ways to streamline the mortgage debt

instrument in order to make it a more attractive investment

to a broader base of investors. In particular, ways were

sought to tap the high volume of financial resources in the

bond and securities markets that never found their way into

the mortgage market because of the complex legalities, the

need to be familiar with local housing markets, the need to

underwrite individual mortgages, and the need to service

individual mortgages. The result of these efforts was the

Government National Mortgage Association-Mortgage Backed

Security (GNMA-MBS) program with its GNMA Pass-Through

Certificate. (Most of the MBS issues are called

"pass-throughs" to indicate the issuers "pass-through" to

the investors the principal and interest payments made each

month on the mortgages.) Through the vehicle of the Federal

guaranty, securities backed by mortgages were to become as

safe, as liquid, and as easy to hold as Treasury securities.





5



By 1975, the GNMA Certificate had emerged as an

immensely successful instrument. As one of the most popular

forms of mortgage investment to reach the secondary mortgage

market, the GNMA-BMS had proven to be very marketable and

highly liquid with its safety virtually unquestioned. The

program represented one of the most significant innovations

in residential finance in the previous 40 years [11].

With the growth of competitive trading of GNMA's in

both primary and secondary markets, the certificate became

competitive with other long-term instruments such as AAA

corporate bonds and long-term government bonds. With GNMA

yields representative of a variety of long-term rates, it

was thought a GNMA futures contract could potentially be

used to minimize interest rate risk throughout the long-term

market. The establishment of an organized futures market in

GNMA securities was the next logical step in the

evolutionary process.



Result. The Commodity Futures Trading Commission Act

of 1975 provided the enabling legislation for trading

mortgage interest rate futures on a commodity exchange. On

May 28, 1975, the Chicago Board of Trade requested

permission from the Commodity Futures Trading Commission in

Washington, D.C., to establish such a market. Trading was

actually begun on October 20, 1975.

By April 20, 1976, the fledgling market's six-month

birthday, total trading volume for the GNMA certificate









contract stood at roughly 46,000 contracts. The comparable

volume for the Chicago Board of Trade's previously most

immediately successful contract, plywood, was

11,400 contracts. By the market's first anniversary on

October 20, 1976, about 114,000 GNMA futures contracts had

changed hands, almost triple the first-year volume in the

successful plywood futures contract [11]. The acceptance

and popularity of financial futures had been solidly

established.

In the brief years that have passed since that

successful inauguration, a veritable trading explosion in

financial futures has spread to other exchanges and a broad

variety of other instruments such as U.S. Treasury bills and

bonds, bank certificate of deposit, foreign currencies, and

even Eurodollars. Chicago Board of Trade and Chicago

Merchantile Exchange trading volumes have increased more

than eightfold in the past decade, with trading in financial

futures now accounting for about 30% of all futures trading

volume, compared to nothing a decade ago. Some believe

trading in financial futures will in the next few years

overtake conventional commodity futures, such as corn,

soybeans, and wheat, in total volume. In 1981, the Chicago

Board of Trade's Treasury bond contract moved to the top of

the list of all futures trading contracts in volume,

dropping corn and soybeans to Nos. 2 and 3.

Today, the big exchanges believe they are on the verge

of a further explosion in trading activity perhaps doubling









the present volume by 1985, and have committed $300 million

for new trading facilities to handle the anticipated load.



Advantages and Disadvantages of the New Interest Rate
Futures Market Over the Existing Forward Market

Forward commitments in financial instruments, like

futures, exist because of the risk of changes in interest

rates over time. Both deal with contracts for future

delivery. However, there are distinguishing characteristics

between the forward market and the futures market that

produce advocates for both contracts and are therefore

important to identify.

Futures contracts specify a standard contract, with a

standard set of terms, which is traded in large volume on an

organized exchange such as the Chicago Board of Trade.

Uniform market quotations are always publically available.

A forward contract is tailored to the particular needs of

the individual buyer and seller by negotiation between those

respective parties. Thus, futures trading creates a

centralized, highly visible market whereas forward

contracts, because they are entered into directly between

individual dealers, lack that attribute. The existence of a

single market, as in the case of futures transactions, can

reduce the search costs of soliciting quotes from numerous

dealers and assures the investor of getting the optimal

price currently available. However, by fixing delivery

date, quantity, coupon, and other factors, futures gain

liquidity at the cost of flexibility. This loss of









flexibility may lead to "basis risk," which will be

addressed in some detail in a later section. With futures,

one is dealing with a stable, recognized, reputable entity

in the Chicago Board of Trade, and there is virtually no

risk that the contract will default and result in

inconvenience and possible litigation as is the case with

forwards.

The futures markets trade in contracts for delivery up

to two and one-half years into the future, whereas cash

market dealers typically limit their trading to the current

month and perhaps six months thereafter. Therefore, the use

of the futures contract is necessary to deal with risks

associated with changes in interest rates and yields during

periods beyond the coming few months.

The futures trade will require a margin deposit and

maintenance margin costs, referred to as "marking to the

market," when paper losses occur. Forward contracts are

generally made without margin for those institutions which

meet the dealer's credit criteria. One of the difficulties

with the forward market is concerned with the fact that it

has enabled individuals and firms to speculate on interest

rate movements without putting up an investment equivalent

to margin. This may have served to make forward commitment

activity more popular than it might otherwise have been.

This research notes that the relative advantage or

disadvantage of the forward commitment vis-a-vis the futures

contract is in some dispute [2,9]. However, the popularity





9



of the new futures markets appears unquestionable, and the

performance of those markets over time provides the focus

for this research.
















CHAPTER II

THE CONCEPT OF HEDGING



Rationale for Hedging



Definition

It has been noted that since the middle 1960's,

institutions that borrow and lend large sums of money may

experience a sizeable increase in risk because of interest

rate volatility. These institutions must in the course of

conducting business commit themselves to lend or borrow

money at rates that may become intolerably costly in just

days or weeks. This condition will likely give them an

incentive to utilize the risk-minimizing characteristics of

the futures market. While the strategies employed by those

who trade in the futures markets are diverse, often those

who attempt to use the futures as a convenient way to

protect the value of fixed-income trading or investment

portfolios from volatility in interest rates use a technique

called "hedging."

Hedging, at least in its classical sense, is an

activity whereby an individual or firm seeks to minimize

price change risk for a given level of return. The

classical notion of hedging is rooted in the concept of









correlation, the statistical measure that indicates the

relationship, if any, between series of numbers. If two

series move together, they are positively correlated; if the

series are countercyclical, they are negatively correlated.

The idea of simple (two variable) linear correlation

suggests that the best representation of perfect correlation

is a straight (linear) regression line fitted to the

observed data. The equation for such a line is the familiar



Y = a + bX. (1)



In order to diversify and therefore minimize or

eliminate systematic risk, projects best combined or added

to the existing portfolio of projects are those that have a

negative correlation with existing projects. By combining

negatively correlated projects, the overall variability of

returns or risk can be reduced. Thus, the gain (or loss) on

position X is offset by the loss (or gain) on position Y.

Obviously, the strategy works best for perfectly negatively

correlated series.



The Classic Short Hedge

Suppose that on August 24, 1979, a savings and loan

association had expected to close $1 million worth of FHA/VA

loans during the next four weeks and create a GNMA pool.

The institution then intends to sell this pool in the

secondary market. If in the interim interest rates rise,









the pool will have to be sold at a discount thus producing a

loss for the institution. (The fact that interest rates

could fall thus allowing the pool to be sold at a premium

producing a gain over the interim is not the point, at least

for now. Traditionally, price change risk is borne by

speculators and is not the domain of the typical financial

intermediary. To gain the risk-reducing advantages of

hedging, the opportunity to profit from favorable interest

rate movements is forfeited.) The risk can be hedged in the

futures market as follows:

On August 24, 1979, the savings and loan association

sells ten GNMA futures contracts for March, 1980, delivery.

This portion will, under the assumptions of the classic

hedge, protect the institution's planned sale in the cash

market. Assume the pool is sold on September 21, 1979. It

is worth noting that on August 24, 1979, the prime rate as

reported by the Federal Reserve Bulletin stood at 12%; on

September 21, 1979, it made its fourth upward move in

28 days and stood at 13%. Although the institution will

have to take a loss in selling the pool at a discount, it

will obtain a hopefully equivalent gain from the futures

position. Since rates had risen between August 24, 1979,

and September 21, 1979, the price of March, 1980, futures

should, according to the assumptions of the classic hedge,

have fallen below the price at which March, 1980, futures

were selling on August 24. A numerical illustration of this

scenario, an example of the classic short hedge, follows:

















Date

Aug 24, 1979


Sept 21, 1979


Result


TABLE 1

The Classic Short Hedge

Cash Market Futures Market
Action Action

Current Cash Sell 10 Mar 80 GNMA's
Price: $895,937.50 Price: $863,906.30

Sell $1 Million GNMA Buy 10 Mar 80 GNMA's
Price: $876,875.00 Price: $844,843.80

$19,062.50 $19,062.50
LOSS GAIN


The given example is referred to as a classic "short"

hedge because the institution sold or "shorted" the March,

1980, futures to initiate the hedge and maintained that

short position until the offsetting purchase at the close of

the hedge.

Note that in this example the cash market result, which

consists of the ending or closing cash price less the

beginning or opening cash price, is represented by Y in

Equation (1) and the offsetting, countercyclical result in

the futures market, consisting of the beginning or opening

futures price less the ending or closing futures price, is

represented by X in the same equation. Thus, when loss

(gain) in the cash market is regressed on gain (loss) in the

futures market,



(P2 l) = a + b(P1 -P2) (2)
s s f f








2
where Ps = the cash or "spot" price at time t2,
S z


Ps = the cash or "spot" price at time tl,


1
Pf = the futures price at time tl, and


2
P = the



In the case of

b = -1,


futures price at time t2.



perfect negative correlation with a = 0 and


(P P) = (P P
s s f f


and



(P2- pl ( 2- pl) = 0
s s f f


which was in fact the case in the example. Stated

alternatively, when the change in the cash market is

regressed on the change in the futures market,


2 1 1 2
X(P P =P a + bXf(P- P )
s s s f f


where Xs = cash or spot market holdings, and

Xf = futures market holdings.

In the case where Xs = -Xf, as in the classic hedge,









(P2 P = a + b (P ). (6)
s s f f


Now with perfect positive correlation, a = 0, b = +1 and

Equations (3) and (4) hold.

It is observed that the change in the cash position has

been matched by an equal change in the futures position.

The resulting net change of zero completes the so-called

"perfect" hedge, often depicted in the literature but in

fact an exceedingly rare phenomenon, as shall be later

observed.



The Classic Long Hedge

Similar to the short hedge, a "long" hedge can be

initiated to insure an investment yield sometime in the

future. For example, an institution or investor who can

forecast his cash inflow over the next investment period may

consider current yields attractive and wish to lock into

this yield. If, when the time comes to actually invest in

the cash market, yields have fallen and the price of the

financial instrument has risen, the investor's loss on his

cash market position will hopefully be offset by a gain in

the futures market position.

For example, if on March 18, 1980, the firm or

individual had concluded that in four weeks there would be

$1 million available for investment in financial instruments

and the current yields of 12.65% were considered attractive,

a purchase of ten September GNMA contracts could have been









initiated. By April 15, 1980, the prime rate peaked at 20%

and cash yields, leading the prime rate as they often do,

had declined to 12.05%. The firm or individual then could

buy the instruments) in the cash market as planned but at a

loss from the March 18 rate. However, the futures market

position can now be liquidated with the offsetting gain

predicted by the classic hedge as depicted below:


Date

Mar. 18, 1980


Apr 15, 1980


Result


TABLE 2

The Classic Long

Cash Market
Action

Current Cash
Price: $720,312.50

Buy $1 million GNMA
Price: $749,062.50

$28,750.00
LOSS


Hedge

Futures Market
Action

Buy 10 Sep 80 GNMA's
Price: $697,187.50

Sell 10 Sep 80 GNMA's
Price: $725,937.50

$28,750.00
GAIN


This second example is referred to as a "long" hedge

because the institution bought or went "long" in September,

1980, futures to initiate the hedge and maintained that long

position until the offsetting sale at the close of the

hedge.

It is observed that the mathematical requirements of

the "perfect" hedge are equally applicable for either the









short or the long hedge, i.e., the change in the cash

position has been matched by an equal change in the futures

position resulting in a net change of zero, as suggested by

Equation (4).

It is important to emphasize that the examples

presented thus far are predicated on the assumption that the

objective is price insurance. The Exchange and the contract

specifications are designed principally to facilitate the

hedging function. Fewer than 1% of all futures contracts

are settled by delivery. The rest have been offset before

the delivery month.



Factors Affecting the Performance of the Hedge

The real world seldom sees the perfect hedge so often

depicted. One reason for not having perfect hedges relates

to price movements over time called "convergence."

Convergence, which suggests that as time passes the futures

price will approach the cash price, is a phenomenon

resulting directly from the aspect of futurity inherent in

any futures market and involves the behavior of "spreads"

over time. Price differentials between different futures

market contracts of the same commodity are called "spreads."

Whereas spreads refer to the price difference between

specified months in the same market, "basis" can refer to a

price difference between specified months in different

markets, i.e., the December cash market vs. the December

futures market.









In GNMA markets, spreads are caused by two principal

factors: the first is the profitability of financing

inventories of securities for later sale, a factor referred

to as "warehousing," and the second is the market's

expectation of price changes for GNMA securities. In

positive carry markets where short-term rates are lower than

long-term rates, the first of these factors is dominant and

acts to offset the convergence phenomenon. Essentially, the

value of warehousing determines the difference between

immediate delivery and futures prices. For example, if one

owns GNMA securities and agrees to sell to a dealer for

delivery one month later, he receives a month's positive

income by financing the securities at a lower rate than the

securities yield. The dealer, in turn, compensates for the

positive carry by bidding a lower price for the one month's

deferred delivery than he would pay for immediate delivery.

Thus while convergence will work consistently against the

short hedge, there is supposedly an equally consistent

offset to the convergence phenomenon--the interest

differential earned by warehousing the closed loans on

GNMA's against which the hedge is placed. If warehousing

profits set the inter-month spreads in both cash and futures

markets, it follows that convergence losses in a short hedge

should equal warehousing profits.

To interpret the results of any hedge, a financial

manager can look at a bottom line consisting not only of the

gain or loss on the sale of the inventory and the futures









market profit or loss, but also interest income and expense,

imputed interest cost on margin funds and all transaction

costs. The inclusion of so many pieces to the short hedge

implies that any individual performance goals placed on a

long-term hedging strategy should be set as part of an

overall marketing goal. However, to seek to recover costs

of transactions from futures activity, one must insert an

element of arbitrage transaction into the equation which

will increase risk from the minimum. Such action is foreign

to the true hedger and not particularly relevant to this

study, for only as basis risk approaches zero is the true

hedger, who has shifted price change risk to basis risk,

fulfilled.



Theories of Hedging



Traditional

The price insurance potential of the futures markets is

the foundation for traditional hedging theory, where those

seeking to minimize price change risk are expected to take

futures market positions equal in magnitude but of opposite

direction or sign to their position in the cash market.

Traditional theory, which continues to underlie many

articles on hedging, is predicated upon the assumption that

cash and futures prices move together in perfect positive

correlation, the difference between the two at any given









time being the "basis." In the case of the so-called

"perfect" hedge, it is observed from Equation (4) that



(P2 P) (P P) = 0
s s f f


or alternatively,



(P2 P) (l Pf) = 0 (7)
s f s f


and the change in the "basis" is zero over the duration of

the hedge. By taking cash and futures market positions of

opposite direction or sign, the desired perfect negative

correlation which eliminates price change risk is supposedly

achieved. What is clear from empirical observation is that

the basis changes so that the great majority of such

"traditional" hedges are not perfect. Many current writers,

while acknowledging this fact, dismiss the question by

making the implicit assumption that such deviations are

distributed around an assumed mean net change of zero.

Therefore, if enough samples are selected from the

distribution of all possible hedges, the distribution of

sample means will be normal and its mean will indeed

approximate zero. According to the Central Limit Theorem,

this will occur only if the true population mean is equal to

zero. It is this critical assumption, in this instance

analogous to a positive slope of 1 for the regression line
2 1
when the change in cash price (P P ) is regressed on the
s s








2 1
change in futures price (P Pf), that has provided one of

several focal points for recent inquiry into the performance

of the GNMA hedge.



Literature Review

In one of the earlier inquires into the theory of

hedging, Working [14] questioned the view that hedgers were

singularly motivated by the price insurance potential of the

futures markets and suggested that most hedging is done in

expectation of a change in spot-futures price relations. He

viewed hedgers as functioning much like speculators who,

seeking to maximize profit, are more concerned with the

relative basis between cash and futures prices than with

absolute price changes. Working reasoned that, depending on

the hedger's future expectations regarding this

relationship, he would be inclined to either hedge

completely his cash position or remain completely unhedged.

However, Ganis [4] observes that trading the cash/futures

basis in an effort to protect an institution's cash position

from loss due to changes in interest rates would be

classical hedging, whereas the very same trades, if part of

an aggressive effort to profit from anticipated changes in

the basis relationship, would be said to constitute

arbitrage transactions. An arbitrage is, of course, a hedge

position taken in anticipation of a change in market

relationships in an effort to realize a gain.









Johnson [6], Stein [12] and more recently Ederington

[1] have used basic portfolio theory to integrate the price

insurance potential of traditional theory with profit

maximization. This application allowed these authors to

explain why hedgers may elect neither the completely hedged

position suggested by traditional theory nor the dichotomus

alternative suggested by Working's hypothesis, but rather a

fractional or partially hedged position. From the

standpoint of this research, Ederington's work is

particularly significant since it is one of the first

attempts to delve into the performance of the fledgling GNMA

hedge. Ederington viewed cash market holdings as fixed and

the decision was how much of the cash market holding to

hedge. There was no presumption as in traditional theory

that Xs = -Xf, where Xs represents cash or spot market

holdings and Xf represents futures market holdings.

Continuing to use Ederington's notation for clarity, it is

noted that in a traditional classic hedge with Xs = -Xf,

b = +1 where b is the slope of the regression line when the
2 1
change in cash or spot price (P P ) is regressed on the
s s
change in futures price (P2 P ). Going back to

Equation (2)



(P2 ) =) a + b(P1 P )
s s f f


and









2 1 1 2
(X)(P P) = a + b(Xf)(P P )



where a = 0


2 1 1
b = (Xs)(P P) / (X) (P P )
s s s f f f


and, if the hedge is perfect, i.e., (P2 p 1) = _(P1 )
s s f f
then



B = Xs / -Xf



and if the hedge is traditional, i.e., Xs = -Xf, then



b = +1.



However, as observed later, the classic perfect hedge

is rarely achieved. In the great majority of cases



(P2 P (P2 P)
s s f f


and the traditional assumption that the population mean is

equal to zero has heretofore been an implicit assumption

rather than a proven fact. It follows that the true

regression line, when the change in cash price is regressed

on the change in futures price, will produce the minimum

variance. Therefore, the risk-minimizing b, b*, is the

slope of the regression line when the change in cash price









is regressed on the change in futures price. This is as

Ederington found it. Optimal b, b as defined by Ederington

[1], will of necessity be a function of each individual's

risk-return relationship. Obviously, if b is greater than

one, an individual takes a position in futures greater than

that in the cash market. If b is less than zero, one has

assumed the same position in both the cash and the futures

market, the structure whimsically known as a "Texas" hedge.

Ederington notes that "while the risk reduction

achieved by any one hedger depends on the chosen b, the

futures market's potential for risk reduction can be

measured by comparing the risk on an unhedged portfolio with

the minimum risk that can be obtained on a portfolio

containing both spot (cash) and forward (futures)

securities" [1, p. 163]. This position corresponds to the

variance of return on a portfolio where b equals b*. The

measure of effectiveness he used was, therefore, the percent

reduction of the variance, or



e = 1 [Var(R*) / Var(U)] = R2



where Var(R*) denotes the minimum variance on a portfolio

containing securities futures; R2 is the familiar population

coefficient of determination between the change in cash

price and the change in futures price. Ederington estimated

e using the sample coefficient of determination,









2
r for two-week and four-week hedges noting both the
2
observed b and r

We have already observed that traditional theory, while

acknowledging that the hedge will not often be perfect,

implicitly assumes movement or volatility in the change in

basis in any given period is random with zero mean and

standard deviation of o, and is independent of changes in

other periods. As such, traditional theory implies the

widely accepted "random walk" model for the movement of the

basis. However, the generalization of this model known as

the "Martingale" model differs from a random walk in that

volatility may change over time, while it is a fixed

constant for a random walk. Thus, volatility is an ideal

measure of basis variation because it captures the intuitive

notion of stability being related to the magnitude of random

fluctuations. It is this volatility that Ederington

captures in r2 or e.

Ederington hypothesized that expectations of the near

future would be more affected by unexpected changes in the

cash price than expectations of more distant futures and

predicted e would decline as one hedges in more distant

contracts. He further hypothesized that e will be greater

for four-week hedges than for two-week hedges because

absolute changes in cash prices should generally be greater

and future prices would have more time to respond over the

longer period.









Ederington confirmed the second hypothesis and

supposedly proved the "lag" in futures, but failed to

conclude, at least for GNMA's, that the near future would be

affected more by unexpected changes in the cash market.

Ederington found that b* was, in most cases, significantly

different from one and in general was less than one.

An important question raised by Ederington is whether

over the long run the expected change in the basis will tend

to be consistently positive or negative. He suggests that

since the basis must be approximately zero at the
delivery date, the expected change in the basis
will generally be positive if the current cash
price exceeds the current futures price and will
generally be negative if the futures price exceeds
the cash price. [1, p. 167]

Ederington felt his results tended to confirm this

hypothesis and, since he had concluded risk reduction to be

approximately the same for nearby and distant contracts, he

suggested that long (short) hedgers would have been well

advised to hedge in the nearby (distant) contracts.

What is perhaps most significant about Ederington's

work, at least from the standpoint of this study, is the

time period observed. His observations were of necessity

confined to the "market experience to date," namely 1976-77,

the first two years of GNMA futures market existence.

Although turbulent by pre-1966 standards, the period may be

characterized as relatively benign when compared with the

years to follow.

Franckle and Wurtzebach [3] refine Ederington's

regression equation









2 1 2 1
(P2 ) = a + b(P2 P )
s s f f


by incorporating E(APs) and E(AP ) where E(APf) = 0,
1 2
i.e., P is an unbiased estimate of P and E(AP )
1 1f
= (P P )[i/(i + j)] where
f s
i = length of hedge

j = time to convergence of spot and futures.

Thus, their equation becomes


2 1 2 1
P2 pl E(AP = a + b[(P P) E(AP)]
S s s f f f


2 1 2 1
P2 Ps E(AP = a + b(P2 -P).
s s s f f


They incorporate, using linear interpolation, the

phenomenon of convergence into the equation regressing

unexpected change on unexpected price change in futures

instead of using total change as in previous research.

Unexpected change A is computed under the assumption

that the futures price is an estimate of the spot price at

either the beginning or the end of the delivery month.

Unexpected change B assumes that the futures price is an

estimate of the spot price on the last day of futures

trading.

These varying assumptions all determine the value of j

or the length of time from the closing of the hedge until

price convergence.









Franckle and Wurtzebach observed that estimated e and

the risk-minimizing hedge ratio, b*, increased during

1978-79 over that period observed by Ederington (1976-77).

This suggests the erosion of the positive change in the

basis characteristic of the earlier period and perhaps the

increased maturity in the markets suspected by Ederington.

They observed that variance of futures price was about twice

as great as variance of cash prices in the less volatile

period of 1976-77 while there was little difference between

the two in the later period. Because



b* = o / ,
s f


this would account for a lower b* in the earlier period.

Interestingly, they conclude that the futures market is most

effective during periods of volatile interest rates.

Working's hypothesis is not without its present day

advocates. Howard and D'Antonio [5], in a recent and as yet

unpublished work, conclude that while one's cash position

may be only partially hedged, the optimal level of futures

contracts held will vary greatly depending on one's

perception on the relative expected performance of futures

to cash holdings. The authors have thus chosen to

concentrate on optimal b, which Ederington defined as b, as

opposed to the risk-minimizing b, which Ederington defined

as b*. The difference between the two has to do with

individual portfolio considerations as contrasted with









market potential for risk reduction. This study is

concerned with the latter.

In a study concentrating on activity throughout the

calendar year 1978, Raleigh [10] took a hypothetical firm

with a cash inventory position through a simulation using

cash forwards four months out and compared results using

futures contracts for four months protection, at all times

being 100% hedged. He then developed a "managed hedge" for

a classic short hedger where futures are used to adjust from

less than 100% coverage in apparent uptrends to more than

100% coverage in apparent downtrends, thus roughly

simulating Ederington's hypothesis that the astute hedger

may not desire a b* = 1 at all times. Trends were

identified through the use of technical analysis. The

arbitrary target was to be 75% covered in uptrends, 100%

covered in sideways markets, and 125% covered in downward

trends. The key, of course, to the success of the managed

hedge was the accurate assessment of the trends. Whereas

Ederington's b* reflected the risk-minimizing hedge ratio

over the observed period (in his case, approximately two

years), Raleigh in effect shortened the periods and altered

the hedge ratio over a much shorter term, producing

apparently successful results which confirm Ederington's

conclusions regarding b*.

The matter of the optimal hedge ratio has been refined

further by Kolb, Corgel, and Chaing [8]. The objective is

development of an optimal hedge ratio which will overcome









some of the limitations of the traditional and portfolio

approaches while taking into account differing price

sensitivities for the hedged and hedging instruments.

The authors contend that all hedging in GNMA's is

essentially "cross-hedging" since price sensitivites rarely

if ever match. Their suggested technique seeks to control

for the "mismatches" that must of necessity arise.

The approach is applied to hedge a particular risk and

therefore is more sharply focused than either Ederington,

Franckle and Wurtzebach, or the other authors mentioned.

The method is more responsive to individual price

sensitivities than Ederington's universal b* which suggests

a single hedge ratio regardless of the nature of one's cash

position.

Much as with Franckle and Wurtzebach [3] and with

Howard and D'Antonio [5], this approach represents a rather

sharp refinement which, while reflecting the continuing

improvement in technique, does not bear directly on this

study, which is more global in character.
















CHAPTER III

THE MARKET ENVIRONMENT (1976-1980)



The Potential of the Prime Rate as a Proxy
for Uncertainty in U.S. Money Markets



The Prime Rate

The GNMA futures market, in existence for five complete

calendar years at the time of this study, has witnessed some

of the most dramatic volatility in the history of U.S. money

markets. While not the only indication of such volatility

and perhaps not even the best, the movement of the prime

rate is likely the most visible and conspicuous of the

indicators of market volatility and uncertainty.

The concept of a prime rate was born in the Depression

to protect the banks against cut-throat competition. Banks

define the prime rate as their lowest interest rate for

their most credit-worthy customers.

In 1974, increases leading to a 12% prime rate ushered

in a massive credit crunch and the worst recession since the

era of the Great Depression. The apex of that historic

credit crunch was reached on July 5, 1974, when the prime

rate reached a relative maximum of 12%. After holding at

that historic level for a period of 94 days, a steady









decline began on October 7, 1974. This decline lasted

284 days and consisted of 20 quarter-point declines, ending

with a quarter-point advance on July 18, 1975.

On October 20, 1975, when trading in GNMA futures was

initiated on the Chicago Board of Trade, the prime rate

stood at 8%. By the first of January, 1976, the beginning

of the period reviewed by Ederington [1], the rate had

receded to 7%%. For the next two calendar years, the range

of the observed market period for the Ederington study, the

market would experience only 14 movements of the prime rate.

All would be at quarter-point intervals with the highest

level of 7 3/4% occurring from October 24, 1977, to

December 31, 1977, and the lowest level of 6% occurring

from December 13, 1976, to May 13, 1977.

A steadily increasing prime rate, actually begun with

the move to 6% on May 13, 1977, was to continue without

interruption throughout 1978. During this calendar year,

the prime rate experienced 15 quarter-point advances, more

absolute movement than had been experienced in the previous

two years combined. A peak was reached on December 26,

1978, with an 11 3/4% prime rate, only 1/4% below the

historic high set on July 5, 1974 (see Figure 1).

The first half of 1979 witnessed a stable prime rate,

although historically high. On August 16, 1979, the prime

rate moved to 12% to equal the record established five years

earlier. It remained there only 12 days before continuing

upward. During the next 17 months, the prime rate would






























1976-1981


Figure 1. Prime Rate Activity.









move on 52 occasions. Thirteen of these movements would

occur in the remaining months of 1979 and an incredible

39 such movements would occur in calendar 1980. The prime

rate would reach another relative maximum of 20% from

April 2, 1980, to April 18, 1980, plunge to a relative

minimum of 11% on July 25, 1980, and peak again at 21% on

December 19, 1980, moving at times in quantum leaps of a

full percentage point. It is this sharp increase in the

volatility and the level of the prime rate that

characterizes the market period of this study.

It is noted that the rise in interest rates which began

midway through 1979 was pointed, regardless of which

interest rates are considered. The three-month Treasury

Bill rate rose from 9% at the end of 1978 to over 12% by

the same period one year later. In the capital markets,

1979 bond rates registered record increases. The movement

of the prime rate was equally symptomatic of the behavior of

other indicative interest rates in 1980. Six-month Treasury

Bills reached a record of 15.7% on March 24, declined to a

low of 6.6% at the June 16 Treasury auction, then climbed to

a new record of 15.42% on December 15, 1980. The late

March-early April period of 1980 registered historically

high interest rates on both short- and long-term securities.

While interest rates have no doubt shown increased

volatility in recent years due to factors such as structural

changes in the financial markets, greater emphasis on

monetary policy as a means of implementing a countercyclical









stabilization policy and higher and more variable rates of

inflation, the greater volatility in 1980 than in previous

years is due in large part to change in the Federal

Reserve's operating strategy of focusing on the behavior of

bank reserve positions and, hence, money supply growth, with

less emphasis on interest rates. The new approach, formally

announced on October 6, 1979, coincides with the sharp

fluctuations in market interest rates. The period since

October 6, 1979, differs significantly from earlier periods

of comparable length. Monetary growth, interest rates, and

the economy have been notably more erratic. The interest

rate fluctuations since that new approach was announced are

unprecedented, at least since the War Between the States.

It is noted that while there appears to be positive

correlation between the movement of the prime rate and

long-term rates, the correlation is by no means perfect.

During the second quarter of 1980, short-term interest rates

plunged 8 to 10 percent, while long-term rates fell 3 to

4 percent. As the prime rate becomes more volatile, it may

be losing its position as the sole base from which other

rates are scaled upward. As recently as a decade ago, rates

seemed to move in tandem with the prime rate. There is some

current evidence that there may be more "side-stepping" of

the prime rate than ever before. The prime rate does appear

to "lag" behind other short term interest rates and, as

already observed, long-term rates are no longer seen as

moving in synchronization with the prime









rate. Admittedly, there is evidence that the linkage

between consumer loans and the prime rate is deteriorating.

Despite these and other recent challenges, the movement

of the prime rate does reflect volatility in the period in

question and, as importantly, does have the characteristic

of high visibility. Therefore, this study will attempt to

utilize characteristics of the movement of the prime rate as

a proxy for uncertainty in financial markets.



The Concepts of Volatility and Stability
in U.S. Money Markets

The concept of absolute stability in money markets

suggests that the regression of interest rates on time will

be linear with slope and variance equal to zero. This

proposition is axiomatic to the discussion and analysis to

follow. Thus, over any given range of observations,

interest rates remain unchanged, each day's quote being

identical to that of the immediately preceding day's quote.

Any curvilinear relationship which would produce a

regression equation that accounted for all variability in

rates would suggest that rates move in a predictable manner,

a condition not supported by logic nor by observation. A

linear regression equation whose variance was indeed zero

but with slope different from zero would likewise imply a

dependable change or movement in rates. It is this

movement, whatever its course, direction, or dependability,

that is antithetical to the concept of absolute stability.

If, therefore, we can infer that absolute stability results









when there is no movement or change in interest rates,

volatility would then infer departure from this norm as

reflected by a variance and/or slope not equal to zero.

Consequently, it is suggested that volatility in money

markets can be characterized over any given range of

observations by departure from the axiom of absolute

stability, i.e., by a slope and/or variance not equal to

zero.

There is considerable intuitive appeal as well as

empirical evidence to support the notion that the

variability of inflation increases when inflation increases.

To the extent that interest rates embody inflation

expectations, higher average levels of interest rates might

also be associated with increased market uncertainty,

however stable the movement of interest rates over the given

range of observations.

Therefore, a third factor which is postulated to

characterize a money market over any given range of

observations is the level of interest rates. An absolutely

stable prime, holding at a historically high level, could

characterize a market possessing a greater degree of

uncertainty than would an absolutely stable prime holding at

some lower level.

Admittedly, many factors may influence a defined

market, making it unreasonable to ascribe all differences in

market behavior between periods to the existence of

uncertainty in the money market. However, to the extent





38



that we are able to define specific market behavior in terms

of uncertainty or volatility in the economy at large, we

will have advanced another step towards the better

understanding of our markets and the complex relationships

that bind them together with macro-economic forces.
















CHAPTER IV

METHODOLOGY



Statement of Objectives

The simplistic and naive assumptions of the classic

hedge as depicted in traditional hedging theory have been

demonstrated earlier. Most notable among these are (1) the

assumption that cash and futures markets are perfectly

positively correlated and (2) the assumption that the astute

hedger will utilize a risk-minimizing hedge ratio, b*, of 1.

Recent empirical research (Ederington [1], Franckle and

Wurtzebach [3]) has shown that, over a given market period,

the degree of positive correlation between movement in cash

and futures markets, while strong, is in fact somewhat less

than perfect (b* not equal to 1) and the efficiency of the

hedge, e (estimated by the sample coefficient of

determination), is in fact less than 1.00. What this

previous research has neglected to consider in any detail

thus far is how the risk-minimizing hedge ratio, b*, and the

measure of hedge efficiency, e, may be altered in different

market periods, periods which may be segmented by the degree

of uncertainty present in the money market. Franckle and

Wurtzebach [3] only touched on the possibilities. No other

known research has yet addressed this particular aspect of









hedge performance. Therefore, an initial objective of this

research will be to develop a methodology which will allow

observation of Ederington's b* and e over time. Such a

series will provide graphic evidence of any changes in hedge

performance which may be occurring as market conditions

change. By developing a series of coefficients descriptive

of the movement of the prime rate over comparable periods,

this research attempts to draw conclusions about the

performance of the hedge relative to uncertainty in the

money market.



Data Collection and Refinement



Sources

The raw data to construct the hypothetical market

transactions necessary to this study are obtained from data

tapes acquired through the Chicago Board of Trade

Foundation. The foundation was able to supply three

separate Chicago Board of Trade Commodity Futures Data Tapes

containing in the aggregate over 243,000 data lines of

information concerning daily open, high, low, and closing

futures prices, as well as other pertinent market

information. A subset of this master database, consisting

of all activity in the original GNMA 8 contract dating from

October 20, 1975, to December 31, 1980, and containing

approximately 13,000 data lines, was generated to produce

the first of two raw data files necessary to this study.









GNMA cash prices from January 1, 1976, to December 31,

1980, were researched from daily quotations published in The

Wall Street Journal. Bid, asked, and yield information was

recorded on a daily basis, creating a 1,346 line raw data

file from which cash prices could be obtained.



Refinement

It is noted that Ederington, in selecting futures

prices for constructing his hypothetical hedges, used

"weekly closing prices" [1, p. 164], presumably Friday's

closing price. Franckle and Wurtzebach also used a weekly

observation, Thursday's settlement price [3, p. 8]. While

the option to use either the closing price or the settlement

price and confine observations to any given weekday were

similarly available here, there was no perceived necessity

to limit observations to a given weekday nor was there

particular intuitive appeal in selecting either the closing

price or the settlement price. Since in practice a

commodity futures transaction can and likely would be made

at various and random times throughout the trading day and

week, this study has utilized the arithmetic mean between

high and low quotations as the hypothetical futures price

and has constructed observations for every day within the

selected range and not just a selected weekday.

Although Ederington presumably dropped paired

observations with missing data and Franckle and Wurtzebach

do not make clear their handling of missing data, this study









utilizes the following criteria: If a futures quotation for

a given day is necessary to either open a hedge or to close

a hedge and the quotation for that day is missing, as would

occur if that day were a holiday, then an appropriate

quotation is simulated by echoing the data from the

immediately preceding trading day. The only exception to

this rule occurs when a closing futures quotation is

required, the data are missing, and the immediately

preceding quote is of a contract not compatible with the

opening hedge data. In that rare instance, the closing

futures quotation is simulated by mirroring the immediately

following trading date.

These criteria for handling missing data points in the

futures quotes will occasionally result in sample hedges of

slightly shorter or longer duration than that originally

specified. The result is considered a more reasonable

reflection of what might actually occur in market trading

and in any case should have negligible impact on the

results.

In selecting cash prices for hypothetical hedges,

Ederington [1], Franckle and Wurtzebach [3], and Figlewski

[2] all utilize prices as quoted in The Wall Street Journal,

as does this study. Ederington apparently used the bid

price for GNMA 8's. The 8% coupon is normally the delivery

security for the futures contract, but different coupon

GNMA's can be substituted according to a set formula.

Figlewski and Franckle and Wurtzebach observed that during









the periods considered in their studies, the structure of

GNMA prices was such that it was nearly always more

advantageous to deliver the 9% coupon. Thus, Franckle and

Wurtzebach used the converted asked price of the GNMA 9%

Certificate. Figlewski used an average price. It is noted

that if bid prices are used for "sale" of inventory and

asked prices are used for "purchase" of inventory, there

would be a change in the price of the security without any

real change in the market rates. This study has elected to

use the arithmetic average of bid and asked in order to

obtain a cash quote.

The criterion for handling missing data in the cash

database is similar to that previously described for the

futures database. There were isolated instances when cash

quotes as reported in The Wall Street Journal were either

unreadable or differed so significantly from surrounding

figures that they were presumed to be misquotes. In those

instances as well as on holidays, the cash quote is

simulated using the immediately preceding day's quote.



Critical Parameters



Hedge Length

Initially Ederington and later Franckle and Wurtzebach

used only two- and four-week hedges when constructing their

sample observations. Ederington's choice was admittedly

arbitrary [1, p. 164]. Presumably, Franckle and Wurtzebach









selected similar lengths in order to compare their findings

more directly with Ederington's initial study. As a means

of more direct comparison, this research has likewise

developed hypothetical four-week (28-day) hedges, although

that is where the similarity ends. It has already been

noted how the handling of missing data and the selection of

both futures and closing quotations differ slightly from

earlier studies. It must also be noted that earlier studies

allowed futures trading to continue into the spot month,

which the researcher was reluctant to do. These subtle

differences in methodology between this and previous

research work to increase the possibility of divergent

results, although perhaps not significantly.

Following the logic of Raleigh [10] and others who have

constructed hypothetical hedges for the purpose of

demonstrating characteristics of the hedge, this study also

develops an 18-week (126-day) hedge.



Hedge Distance

With the four-week (28-day) hedge, this study will make

observations, as did the previous researchers, using futures

contracts three, six, nine, and twelve months distant.

Because there are only four annual delivery months available

to the hedger, it is obvious that not all hedges can be

initiated in contracts exactly x months distant. Therefore,

this research has constructed hypothetical hedges according

to the following criteria: If a 28-day hedge in the nearby









or three-month contract is originated in November, December,

or January, the March contract is utilized. Similarly, if a

hypothetical 28-day hedge in the nearby or three-month

contract is originated in February, March, or April, the

June contract is utilized. The logic is similar for all 28-

and 126-day hedges constructed in either the three, six,

nine, or twelve-month contracts. In the extreme case, a

28-day hedge in the three-month or nearby contract initiated

on July 31 would close out on August 27, still prior to the

September spot or delivery month.

In the case of the 18-week hedge, the three and six

months contracts are ignored and only the nine and

twelve-month contracts are examined.



Range of Observations

The selection of the range of observations is one of

the more critical decisions in the study. Ederington chose

a two-year frame [1, p. 164] to examine his b* and e,

presumably because this was the extent of "market experience

to date" [1, p. 163] and there was no compelling reason to

attempt to segment the market period. Franckle and

Wurtzebach also used market experience to date (1976-79) to

come up with their initial results but then, to compare more

directly with Ederington's effort, divided their

observations into two identical two-year periods possessing

obviously differing characteristics with respect to interest

rate volatility. Once again, market experience to date









appeared to be the primary deciding factor for aggregating

1976 through 1979 data, and Ederington's two-year

observations fit neatly into Franckle and Wurtzebach's

four-year frame, providing two equal observation periods.

This study does not rely completely on the precedents

established by Ederington and by Franckle and Wurtzebach,

partly because the selection appears more expedient than

well-conceived.

A glance at money market activity over the first five

year operating history of the Chicago Board of Trade GNMA

futures market would indicate major market movements can be

roughly segmented into 18-month intervals when a new degree

of uncertainty was actively influencing the market. For

instance, the steady rise from the market low of a 6%% prime

rate began on May 13, 1977, and reached an obviously stable

plateau on December 26, 1978; the severe dislocations in

late 1979 and 1980 can be traced to a beginning on June 19,

1979, when prime first moved following a six-month lethargy,

and a peak on December 19, 1980. The objective, then, is to

choose a range that will be short enough to capture the full

essence of well-defined market periods without the diluting

or excessive smoothing that would result from distant

historical observations and yet long enough to avoid

distorting aberrations and extremes. An 18-month range is

considered adequate to accomplish these goals and yet remain

reasonable consistent with earlier efforts.









Measures of Hedging Performance

This study utilizes Ederington's b* and e to assess

hedge performance where b* is in effect the slope of the

linear regression line when the change in cash or spot price

is regressed on the change in futures price and e is the

sample coefficient of determination. The propriety of this

choice is dictated by the nature of this study. Admittedly,

more refined measures such as those suggested by Kolb,

Corgel and Chaing [8] or by Howard and D'Antonio [5] could

likely be incorporated into future, more sharply focused

efforts. For measuring the potential of these markets to

minimize price change risk, Ederington's measures have

considerable practical, intuitive appeal.



The Concept of a Moving Performance Parameter

It is noted that Ederington, in using "market

experience to date," selected hypothetical hedges from

within that defined period and drew conclusions about market

performance applicable to that period. The effect was to

stop or freeze attention on a single frame in time. If, for

instance, days were numbered beginning at some arbitrary

starting point, say, July 1, 1974, and Ederington's

observations and conclusions relate to a single two-year

period ending with activity on December 31, 1977, he in

effect froze attention at frame number 1280. Rather than

allowing the range of observations to constantly expand to

"market experience to date," he could have on the following









day deleted an observation from January 1, 1976, and

simultaneously added an observation from January 1, 1978,

effectively freezing attention on frame number 1281.

Effectively, this is what Franckle and Wurtzebach do when

they discard the notion of "market experience to date" and

segment their observations into two well-defined market

periods, 1976-77 and 1978-79, thus using a two-year range of

observations. Franckle and Wurtzebach effectively froze

attention at frames 1280 (December 31, 1977) and 2010

(December 31, 1979). What this study does is construct a

series of "moving" performance indicators, namely bt and et,

with each indicator computed in a manner not dissimilar to a

moving average.

As the name implies, a moving average is a series of

averages computed from the terms in a series by successively

dropping one old term and adding one new term for each

average. Moving averages tend to smooth or eliminate

erratic movements from the series, the degree of smoothing

being a function of the number of terms used in computing

the moving average. The primary use of such a smoothing

technique is to provide a pictorial description of the time

series secular trend. In this case, the selection of an

18-month observation range determines the computed value for

b* and et similar to the way the two-year observation range

did for Ederington and for Franckle and Wurtzebach. The

difference is that instead of selecting one frame for

viewing as did Ederington or even two frames as did Franckle










and Wurtzebach, this study computes b* and et for all such

"frames" beginning with frame number 1096, which is

descriptive of the period from January 1, 1976, through

June 30, 1977, and ending with frame number 2376,

descriptive of the period from July 1, 1979, through

December 31, 1980. The actual equations, then, for

computing the respective series are as follows:










T T T
[ mE (X -X) (Y -Y) E (X -X) E (Y -Y) ]
j=t-m+l j=t-m+l j=t-m+l
t T T T T
[ m (X.-X) ( (X.-X))2] [ mE (Y.-Y) ( E (Y i- ))2]
j=t-m+l j=t-m+l j=t-m+l j=t-m+l






T
Z (X.-X) (Y-Y)

[ E (X.-X))
j=t-m+l











where M = range of observations,

t = 1097, 1098, . ., T









The observed values of the chosen performance indicators, b*
t
and et, are connected using a Hewlett-Packard Model 7221C

Digital Plotter to depict graphically the movement or

pattern of changes in the respective performance indicators

which, in the case of Franckle and Wurtzebach's

observations, showed significant change between market

periods.



Statistical Model



Bivariate Regression



The Model. The basis for the statistical model which

is used to examine characteristics of the performance of the

GNMA hedge over volatile money market eras is found in

bivariate regression, a straightforward technique which

involves fitting a line to a scatter of points. The

simplest such relationship between an independent variable

and a dependent variable is the straight line expressed by

equation (1). Because relationships in the social sciences

are almost always inexact, the simple equation for a linear

relationship is more realistically written as



Y. = a + bX. + e. (8)
1 1 1


where e represents the error term.









The familiar least square principle, in which the

optimal line is the one which minimizes the sum of the

squares of the error terms, is appropriate to apply in this

research. Lacking the resources to review all possible

hedges which could have been constructed during the period

from 1975 through 1980, a total that would surely be

astronomical, a stratified, systematic sample was selected

from the enormous, although finite, population of all

possible hedges. The sample is systematic in that the

hypothetical hedges constructed are assumed to be executed

at the mid-point of the range of each day's quotations. It

is stratified in that the population of all possible

hypothetical hedges is divided into strata consisting of

either 28-day hedges or 126-day hedges in contracts ranging

from three to twelve months distant at three month

intervals.

The statistic b in this model, the estimate of the

slope of the true population regression line, indicates the

estimated average change in the dependent variable Y

associated with a unit change in the independent variable X.

(A causal process is not established, however, by the

regression of Y on X and is more appropriately determined

outside the estimation procedure. Often, it is based on

theoretical considerations, good judgment, and past

research.)

The statistic a, the intercept, is of lesser interest

to this study. In the application this research is to make









of bivariate regression, this statistic should, as

traditional hedging theory suggests, be close to zero,

except for the effect of the convergence phenomenon.

Generally, social scientists stress explanation rather

than prediction. The research question at this point

suggests emphasis on the former. To examine how powerful an

explanation the bivariate regression model provides, a

formal measure, the coefficient of determination (R2), is

essential. This population coefficient of determination

(R2) is estimated by the sample coefficient of determination

(r2), the same measure referred to by Ederington as e and

assumed by traditional hedging theory to equal 1.00.



Assumptions and inferences. The basic assumptions of

the classical linear regression model, never properly

ignored or overlooked, suggest

1. no specification error (linearity): the

relationship between Y. and X. is linear;
1 1
2. no measurement error (nonstochastic X and Y): the

variables X. and Y. are accurately measured;
1 1
3. zero mean: the error term, ei, has the

characteristic that the sum of all the error terms

from 1 to n is equal to zero;

4. constant variance (homoscedasticity): the variance

of the error term is constant for all values of X.;

and









5. no autocorrelation: the error terms are

uncorrelated.

By adding the following assumption we have the

classical normal linear regression model.

6. Normality: the error term is normally distributed.

The assumption of linearity is common in postulating

relationships among social science variables. Although not

always correct, its adoption is at least a starting point

that might be justified on several grounds. First,

empirical research has found numerous such relationships

among social science variables to indeed be linear.

Secondly, theory has not suggested thus far what the

nonlinear specification would be. Most importantly,

inspection of the data in this case fails to suggest a clear

alternative to the linear model. While alert to the

possibility that our bivariate relationship may actually be

nonlinear, the assumption of linearity expressed in

Equation (8) is entirely plausable.

The importance of the second assumption is

self-evident. The researcher is satisfied that the data

supplied by the Chicago Board of Trade Foundation and

researched from the library microfilm are as accurate as can

be reasonably expected. Therefore, the possibility of

measurement error can, as a practical matter, be ruled out.

The remaining assumptions involve the error term. The

initial one, a zero mean, is of little concern because the

least square estimate of the slope will be unchanged









regardless. It is true that, if this assumption is not met,

the intercept estimate will be biased. However, since the

intercept estimate is of secondary interest in this

research, this potential source of bias is relatively

unimportant.

Violation of the assumption of homoscedasticity is more

serious. While the least squares estimates remain unbiased,

significance tests would be inaccurate. Diagnosis of

heteroscedasticity depends upon observation and analysis of

residuals. After visual analysis of scattergrams and review

of previous research, there is no reason to suspect a

condition of heteroscedasticity.

The assumption of no autocorrelation suggests that the

error corresponding to an observation is not correlated with

any of the errors for the other observations. When

autocorrelation is present, the least square parameters

estimates are still unbiased; however, the formulas used by

most regression computer programs are no longer appropriate.

Where there is evidence of positive autocorrelation, as is

often the case in political and economic data observed over

time, this means the estimated variances of a and b will be

seriously underestimated and the sample coefficient of

determination, critical to this and to previous research in

measuring the effectiveness of the GNMA hedge, will be

overstated. It is critically important to check for

violation of this assumption when using economic data

collected over time. Observation and tests conducted during









this research suggest strong positive autocorrelation

requiring corrective action.

The normality assumption, necessary only for the

statistical testing of the model, is not crucial as long as

one is willing to believe that individual errors due to

measurement and to omission are small and independent of

each other. Furthermore, the normality assumption can be

ignored when the sample size is large enough, for then the

Central Limit Theorem can be invoked.

Significance of violation of the autocorrelation

assumption. There is some disagreement in the statistical

literature over how serious the violations of the regression

assumptions actually are. Often, the question turns on

whether one's perspective on regression analysis is "robust"

or "fragile." The "robust" perspective on regression

suggests the parameter estimates are not significantly

influenced by violations of the regression assumptions. At

the other extreme, the "fragile" view of regression analysis

suggests violations of the assumption render the regression

results almost useless. Clearly, some of the assumptions

are more likely to be critical than others. The

consequences of violation of the nonautocorrelation

assumption are so serious in this case due to the impact

upon the estimate of the population coefficient of

determination (the measure of hedge effectiveness in this

and previous research), its possibility cannot be ignored.

Previous research (Ederington [1], Franckle and Wurtzebach









[3]) did not mention the possibility of autocorrelation of

the error terms in their regression equations, despite the

fact that they did indeed observe their economic data over

time, as does the research. Their failure to mention the

possibility and the likely effect on their findings may have

resulted from a "robust" perspective of regression in

general or from other considerations not readily apparent.

Nevertheless, evidence of violation of that assumption

prompts consideration of modification of the simple

bivariate equation.

Correction for autocorrelation. The focus on the

nonautocorrelation assumption is appropriate because of the

time-series context implied by the research question. The

problem arises in a time-series context because the

disturbances, which are a summary of a large number of

theoretically random factors that enter into the

relationship under study, are likely to carry over into

subsequent time periods.

Virtually all work in regression of this type assumes

that a first order autoregressive process generates the

disturbance. While not the only process possible, the first

order autoregressive process is often studied because of its

statistical tractibility and because it yields a crude

approximation to the process in which we are interested.

The equation for a first order autoregressive process is


et = Pet + vt
St-1









where P is the coefficient of correlation between et and

et-l and is the basic indicator of whether the

nonautocorrelation assumption is violated.

In correcting for evidence of positive autocorrelation,

one of several approaches available to the researcher, an

alternative identified as the Cochrane-Orcutt method [7],

was used. The procedure begins with the familiar bivariate

regression of Equation (8) where previous research has

apparently left off. The estimated residuals are used to

obtain a "first round" estimate of P which is defined as


^ ^ ^ ^ 2
P = Zee /Zet t=2,3,....,T



Transformed data points are constructed yielding "second

round" residuals which are then used to obtain a new

estimate of P. This iterative procedure is continued until

the values of the estimators converge. The resulting

transformed data points are free from the effects of

autocorrelation as is reflected by a P of approximately

zero.



The Multivariate Regression Model

The basis for the statistical model which is used to

examine the relationships between the characteristics of

performance of the hedge, bt and et, and the chosen

indicator of uncertainty in money markets, the prime rate,









is multiple regression. The elementary four-variable case

which this research uses is written



Y = a0 + blX1 + b2X2 + b3X3 + e (9)



where

Y = a performance indicator, either b* or e

X1 = an uncertainty indicator

X = an uncertainty indicator

X = an uncertainty indicator

The bivariate regression assumptions are carried over

to the multivariate case. However, for multiple regression

to produce the best linear unbiased estimates, it must meet

one additional assumption--the absence of perfect

multicollinearity. Observation of the plot of the

uncertainty indicators, to be developed shortly, does not

suggest multicollinearity in the independent variables.

Using the same range of observations thought

justifiable for examining the performance of the GNMA hedge,

performance characteristics have been developed for the

movement of the prime rate, the "proxy" for uncertainty in

today's money markets. A parameter called prime rate trend

(PRMTND) is, in fact, a series of coefficients which reflect

the slope of the regression line of prime rate on time for

each "frame" from 1097 to 2376. It is important to realize

that these coefficients reflect changes in the slope of the

regression line of the prime rate on time and not in the









prime rate itself. Otherwise, misinterpretation of the

resulting curve might occur. For instance, in early 1979 a

plot of these coefficients reveals the prime rate trend

decreasing when in fact the prime rate had only stabilized

after approximately 18 months of uninterrupted upward

movement. Thus, the rate of increase of the prime rate was

decreasing although the prime rate itself was not.

A parameter called prime rate volatility (PRMVOL) is a

series of variances associated with the mentioned regression

lines. Thus, prime rate could be rising steadily,

uniformly, and predictably, and prime rate volatility could

be approaching zero, for it takes uncertainty reflected by

undulating patterns to result in higher levels of

volatility.

Finally, a parameter called prime rate average (PRMAVE)

is a series of weighted averages which allow the insertion

of the general level of the prime rate into Equation (9).

In this case the relationships are not so obvious as in

the bivariate case. Therefore, we confront the null

hypothesis which states there is NO linear relationship

between the parameter and the performance of b* and e, as

opposed to the alternative hypothesis which states there IS

a linear relationship.

The main focus in the use of this technique as a

descriptive tool is the evaluation of measurement of overall

dependence of a variable, namely, b* or e, on a set of other

































Figure 2.


Market Period Indices.
Coefficients Developed
Prime Rate, 1976-1981.


25


I
20 N
T
E
R
E
15 S
T

R
T
10 E
S


A Plot of Descriptive
from the Movement of the





61



variables, the uncertainty indicators of PRMTND, PRMVOL, and

PRMAVE.
















CHAPTER V

ANALYSIS AND INTERPRETATION



The Performance of the 28-Day Hedge
in the Near-Term Contract



Explanatory Results

From the 12,848 line database containing a daily record

of market activity of all GNMA futures contracts for

1976-80, inclusive, a total of 1,284 hypothetical beginning

hedge positions were observed according to the previously

defined selection criteria. This includes a hedge for every

business day during the period. Of this total,

approximately 3% are simulated. These hypothetical

beginning hedge positions provide the first of four input
1
variables, specifically Pf, necessary to construct the

hypothetical hedges requisite to this empirical observation.

Using the same 12,848 line master database of all GNMA

futures activity and the 1,284 line data base just created

containing beginning hedge positions, a matching 1,284 line

database containing hypothetical ending hedge positions was
2
spawned. The observations, corresponding to Pf, provide a

second input variable for the hypothetical hedge.









Similarly, approximately 3% of these observations were

simulated.

To construct the hypothetical beginning and ending cash
1 2
positions, P and P the database containing cash activity
s s
as reported daily in The Wall Street Journal was utilized

according to predefined selection criteria. Two 1,284 line

files were generated completing the selection of the

possible parameters of 1,284 hypothetical 28-day hedges in

the near-term contract.

A summary of these hypothetical hedge transactions was

then created by merging the previous four data files. This

summary file was embellished by the addition of the observed

basis change, expressed both fractionally, as the numerator

of a 32nd, and decimally. This latter observation

corresponds to the error, or residual, when the observed

change-in-basis differed from the predicted change-in-basis,

namely zero, where the regression coefficient is +1. A plot

of these residuals on time, smoothed by reducing them to

weekly averages, is reflected in Figure 3. Before

commenting on that display, some characteristics of this

particular series of hypothetical hedges are worthy of

comment.

Of the 1,284 hypothetical hedges observed,

approximately 6% contain simulated data points. These

observations, while admittedly differing slightly from the

established selection criteria, do closely approximate the

others.








250

200

150

100

50


P 0
0
I
N -50
T
S-100


-150

-200


Figure 3.


Weekly Average Change in Basis GNIA8/CBOT/4 Week
Hedge/3 Month Contract, 1976-1981.









There were only 15 observed instances of the so-called

perfect hedge, slightly over 1% of the sample total.

There were surprisingly 127 observed instances, nearly

10% of the total, when cash and futures price movement

exhibited negative correlation rather than the expected

positive correlation. In these cases, the short (long)

hedger would have gained (lost) on both cash and futures

transactions on 29 occasions while losing (gaining) in both

markets on 98 occasions.

There were 316 observed instances, nearly 25% of the

sample total, when the short (long) hedger's cash position

improved (deteriorated) but the futures position

deteriorated (improved) more rapidly, producing a net loss

(gain); there were 375 observed instances, nearly 30% of the

sample total, when the short (long) hedger's cash position

deteriorated (improved) while the futures position improved

(deteriorated) less rapidly, thus failing (succeeding) in

covering (preserving) the hedger's cash market loss (gain).

Lastly, there were 168 observed instances, over 13% of

the sample total, where the short (long) hedger's cash

position improved (deteriorated) with the futures position

deteriorating (improving) less rapidly, thus preserving

(covering) the hedger's cash market gain (loss); there were

283 observed instances, over 22% of the sample total, where

the short (long) hedger's cash position deteriorated

(improved) with futures positions improving (deteriorating)

more rapidly, thus producing a net gain (loss).









Admittedly, any one hedger's net results from employing

a series of traditional hedges would be a function of the

magnitude of each transaction and the degree of the change.

Nevertheless, these observations provide insight into the

workings of the market over the 1976-80 period. From the

viewpoint of the classic short hedger, there were 1,269

opportunities (99% of the sample total) to hedge one's cash

inventory position and experience a disconcerting basis

change. On 702 occasions, over 55% of the sample total, the

futures position added to the yield on an unhedged position

or perfectly hedged the position. On 582 occasions, about

45% of the sample total, the futures position subtracted

from the yield on an unhedged position. The consideration

of transaction costs could be expected to narrow the

apparent margin favoring the hedge.

What is noteworthy is that the expected positive change

in the basis, observed by Ederington [1] to generally

characterize the market during the 1976-77 period and

attributed to the convergence phenomenon, has not subtracted

from the short hedger's performance opportunities with the

frequency that might have been expected.

Close examination of Figure 3, the plot of residuals on

time, suggests the dominance of the positive change in the

basis, clearly observed for 1976-77, may have been broken in

1978-80. Obvious from the plot is the increased volatility

in the performance of the classic traditional hedge in the

1978-80 period and particularly from October, 1979, through









the end of 1980. If all hedges were perfect, as traditional

theory suggests, the plot of residuals would be the

reference line with a slope of +1. But Figure 3 reveals

such is not the case nor can the variance or volatility over

time be considered constant. (This should not be construed

as suggesting the presence of heteroscedasticity, which is

best observed by a scattergram and not by a plot of

residuals over time. Increase in volatility in the

performance of the hedge may be caused by any combination of

relative change in cash or futures and is not necessarily

suggestive of large changes in futures or cash being

associated with large residuals. The large residual could

result when either the change in cash or futures is quite

small.)

Having constructed a sample of 1,284 hypothetical

hedges in the near-term contract and examined some of the

characteristics of the performance of the hedge assuming

traditional hedging theory, it is appropriate to examine

the performance of the hedge given the remaining assumptions

of this research. This requires construction of a moving

546-day observation range which begins at frame 1097 and

observes 390 hypothetical hedges that could have occurred in

the previous 546-day period. After observing

characteristics of performance during that frame (namely, bt

and et), the moving observation range is stepped forward

one frame to repeat the process. This continues until

frame 2349, the last possible observation point for









28-day hedges during the 1976-80 period. The result is 895

observation platforms on which to stand and examine hedge

characteristics over the immediately previous 18-month

period.

A summary of these observations was produced utilizing

the data files generated earlier. With each of the 895

frames containing 390 overlapping observations, the summary

can be embellished with such descriptive statistics as the

sample regression coefficient (Ederington's b*) and the

sample coefficient of determination (Ederington's e).

Frame 1097 corresponds, if somewhat roughly, to

Ederington's observations for the 1976-77 period. His

observed measure of hedging efficiency for this period was

.785, whereas this study produced an et of .812. Franckle

and Wurtzebach [3], in examining the 1976-77 period,

produced an e of .871, explaining the discrepancy between

their findings and Ederington's results for the same period

by noting differences in data collection, a factor mentioned

earlier. This study's findings of .812 are not inconsistent

with earlier findings, given the varying techniques of data

collection and the other assumptions previously mentioned.

Ederington noted b* at .848 for this period, whereas

Franckle and Wurtzebach found .697, again attributing the

difference to data collection. Observation of the slope at

.907 in this research is compatible with Ederington's

findings.









Franckle and Wurtzebach provide one more opportunity

for comparison. In dividing their sample into two equal

periods, 1976-77 and 1978-79, they provide a second frame or

platform from which to observe. This platform corresponds

roughly to frame 2010. Franckle and Wurtzebach observed b*

and e at .936 and .898 for third period, whereas this

research found b* and e at frame 2010 to be .948 and .937.
t t
The last such frame observed in the case of the 28-day hedge

is frame 2349.





TABLE 3

Summary of Current and Previous Findings
28-Day Hedge in the Near-Term Contract
1976-77

Estimated Estimated
b* e

Ederington .848 .785
Franckle and Wurtzebach .697 .871
Earle (t=1097) .907 (.835) .812 (.614)
1978-79

Franckle and Wurtzebach .936 .898
Earle (t-2010) .948 (.888) .937 (.802)
1980

Earle (t=2349) 1.032 (.860) .891 (.680)






Having made 893 additional observations of b* and e to
t t
supplement the two observations noted by Franckle and

Wurtzebach, they can now be plotted on a graph with time as









the x-axis and the coefficient of determination or the

regression coefficient on the Y-axis. The results are

depicted in Figures 4 and 5.

The plots in these figures reveal a pattern of

performance that can be attributed to the hedge given the

assumptions. Note the efficiency of the hedge (e) was

improving steadily at the time of the initial observation

(frame 1097) until the end of calendar 1977. Ederington [1]

suggested that continuing maturity of these fledgling

markets could result in increased efficiency. Note that

this period of increasing e corresponds to a period of

decreasing b* at a time when the market was exhibiting

consistent positive change in the basis. Therefore, as b*

was continually being lowered in a positive change

environment, e was predictably increasing. The

stabilization of hedge efficiency from early 1978 until mid-

to late-1979 may have reflected near optimal efficiency

under the given conditions. (The Federal Reserve action in

October, 1979, corresponds suspiciously with the dramatic

increase in efficiency indicated by the data in mid- to

late-1979, but this author discounts any significance in

this apparent relationship. More likely, the increased

efficiency results from a combination of a relatively low b*

and the elimination of the last vestiges of the positive

change in the basis characteristic which occurred about

early 1978. Thereafter, a new, higher level of market









1.1-
1-



D 1.0-
j -



S0.9-
I
I w

0.8-




0.7-






Figure 4.


I I I I I
DEC DEC DEC DEC DEC


Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/3 Month Contract,
1976-1981.


DEC








1.50--




H 1.25-
E
D
G
E1.00
R
A -
T
I
0 0.75-



0.50
DEC DEC DEC DEC DEC DEC





Figure 5. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/3 Month Contract,
1976-1981.









efficiency dominated until the effects of the turbulent 1980

produced a sharp decline in that year.

These findings confirm Franckle and Wurtzebach's

conclusion for 1978-79 vis-a-vis 1976-77. The markets

apparently were more efficient in times of increasingly

higher interest rates (although causation is not necessarily

established). However, those conclusions may not be safely

projected beyond October, 1979, when volatility was combined

with overall high levels of interest rates.

The series of risk-minimizing hedge ratios (b*)

exhibits a pattern of generally increasing values,

suggesting that the risk-minimizing proportion hedged may,

over time, be approaching that suggested by traditional

theory. Indeed, as positive change-in-basis markets are

balanced by negative change-in-basis markets over long

periods of time, this can be anticipated. Observe the

correlation between the performance of the risk-minimizing

hedge ratio and weekly average change-in-basis. Severe

negative change-in-basis (indicating futures are moving

slower than cash) is matched by increases in the

risk-minimizing hedge ratio. In 1980, with the prime rate

falling during the first half of the year, futures prices

rose slower than cash prices resulting in a negative

change-in-basis for the first half of 1980. However, in the

second half of 1980 with the prime rate rising, futures

prices fell faster than cash resulting in a positive

change-in-basis for the second half of 1980. This explains









the leap in b* at about February, 1980, and the violent

negative spike in the weekly average change-in-basis at

about the same time.

The violent positive spike in the weekly average

change-in-basis occurring in mid-1980 leveled off b* (not

reduced it) since it was having to "offset" the effects of

the immediately earlier opposite spike. Efficiency (e),

having leaped to a new level in October, holds until

mid-1980 when return of a strong positive change-in-basis

condition (suggesting an immediately lower b*) catches b* at

high levels (because of the 18-month range). The result is

a dramatic decrease in et.

Franckle and Wurtzebach [3] observed a sizeable

increase in b* between the 1976-77 period and the 1978-79

period. A declining b* as experienced from mid-1977 to

mid-1978 would suggest a more rapid change in futures prices

than in cash prices, consistent with the generally positive

change-in-basis characteristic of this period. However,

with erosion of the dominance of the generally positive

change-in-basis over 1978-80, it is noted that the b* has

indeed approached or even exceeded that stipulated by

traditional hedging theory.



Inferential Results

Multiple regression, using PRMVOL, PRMTND, and PRMAVE

as independent variables to predict the value of both b* and

e, is a technique apparently unexplored by previous









research. The results of an SPSS run to evaluate and

measure the overall dependence of b* on these three

variables is summarized in the following table:





TABLE 4

Selected Statistics for Multivariate Regression

Multiple R 0.92433 ANOVA DF SS F
R Square 0.85439 Regression 3 6.30608 1742.68940*
Std Error 0.03473 Residual 891 1.07472

Variable B Beta Std Error B F
PRMVOL -0.0272943 -0.53319 0.00190 206.083*
PRMAVE 0.0600282 1.75613 0.00168 1273.127*
PRMTND -16.5203899 -0.76201 0.73349 507.291*
Constant 0.4534595


*Significant at the .05 level.



Since the computed F value is larger than the

statistical tables value for a level of significance of .05

for 3 and 891 degrees of freedom, the observed linear

association is statistically significant, although not

necessarily causal. Similarly, each of the independent

variables exhibits a coefficient significantly different

from zero at the .05 level, implying a linear relationship

does exist between each of these independent variables and

the dependent variable, b*. Reference to the multiple r

leads to the initial conclusion that a significant

proportion (85.439%) of the variation in b* can be explained

by the independent variables.









Because of the different units of measure used for the

independent variables, reference to the beta values provides

a more sensible way to compare the relative effect on the

dependent variable by the independent variables. Other

things being equal, the betas indicate that one standard

deviation per unit change of PRMAVE would produce the

greatest change in b* and one unit change of PRMVOL would

produce the least.

The results of the SPSS run to evaluate and measure the

overall dependence of e on the three independent variables

are summarized in the following table:





TABLE 5

Selected Statistics for Multivariate Regression

Multiple R 0.80119 ANOVA DF SS F
R Square 0.64190 Regression 3 0.54765 532.38332*
Std Error 0.01852 Residual 891 0.30552

Variable B Beta Std Error B F
PRMVOL -0.0021678 -0.12456 0.00101 4.573*
PRMAVE 0.0081887 0.70461 0.00090 83.339*
PRMTND 1.6598608 0.22519 0.39208 507.014*
Constant 0.8106573


*Significant at the .05 level.



The observed linear association is statistically

significant at the .05 level as are each of the partial

coefficients. The strength of the relationship as evidenced

by a multiple r2 of 64.190% is not nearly so strong as was
by a multiple r of 64.190% is not nearly so strong as was









the case with b*. Again the observed beta weights suggest

PRMVOL could be dropped as a predictor variable with little
2
impact on the multiple r

For purposes of comparing different market

environments, the 895 item data set was subdivided and

examined in separate parts. The first data set contained

the first 598 observations, roughly spanning the period from

1976 to 1978, whereas the second data set contained the

remaining 297 observations roughly corresponding to the

relatively volatile 1979-80 period. Selected results

follow:





TABLE 6

Multiple Coefficient of Determination (r2)

Dependent Variable b* e
Combined Subsets 0.85439 0.64190
Subset 1 (1976-78) 0.72711 0.33360
Subset 2 (1979-80) 0.89796 0.83220





What is notable is the significantly increased strength

of the relationships during the relatively volatile 1979-80

period as contrasted with the relatively benign 1976-78

period.









Detection of and Correction for Positive Serial Correlation
in the Data Observations

Detection. Spurred by the intuitive notion that the

data points collected and observed in previous research and

thus far in this study could likely be affected by serial

correlation, the researcher generated a plot of residuals by

an SPSS run on selected samples of hedges. The null

hypothesis was NO evidence of serial correlation (P=0)

whereas the alternative hypothesis was positive serial

correlation (P > 0). The decision rule was to reject the

null if the Durbin-Watson d-statistic was less than 1.52.

The computed d-statistic of .48981 was indeed less than 1.52

suggesting significance at the .01 level. Therefore, the

null was rejected and the conclusion was evidence of

positive serial correlation. Initial P on selected samples

ranged from .45 to .80, further confirming the evidence of

strong positive autocorrelation in the data points.



Correction. Using the Cochrane-Orcutt technique [7]

through three iterations to eliminate positive

autocorrelation in the residuals produced transformed data

points that consistently reflected -0.03 < P < 0.03 where

any -0.20 < P < 0.20 is considered relatively free of serial

correlation in the error terms. (It should be noted that

from this point only every third data point was observed,

reducing the sample from 895 observations to 299

observations.)









The b* and e are recalculated using the transformed

data points thus obtained. The results are predictable and

are depicted in Figures 6 and 7.

We expect the intercept and slope to remain relatively

unchanged after the removal of positive autocorrelation in

the residuals. However, the r2's are predictably reduced

and greater exaggeration is obtained in the plot of the

efficiency index.

Note from Table 3 on page 69 the efficiency index of

.812 reported at t=1097 is reduced to .614. In fact,

Figure 6 indicates the entire family of efficiency indices

is noticeably modified, including the observations at t=2010

and t=2349 reported in Table 3. While the general

characteristics of the performance of the efficiency index

are recognizable, the efficiency index now operates over a

greater range with increased volatility and substantially

reduced magnitude.









1.0


0.9-



0-8--



0.7-



O.R--


0.5


I I I I I
DEC DEC DEC DEC DEC


DEC


Figure 6. Performance of Hedge Efficiency Index
GNMA8/CBOT/4 Week Hedge/3 Month Contract
(Autocorrelation Corrected), 1976-1981.


I,.- *

.wI


---------


I








1.50




H 1.25-
E
D
G
E
1.00-


I -
0 0.75-



0.50
DEC DEC DEC DEC DEC





Figure 7. Performance of Risk-Minimizing Hedge Ratio
GNMA8/CBOT/4 Week Hedge/3 Month Contract
(Autocorrelation Corrected), 1976-1981.









New multiple regressions utilizing the revised estimate

of b* are summarized below:



--------------------------------------------------------

TABLE 7

Selected Statistics for Multivariate Regression
(Autocorrelation Corrected)

Multiple R 0.84184 ANOVA DF SS F
R Square 0.70869 Regression 3 0.69748 239.21789*
Std Error 0.03118 Residual 295 0.28671

Variable B Beta Std Error B F
PRMVOL -0.0017121 -0.53151 0.00030 33.461*
PRMAVE 0.0342306 1.58710 0.00262 170.947*
PRMTND -0.0081647 -0.59582 0.00114 51.162*
Constant 0.5893686


*Significant at the .05 level.



The table compares directly with Table 4 on page 75.

Note the strength of the relationship is weakened by the

effect of the autocorrelation in the original data.









The revised multiple regression run utilizing e as the

dependent variable produces the following:


TABLE 8

Selected Statistics for Multivariate Regression
(Autocorrelation Corrected)

Multiple R 0.39091 ANOVA DF SS F
R Square 0.15281 Regression 3 0.14354 17.73652*
Std. Error 0.05194 Residual 295 0.79583

Variable B Beta Std Error B F
PRMVOL 0.0009501 0.30192 0.00049 3.713
PRMAVE -0.0047759 -0.22665 0.00436 1.199
PRMTND 0.0066992 0.50040 0.00190 12.409*
Constant 0.7475657

*Significant at the .05 level.
*Significant at the .05 level.


The table compares directly with Table 5 on page 76.

There is considerable loss in goodness-of-fit as reflected

by a reduced r2 from 0.64190 to 0.15281. Although a linear

relationship may be said to exist, it is weak.

Selected summary statistics are as follows:


TABLE 9

Multiple Coefficient of Determination (r2)

Dependent Variable b* e
Combined subsets 0.70869 0.15281
Subset 1 (1976-78) 0.48698 0.46434
Subset 2 (1979-80) 0.88447 0.73295









This table may be compared directly with Table 6 on

page 77. The pattern is similar to the one obtained with

the original data points. The relationship between b* and e

and the three independent variables, although weaker,

appears much stronger in the latter, more volatile period.



The Performance of the Hedge Under
Selected Alternative Conditions



The Performance of the 28-Day Hedge
in the Distant Contracts

As did Ederington [1], this effort has constructed and

observed hypothetical hedges in the so-called distant

contracts, those six, nine, and twelve months removed from

the originating date of the hedge. The criterion for

selecting the hedge parameters is identical to that observed

for the near-term or three-month contract.

In the case of the 28-day hedge, a total of 1,284

hypothetical transactions were constructed in each of the

respective contracts. The measures of hedge performance, b*
t
and et, are developed similar to the previous case.

Table 10 summarizes from the viewpoint of the classic

short hedger certain characteristics of the performance of

the 28-day hedge in the various contracts, including the

near-term contract.

There is an apparent increasing incidence of unexpected

negative correlation between the movement of cash and

futures prices as one hedges in increasingly distant











TABLE 10

Summary of Selected Hedge Characteristics from the
Viewpoint of the Classic Short Hedger
28-Day Hedge, All Contracts

Category Description 28-Day 28-Day 28-Day 28-Day
(+) Adds to the Yield Hedge Hedge Hedge Hedge
of an Unhedged Position 3-Mo 6-Mo 9-Mo 12-Mo
(-) Subtracts from the Yield Cntrct Cntrct Cntrct Cntrct
of an Unhedged Position

Observed Instances of Both
Cash and Futures Positions
Improving (+) 29 36 46 48

Observed Instances of Both
Cash and Futures Positions
Deteriorating (-) 98 86 92 108

Observed Instances of the
Perfect Hedge 15 11 11 10

Observed Instances of Cash
Position Improving with
Futures Position
Deteriorating Faster (-) 316 305 272 245

Observed Instances of Cash
Position Deteriorating
with Futures Position
Improving Slower (+) 375 366 358 360

Observed Instances of Cash
Position Improving with
Futures Position
Deteriorating Slower (-) 168 176 200 224

Observed Instances of Cash
Position Deteriorating
with Futures Position
Improving Faster (+) 283 304 305 289









contracts. As observed earlier, there were 127 such

occurrences in the near-term contract, comprising

approximately 9.9% of the sample total. This instance

increases in the nine-month and twelve-month contracts to

138 (10.7%) and 156 (12.2%), respectively. A confidence

interval on the first proportion suggests the statement that

the true proportion of negatively correlated hedges is

between 8.3% and 11.5% is correct with a probability of

.95. Thus, there appears to be a significant increase in

the proportion of negatively correlated hedges in the most

distant contract. The puzzling dominance of instances in

this set where cash prices are decreasing while futures

prices are increasing appears uniform across all contracts.

The observed instance of the so-called "perfect" hedge

appears consistently in the range of 0.8% to 1.2% of the

sample total.

Note the decreasing incidence of futures market

deterioration (increasing futures prices) being sufficient

to override cash market improvement (increasing cash prices)

as one hedges in the more distant contracts. It was

observed in the analysis of the positive/negative

change-in-basis characteristics of the market that when cash

prices rise, as they may be expected to do when interest

rates are falling, futures prices may rise more slowly

suggesting long-term pessimism on the part of the market and

generating negative change-in-basis characteristics. For a

classic short hedger, increasing cash prices would reflect









improvement in the cash position, while increasing futures

prices would reflect deterioration in the futures position.

Thus, on the basis of trend alone, this decreasing incidence

of futures market deterioration being sufficient to override

cash market improvement as one hedges in increasingly

distant contracts may suggest the short hedger would be well

advised to hedge in the distant contracts.

As observed earlier, there were 316 such occurrences in

the near-term contract, comprising approximately 24.6% of

the sample total. This instance decreases in the six-month,

nine-month, and twelve-month contracts to 305 (23.8%), 277

(21.2%), and 245 (19.1%), respectively. A confidence

interval on the first proportion suggests the statement that

the true proportion of such hedges is between 22.3% and

27.0% is correct with a probability of .95. There appears,

then, to be a significant difference in the proportions

experienced in the more distant contracts.

This result is not inconsistent with the conclusion

that might be drawn from examination of the other

significant set where the short hedger's yields are reduced

by futures market participation. Note the increasing

incidence of futures market deterioration (increasing

futures prices) being insufficient to override cash market

improvement (increasing cash prices) as one hedges in the

more distant contracts. As observed earlier, there were 168

such occurrences in the near-term contract, comprising




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