Hedging against commodity price inflation

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Hedging against commodity price inflation a security market approach
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Hedging (Finance)   ( lcsh )
Inflation (Finance)   ( lcsh )
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Thesis--University of Florida.
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Includes bibliographical references (leaves 102-104).
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by Gerald Douglas Gay.
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Typescript.
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Vita.

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HEDGING AGAINST COMMODITY PRICE INFLATION:
A SECURITY MARKET APPROACH





BY

GERALD DOUGLAS GAY


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


1980













ACKNOWLEDGEMENTS


The writer is indebted to Dr. Richard H. Pettway, chairman of

nis supervisory committee, and to Dr. Steven Manaster, Dr. Robert W.

Kolb, Dr. David A. Denslow, Jr., and Dr. H. Russell Fogler, members of

the committee, for their counsel and assistance in the preparation of

this dissertation. The writer is especially obligated to Dr. Steven

Manaster for his guidance and many helpful suggestions.













TABLE OF CONTENTS


PAGE

ACKNOWLEDGEMENTS................................................. ii

ABSTRACT.... ...... ..................................... iv

CHAPTER

I. INTRODUCTION... ............... .......................... 1

A. Overview.................. ..................... 1
B. Previous Work in Commodity Pricing.................. 2
C. General Outline..................................... 6

II. A LITERATURE REVIEW OF MULTI-PERIOD PRICING MODELS....... 9

A. Long's Multi-Period Pricing Model................... 10
B. A Test of the Long Multi-Period CAPM.................... 17

III. METHODOLOGY FOR CREATING "QUASI-FUTURES" CONTRACTS....... 20

IV. THE FORMATION OF "QUASI-FUTURES" CONTRACTS .............. 28

A. The Data............................. .............. 28
B. Empirical Estimation of the Regression Coefficients.. 38
C. Computation and Analysis of the Portfolio Weights.... 42

V. TESTS OF THE PORTFOLIOS AS HEDGING INSTRUMENTS........... 52

A. Testing Price and Risk Characteristics .............. 52
B. Effect of the Nixon Wage and Price Controls.......... 69
C. Quarterly and Semiannual Rebalancing................. 85

VI. SUMMARY AND CONCLUSION................................. 90

A. A Summary of this Research.......................... 90
B. Suggestions for Further Research.................... 95

APPENDICES

A. CREATING A "QUASI-FUTURES" CONTRACT: AN EXAMPLE........ 98

B. A GENERAL SOLUTION FOR THE PORTFOLIO WEIGHTS............. 100

BIBLIOGRAPHY.................................................. 102

BIOGRAPHICAL SKETCH.............................................. 105
iii












Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


HEDGING AGAINST COMMODITY PRICE INFLATION:
A SECURITY MARKET APPROACH

By

Gerald Douglas Gay

June, 1980
Chairman: Richard H. Pettway
Major Department: Finance, Insurance, and Real Estate


Investors often hedge against price inflation in a particular

commodity by taking a position in a futures contract, an action that

protects the investor from any price fluctuations in the commodity during

the period before delivery. This dissertation develops portfolios com-

posed of default-free bills of various maturities and shares of common

stock which allow an investor to hedge against commodity price inflation,

without actually entering the futures markets. This hedging alternative

can be of use to investors who wish to hedge against price inflation in

commodities for which organized futures trading does not exist.

This study develops hedges by purchasing existing security market

instruments, using a previously suggested technique. These hedge port-

folios, or "quasi-futures" contracts, for a particular commodity are

constructed such that they are not only highly correlated with the

commodity, but also have the same price and risk properties. The port-

folios and the commodities are shown to have the same expected price at

delivery, and the same covariances with the stock market, all other

commodities, and long-term bills.
iv







The hedging portfolios developed for ten various commodities over

the period 1965-1976 are shown to be unbiased substitutes for the

commodities themselves. The techniques explored in this dissertation

allow investors to hedge against price inflation in any commodity.

Consequently, the existence of these "quasi-futures" contracts has

important implications for the necessity of futures markets and for the

development of a multi-period capital asset pricing model. If markets

are perfect and securities are traded costlessly, then futures markets

do not provide an investor with a service that is not already available

in the existing markets for common stocks and Treasury bills. Additionally,

since these "quasi-futures" contracts can be created with existing

securities, a pricing model, based on a multi-period economy which allows

for shifts in commodity prices and the term structure of interest rates,

may well lead to a more complete and realistic view of capital market

equilibrium. Finally, the "quasi-futures" contracts are shown to require

frequent rebalancing. Thus, futures markets may be economically valuable

since they allow investors to hedge more efficiently in terms of trans-

action costs.













CHAPTER I
INTRODUCTION


I. A Overview

Investors often hedge against price inflation in a particular

commodity by taking a position in a futures contract, an action that pro-

'ects the investor from any price fluctuations in the commodity during the

period before delivery. This dissertation investigates whether portfolios

composed of default-free bills of various maturities and shares of common

stock allow an investor to hedge against commodity price inflation, with-

out actually entering the futures markets. This hedging alternative will

be especially appealing to investors who wish to hedge against price

inflation in commodities for which organized futures trading does not

exist.

This study develops hedges by purchasing existing security market

instruments, using a technique suggested by Long (1974). These hedge

portfolios, or "quasi-futures" contracts,1 for a particular commodity will

not only be highly correlated with the commodity, but will have all the

same price and risk properties. The portfolios and the commodities will

have the same expected price at delivery, and the same covariances with

the stock market, all other commodities, and long-term bills.



These portfolios are not true futures contracts for two reasons;
(1) they require a positive net investment, and (2) they involve taking
a current position in the markets for common stocks and Treasury bills.
However, these portfolios will be called "quasi-futures" contracts to
be consistent with the terminology of Long.





2

The hedging portfolios developed for ten various commodities over

the period 1965-1976 will be shown to be unbiased substitutes for the

commodities themselves. Consequently, their existence has important impli-

cations for the necessity of futures markets and for the development of

a multi-period capital asset pricing model. If markets are perfect and

securities are traded costlessly, then futures markets will not provide

an investor with a service that is not already available in the existing

markets for common stocks and Treasury bills. Additionally, if these

"quasi-futures" contracts can be created with existing securities, Long's

pricing model, based on a multi-period economy which allows for shifts

in commodity prices and the term structure of interest rates, may well

lead to a more complete and realistic view of capital market equilibrium.

I. B Previous Work in Commodity Pricing

Futures markets integrate the actions of two types of investors who

are typically described as being either hedgers or speculators. In order

to avoid the risks of price fluctuations in the spot commodity, a hedger

will initiate a futures market transaction. Thus an investor who desires

a particular commodity for future consumption or production purposes will

purchase a claim for future delivery of the specified commodity. This is

a riskless claim for consumption of the commodity even though the future

spot price of the commodity is highly uncertain. On the other side of

the market, the speculators underwrite the risks of price fluctuation in

the spot commodity in hopes of receiving some compensation.

Keynes (1930) first analyzed futures markets as constituting an

insurance mechanism. According to Keynes, hedgers pay a significant

premium to the speculators for underwriting the risks of price fluctuation

in a commodity. Hardy (1940) has argued to the contrary, that futures








markets are a socially acceptable form of gambling whereby speculators may

actually be willing to pay for this opportunity to gamble. Thus the

premium they receive should be zero or possibly negative.

Attempts have been made to analyze the returns to holders of futures

contracts for the purpose of interpreting the actual need for futures

markets. Dusak (1973) presents a portfolio approach and argues that futures

markets are no different in principle from the markets for any other risky

portfolio assets. Since all assets are candidates for inclusion in an

investor's portfolio, the return on any risky asset should be governed by

the asset's contribution to the risk of a large and well-diversified port-

folio of assets. In her paper Dusak investigates the risk-return relation-

ship to holders of futures contracts in a capital asset pricing framework.

The purchase of a futures contract is like buying a capital asset on

credit since the buyer has no capital of his own invested. The margin

paid by an investor is merely a good-faith deposit to acknowledge a later

commitment to the contract and thus cannot be treated as a capital invest-

ment. Thus, in order to approximate the risk premium earned on the spot

commodity, Dusak uses the percentage change in the futures price over a

given interval. Her results indicate that the returns and systematic

portfolio risk are both close to zero for each of the commodity futures

studied (wheat, corn, and soybeans) despite the fact that each commodity

had a large price variability during the sample period of May 1952 through

November 1967. These findings contradict the Keynesian theory which says

an investor in commodity contracts should earn a substantial positive

return. In addition, the findings only partially support the Hardy gambling

casino theory (which predicts a mean return of zero) since the systematic

risk was close to zero.








Black (1976) also discusses the behavior of futures prices in a

model of capital market equilibrium and states that the returns on

commodity holdings should obey the capital asset pricing model like any

other asset. He develops an expression which states that the expected

change in the futures price is proportional to the "dollar beta" of the

futures price. If the change in the futures price is uncorrelated with

the return on the market portfolio, thus producing a zero beta for the

futures price, then one would expect a zero change in the futures price.

Had Black empirically tested his equations, he would have expected the

same zero returns to holders of futures contracts that Dusak found, since

in Dusak's paper covariances with the stock market were close to zero for

wheat, corn, and soybean futures.

Black also states that since commodity holdings appear to be priced

like other assets, then investors who own commodities should be able to

diversify away any unsystematic risk. One way this may be done is through

futures markets. However, since the majority of commodity holdings is by

corporations, the risk may be passed on to shareholders who should hold

well-diversified portfolios. This implies that futures markets do not

have a unique role in the allocation of commodity price risk since corpor-

ations can do a more efficient job, especially in the cases where organized

futures markets are nonexistent for many commodities.

Finally, on the need for futures markets, Black refers to the infor-

mation content of futures markets. Black (1976, p. 176) states "I believe

that futures markets exist because in some situations they provide an

inexpensive way to transfer risk, and because many people both in the

business and out like to gamble on commodity prices. Neither of these

count as a major benefit to society. The big benefit from futures markets





5


is the side effect: the fact that participants in the futures markets

can make production, storage, and processing decisions by looking at the

pattern of futures prices even if they don't take positions in that

market."

Stoll (1978) also maintains that traditional explanations of hedging

fail to take proper account of the available risk spreading opportunities

in the capital market as a whole as opposed to futures markets alone.

His rationale for hedging is the inability or reluctance of individuals

such as farmers or privately held firms to trade ownership claims on cer-

tain assets or production techniques with which they are endowed.

Stoll describes two types of risk associated with a commodity:

(1) price risk arising from future supply and demand uncertainties, and

(2) the risk due to uncertainties in storage costs. Futures markets only

allow the price risk to be passed on, but both the price and storage risks

could be passed on in the stock market if the process has shares traded.

Stoll develops a model of futures prices in a capital market

equilibrium framework in which there are non-tradeable assets. He relates

the expected dollar return on a futures contract to the market price of

risk and the risk of the futures contract which is measured by the co-

variance of the commodity return with the return of all other assets.

However, even if this systematic market risk is zero as Dusak found, the

expected return on futures contracts may not be zero depending on the

size of the market value of commodities relative to the market value of

all shares of stock. He concludes that in a world of perfect capital

markets there is no need for hedging if futures contracts and shares in

the production or storage process are traded at no cost.








It appears there is beginning to be some success in developing a

pricing framework to analyze futures markets. However, there is a lack

of any empirical testing of the models in the literature, and even less

to substantiate the different authors' explanations for the actual need

of futures markets. In their papers, neither Black nor Stoll empirically

tests his model. Moreover, Stoll's pricing model for futures contracts,

to be properly tested, requires pricing information on non-tradeable

assets. Dusak did construct and perform some tests, but limited her

investigation to three commodities.

Correct development of an equilibrium pricing model for futures

contracts and subsequent empirical analysis of the returns to holders of

futures contracts would not be adequate criteria for justifying the need

for futures markets as other authors have claimed. The necessity of

futures markets depends on the contribution of futures markets to the

completeness of markets. That is, are the services and investment oppor-

tunities provided by futures markets unique in that they are not available

elsewhere?


I. C General Outline

This dissertation investigates whether there are assets in existing

stock and bill markets which can be combined in such a way that the resulting

portfolio will have the same price and risk characteristics as does a

particular commodity. A stock-bill portfolio of this type which serves

as a substitute to holding a good itself will be referred to as a "quasi-

futures" contract. These "quasi-futures" contracts for a particular

commodity should have (1) the same "with-dividend" value at delivery as

the spot commodity and (2) the same covariance with the stock market,

all other goods, and all long-term bills as does the gooa itself.








The concept of a "quasi-futures" contract was first presented by

Long (1974) in his development of a multi-period capital asset pricing

model. The next chapter presents Long's theoretical discussion for the

development of his model from which the concept of a "quasi-futures"

contract is taken. The economy in Long's model is very realistic in that

there is a stock market, a market for default-free bills of different

maturities, and many consumption goods whose future prices are uncertain.

Long relates the price of an asset to not only the systematic market

risk, but also to the risk due to changing consumption opportunities

(inflation risk) and changing investment opportunities (interest rate

risk).

Chapter III presents the methodology for creating "quasi-futures"

contracts. The steps needed to attain the correct expected price and

covariance properties of the hedge portfolios are described in detail.

Chapter IV describes the actual formation of "quasi-futures" con-

tracts for ten different commodities using asset data from the period

January 1961 through March 1976. Selection of the various commodity,

bill, and stock data to be used, as well as the formation of a market

index, will be discussed. The econometric difficulties encountered in

creating the asset weights for the hedging porfolios are also presented.

Finally, the composition of the "quasi-futures" contracts is examined

with regards to the relative weights of the various stocks and bills con-

tained in each period's hedge. These findings are then compared with

those of Fama and Schwert (1977a), who investigate the success of various

assets as hedging devices against the different components of the in-

flation rate.








Chapter V outlines the various tests that are conducted in order to

verify that the "quasi-futures" contracts constructed are indeed true

substitutes for the goods themselves. Hypotheses are tested to determine

whether each hedging portfolio and good had the same subsequently observed

prices and covariances with the stock market, all other goods, and all

long-term bills. Interpretation of these results and the implications for

the necessity of futures markets is discussed. In addition, the sensi-

tivity of the results to the Nixon wage and price controls is tested.

Since the "quasi-futures" contracts are one month hedges which

require extensive and costly rebalancing, the tests of hypotheses are

repeated for the cases where the portfolios are rebalanced only at

quarterly and semiannual intervals. The results from these tests indicate

that futures markets provide a less expensive means for hedging against

commodity price inflation versus the use of "quasi-futures" contracts.

The final chapter presents the conclusions of the dissertation and

draws the practical implications of the research for hedging. In

addition, potential extensions of the dissertation are discussed.












CHAPTER II
A LITERATURE REVIEW OF MULTI-PERIOD PRICING MODELS


The capital asset pricing model as developed by Sharpe (1964) and

Lintner (1965a,b) abstracts from reality by assuming consumers act to

maximize the expected value of a utility function whose only arguments

are consumption at time 0 and nominal wealth at time 1. To make this

assumption consistent with consumer maximization of the expected utility

of a lifetime consumption stream,it becomes necessary to assume future

prices of consumption goods are known with certainty and no unpredictable

changes occur in the investment opportunities over time. Uncertainty in

the rate of commodity price inflation is thereby eliminated. In addition,

the capital market cannot contain assets whose future rates of return

over a time interval may depend on unanticipated events in the interim.

Thus, an economy with a bill market is not allowed. However, commodity

price inflation and the term structure of interest rates may play an

important role in the determination of equilibrium asset prices.

Roll (1973) recognizes that inflation of commodity prices has been

almost completely neglected in the literature of asset pricing. He

develops a capital asset pricing model that includes the risk of currency

inflation and attempts to show how assets and commodities acquire

equilibrium prices in competitive markets. Roll points out that the

simple Fisherian equation will not correctly specify the relation between

nominal interest rates and expected rates of commodity price inflation.

His analysis indicates that the nominal expected rate of return on assets

will depend on the covariance between nominal asset returns and the rate







of inflation. Roll's economy, however, has only one future date and thus

the term structure issue is ignored.

Merton (1972) presents a continuous time analysis of the demand for

assets in an economy where both consumption good prices and the investment

opportunity set are allowed to vary randomly over time. He derives a

formula that expresses the consumer's demand for risky assets in term of

parameters describing his consumption preferences and parameters of the

stochastic process governing commodity and asset prices. Like Roll,

however, Merton's paper fails to provide testable propositions in the

form of precise relations between well defined and readily measurable

variables.


II. A Long's Multi-Period Pricing Model

Long (1974) provides a very realistic view of capital market

equilibrium, by presenting a multi-period discrete time analysis which

deals directly with uncertainty in future commodity prices and future

investment opportunities from which he develops empirically testable

price formulas for common stock and long-term bills. These formulas are

developed such that the relation between equilibrium prices and parameters

describing consumer preferences can be directly analyzed. The price of

an individual asset can be interpreted in terms of its marginal contribu-

tions to portfolio characteristics that concern investors such as mean,

variance, and covariance.

The economy in Long's model contains three markets: a stock market

where the shares of N firms are traded, a consumption goods market

containing K non-storable commodities available to consumers, and a market

containing default-free bills for any maturity date up to and including

time T. For each of these markets, the following assumptions are made:








(1) markets are perfect in the sense that all items are infinitely

divisible, there are no transaction costs, and all traders acts as price

takers; (2) on any date all traders have free and equal access to all

information which is relevant to assessing the subjective joint proba-

bility distributions of prices which prevail on subsequent trading dates

and, furthermore, all consumers form identical expectations regarding

prices to be realized on subsequent dates; (3) markets are only open on

trading dates which are equally spaced in time; (4) all production in

the economy is accomplished by firms; and (5) the only inputs to produc-

tion supplied directly by consumers are capital funds supplied by the

purchase of the firm's shares and bills.

Next, a brief development of the pricing formulas is presented. The

notation that will be used is given as follows:

1kt = the price per unit of good k at time t;
Cikt = the quantity of good k purchased by consumer i at time t;

P, = the ex-dividend price per share of stock in firm j at time t;

Djt = the dividend per share paid at time t to shareholders in

firm j;

Vjt = the "with-dividend" price per share of stock in firm j at

time t;

X.j = the number of shares in firm j that consumer i chooses at

time t to hold during the (t+l)st period;

3tm = the price at time t of a bill which matures and pays one
dollar at time m, (O
Yitm = the number of bills maturing at time m that consumer i
chooses at time t to hold during the (t+l)st period.








A vector of prices or quantities will be referred to by omitting
the subscript which indexes the elements of the vector. For example,

the bundle of goods consumed at time t by consumer i is denoted by
Cit = (Cilt, Ci2t, ..., CiKt)'

Consumer i is assumed to act at time 0 as if he is maximizing the
expected value of a utility function of the form U (Ci0, Ci, ..., CiT)

where U is monotonically increasing, strictly concave, continuous, and

twice differentiable with respect to its argument. The maximization is

done subject to a set of budget constraints which will be given later.

Fama (1970b) shows how this problem can be recharacterized as one
in which consumer i acts at time 0 as if he is maximizing the expected

value of a semi-indirect utility function of the form Fi(CiO, wil' 1)'

F is defined to be the maximum attainable value of E(Ui) given that Ci0

is the bundle of consumption goods chosen at time 0, wil is the realized

value of time 1 nominal wealth, and that I1 is the realized value of the

vector of time 1 prices and dividends I- (n, P1, D1, B1)

The variables wil and jl serve to summarize the opportunity set
the consumer will face at time 1. However, it is not necessary to have

all of the data specified by wil and 1l in addition to those items known

to the consumer at time 0 in order to fully specify the opportunity set

seen at time 1. Empirical evidence (see Fama, 1970a) suggests that

observed stock prices and dividends do not convey new information about
the distribution of rates of return to be earned over subsequent periods

that is not already provided by observation of good and bill prices alone.

P1 and D1 may then be eliminated as arguments of the function Fi and,
therefore, we are left to maximize E [Fi (C 10 l' wi B1)] with

respect to (Ci0, Xio, Y i).





13

In order to simplify the problem further, the consumer's subjective
joint probability distribution on nl, B1, and w1 is assumed to be multi-

variate normal at time 0. The expected value of Fi then becomes a function
of Cio and the parameters which identify the particular multivariate normal

distribution of (wil, nl' 31). The only parameters of the distribution

that are affected by the consumer's portfolio choice are 1) the expected

value of wil, 2) the variance of wil, 3) the covariance of wil with each.

of the time 1 consumption good prices {nkl' k=l, ..., K}, and 4) the

covariance of wil with each of the time 1 bill prices {Blm, m=2, ..., T}.

Thus there exists a function Gi that can now be used in place of the

expected value of Fi as the objective function such that


Gi(Cio ei' vi Hi, Ji) = E[F1(Ci0 Wil, n B1)]

where

ei E(wil);

vi = var(wil);

H-= (Hil, ..., H, ... HiK)' with Hik = cov(wl, kl);

and
im= (0 .' with J o
i i2' im' iT) with Jim = cov(il Blm)

Consumer i's current consumption-investment decision problem at
time 0 will then be to maximize Gi subject to the constraints:

K N T
C C kO kO + X + Yi0m Om io;
k=l j=1 m=l

CikO > 0, k = 1, ., K;







iN T
11 E ojl V iO m:2 iOm Blm
ii i ovil + Yi0i + M- i0m lm
j=l m=2
By solving the above maximization problem it can be shown that at
equilibrium the resulting pricing equation for stocks and bonds is1

P =B [V + 2v ev- M + Vb)+ eH + \0o (II-1)
0 01 1 ev(-aM +eH + eJ
-e1
B = B [B + 2v- e (S + b) + YeH + e] (II-2)
0 01 1 ev -i + B eH -e


where

v = the number of consumers,
e = a weighted average of individual consumers' marginal rates

of substitution (MRSs) of expected nominal wealth for variance

in nominal wealth,

GeH = a vector of weighted averages of individual consumers' MRSs
of expected nominal wealth for covariance between nominal

wealth and the price at time 1 of each good k,
eeJ = a vector of weighted averages of individual consumers' MRSs

of expected nominal wealth for covariance between nominal

wealth and the price at time 1 of each bill m,
b = a vector of the supplies of long-term bills,
and

m', 4 ', S, ', and z are vectors of covariances whose elements
are listed in Figure III-1 on page 21.



See Long, Appendix A, for the derivation of the first-order conditions
and the resulting price formulas.








It is possible to give economic interpretations to each of the

above terms. B01, the price of a risk-free one period bill, equals the

MRS of current nominal wealth (Wi0) for expected nominal wealth at

time 1 (ei). V1 is the marginal contribution per share of stock to the

consumer's expected nominal wealth at time 1. The term 2v-le ,( + Vb)
ev -m
measures the "expected wealth equivalent" to the average consumer of the

marginal nominal risk of a share of stock. The term eOeH measures the

"expected wealth equivalent" of the marginal contribution per share of

stock to covariance between consumer's time 1 wealth (wil) and the price

of each consumption good k, (Ikl). Similarly, 'eJ measures the "expected

wealth equivalent" of the marginal contribution per share of stock to

covariance between wil and the price at time 1 of bills maturing at time

m, (Bm).

The price formula for long term bills (11-2) is interpreted in the

same way as the stock price formula (II-1) with the words "bills maturing

at time m" substituted for "share of stock."

Using historic data, estimations can be formed of the expected

values and covariances in equations (II-1) and (11-2). To solve for the

unobservable e's, {eev, eHk' 0eJm; k = 1, ..., K; m = 2, ..., T} in the

formulae, there is a restriction for a non-trivial solution that the

number of stocks and long-term bills for which there are pricing formulae

must equal or exceed the number of unobservable O's. In other words, it

is required tnat N + (T 1) > 1 + K + (T 1), or equivalently, that

N > K + 1. If not, a solution will exist for any set of current prices

and the model would not have any empirical content.








By solving for the unobservable e's, it is possible to derive the

following reduced form pricing model2 which not only prices the systematic

market risk of a share of stock, but also the inflation risk from changing

good prices and the interest rate risk from changes in the term structure:

1 K -1
Pj0 = B1[Vj MVM B 0 MO- jk kl 01 FkO

T
jm (Blm- B 01 Bm)], j = 1, ..., N. (11-3)
m=2 m 1
In the above equation VM1 is the mean of the "with-dividend" value of the

stock market portfolio at time 1 and PMO is its current ex-dividend price.

The assumption that (VM1l, n1' B1) is multivariate normal guarantees the

existence of linear regressions within this set of random variables.

The symbols 8jM', {k' k = ..., K}, and {6jm, m = 2, ..., T} are,

respectively, the coefficients of V M, {1kl, k = 1, ..., K} and

{Blm, m = 2, ..., T} in the following multiple regression:

K T
Vj = tj + j VM + E Ejk kl + EZ jmB + ., j = L, ..., N.
k=l m=2
(11-4)
N .
In the above regression, VMi1 ` Vjl, the "with-dividend" value at time
j=1 l
1 of the stock market portfolio. Also, E(ej) = 0 and ej is independent

of (VM 1, B1). Finally, FkO is the current ex-dividend price of any

stock-bill portfolio whose "with-dividend" value at time 1 has a mean
equal to Ikl and has the same covariance with the elements of

(VM1' I,' B1) as does Hkl* This stock-bill portfolio is referred to as
a "quasi-futures" contract for good k.



See Long, Appendix B.








II. B A Test of the Long Multi-Period CAPM

Gouldey (1977) presents a test of the Long model. The purpose of

Gouldey's study was to test the implications of the Long model, which

suggested that investors are concerned with three types of risk when

making investment decisions: the traditional systematic market risk,

the risk due to a stochastic consumption opportunities set, and the risk

due to stochastically changing investment opportunities.

Whereas the traditional mean-variance CAPM relates the return on a

security to only its systematic market risk, the Long CAPM relates the

return on a security to 1) the systematic risk of the security in the

stock market, 2) the risk of the security due to expected price changes

in each commodity k (k = 1,..., K), and 3) the risk of the security

with respect to a bill of maturity m (m = 2, ..., T), due to anticipated

shifts in the yield curve. Since there are thus K + T types of risk, each

security can be represented by a point in (K + T + 1) space. Thus, a

natural generalization of the security market line (SML) associated with-

the single-period CAPM is the security market hyperplane (SMH) on which

each security in equilibrium must lie. The SMH will intersect the

expected return axis at the riskless rate just as the SML does in the

two-dimensional case.

Gouldey first tests the Long model using cross-sectional methods

across individual securities over the period January 1953 through

July 1971. He selected 1953 as a starting date since earlier price

indices compiled by the Bureau of Labor Statistics (BLS) are inaccurate

and misleading due to poor sampling techniques. Also, before 1951, the

Fed pegged the interest rates on Treasury bills, thus not allowing

Treasury bill rates to adjust to anticipated variation in inflation rates.








The tests ended in July 1971 since wage and price controls were imposed

in August 1971 which caused the various price indices not to reflect the

true cost of consumption goods.

Gouldey's data consisted of monthly returns on common stock taken

from the monthly returns file of the Center for Research in Security

Prices (CRSP) at the University of Chicago. The Standard and Poors

Combined Index was used to compute a proxy for the return on the market

portfolio. Price indices of the different groupings used by the Bureau

of Labor Statistics in compiling the Consumer Price Index (CPI) were

used for computing monthly returns for various consumption goods. The

consumption bundles selected were food, housing, apparel and upkeep,

health and recreation, transportation, and other goods and services.

Finally, one month holding rates of returns for U.S. government debt

obligations ranging in maturity from one month to twenty years were used.

Results of Gouldey's tests using individual stocks indicate the

following: 1) the intercept of the SMH is significantly positive,

2) the estimated premium for market risk is less than predicted by the

model, and 3) the risk premiums due to unpredictable commodity price

inflation and changing interest rates are as predicted by the model. As

Gouldey points out, however, the results are suspect due to non-stationarity

of many of the parameters. In addition, the results are not conclusive

because of the presence of some specification error and also because the

residuals may not be independent and identically distributed due to the

presence of an industry factor. Therefore, in order to examine the

effects of this possible dependence in the residuals, Gouldey repeats the

tests using industry portfolios. When portfolio data are used the risk

parameters tend to be more stable than those of individual stocks and








much of the risk peculiar to individual stocks is diversified away in

portfolios. Results of these tests indicate that the implications of the

Long CAPM cannot be rejected using industry portfolios. However, the

premium earned for market risk is less than predicted by the model. This

may be due to other types of risk associated with omitted commodities or

bills that investors consider relevant which would cause the estimated

market risk premium to be biased downward.

Although the Long model did not fare well in his tests, Gouldey

states thatthe evidence does not necessarily refute the model, but instead

may cast doubt upon the abilities of investors to correctly predict future

inflation and interest rates. Again, however, the results of the tests

using portfolio industry data indicate that average rates of returns on

capital assets do contain risk premiums for systematic market risk and

risk due to stochastic consumption and investment opportunities. Those

results imply that in principle investors can use stocks and bills to

create a hedge against commodity price inflation and rising interest rates.

Even though Long suggests that these "quasi-futures" contracts exist

in principle, there needs to be further development and testing of these

hedge portfolios. Gouldey attempted to obtain estimates of the costs of

forming "quasi-futures" for food, housing, and transportation price

indices, but he failed to provide any information concerning the

composition of the contracts nor did he test the success of the portfolios

as hedging instruments using subsequently observed data. This disserta-

tion intensively examines the construction and composition of "quasi-

futures" contracts for ten consumption goods over the period 1965-1976.

The "quasi-futures" contracts are subsequently tested for their adequacy

as hedging instruments against commodity price inflation.












CHAPTER III
METHODOLOGY FOR CREATING "QUASI-FUTURES" CONTRACTS

This chapter presents a general methodology for the construction of
"quasi-futures" contracts for various consumption goods. In order that

a stock-bill portfolio can be properly called a "quasi-futures" contract
for a particular good k, it must have the following two properties:

(1) it should have the same expected "with-dividend" value at time 1 as
the good, k1, and (2) its covariance with ('l' ~1' $1) should be equal
to the covariance of ?kl with (M1, 1' i, 1).

The first step will be to select the stocks and long-term bills in
such a way that the covariance property is attained. Let C be a

[(N+T-1)X(K+T)] matrix of the covariances appearing in the equilibrium

pricing equations (II-1) and (11-2). The elements of C are given in
Figure III-I. Let z be the [(K+T)X(K+T)] variance-covariance matrix of

(~M1' 1 1) whose elements are presented in Figure 111-2. Finally, let
P be a [(N+T-1)X(K+T)] matrix whose elements are given in Figure 111-3.

Note that the first N rows of n contain the coefficients taken from the

multiple regression of equation (11-4) for each of the N stocks.

The matrices are C, z, and n are related such that

C = nz. (III-1)
For example, this implies that the first element of C is















-M
(Nxl)

C ( x
j(T-I)xl


(T-1)xK (T-1)x(T-1)

(N+T-1)x(K+T)
(N-+T-I)x(K+T)


COI(V ,v ) vcov ,
I Oi V11 ,..l


S N.,xl1) I:COV(V ? k
NxK



COV(V .V I ) COV(Vt ) COV(V ; )


i
Scov(3, ,V) cOv(B ,i ) covV(,,Ia )

COV(S3.,V I) COV(,83,,11 .






( V:(T-1)xl) :COV(B ,, 1
I
(T-l)xK




CO T,VM) COV( COV )
I V(312,:1)


CCV(Vi!, ) COV(V.,B!T)



:COV(Vjl,3 1m,
Nx(T-;



COV(V ,3.; COV(CNv,D .5


COV(B12,312 CO


1COV(BV3, 12),






C:COV(V I' m B





COV(B-,,S2) Co


17, '


Figure III-1
Elements of the Covariance Matrix C


(NxK)


S(-1

Nx(T- )


. ov(v ,r i
K














(1x1) (1xK)


(KxK) Kx(T-1)


T-1)xK (T-1)x(T-1)


COV(VM, Vh )




I I
coVAR(V )





COV(
1











COV(E x ,V !a
i COV( V
I 2'




COV(E.3 VMK


( )x
(T-1 )x1


iCOv(v )


I I


.COV(vi ,r.KI viiC (BV ,M12 ) .


(lx)
(IxK)


COV 2T' 1, ) .
SCDV(1 :2141.)CO~~:c2


i covr )




COV(B '
I; :-


COV(B
(T- )x


* OV IT'BV)
17'


(1x(T-1))


COV( ,'k ,l)1 COV(E,12'.: )COV(B.

COV(BE2,21)
I 21


i i

COV(l ) COV(E1, )
I I



COV(,13, 12)

Im'"kl I "

K
!


W':COV(
Kx(











:: COV
(T-1


COV(B T,rK1) COV(BIT,B1) 2
KI 1


3%11 OV( )j,




B '
m' r.kl


1,T '"KI i i
COV(E-,K);







(1m' n 1 *
)x{7-1)


S COV(BT1,B7T)


Figure III-2
Elements of the Covariance Matrix E


*'i
(Kxl)


(T-I)xl


(1x(T-I))


OV(BI j ,'V ) icov (B IT'rl


i I






23














(Nxl) (NxK) (NxT-1)


(T-l)xi (T-I)xK (T-1)x(T-.)j


S1K


* 2K










i
N
i

.0I
* 0
i


&12


022











6N2


0

0




0
o


13


'-i













'NT


L
Nx(T-1)





0N3


0 0 .


1

0


1MI


i














0






(-)xl




o 0


Figure I1-3
Elements of the Augmented Coefficient Matrix n


!2 *


'Z2





(NxK)


CNi


0

0


,N2


0

0 .


0
o .
1




(T-1)x(-1;



I


0
(T-1)xK




0 .


i ^


0 i






K
cov (~ = 1Mvar(,, ) + jk cov( Ml k)
k=l

T
+ E jmcov(im' 'Ml (111-2)
m=2
which is equivalent to the covariance of equation (11-4) with V., If the
value of the stock market portfolio is unrelated to the price of goods
or bills, then equation (111-2) will reduce to the more traditional
expression as given in the single-period model for the covariance of
the value of a stock with the market portfolio.



To demonstrate this point let
Yi = a + 1Xli + B2X2i + i
Our estimate for the vector of regression coefficients, 8, is
1XIx XIX2 -1 7, IT
'X X 'X X Y
1 1 1 2 X1
a-
X2X1 X2X2 X2 ,

or equivalently
- = TX1 2' )1 (X1M 2X)lX1X2(X2'X2)1 X1 'Y

I-(X2'2)-X'X1(X1 2'rX1)-1 (X21X2)-1+(X2'X2) 1A(X22') X2'Y

where
A = X2'X1(X1I 2X1)-1X'X2; and

M2 = I-X2(2'X2)-2'

Now, if 1) X2'X2=0 (a trivial case), or 2) X1'X2=O, which would imply
for this paper that the market portfolio (X1) was orthogonal to the vector
of good and bill prices (X2), then our estimate of a1 would reduce to

S6 = (XI'X1)-1x'Y,
the traditional measure of the risk of a security relative to the market
portfolio.







It can be shown that the sum of the first N rows of C is equal to

the first row of z by applying the following weighting scheme:


1':.0'] C = [ '11 '] n

= [0 0 ... 0]

= el (111-3)

where 1' is a (1XN) vector of ones and 0' is a [1X(T-1)] vector of zeros.

The above relationship implies the following:

N
E 1jm (111-4)
j=l

N
j Sjk = 0, k=1,...,K, (III-5)
j=1

N
E 6S = 0, m=2,...,T. (III-6)
j=l

The validity of these equations can be demonstrated by summing

equation (11-4) across all N securities and by recalling the definition of
N -
the value of the market portfolio, VM1 E- V.. These conditions, (111-4),
j=1 J
(111-5), and (11-6), must hold during the empirical analysis in the

next chapter in order to verify that the estimation procedure used is

correct.

Let e'l+k be a [1X(K+T)] vector whose (l+k)th element is 1, with

all other elements equal to zero. The index k on el+k, k=1,...,K,

indicates that e' +k is being associated with the kth consumption good.

For example, when k=0, vector el' will refer to the "market" as was

previously shown in (111-3). The next step is to find the k weighted

combinations of the rows of n that will solve for the K row vectors,








el+k, k=1,...,K. These weights can be found by solving the following
system of equations for bk where bk is a [IX(N+T-1)] vector:

b' := e'
k l+k

b'k = e l+k "

b'k = e'l+k -1 k=1,...,K. (III-7)

Each of the K row vectors, b'k can be interpreted as the unit quantities

of the respective shares of common stock and long-term bills which

correspond to a portfolio whose "with-dividend" value at time 1 has a

covariance with the vector (VM1, ill B1) equal to the covariance of 1nkl

with (VMl, l1, B ). The first N elements of bk refer to the unit

quantities of shares of each stock and the last (T-l) elements of b'
k
refer to the number of each of the long-term bills.

Now that the covariance property has been attained, the next step
adjusts the expected value of each of the K stock-bill portfolios to equal

E(nkl), the expected next period's value of the kth good. To set the

expected value of the portfolio equal to E(Irkl), a quantity of short-term

bills (m=l) can be added to or subtracted from the portfolio without af-

fecting its covariance with (V1 1,' Bl). This is possible since the es-

timated regression coefficients from (11-4) that are used in solving for

bk are independent of the price of a one-period bill. Therefore, the
quantity of short-term bills, Yolk' to add to the hedging portfolio is


Y0lk = B01 (Ikl bk [P1 Bl]'), k=l,...,K. (III-8)

A negative value of Y0lk refers to a short position in one-period bills

or a borrowing of funds at the short-term bill rate. Thus, a mean-adjusted








portfolio with a current value of FkO can be created and is referred

to as a "quasi-futures" contract for good k. A simple example to help

clarify the methodology used in solving for the vector of portfolio

weights, bk, is presented in Appendix A for an economy containing the shares

of two firms, one consumption good, and one long-term bill. It will be

the convention during the empirical analysis in this paper to select N,

the number of different stocks in the market portfolio, to be equal to

one plus the number of consumption goods in the economy. That is, N=K+1.

By doing so, there will exist only one "quasi-futures" contract per good

each period. If N>K+1, then there will exist an infinite number of port-

folios which could serve as "quasi-futures" contracts for a particular

good.2 However, of all such portfolios, only that portfolio which had

the minimum variance about its next period's "with-dividend" expected

value would be chosen as the "quasi-futures" contract for a particular

good.

When constructing the hedging portfolios, it is interesting that

the number of long-term bills in the economy assumed does not impose any

empirical restrictions on the model as does the number of shares and

consumption goods assumed. Also, it is shown in Appendix B that the

number of shares of each firm held in the hedge portfolio does not depend

directly on the regression coefficients, A, associated with the long-

term bills. However, one can not conclude that bills are unimportant in

calculating the share weights. Exclusion of bills in the multiple

regression (11-4) would change the values of B and = and thus would have

an effect on the share weights.



2There will exist N-K linear independent solutions. Any linear
combination of these solutions will also be a solution.












CHAPTER IV
THE FORMATION OF "QUASI-FUTURES" CONTRACTS

IV. A The Data

In order to select the proper quantities of stocks and long-term

bills such that the covariance property of each "quasi-futures" contract

is attained, the first step is to run the multiple regression of equation

(11-4). The following time series data are required to perform the

regression: (1) monthly prices for N=K+1 common stocks, (2) monthly

prices for the value of the stock market portfolio, (3) monthly prices

for K consumption goods, and (4) monthly prices for T-1 default-free long-

term bills. The price data for the above assets were collected for the

period January 1961 through March 1976. An explanation for the choice of

this time period will be discussed later in this section.

Previous studies concerning commodity price inflation (Dusak (1973)

and Gouldey (1977)) were somewhat limited in the number of different

commodities used. If several goods are used in the analysis, and all the

goods were to experience the same relative price changes or inflation

rates, then one would expect the same hedging portfolio to be derived for

each good except for the amount of short-term bills needed to adjust the

expected value of each good. However, it appears that all goods do not

experience the same relative price changes (see Fama and Schwert, 1977b)

and thus the composition of each "quasi-futures" contract should be

different for each good. Therefore, to test the success of "quasi-futures"

contracts properly, the study should include a wide variety of consumption

goods in the analysis.







The data concerning the consumption goods to be used presented two

main problems. First, to be theoretically consistent with the Long model,

all consumption goods should be included in the analysis. Including all

these variables as independent variables in the regression (11-4) may

present severe multi-collinearity problems. However, failure to include

enough of these variables may result in misspecification of the model and

missing-variable problems. The second problem concerns finding accurate

and available commodity price data. For this purpose prices of seven

various groupings containing closely related bundles of consumption goods

used by the Bureau of Labor Statistics in compiling the Consumer Price

Index (CPI) will be used to proxy for commodity prices. Price indices

for these various groupings are readily available. In addition, due to

problems to be discussed in some of the CPI components, price indices for

three components of the Ulholesale Price Index (WPI) will be used in order

to have a larger cross-section of commodity data.1 The various component

indices selected to proxy for commodity prices are given in Table IV-1.

In addition to the reasons previously discussed for not using a

single good for the analysis, one would not try to use the overall CPI as

a proxy to relect the price changes for a particular good. These reasons

are: (1) periodic revisions in the weighting of subcomponents, (2) insen-

sitivity of the CPI to price changes during periods of low mean rates of

inflation due to rounding or truncation to one digit after the decimal,

(3) differences in the accuracy of measurement across components, and



1The following discussion concerning the CPI components is taken
heavily from Fama and Schwert (1977b).







Table IV-1
Selected Consumption Bundles

Component Source Symbol

1. Food CPI FD

2. Gas and Electricity CPI GE

3. Apparel and Upkeep CPI AU

4. Private Transportation CPI PT

5. Reading and Recreation CPI RR

6. Medical Care CPI MC

7. Household Furnishings CPI HFO

8. Metal and Metal Products WPI MMP

9. Lumber and Wood Products WPI LWP

10. Chemicals and Allied Products WPI CAP


(4) problems in defining the overall inflation rate if relative price

changes induce substitution effects causing consumers to consume goods in

different proportions at different times.

To retain the uniqueness of each price series, monthly price data

for the selected consumption bundles were used. Fama and Schwert (1979)

show that inflation rates of different goods can be broken into a part

common to all goods and a part peculiar to each good itself. An example

of a part peculiar to a particular good is one that may be due to

seasonals. If production for a good is seasonal whereas demand occurs

smoothly throughout the year, then seasons in the price of such a good

may be observed to offset the cost of storing the output. However, as

one goes from using monthlyprices to prices of longer intervals, the

variability of the price series of a component becomes more and more like








that of the CPI. Thus, the variability of price indices of various goods

will become more and more similar as they are measured over longer

intervals.

Final selection of the consumption bundles used in this study

depends in many ways on the construction of the CPI. An overall break-

down of the major groupings composing the CPI is given in Table IV-2.

Since the data to be used in the study are on a monthly basis, it will be

desirable to have the selected CPI components sampled and priced monthly.

In addition, it is desirable for each component chosen to be a fairly

homogeneous grouping of goods. Approximately 50 percent of the items

and locations used to construct the CPI are sampled every month. The

rest of the component prices are collected on a quarterly basis, but on

a rotating basis so that there is some monthly revision of prices. How-

ever, components which are sampled on quarterly intervals will reflect

changes in prices which actually occurred during the preceding two months.

Therefore, some components at times will be incorrectly calculated as

being unchanged. These lags in the updating of prices may introduce

autocorrelation in the price series.

The Food component which represents 22.4 percent of the CPI is

priced monthly in all locations and is probably the cleanest series used

in the study. The Gas and Electricity index which is a subcomponent of

the Fuel and Utilities index represents about 3 percent of the CPI and is

also priced monthly in all locations. However, since most of this

component depends on utility rates determined by governmental agencies,

the behavior of its price series may be different had the prices been

determined in a free market as the other components. Despite this

shortcoming, this series was retained in the study due to its importance

as an everyday consumption item.






















to a
-i- k




eI C Ln n
I u c i a I
j i L io co o n




> W
V, c io
L; 4 ea a1(A
3Si QIn V v
0 0 C 0 -
S6 >n .
0ga c- D r I
--'* > i- ci 0, ^' C SI = La S i -
u I- c >d i. 3 C >< 1 C

C. 00 i = C U0.5. 0
C C OL ci o c 4
I-' o a a a 3 -c -
va c0 -ci r

r- 0 C -- n 0- C e i ; O )
x -aa in = Q a i c ? oa u=o i
,I = --o u 1- 3 e a o u o -


S- su
1 ) 0- 0 ,'
a- ac c o
U =i w 0 (v 0 I

L,

Q I 0




























-6 w
ia c
CM E I o















1 3 C I ci2












'V 0 0 0 0 L. C X C
1 0 -C S M C- C c











c- sO ci .- c i = S.



SQ C 0 ( m C W0 C
4.'. C C. ci = ; i
1-- -r 0n "^ L O C QC O

0e1 c\iomcM < c me c xQ



Se t =i
























-t V C 00
Ei 0 0 0













01 0 0 C
c O l 2 u
a- 0 1 ) J \








It seemed desirable to include the Homeownership series in the

list of components chosen for the study. However, there are many problems

with this series due to its subcomponents such as Mortgage Interest

Expenses and Real Estate Taxes. The expense incurred in financing a good

is not a factor of its price. In addition, government agencies, and not

a free market, determine real estate taxes. A third subcomponent of the

Homeownership series is the Home Purchase Price Index. This index is a

three month moving average of newly insured FHA housing prices and thus

suffers from the problem of built-in lags. Finally, another shelter

related index, Rent, was also not included in this study, since this index

is based on contract rents for a fixed sample of apartments, where the rent

for a given apartment is sampled every six months with all unsampled

months assumed to be unchanged in price. In addition, since most rental

contracts are negotiated on an annual basis, this component does not truly

reflect the actual price changes in the rental market. Household

Furnishings (about 7.8% of the CPI) is a fairly homogeneous grouping and

was selected for the study since it did not suffer from the shortcomings

previously discussed.

Apparel and Upkeep which comprises about 10.6% of the CPI is a

fairly clean and homogenous grouping and was selected, as was Private

Transportation. Private transportation (about 12.6% of the CPI) reflects

the cost of new and used cars, and the price of gasoline, motor oil, and

auto parts.

The Health and Recreation index is a very heterogeneous mix and

contains many built-in lags. Two of its subcomponents, Medical Care

(5.7%) and Reading and Recreation (5.9%) are much cleaner indices and were

thus selected.







Due to the lack of correctly measured CPI components, three price

indices from the Wholesale Price Index (WPI) were selected to enlarge

the sample of goods used. The three selected series are Metal and Metal

Products, Lumber and Wood Products, and Chemicals and Allied Products.

Despite the fact that these series are not truly consumer prices, they are

homogeneous groupings and appear to accurately reflect price movements in

the particular goods.

In summary, monthly price data for the period January 1961 through

arch 1976 weregathered for K=lO consumption bundles taken from the

Consumer Price Index and the Wholesale Price Index to be used as proxies

for various commodity prices. One reason for selecting January 1961 as a

starting point for the study was due to an important change in the way the

CPI was constructed beginning in 1964. At this time the coverage of the

index was extended and the weights assigned to the different items are

updated in line with the 1960-1961 Consumer Expenditure Survey. However,

it was still possible to gather revised data for the selected price series

back to January 1961 according to the 1964 updating scheme.

One final point related to the commodity price indices concerns the

Nixon wage and price controls. Beginning in August 1971, the Nixon

administration instituted price controls which were not lifted until

1973-1974. Since the controls led to queues and shortages, reported

inflation rates probably understated true changes in purchasing costs to

consumers. After the controls were lifted, the reported inflation rates

probably overstated the true inflation rates. Tests will be performed

in Section V. B to see if the controls had any significant effect on the

success of the "quasi-futures" contracts as hedging devices.







Based on the decision to use K=10 commodities in the study, monthly

price data on N=ll (K+1) common stocks are required. This empirical

restriction that the number of stocks to be used equals one plus the

number of goods was discussed in Section II. A. Recalling that if N>K+1,

then there will exist an infinite number of hedging portfolios which have

all the properties of a "quasi-futures" contract for a particular good.

However, of all such portfolios, only that portfolio which had the minimum

variance about its next period's "with-dividend" expected value would be

chosen as the "quasi-futures" contract for a particular good. Despite

not being the optimal approach for creating a "quasi-futures" contract,

the problem of searching for a minimum variance portfolio will be avoided

by setting N=K+1, whereby, only one solution is produced.

As Gouldey (1977) points out, the risk parameters using portfolio

data tend to be more stable than those of individual stocks and much of

the risk peculiar to individual stocks is diversified away in portfolios.

Instead of using individual securities in the analysis, industry portfolios

are formed.2 Various industry classifications as provided by the Compustat

files will be used to create the industry portfolios. The eleven industry

groupings to be used are listed in Table IV-3. The industries selected

are widely varied and an attempt was made to have all the industries

correspond to each of the consumption bundles selected. For example, the

"Motor Vehicles and Auto Trucks" portfolio corresponds to the Private

Transportation component. The purpose of this is to see if the best

hedging strategy against inflation in a particular good consists of buying

the stock of a firm in a related industry.


2
It would be desirable to use individual stocks. However, due to the
instability of the regression estimates when individual stocks are used,
industry portfolios are created. It is realized that industry portfolios
may not be fully diversified.













Table IV-3
Industry Portfolios


Name
1. Chemicals-Major
Chemicals-Minor

2. Textile Apparel MGF

3. Forest Products

4. Home Furnishings

5. Drugs-Ethical
Drugs-Proprietary
Drugs-Medical Supply

6. Steel-Major
Steel-Minor

7. Motor Vehicles
Auto Trucks

8. Elec Utilities-Normalized
Elec Utilities-Flow Thru

9. Retail-Food Chains

10. Leisure Time Products
Amusement & Recreation
Prof. Sports & Arenas

11. Natural Gas Companies


Compustat
Industry Code
2801
2802

2300

2400

2510

2835
2836
2837

3310
3311

3711
3713

4912
4911

5411

3948
7949
7941

4924


Symbol
CH


TA

FP

HF

D



ST








A price index was created to represent a set of prices for each of

the industry portfolios. The following procedure was used to create each

price index. First, each company within an industry grouping was checked

to see if it had a monthly return (RET1) listed in the monthly returns

file of the Center for Research in Security Prices (CRSP) at the Univer-

sity of Chicago. For all companies that had a monthly return listed in a

given month, the returns were summed and an average monthly return was

computed for that industry. This procedure was repeated for each month

from January 1961 through March 1976. Firms were frequently observed to

enter and leave the sample when computing each industry average monthly

return. This method allowed the maximum number of companies to be used

each month in the calculation of the industry average monthly return.

The regression in equation (11-4) requires time series data in the

form of prices rather than returns. To convert the eleven industry

average return series into price indices, the following steps were taken

for each industry. First, each industry was assigned a base value of 100

at the beginning of the time period. Then, the value of an industry

portfolio in any subsequent month t was calculated by multiplying the

price in month t-l by one plus the portfolio return in month t. By per-

forming these calculations for all months, eleven industry price indices

were created.

To be consistent with the theory underlying the model, the value of

the stock market portfolio in month t is defined to equal the sum of the
N
values of all stocks in month t. That is VMt = E Vjt, for all months t.
j=1
Therefore, a stock market price index was created by summing each industry

price index across industries.

Finally, Long's model requires data for default-free coupon-less

bills of all maturities. The prices of U.S. Government Treasury bills were







used because of their availability and reliability. The interest rate on

Treasury bills was pegged by the Fed before 1951, thus not allowing

Treasury bill rates to adjust to anticipated variation in inflation rates.

Price data were available on bills with maturities from one to three

months until March 1959, at which time they became available for maturi-

ties up to six months. Price data on Treasury bills with maturities up

to twelve months became available beginning in August 1964. Since the

data on the consumption bundles werecollected back to 1961, monthly prices

for Treasury bills with maturities ranging from one to six months were

collected for the period January 1961 through March 1976.3 It will be the

convention to treat the one month bill as a short-term bill. The Treasury

bills ranging in maturity from two to six months are treated as long-term

bills. Thus, there are five (T-l) long-term bills and one short-term

bill used in the study.

IV. 3 Empirical Estimation of the Regression Coefficients

Following the collection of the various monthly price data, the next

step is to estimate the regression coefficients in the following multiple

regression whose parameters were discussed in Chapter II:

S K T
V1 = *j + 'Ml + Z jk + = m B + j j=,... N. (II-4)
jk=l m=2

The above equation requires using realizations of time 1 values of the

variables. Since we do not have perfect foresight, the empirical counter-

part to equation (11-4) will be the following:



See Fama (1975) for a description of the Treasury bill data used in
this study.








^K ^ T
E(Vjl) = + jME(VMI) + z jk E(nkl) + m E(Bl ) + Wj,
k= M=2 jm

j = 1,..., N. (II-4a)

A naive expectations model is used to estimate each variable's expected

value. Thus, the convention in this study will be: (1) to use today's

stock and commodity prices as estimates of next period's value; (2) to use

today's value of the stock market portfolio as an estimate of next period's

value; and (3) to use today's forward prices as implied by the term

structure as the best estimates of next period's bill prices. Conventions

(1) and (2) assume that stock and commodity prices follow a martingale.

Convention (3) assumes the expectations theory of the term structure.

Today's forward price for each bill is then computed according to

-1
E(Bm) = B1 Bm, m = 2,..., T. (IV-1)

The number of observations used in each of the N=11 regressions

performed over each time interval must exceed the number of coefficients

(K+T+1 = 17) to be estimated. Five years of monthly observations will

be used in each time series regression. The first set of N regressions

will be performed on sixty months of observations extending from January

1961 through December 1965. The estimated coefficients from this time

interval are then used to compute the one period or one month "quasi-

futures" contracts for each of the goods according to the method dis-

cussed in Chapter III. Thus, the first sixty months of observations are

used to create portfolios which serve as hedging devices against price

inflation in the various selected goods during January 1966. Since the

"quasi-futures" contracts are one-period contracts, new estimates of the

regression coefficients must be computed each month in order to rebalance







the portfolios. This is done by repeating the regression after first

dropping the observations from the oldest month and adding observations

from the latest month. By using this updating scheme, observations from

the most recent sixty months are used in each regression. For example,

the portfolio weights of "quasi-futures" contracts for goods to be

delivered in February 1966 are computed using the estimated regression

coefficients from the period February 1961 through January 1966.

During the initial runs of the regressions, serial correlation in

the residuals was found. In order to get unbiased estimates of the

regression coefficients, the data were transformed into first differences.

When the method of first differences is used, it is believed that rho,

the first order serial coefficient of the regression disturbances, is

close to unity. In order to justify the assumption that the value of

rho is sufficiently close to unity, the Hildreth-Lu4 maximum likelihood

scanning procedure was used in regressions over various selected time

intervals. This technique transforms the data by rho (e.g.: Xt PXt-1)

and selects the value of rho which results in the lowest transformed

error sum of squares. A sample of the estimated values of p for each of

the eleven regressions over the interval January 1961 through December

1965 is presented in Table IV-4. Since p was sufficiently close to unity

in the sample regressions, the method of first differences was used in

all regressions.5 In addition, the constant term was omitted from the

regressions since there is no reason to include a trend variable.



4See Hildreth and Lu (1960) for a description of this procedure.

It is assumed that the residuals follow a first-order autoregressive
process. Since the values of rho are sufficiently close to unity, a
first-difference transformation of equation (Il-4a) is actually used
to estimate the regression coefficients.













Table IV-4
Estimation of Equation II-4a:
Hildreth-Lu Scanning Technique
January 1961 to December 1965

Dependent
Variable RHO R

CH .99 .9948

TA .97 .9955

FP .80 .9957

HF .91 .9958

D .97 .9893

ST .82 .9779

MV .99 .9918

EU .95 .9927

F 1.00 .9703

LT .70 .9620

NG .81 .9824








In order to verify that the estimation procedure used to calculate

the regression coefficients is correct, three conditions must hold over

each time interval. Recalling from Chapter III, these conditions are as

follows:

N
j Bjm 1 (111-4)
j=l
N
j Sjk = 0, k = 1,...,K, (III-5)
j=1
N
z 6j = 0, m = 2,...,T. (III-6)
j=1 Jm

These qualities exist due to the definition of the value of the market

index. The estimation procedure used proved to be quite accurate as demon-

strated in Table IV-5, which presents a summary of the regression coef-

ficients and their totals across industries from the eleven regressions

over the sample interval March 1971 through February 1976.

IV. C Computation and Analysis of the Portfolio Weights

Following the estimation of each set of regression coefficients, the

next step is to create the matrix n from which the monthly portfolio weights

are computed. The matrix 0 is a [(N+T-1) X (K+T)] matrix whose elements were

given in Figure III-3. For each time interval, the regression coefficients

from each set of N = 11 regressions are placed in the first N rows of n.

The last 5 (T-1) rows are completed as given in Figure III-3.

Recalling from Chapter III, let e'+k be a [Ix(K+T)] vector whose

(l+k)th element is 1 with all other elements equal to zero. The index k

on el+k, k=1,...,K, indicates that the vector e+k is associated with the

kth consumption good. The next step is to find the K = 10 weighted com-

binations of the rows of Q that will solve for the K row vectors,







43














SO 0 0 0 0 0 0 O 0 N-
SCO m O O C) o L. LO O r- CO O
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a o Ln eq o Ln o t o cr o

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I I I Il i M








el+k, k = ..., 10, from the following system of equations:

bh = e+k "-1, k = 1, ..., 10. (111-7)

The vector bk then contains the unit quantities of the respective shares

and long-term bills which correspond to a portfolio whose "with-dividend"

value one month later has a covariance with the vector (VnM1, i1, B) equal

to the covariance of nkl with (V,1, 1, B1).

After attaining the correct covariance properties for each stock-
bill portfolio, the expected value for next month is set equal to the next

month's expected value of the good for which it is hedging. Adding a

quantity of bills with one month to maturity to the portfolio accomplishes

this. These short-term bills will not disturb the covariance of the port-

folio with (VM1', B1). The quantity of one-month bills, YOlk' to add

to each portfolio is


Yolk = 801 (kkl bk [P1 1]'), k = 1, ..., 10.6 (III-8)

A negative value of YOlk refers to a short position in one month bills.

After the quantity of one month bills is computed and added to each port-

folio, a "quasi-futures" contract for each good is created which will have

all the same desirable risk and return properties that concern investors

as the goods themselves.

The "quasi-futures" contracts for each good are of one month in
length. Their portfolio weights are calculated using the regression
coefficients from the sixty most recent months of price observations.



6The bars over the variables indicate time 1 expectations.








Therefore, every month starting from December 1965 and extending to

February 1976, a new "quasi-futures" contract is constructed for each

good for delivery one month later.7

The quantities of each of the shares and bills in the hedging

portfolios for a particular good changed significantly from month to

month, thus indicating a need for rebalancing. Table IV-6 presents a

typical example of the fluctuations in the portfolio weights of the "quasi-

futures" contracts for Food (FD) over the interval September 1969 through

December 1969. As one might expect, the fluctuations are more apparent

in the quantities of the various bills due to their high degree of

correlation and substitution. The next chapter investigates the need for

rebalancing further. Fama and Schwert (1977a)investigate the question of

which assets provided effective hedges against inflation during the

1953-1971 period. By regressing the returns on various assets against

both the anticipated and unanticipated components of the inflation rate,

they conclude that U.S. Government bonds and bills were a complete hedge

against expected inflation and that common stocks were negatively related

to the expected component of the inflation rate, and probably also to the

unexpected component. These results imply that bills serve as a better

hedge against inflation than do common stocks during the 1953-1971

inflationary period. In addition, the "quasi-futures" contracts which

serve as hedging devices should therefore consist mostly of bills. In fact,

if returns on common stock were negatively related to the inflation rate,

one would expect to observe a short position in common stocks each month.



Tables specifying the composition of each "quasi-futures" contract
are available from the author upon request.












Table IV-6
Composition of "Quasi-Futures" Contracts for Foodl
September 1969 through December 1969


Months
Industries 9/69 10/69 11/69 12/69


- .217
.014
- .269
- .139
- .035
.264
.244
- .453
.718
.063
.546


Bills2
2-Month
3-Month
4-Month
5-Month
6-Month

1-Month3


10.085
-13.168
-40.013
1.261
11.987

29.960


- .160
.099
- .310
- .237
- .029
.777
- .121
- .025
.863
.071
- .417


18.990
-30.131
-39.643
-12.041
29.916

33.716


.468
.044
.194
- .069
- .077
.560
- .940
.094
.202
.071
- .701


1.880
-34.815
9.057
-14.245
17.706

22.342


.525
.063
.012
- .104
- .093
.627
- 1.053
.083
.279
.086
- .752


3.816
-40.306
8.498
-17.365
20.889

26.443


Numbers in table
and bills.


represent quantities of the respective shares of stock


Bills are assumed to have a face value of $100.

1-month bills are used only for adjusting the expected value of the
portfolio.








Examining the percentage of each of the two types of assets in

each monthly portfolio confirms these implications. Table IV-7 presents

the fraction of the total dollar investment in common stock and in bills

in each of the monthly "quasi-futures" contracts for the consumption

bundle "Lumber and Wood Products" from December 1965 through February

1976. In all but 14 of the 123 months there was a larger dollar invest-

ment in bills. In fact, in more than half of the months there was a

negative dollar investment or a short position in common stock. The

results for all of the other consumption goods were similar to those for

"Lumber and Wood Products." Thus it appears that bills do serve as a

better hedge against commodity price inflation than do common stocks.

While bills were a better hedging mechanism than common stocks, no

conclusion can be drawn as to which of the bill maturities is better.

Each of the various bills were frequently observed to be held short from

month to month. Finally, the results imply that purchasing the common

stock of a firm that produces a good similar to the hedged commodity

would not contribute to the hedging efficiency of the portfolio.




























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CHAPTER V
TESTS OF THE PORTFOLIOS AS HEDGING INSTRUMENTS


Following their construction, the monthly "quasi-futures" contracts

are tested to determine their success as hedging devices against commodity

price inflation. As discussed previously, a "quasi-futures" contract for

a particular good is constructed such that its expected value at the

delivery date is equal to nkl. In addition, the portfolio should also

have a covariance with (~M1' i) equal to the covariance of tk with



V. A Testing Price and Risk Characteristics

Two tests were designed to investigate whether each series of "quasi-

futures" contracts were indeed true substitutes for owning the goods them-

selves. The first of these tests was to indicate if the subsequently

observed value at delivery of each "quasi-futures" contract was identical

to the observed value of the good at the same delivery date. This was

accomplished by testing the significance of the estimated regression

coefficients in the following time series regressions for each of the 10

consumption goods:


Fkt = IkO + Ykl "kt + Ekt' k = 1,...,10, (V-l)

where Fkt is the actual observed value at delivery date t of a "quasi-

futures" contract which was purchased one month earlier. The value of

Fkt at delivery is computed according to








Fkt = bt-l Pt Bt] + 100t-tk k = l,...,10. (V-2)

Let a perfect hedge be defined as one where the hedging portfolio

and the good have identical observed values each period. This would

require the intercept and slope coefficients in equation (V-l) to be

exactly zero and one, respectively, with zero standard errors. In

addition, the R2 of each regression should equal one. Let an unbiased

hedge be defined as one in which the estimated slope and intercept coef-

ficients are not statistically different from zero and one, respectively.

Thus, the hypothesis of whether the "quasi-futures" contracts do indeed

have the same subsequently observed values as the goods is tested by

examining the regression coefficients in equation (V-l) which should have

the following expected values:


E(ykO) = 0, k = 1,...,10,
and

E(ykl) = 1, k = 1,...,10.

Estimates of the regression coefficients in equation.(V-l) from the

period January 1966 to rlarch 1976 are presented in Table V-l for each of

the consumption goods. The estimates of the intercepts coefficients,

YkO' k=1,...,10, are all within one standard error from zero, with three
exceptions, as indicated by the t statistics. The three exceptions are

Gas and Electricity (t = 1.04), Apparel and Upkeep (t = -1.71), and

Household Furnishings (t = -1.18). However, none of the t values are

significant at a .05 significance level. Similarly, the estimates of the

slope coefficients, ykl' k=1,...,10, are all within one standard error

from one, with one exception (Apparel and Upkeep: t = 1.62). Again,















Table V-1
Portfolios as Substitutes for Consumption Goods:
Ordinary Least Squares

Fkt = YkO + Ykl kt + :kt
January 1966 March 1976, T=123
(standard errors in parenthesis)


SDurbin-
Ykl t(Ykl1)a Watson
1.15 .63 2.26
(.24)
.83 -.81 2.36
(.21)
1.42 1.62 2.00
(.26)
1.01 .04 2.16
(.23)
.91 -.75 2.32
(.12)
1.07 .39 2.15
(.18)
.87 -.68 2.35
(.19)
1.37 .59 2.21
(.63)
1.11 .92 2.25
(.12)
1.10 .83 2.07
(.12)


R2

.16

.11

.20

.14

.31

.23

.15

.04

.41

.43


F(Yko=0:, Yll)b
.19

1.29

1.80

.04

.89

.99

.70

1.18

.43

1.53


aCritical t.05,121 1.980

bCritical F.052,121= 3.07
05;2,121'230


Good

FD

GE

AU

PT

RR

MC

MMP

LWP

CAP

HFO


YkO
-19.03
(31.25)
27.63
(26.33)
-53.39
(31.20)
.08
(26.86)
8.84
(14.68)
-13.96
(22.75)
21.58
(24.67)
80.32
(88.75)
-13.25
(14.57)
-16.59
(14.12)


t(YkO=0)a
-.61

1.04

-1.71

.00

.60

-.61

.87

-.90

-.91

-1.18







none of the t values are significant at a .05 significance level. Finally,

an F test can be conducted (see Theil, p. 133) which will test simultane-

ously the joint hypothesis that YkO = 0 and Ykl = 1 for each good. This

statistic is determined according to


F2,T-2(YkO' Ykl) = :[kO YkO kl Ykl] (s2C)- O kO kl Ykl /2

where s C is the variance-covariance matrix of the regression coefficients.

The values of F with 2 and 121 degrees of freedom for each regression are

clearly insignificant at a .05 significance level as indicated in Table

V-1.

The intercept and slope coefficients in equation (V-1) are re-

estimated using seemingly unrelated estimation. This procedure will

provide better estimates whenever the residual terms are contemporaneously

correlated across regressions. Table V-2 presents these estimates of the

intercept and slope coefficients along with the t statistics. None of

the t values are significant at a .05 significance level. Table V-2 also

presents an F statistic which differs from the previously described F

statistic. This F statistic tests the general linear hypothesis that the

intercept and slope coefficients across regressions are jointly equal to

zero and one, respectively; see Zellner (1962). The F value is clearly

insignificant at a .05 significance level.

The evidence supports the claim that each hedging portfolio and

consumption good had statistically equivalent observed values each month.

Although the results indicate that the portfolios were not perfect sub-

stitutes for the goods, the portfolios did serve as unbiased hedges

against commodity price inflation in each good.













Table V-2
Portfolios as Substitutes for Consumption Goods:
Seemingly Unrelated Estimation
Fkt = YkO+ Ykl kt+ Ekt
January 1966-March 1976, T = 123
(standard errors in parenthesis)


Yk1
1.15
(.20)
.92
(.14)
1.36
(.22)
1.10
(.16)
.96
(.09)
1.05
(.13)
.96
(.12)
1.30
(.36)
1.08
(.10)
1.09
(.09)


t(kl=)a
.75

-.57

1.64

.63

-.44

.38

-.33

.83

.80

1.00


aCritical t.05,121 = 1.980

F20,1210 = .69; Critical F.05 = 1.58


Good

FD

GE

AU

PT

RR

MC

MMP

LWP

CAP

HFO


^0
YkO
-19.60
(25.64)
16.72
(17.74)
-46.36
(25.89)
-10.28
(18.84)
3.37
(11.24)
-11.50
(16.67)
11.24
(16.06)
-69.71
(53.25)
-9.74
(12.50)
-14.09
(11.46)


t(YkO=)a
-.76

.94

-1.79

-.55

.30

-.69

.70

-1.31

-.78

-1.23







The second step to indicate whether the "quasi-futures" contracts
were true substitutes for the consumption goods is to test whether the
relative risk properties of the stock-bill portfolios were similar to
that of the goods. That is, the "quasi-futures" contract for good k
should have a covariance with (V' M1' 1 ) equal to the covariance of

,kl with ( s i ). This can be stated as

COV *,kl (11'' 1) } = COV {0kl' ( t' ) ,) } k = 1,...,K.

(V-3)

Since the previous tests indicated that the portfolios had equiva-
lent observed values at each delivery date, then any differences in the
actual monthly values should be uncorrelated with (~1' f1' 1S). If
equation (V-3) is true then the following can be stated:

COV {( kt- kt) (VI' .11 1 I)} = 0, k = 1,...,K. (V-4)

Letting Dkt be equal to Fkt Ikt, the difference in the observed monthly

prices between the hedging portfolio and good k, the following set of 16
(K+T) regressions is run for each good k, k = 1,...,K.

D 1 1 1
Dkt= 0kO + kI Vt + pkt'

j+ + j+l + j+l
kt =kO + kl jt "kt, j =

K~ti K+i K+i
k = k+ + "Ki B + Ki i = 2,...,T. (V-5)
kt kO kl t,t+i-l kt,

If the differences, Dkt, are truly uncorrelated with (V5M1 l' il ), then
all the intercept and slope coefficients in equation (V-5) should equal
zero. Thus, the hypothesis to be tested is








1 2 K+T
HO : "kO = "kO : "'= = kO = 0
0 kO kO k 0

1 2 K+T
"kl kl ~ = .'" : k1 : O, k = 1,...K.

An F test can be conducted (see Maddala, p. 323) which will test

the above hypothesis. The F ratio is


F = (S2 Sl)/ 2(K+T)
S/ K+T
z M.r 2(K+T)
i=1

where

1) M. is the number of observations in the ith regression,

2) S, = the sum of the unrestricted residual sum of squares from

each regression

K+T K+T
E RSS. with df = S M. 2(K+T),
i= 1 i=I 1
and

3) S2 = the restricted residual sum of squares from a pooled

regression of the data

2 K+T
= (K+T) Z Dt with df = z M..
t i= 1

Estimates of the regression coefficients in equation (V-5) from the

period January 1966 to March 1976 are presented in Tables V-3 through

V-12 for each of the 10 consumption goods. In addition, the t statistics

for the coefficients are given along with the R2 and the residual sum of

squares from each regression. When trying to reject a null hypothesis,

selecting a larger significance level produces a more stringent test.

For all of the consumption goods, with the exception of Apparel and Upkeep,

none of the estimated intercept or slope coefficients were greater than













Table V-3
Covariance Properties of Contracts
Fit "it = a0 + all (Ind Var)t
January 1966 March 1976, T


t(al0=0)


all


.37 -.01


-.61
-.47
-.33
-.51
-.34
-.36
-.53
-.34
-.79
-.50
.87
.51
.39
.62
.67


.15
.12
.14
.19
.14
.10
.11
.07
.18
.17
-59.01
-16.05
- 7.91
- 9.43
- 8.15


t(all=0)

-.38
.61
.47
.33
.51
.34
.36
.53
.34
.81
.50
-.87
-.51
-.39
-.62
-.67


Residual
Sum of
R2 Squares

.001 613715.5


.003
.002
.001
.002
.001
.001
.002
.001
.005
.002
.006
.002
.001
.003
.004


612553.1
613356.6
613909.9
613139.1
613878.3
613803.4
613009.0
613870.7
611166.4
613194.2
610615.2
613124.4
613687.4
612501.1
612180.4


S1 = 9807704.7

S2 = 9831382.4

F32,1936 15

Critical F.05 = 1.45
05


df = 1936

df = 1968


for Food

+ 1It
= 123


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


a10
12.10
-19.03
-15.30
-17.10
-22.75
-17.20
-12.62
-14.74
9.49
-21.39
-20.12
5878.04
1591.37
779.82
924.96
795.53













Table V-4
Covariance Properties of Contracts for Gas and Electricity

F2t 2t = 20 + a21(Ind Var)t + "2t
January 1966 March 1976, T = 123


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


"20
10.05
26.91
27.63
47.07
34.82
42.69
30.79
24.78
24.95
18.61
32.54
1182.28
-631.33
-628.49
-426.53
-290.78


t(ci20=0)

.38
1.08
1.05
1.14
.98
1.05
1.10
1.11
1.12
.86
1.01
.21
-.25
-.39
-.36
-.31


a21
-.01
-.16
-.17
-.34
-.24
-.30
-.19
-.14
-.13
-.10
-.21
-11.25
6.44
6.45
4.42
3.05


t(a21=0)

-.10
-.80
-.79
-.97
-.78
-.88
-.85
-.81
-.81
-.54
-.79
-.21
.26
.40
.36
.31


R2

.000
.005
.005
.008
.005
.006
.006
.005
.005
.002
.005
.000
.001
.001
.001
.001


Sl = 6295925.9


S2 = 6424353.6


F32,1936 = 1.23


df = 1936


df = 1968


Critical F05 = 1.45
.05


Residual
Sum of
Squares

394886.6
392847.4
392914.3
391882.3
393949.7
392406.2
392567.7
392816.6
392784.9
393982.2
392887.3
394782.8
394708.3
394413.2
394493.0
394603.4













Table V-5
Covariance Properties of Contracts for Apparel and Upkeep

F3t 3t = 930 + a31(Ind Var)t + 3t
January 1966 March 1976, T=123


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


a30
.16
-33.89
-28.48
-53.40
-43.92
-47.71
-34.78
-28.23
-27.24
-25.32
-39.11
8791.19
3993.25
2224.94
1704.25
1509.15


t(a30=0)

.01
-1.80
-1.43
-1.71
-1.63
-1.56
-1.64
-1.68
-1.62
-1.55
-1.60
2.18
2.15
1.85
1.90
2.12


a31
-.01
.24
.20
.42
.34
.37
.24
.19
.17
.18
.29
-88.30
-40.32
-22.59
-17.40
-15.50


t(a31=0)

-.21
1.62
1.25
1.59
1.50
1.44
1.48
1.48
1.42
1.34
1.46
-2.18
-2.15
-1.85
-1.90
-2.13


R2

.000
.021
.013
.021
.018
.017
.018
.018
.016
.015
.017
.038
.037
.028
.029
.036


Residual
Sum of
-Squares

227742.5
222999.0
224913.8
223136.2
223679.6
223986.7
223780.1
223772.9
224116.7
224477.2
223884.7
219232.9
219441.1
221568.3
221169.8
219606.8


= 3567508.3


= 3677036.8


df = 1936


df = 1968


32,1936 1.86


Critical F. 5 = 1.45













Table V-6
Covariance Properties of Contracts for Private Transportation

F4t 4t = a40 + 41 (Ind Var)t + 4t
January 1966 March 1976, T=123


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


a40
12.72
-2.75
.75
6.08
.08
4.32
2.54
1.44
-6.18
-1.99
1.11
5749.06
2737.57
1480.92
1025.41
800.91


t(a40=O)
.64
-.15
-.04
.20
.00
.14
.12
.09
-.37
-.12
.05
1.42
1.47
1.23
1.15
1.12


a41
-.01
.03
.01
-.04
.01
-.03
-.01
-.01
.05
.03
-.01
-57.71
-27.60
-15.00
-10.44
-8.19


t(a41=0)

-.60
.20
.09
-.16
.04
-.11
-.07
-.03
.44
.19
-.00
-1.42
-1.47
-1.23
-1.15
-1.12


2
R2

.003
.000
.000
.000
.000
.000
.000
.000
.002
.000
.000
.017
.018
.012
.011
.010


Sl = 3548072.8

S2 = 3566366.8


F32,1936 = .31


df = 1936


df = 1968


Critical F.05 = 1.45


Residual
Sum of
Squares

222115.1
222696.9
222758.7
222724.6
222771.6
222752.0
222763.9
222772.6
222417.0
222707.2
222773.8
219103.4
218843.8
220015.1
220380.1
220477.0













Table V-7
Covariance Properties of Contracts for Reading and Recreation
F5t "5t = 50 + 51 (Ind Var)t + St
January 1966 March 1976, T=123


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


"50
5.09
2.02
3.91
8.37
7.14
8.84
5.11
3.53
.32
1.87
5.82
2258.23
1062.91
808.43
483.15
377.80


t(a50=0)
.53
.22
.41
.56
.55
.60
.50
.44
.04
.24
.50
1.16
1.18
1.40
1.12
1.10


"51
-.01
-.03
-.05
-.09
-.08
-.09
-.05
-.04
-.01
-.03
-.06
-22.69
-10.74
-8.21
-4.94
-3.89


t( 51O0)
-.73
-.42
-.60
-.68
-.69
-.73
-.69
-.67
-.26
-.47
-.65
-1.16
-1.18
-1.40
-1.12
-1.10


R2

.004
.002
.003
.004
.004
.004
.004
.004
.001
.002
.004
.010
.012
.016
.010
.010


= 825262.6


= 836043.2


df = 1936


df = 1968


F32,1936 = 79


Critical F05 = 1.45
05


Residual
Sum of
Squares

51656.0
51804.2
51725.1
51684.1
51675.2
51655.3
51679.7
51688.8
51851.5
51784.6
51697.5
51313.2
51285.8
51053.8
51344.3
51363.5













Table V-8
Covariance Properties of Contracts for Medical
F6t "6t = a60 + a61 (Ind Var)t + 6t
January 1966 March 1976, T=123


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


060
9.18
-18.26
-16.64
-19.74
-19.99
-16.83
-13.96
-15.64
-10.06
-19.28
-18.95
3686.31
1873.08
1323.96
1049.99
785.51


t(a60=0)

.43
-.90
-.78
-.59
-.69
-.51
-.61
-.87
-.55
-1.10
-.72
.84
.93
1.02
1.09
1.02


"61
-.01
.10
.09
.12
.12
.10
.07
.08
.03
.12
.11
-37.06
-18.95
-13.48
-10.75
-8.10


t(a61=0)

-.70
.64
.53
.42
.50
.34
.37
.57
.25
.81
.52
-.84
-.93
-1.02
-1.09
-1.02


= 4131077.2

= 4209499.2


df = 1936

df = 1968


F32,1936 = 1.15


Critical F 05 = 1.45
.05


Care


Residual
Sum of
Squares

258216.2
258395.9
258670.2
258880.0
258724.9
259011.2
258965.0
258565.6
259127.5
257881.1
258693.0
257751.4
257413.4
257038.9
256723.9
257019.0


R2

.004
.003
.002
.002
.002
.001
.001
.003
.001
.005
.002
.006
.007
.009
.010
.009












Table V-9
Covariance Properties of Contracts for Metal and Metal Products
F7t 7t = a70 + a71 (Ind Var)t + "7t
January 1966 March 1976, T=123

Residual
Sum of
Ind. Var. a70 t(a70=0) a71 t(a71=0) R2 Squares

MKT 14.14 .48 -.01 -.30 .001 483556.9
FD 21.39 .77 -.13 -.58 .003 482556.2
GE 22.01 .75 -.14 -.57 .003 482595.6
AU 44.21 .97 -.33 -.85 .006 481038.2
PT 30.93 .78 -.22 -.65 .004 482235.4
RR 38.55 .85 -.28 -.74 .005 481722.8
MC 28.08 .90 -.18 -.74 .005 481744.7
MMP 21.58 .87 -.13 -.67 .004 482138.4
LWP 19.46 .79 -.10 -.58 .003 482584.1
CAP 14.38 .60 -.08 -.38 .001 483337.7
HFO 28.70 .80 -.19 -.66 .004 482197.3
B1 1855.61 .31 -18.57 -.31 .001 483530.1
B2 151.93 .06 -1.48 -.05 .000 483899.1
B3 14.31 .01 -.09 -.00 .000 483910.2
B4 -44.64 -.03 .51 .04 .000 483904.6
B5 -69.15 -.07 .77 .07 .000 483890.3



SI = 7724841.6 df = 1936

S2 = 7803676.8 df = 1968

F32,1936 = .55


Critical F = 1.45
.05













Table V-10
Covariance Properties of Contracts for Lumber and Wood Products

F8t X8t = a80 + a81 (Ind Var)t + "8t
January 1966 March 1976, T=123


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


c80
-55.01
-110.51
-106.49
-204.64
-144.83
-177.49
-126.47
-111.62
-80.32
-92.44
-142.03
3326.18
3214.50
2723.63
2181.21
2122.31


t(a80=O)

-.52
-1.11
-1.02
-1.25
-1.02
-1.10
-1.14..
-1.26
-.90
-1.08
-1.11
.15
.32
.43
.46
.56


c81
.01
.65
.64
1.48
.99
1.26
.77
.65
.37
.54
.94
-33.68
-32.72
-27.90
-22.52
-22.03


t(a81=0)

.25
.84
.75
1.08
.83
.93
.89
.96
.59
.76
.89
-.16
-.33
-.43
-.47
-.57


R2

.001
.006
.005
.010
.006
.007
.007
.008
.003
.005
.007
.000
.001
.002
.002
.003


Residual
Sum of
Squares

6225374.
6192771.
6199474.
6169336.
6193731.
6184320.
6188088.
6181574.
6210587.
6199034.
6187793.
6227339.
6223068.
6219045.
6217445.
6211973.


S1 = 99230952

S2 = 101330400.0

F32,1936 = 1.28


df = 1936

df = 1968


Critical F05 = 1.45
05













Table V-11
Covariance Properties of Contracts for
Chemicals and Allied Products
F9t H9t = a90 + a91 (Ind Var)t + 19t
January 1966 March 1976, T=123


^o
"90
-17.53
-17.69
-20.15
-28.61
-29.12
-30.83
-22.09
-12.73
-13.17
-13.25
-24.13
-1146.73
-285.07
-141.67
-34.42
-145.54


t(a900)

-.98
-1.05
-1.14
-1.03
-1.21
-1.13
-1.17
-.85
-.87
-.91
-1.11
-.31
-.17
-.13
-.04
-.23


a91
.01
.14
.17
.24
.25
.26
.17
.10
.09
.11
.20
11.51
2.87
1.43
.35
1.49


t( 91 =0)

.99
1.06
1.15
1.03
1.22
1.13
1.18
.86
.89
.92
1.12
.31
.17
.13
.04
.23


= 2862602.3

= 2881004.8


df = 1936

df = 1968


F 1936 = .39
32,1936 j


Critical F0 = 1.45
.05


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


Residual
Sum of
Squares

178612.7
178401.5
178119.7
178505.3
177879.3
178171.4
178007.9
178971.8
178900.8
178800.2
178223.7
179914.0
180017.5
180034.9
180057.4
179984.2


R2

.008
.009
.011
.009
.012
.011
.011
.006
.006
.007
.010
.001
.000
.000
.000
.000












Table V-12
Covariance Properties of Contracts for
Household Furnishings
Flot l0t = a10,0 + a10,1 (Ind Var)t + 10tt
January 1966 March 1976, T=123


t(al0,o=0)
-.00
-1.40
-1.15
-1.09
-1.18
-1.00
-1.16
-1.22
-1.19
-1.39
-1.18
1.52
1.60
1.56
1.62
1.56


"10 1
-.01
.09
.08
.14
.13
.12
.08
.07
.06
.08
.11
-35.91
-17.53
-11.05
-8.60
-6.65


t(a l01=0)
-.30
1.11
.87
.90
.96
.81
.89
.89
.89
1.06
.94
-1.52
-1.61
-1.56
-1.63
-1.57


= 1200515.9

= 1237188.8


df = 1936

df = 1968


F32,1936 = 1.85


Critical F = 1.45
.05


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


10,0
-.05
-15.31
-13.28
-19.71
-18.36
-17.72
-14.20
-11.92
-11.62
-13.15
-16.59
3573.56
1734.89
1086.31
840.49
646.29


Residual
Sum of
Squares

75796.2
75092.4
75382.1
75344.1
75273.7
75442.9
75358.6
75357.2
75394.0
75158.8
75299.5
74430.6
74266.1
74356.0
74227.3
74336.4


R2

.001
.010
.006
.007
.008
.005
.007
.007
.006
.009
.007
.019
.021
.020
.021
.020








1.63 standard errors from zero. Thus, the hypothesis that each of the

regression coefficients is individually equal to zero cannot be rejected

as indicated by the critical t val-e of 1.658 at a .10 significance level

with 121 degrees of freedom. Only three of the regressions pertaining to

Apparel and Upkeep contained t values which were slightly greater than 2.

The hypothesis that all the intercept and slope coefficients are

jointly equal to zero cannot be rejected for eight of the ten consumption

goods as indicated by the F statistic at the bottom of each table. All

the F values with the exception of Apparel and Upkeep (AU) and Household

Furnishings (HFO) are insignificant at a .05 significance level. Finally,

the values of R2 in all the regressions are extremely small (the highest

in any being .037) indicating almost no relationship between the difference

in the value of the hedging portfolios and goods each period and the

vector of prices (VMl1' ,I B1).

Despite two significant F values, the findings essentially indicate

that each series of "quasi-futures" contracts had the same covariance with

the vector of prices (VM1, nl, B1 ) as did each good. In addition, the

neglible values of R2 in each regression indicate that any observed

difference each month between the value of the portfolio and the good was

non-systematically related to (VM1' 1 B1).

V. B Effect of the Nixon Wage and Price Controls

On August 15, 1971, President Nixon announced his New Economic

Policy intended to keep wage increases down to a 5.5 percent annual rate and

also to limit price increases, and thus inflation, to a 2.5 percent annual

rate. Economists thought that the 3 percent difference would result from a

rise in productivity and thus curtail the rising inflation rate in addition

to stimulating real growth. They also believed at the time that if the







inflation was of the cost-push variety, then controls could be a success

since rising costs of production would be pushing prices higher. Under

demand-pull inflation, economists thought controls would be a waste of

time since the demand itself requires limiting. Although the freeze

applied to prices and wages, prices of stocks and bondswere not included.

Interest rates were not frozen, but bankers and other lenders were urged

to hold the line. The impact of these wage and price controls on the

ability of the "quasi-futures" contracts to serve as successful hedging

instruments against commodity price inflation is examined next.

The controls which went into effect beginning on August 16, 1971,

led to queues and shortages which caused reported inflation rates through

the price indices to understate the true changes in purchasing costs to

consumers. August 1971 will be used as the starting date for the controls.

As the controls were lifted, the reported inflation rates probably over-

stated the true inflation rates. For instance, prices of many goods on

the commodity exchanges frequently reached their permissible daily price

increases within a few minutes of the opening of the exchanges. During

the ending months of the controls, the Administration tried to stagger

price increases by gradually lifting the controls from various industries

at a time. December 1974 will be used as the ending date when the con-

trols were lifted from almost all industries.

The tests described in Section V. A will be used again to examine

the success of the portfolios as hedging devices during the period

August 1971 through December 1974. Table V-13 presents the results of

the first test which investigates whether the portfolios had the same

observed value each month as each of the goods. The hypothesis is that

the intercept coefficient in equation (V-1) is equal to zero and the






71







Table V-13
Portfolios as Substitutes for Consumption Goods:
Ordinary Least Squares

Fkt = YkO + klkt + kt
August 1971 December 1974, T=41
(standard errors in parenthesis)


Good

FD


YkO
- 87.19
(102.23)


GE 24.45
(53.89)
AU -162.16
(122.20)
PT -35.59
(122.77)
RR -57.58
(111.95)
MC -153.63
(141.79)
MMP 6.17
(39.21)
LWP .50
(217.49)
CAP 23.08
(24.26)
HFO -53.15
(55.70)


t(Yko=O)a
-.85


Ykl
1.59
(.73)


.45 .84
(.42)
-1.33 2.24
(.96)
-.29 1.26
(.99)


-.51


1.42
(.88)


-1.08 2.02
(1.02)


.16

-.00


.95
(.28)
.86
(1.31)


.95 .81
(.20)
-.95 1.37
(.44)


t(kl=1)a
.81

-.38

1.29

.26

.48

1.00

-.18

-.11

-.95

.84


Durbin-
Watson
2.13


R2 F(YkO=O Ykl=1)b
.11 .41


2.16 .09

2.49 .12

2.16 .04

2.46 .06


.27

.39

.22

1.05


2.31 .09 1.17


2.32 .23

2.38 .01

2.57 .29

2.56 .20


.01

.30

.46

2.39


aCritical t.10,39= 1.684

Critical F052 3.23
.05;2,39=








slope coefficient is equal to one. The estimates of YkO' k = 1,...,10,

are all within one standard error from zero, with two exceptions, as

indicated by the t statistics. None of the t values are significant for

a critical value of t = 1.68 at a .10 significance level with 39 degrees

of freedom. Similarly, the estimates of Ykl' k = 1,...,10, are all within

one standard error from one, with one exception. Again, none of the t

values are significant at a .10 significance level. The values of F in

each regression, which test the joint hypothesis that YkO = 0 and Ykl = 1

for each good k, are all insignificant for a critical value of F = 3.23

at a .05 significance level with 2 and 39 degrees of freedom. Finally,

the values of R2 from each regression appear to be slightly lower than

those from the January 1966 to March 1976 period.

The intercept and slope coefficients are re-estimated using seemingly

unrelated estimation. Table V-14 presents these estimates of the intercept

and slope coefficients along with the t statistics. None of the t values

are significant at a .10 significance level. The F statistic which tests

the general linear hypothesis that the intercept and slope coefficients

across regressions are jointly equal to zero and one, respectively, is

also presented in Table V-14. The F value is insignificant at a .01

significance level.

The evidence again supports the claim that each hedging portfolio

and consumption good had statistically equivalent values each month. The

wage and price controls appear to have had little or no effect on the

success of the portfolios to serve as unbiased hedges for the consumption

goods.












Table V-14
Portfolios as Substitutes for Consumption Goods:
Seemingly Unrelated Estimation
Fkt = Yk + Ykl Ikt + kt
August 1971-December 1974, T = 41
(standard errors in parenthesis)


t(YkO0O)a
-1.55

-.97

-.23

.07

-.10

.23

-.43

-.59

-.43

-.48


Ykl
1.39
(.26)
1.26
(.24)
1.08
(.51)
.95
(.45)
1.00
(.38)
.81
(.46)
1.06
(.13)
1.03
(.24)
1.06
(.12)
1.03
(.17)


t(kl=1)a
1.50


1.08


-.11


-.41


YkO
-59.06
(38.02)
-29.75
(30.80)
-14.97
(65.79)
3.80
(56.87)
-4.95
(47.84)
14.97
(64.29)
-8.34
(19.30)
-28.97
(48.93)
-6.29
(14.49)
-10.82
(22.48)


t.0,39= 1.684

1.83; Critical F.01 = 1.92


Good


.18


MMP

LWP

CAP

HFO


aCritical

F20,390







The second set of tests for the wage and price control period will

check to see if the covariance properties of the stock-bill portfolios

were similar to that of the goods. Tables V-15 through V-24 contain the

results of regressing the monthly observed price difference between the

hedging portfolios and each good against each of the variables in

(VMI, 111 B1). The hypothesis is that each of the intercept and slope

coefficients in equation (V-5) should jointly equal zero. That is,

1 2 K+T
HO: akO akO "'." = kO : 0

1 2 K+T
k1 : 2k1 "' aK+T 0 k = 1,...K.
ckl kl kl

In the tables for each good, none of the estimated intercept or

slope coefficients are significantly different from zero as indicated by

the critical t value of 2.02 at a .05 significance level with 39 degrees

of freedom. The hypothesis that all the intercept and slope coefficients

are jointly equal to zero cannot be rejected for nine of the ten con-

sumption goods. With the exception of Household Furnishings (HFO), all

the F values are insignificant at the .05 significance level. The findings

essentially indicate that each series of "quasi-futures" contracts had

the same covariance with the vector of prices (VM' 1 1, B1) as did each

good. Any observed difference between the value of the portfolio and the

good each month was non-systematically related to (VM1, 11 1)

Some care must be given in the interpretation of these results. The

hedge portfolios appear to provide successful hedges during the price

control period. However, if the price index numbers for the commodities

do not reflect true transaction prices, the portfolios only provide hedges

against changes in the government reported price levels and not hedges

against actual price changes in the market place.













Table V-15
Covariance Properties of Contracts for Food
Flt l t = a10 + a11(Ind Var)t + "lt
August 1971 December 1974, T = 41


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


al0
28.07
-87.19
-86.60
-251.02
-124.66
-263.71
-183.16
-59.74
-70.89
-53.86
-139.22
3180.74
1617.98
1214.28
1275.07
1244.98


S1 = 3983398.8

S2 = 4048830.0

F32,624 = .32


t(al0=0)

.41
-.85
-.63
-1.05
-.71
-.90
-.90
-.76
-.74
-.77
-.83
.30
.35
.41
.57
.70


all"
-.01
.59
.63
1.93
.96
2.04
1.28
.39
.40
.41
1.05
-31.99
-16.38
-12.37
-13.06
-12.82


t(all =0)

-.49
.81
.60
1.30
.68
.89
.88
.71
.70
.70
.81
-.30
-.35
-.41
-.57
-.70


df = 624

df = 656


Critical F.05 = 1.47
.05


R2

.006
.017
.009
.026
.012
.020
.019
.013
.012
.013
.016
.002
.003
.004
.008
.013


Residual
Sum of
Squares

250464.1
247838.6
249730.8
245385.5
249030.9
247038.8
247134.0
248806.8
248897.8
248837.3
247880.9
251428.9
251220.6
250935.9
249916.0
248851.9













Table V-16
Covariance Properties of Contracts for Gas and El

F2t 2t = "20 + a21(Ind Var)t + 2t
August 1971 December 1974, T = 41


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


"20
-15.18
17.76
24.45
37.10
23.70
35.52
30.18
11.35
11.42
9.44
21.32
-1274.99
-733.12
-491.35
-392.49
-150.71


SI = 614349.8

S2 = 623216.6

F32,624 = .28


t(a20=0)

-.57
.44
.45
.39
.34
.31
.38
.37
.31
.34
.32
-.31
-.40
-.42
-.45
-.22


"21
.01
-.10
-.16
-.27
-.16
-.25
-.19
-.06
-.05
-.05
-.14
12.84
7.43
5.02
4.04
1.58


t(a21=0)

.70
-.36
-.40
-.36
-.30
-.28
-.34
-.27
-.22
-.23
-.28
.31
.40
.42
.45
.22


ectricity


R2

.012
.003
.004
.003
.002
.002
.003
.002
.001
.001
.002
.002
.004
.005
.005
.001


df = 624

df = 656


Critical F.05 = 1.47


Residual
Sum of
Squares

38052.7

38396.3
38372.9
38401.4
38439.8
38449.6
38415.4
38456.2
38478.7
38475.5
38451.9
38434.7
38366.2
38351.6
38327.7
38479.2












Table V-17
Covariance Properties of Contracts for Apparel and Upkeep
F3t 3t = a30 + 31 (Ind Var)t + "3t
August 1971 December 1974, T = 41


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


030
42.28
-76.39
-79.81
-162.16
-111.96
-199.35
-137.93
-50.12
-76.75
-41.03
-102.80
9228.92
3753.98
1881.52
1538.71
1425.97


S1 = 1012352.3

S2 = 1072020.0

F32,624 = 1.15


t(a30=0)
1.22
-1.48
-1.14
-1.33
-1.26
-1.35
-1.34
-1.26
-1.61
-1.14
-1.21
1.75
1.62
1.25
1.36
1.60


(31
-.01
.52
.59
1.24
.87
1.54
.96
.33
.44
.31
.77*
-92.72
-37.93
-19.13
-15.74
-14.67


t(a 31=0)

1.37
1.41
1.09
1.29
1.21
1.32
1.30
1.17
1.53
1.04
1.16
-1.75
-1.62
-1.25
-1.37
-1.61


R2

.046
.048
.029
.041
.036
.043
.041
.034
.057
.027
.034
.073
.063
.039
.046
.062


df = 624

df = 656


Critical F 05 = 1.47


Residual
Sum of
Squares

63210.2
63039.3
64299.5
63522.2
63840.1
63425.3
63507.0
64003.2
62487.3
64454.5
64026.1
61436.8
62059.7
63698.7
63217.9
62124.5












Table V-18
Covariance Properties of Contracts for Private Transportation
F4t 4t = a40 + 41(Ind Var)t + v4t
August 1971 December 1974, T = 41

Residual
Sum of
Ind. Var. 40 t(a40=0) a41 t(41=0) R Squares

MKT 25.20 .53 -.01 -.60 .009 120573
FD -50.93 -.-72 .34 .68 .012 120269
GE -35.19 -.37 .25 .34 .003 121333
AU -65.44 -.39 .49 .37 .004 121260
PT -35.59 -.29 .26 .27 .002 121466
RR -90.73 -.44 .69 .43 .005 121116
MC -53.56 -.38 .36 .36 .003 121294
MMP -12.42 -.23 .07 .17 .001 121592
LWP -97.07 -1.50 .57 1.46 .052 115348
CAP -4.30 -.09 .01 .03 .000 121685
HFO -24.68 -.21 .17 .19 .001 121579
81 11964.60 1.67 -120.18 -1.67 .066 113604
B2 5422.77 1.74 -54.76 -1.74 .072 112958
B3 3324.03 1.65 -33.76 -1.65 .065 113752
84 2174.45 1.42 -22.21 -1.43 .050 115653
85 1781.66 1.47 -18.31 -1.47 .053 115267



SI = 1898749 df = 624

S2 = 1952864 df = 656

F32624 = .56


Critical F 1.47
.05













Table V-19
Covariance Properties of Contracts for Reading and Recreation
F5t 5t = "50 + "51 (Ind Var)t + 5t
August 1971 December 1974, T = 41

Residual
a2 Sum of
Ind. Var. a50 t(a50=0) 51 t(a51=0) R Squares

MKT 3.12 .12 -.01 -.31 .002 36312.5
FD -30.62 -.79 .19 .67 .001 35988.2
GE -23.42 -.45 .14 .36 .003 36281.4
AU -43.01 -.47 .30 .41 .004 36240.3
PT -16.58 -.25 .09 .18 .001 36271.1
RR -57.58 -.51 .42 .47 .006 36193.2
MC -37.05 -.47 .23 .41 .004 36240.3
MMP -9.11 -.30 .03 .15 .001 36380.0
LWP -51.12 -1.43 .28 1.31 .042 34862.4
CAP -5.40 -.20 .01 .02 .000 36399.5
HFO -18.16 -.28 .10 .21 .001 36359.1
B1 4172.33 1.04 -41.95 -1.04 .027 35415.3
B2 2000.95 1.15 -20.24 -1.15 .032 35207.1
B3 1436.35 1.29 -14.62 -1.29 .041 34911.2
B4 943.25 1.12 -9.67 -1.12 .031 35256.1
B5 723.24 1.08 -7.47 -1.09 .029 35331.6



S1 = 573749.3 df = 624

S2 = 597444.3 df = 656

F32,624 = -81


Critical F.05 = 1.47













Table V-20
Covariance Properties of Contracts for Medical

6t 6t = 60 + a61(Ind Var)t + 6t
August 1971 December 1974, T = 41


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


a60
25.63
-82.87
-94.37
-202.41
-106.13
-210.45
-143.62
-54.94
-79.72
-46.43
-111.95
3968.58
2411.99
1781.24
1476.00
1054.09


s1 = 1928744.3

S = 2062723

F32,624 = 1.35


t(a60=O)
.54
-1.17
-.99
-1.21
-.87
-1.03
-1.08
-1.01
-1.21
-.94
-.96
.53
.75
.86
.95
.85


a61
-.01
51
.64
1.49
.76
1.57
1.02
.31
.41
.29
.78
-39.97
-24.47
-18.20
-15.18
-10.94


t(a61 =0)

-.80
1.00
.86
1.14
.77
.97
1.00
.80
1.03
.71
.86
-.53
-.75
-.86
-.96
-.86


df = 624

df = 656


Critical F05 = 1.47


Care


R2

.016
.025
.019
.032
.015
.024
.025
.016
.027
.013
.019
.007
.014
.019
.023
.019


Residual
Sum of
Squares

120950.6
119849.0
120629.1
118980.5
121105.4
120023.2
119867.9
120978.8
119665.0
121374.6
120658.9
122048.3
121200.2
120637.2
120124.3
120651.3












Table V-21
Covariance Properties of Contracts for Metal and Metal Products

F7t "7t = 70 + a71 (Ind Var)t + "7t
August 1971 December 1974, T = 41


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


a70
-7.85
-10.00
1.24
5.11
11.24
-15.81
-1.84
6.17
-37.60
7.39
8.87
2773.82
1406.69
1014.10
600.30
513.11


= 995736.0


S2 = 999851.1

32,624 = .08


t(a70=0)

-.23
-.19
.02
.04
.13
-.11
-.02
.16
-.79
.21
.11
.52
.61
.68
.54
.58



df = 624


df = 656


Critical F.05 = 1.47


a71
.01
.07
-.01
-.04
-.09
.12
.01
-.05
.23
-.06
-.07
-27.86
-14.20
-10.29
-6.13
-5.27


t(a71=O)

.23
.19
-.02
-.04
-.13
.11
.02
-.17
.80
-.22
-.11
-.52
-.61
-.68
-.54
-.58


Residual
Sum of
Squares

62407.3

62429.6
62487.7
62485.3
62461.0
62470.4
62488.0
62444.5
61488.8
62411.1
62469.4
62054.1
61901.4
61750.8
62029.4
61957.2


R2

.001
.001
.000
.000
.000
.000
.000
.001
.016
.012
.000
.007
.009
.012
.007
.009













Table V-22
Covariance Properties of Contracts for Lumber and Wood Products

F8t 8t = a80 + "81 (Ind Var)t + "8t
August 1971 December 1974, T = 41


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
84
B5


a80
-4.08
-93.97
-165.19
-367.43
-224.60
-325.75
-267.07
-134.36
-.50
-120.35
-241.80
-13172.8
-5385.3
-3631.57
1634.4
-1065.81


S1 = 20666073

S2 = 21148416

F32,624 = .46


t(a80=0)

-.03
-.40
-.53
-.63
-.56
-.49
-.57
-.76
-.00
-.75
-.63
-.54
-.51
-.53
-.32
-.26


881
-.03
.50
1.10
2.70
1.62
2.39
1.75
.79
.14
.82
1.71
132.04
54.11
36.61
16.43
10.69


t(a81=0)

-.13
.30
.45
.63
.50
.45
.52
.63
-.10
.61
.57
.54
.51
.53
.32
.26


R2

.000
.002
.005
.010
.007
.005
.007
.010
.000
.010
.008
.008
.007
.007
.003
.002


Residual
Sum of
Squares

1298446
1295921
1292129
1286048
1290585
1292205
1289881
1285864
1298596
1286537
1288075
1289221
1290454
1289646
1295676
1296789


df = 624

df = 656


Critical F.05 = 1.47












Table V-23
Covariance Properties of Contracts for
Chemicals and Allied Products
F9t 9t = "90 + a91 (Ind Var)t + 9t
August 1971 December 1974, T = 41


-19.66
41.24
50.84
93.02
62.89
122.67
84.96
29.77
34.94
23.08
61.12
-3072.94
-1023.48
-335.23
-439.32
-444.68


= 471743.2

= 483588.1


t(90=0) "91
-.83 .01
1.18 -.29
1.08 -.39
1.12 -.72
1.04 -.50
1.22 -.96
1.22 -.60
1.11 -.20
1.07 -.21
.95 -.19
1.06 -.47
-.84 30.87
-.64 10.34
-.32 3.41
-.57 4.49
-.72 4.57


t(91=0))

.89
-1.15
-1.06
-1.11
-1.03
-1.21
-1.20
-1.08
-1.04
-.92
-1.05
.84
.64
.32
.57
.72


R2

.020
.033
.028
.031
.026
.036
.036
.029
.027
.021
.027
.018
.010
.003
.008
.013


df = 624

df = 656


32,624 = .49


Critical F05 = 1.47
.05


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
82
B3
B4
B5


Residual
Sum of
Squares

29573.7
29180.9
29330.7
29252.1
29383.0
29079.7
29096.8
29297.1
29355.2
29533.4
29351.2
29643.2
29865.2
30095.4
29929.6
29776.0













Table V-24
Covariance Properties of Contracts for
Household Furnishings
F0,t 10,t = "10,0 + al0,1(Ind Var)t + v10,t
August 1971 December 1974, T = 41


t(a10,0 =0)

.55
-1.37
-1.07
-1.18
-.89
-1.09
-1.12
-1.04
-1.68
-.94
-.95
1.07
1.27
1.37
1.34
1.30


"10,1
.01
.29
.33
.69
.37
.79
.50
.15
.28
.13
.37
-37.72
-19.57
-13.64
-10.12
-7.84


t(al O,1=)

-.85
1.19
.93
1.10
.79
1.03
1.02
.80
1.49
.68
.84
-1.07
-1.27
-1.37
-1.35
-1.31


Residual
S Sum of
R Squares

.018 27542.6


.035
.022
.030
.016
.026
.026
.016
.054
.012
.018
.028
.040
.046
.045
.042


27074.4
27443.5
27206.9
27612.1
27310.2
27314.7
27599.0
26546.1
27725.5
27550.4
27253.6
26934.6
26753.8
26797.4
26873.2


S1 = 435538

S2 = 476083.4

F32,624 = 1.82


Critical F.05 = 1.47
.05


Ind. Var.

MKT
FD
GE
AU
PT
RR
MC
MMP
LWP
CAP
HFO
B1
B2
B3
B4
B5


"10,0
12.58
-46.20
-48.58
-94.25
-52.36
-106.30
-75.67
-26.99
-52.27
-22.07
-53.15
3749.76
1932.97
1338.18
985.59
757.59


df = 624

df = 656







V. C quarterly and Semiannual Rebalancing

From the conclusions reached in the previous hypothesis testing, it

appears that one can successfully create an unbiased hedge against

commodity price inflation using shares of common stock and Treasury bills

of various maturities. These hedging portfolios or "quasi-futures" con-

tracts had the same observed price and risk characteristics each month as

did the goods. Theoretically, since the portfolios serve as one month

hedges, new portfolios must be created each month in order to maintain

the proper hedge. One may speculate that some minor rebalancing each

month is necessary due to the realization of events. An example of the

fluctuations in the portfolio weights for a typical series of contracts

was presented in Table IV-5. The portfolio weights appear to be very

sensitive to small changes in the data used in the multiple regressions.

Multicollinearity, due to the bills, was probably introduced into the

regressions, since price movements of bills with close maturities are

strongly interrelated. Whenever a high degree of multicollinearity is

encountered, the estimates of the regression coefficients will be highly

imprecise and non-stationary over successive time intervals. This could

possibly explain the large observed changes in the portfolio weights each

period.

Adjusting the portfolio weights each month by the indicated amounts

would involve substantial transaction costs, but it might be possible to

reduce these costs and see how important the shifts in the portfolios

weights are, by reducing the frequency of the rebalancing. That is, the

success of the "quasi-futures" contracts as hedging instruments will be

examined when the stock-bill portfolios are rebalanced: 1) every 3 months





86

or at quarterly intervals; and 2) every 6 months or at semiannual inter-

vals. The procedure will be to keep the same position in each stock as

determined at the beginning of the interval until the interval elapses,

at which time the portfolio is rebalanced based on the sixty previous

months of price data. As for the bills, the proceeds from each bill when

it matures will be reinvested in the bill of the longest maturity. That

is, at maturity the funds from the one month bill wil.1 be placed in a

six month bill.

A comparison of the observed values of the hedging portfolios and

the goods will first be made for the quarterly rebalancing case and then

for the semiannual case. Table V-25 contains the results of the time

series regressions of equation (V-l) for the period January 1966 through

March 1976. The hypothesis that YkO = 0 for each good is rejected for

two of the ten goods (Apparel and Upkeep: t = -4.03, and Household

Furnishings: t = -2.26) at a critical t value of 1.658 for a .10 signif-

icance level with 121 degrees of freedom. The hypothesis that Ykl = 1

for each good is also rejected forthe same two goods. The values of F,

which test the joint hypothesis that YkO = 0 and Ykl = 1 for each good

are presented in the last column. The hypothesis is rejected for the

two goods, Apparel and Upkeep and Household Furnishings, at a critical

F value of 3.07 for a .05 significance level with 2 and 121 degrees of

freedom. Finally, the values of the R2 of each regression are lower than

when the portfolios were rebalanced monthly.

Before concluding that the portfolios still serve as an unbiased

hedge for eight of the ten goods, the values of the Durbin-Watson statis-

tics should be carefully examined. The critical Durbin-Watson value at

a .05 significance level is 1.65 for 123 observations. Thus, each of the











Table V-25
Portfolios as Substitutes for Consumption Goods:
Quarterly Rebalancing
Fkt = YkO + Yklkt + kt
January 1966 March 1976, T=123
(standard errors in parenthesis)

Good kO t(kOO)a kl t(kl)a WDurbin- 2 F(kO=0, y b
Good k0_ tkO) tk1 tkl'- Watson R2 (YkO ^^kl=
FD -18.58 .37 1.24 .62 1.01 .08 .85
(49.89) (.39)
GE 19.91 .49 .93 -.20 1.00 .06 1.40
(40.26) (.33)
AU -235.43 -4.03 2.89 3.85 .96 .22 8.91
(58.48) (.49)
PT 16.22 .35 1.19 .47 .83 .07 .55
(46.07) (.39)
RR 21.79 .78 1.12 .51 .92 .16 2.42
(28.09) (.24)
MC 15.06 .49 1.04 .17 1.21 .14 1.51
(30.74) (.24)
MMP 44.92 1.04 .72 -.84 .67 .04 .84
(43.37) (.33)
LWP 37.55 .37 .89 -.15 .84 .01 2.53
(101.42) (.72)
CAP 24.06 .98 1.22 1.06 1.15 .23 .59
(24.51) (.20)
HFO 56.55 -2.26 1.41 2.00 .98 .28 3.52
(25.06) (.21)



aCritical t = 1.658
S 10,121

Critical F = 3.07
.05;2,121







regressions exhibit positive autocorrelation of the residuals. This

fact alone is sufficient to conclude that the "quasi-futures" contracts

did not provide an unbiased hedge in the months they were not rebalanced.

When the portfolio is not rebalanced in any given month, there is much

information contained in the previous residual that is not being used by

the investor to adjust the expected value of the portfolio to that of the

good.

The results for the semiannual case are presented in Table V-26,

The results indicate a further deterioration of the success of the port-

folios as hedging instruments. The hypothesis that the estimated inter-

cept and slope coefficients are equal to zero and one, respectively, can

be rejected for nine of the ten goods. In addition, the values of the

Durbin-Watson statistics are somewhat lower. It appears that rebalancing

at quarterly or semiannual intervals in order to avoid frequent brokerage

commissions is a poor strategy for an investor who wishes to maintain an

unbiased hedge. The realization of events each month appears to signi-

ficantly influence the portfolio weights.

Futures markets allow investors to maintain a perfect hedge against

commodity price inflation. This dissertation demonstrates how an investor

can create an unbiased hedge, on a monthly basis, using the markets for

common stocks and Treasury bills. Thus, the amount contributed by futures

markets to the overall completeness of financial markets is questionable.

In addition, trading in futures contracts does not exist for many commodi-

ties. However, the techniques explored in this dissertation allow inves-

tors to hedge against price inflation for any commodity. In order to

maintain an unbiased hedge, frequent rebalancing of the portfolios is

required. Thus, futures markets may be economically valuable since they

allow investors to more efficiently hedge in terms of transaction costs.












Table V-26
Portfolios as Substitutes for Consumption Goods:
Semiannual Rebalancing
Fkt =kO +klukt + kt
January 1966 March 1976, T=123
(standard errors in parenthesis)


Good YkO

FD -165.51
(74.17)
GE 33.81
(58.81)
AU -443.56
(74.38)
PT 92.23
(75.02)
RR 15.63
(28.79)
MC 35.17
(53.25)
MMP 50.16
(66.03)
LWP 92.87
(171.18)
CAP -162.73
(39.16)
HFO -132.94
(33.56)


t(ko0)a kl
-2.23 2.63
(.58)
.57 1.07
(.48)
-5.96 4.77
(.62)
-1.23 2.03
(.63)
.54 1.21
(.24)
.66 1.32
(.41)
.76 .90
(.50)
.54 -.44
(1.21)
-4.16 2.44
(.33)
-3.96 2.17
(.28)


t(kl=l )a
2.81

.15

6.08

1.63

.88

.78

.20

-1.19

4.36

4.18


Durbin-
Watson

.85

.55

.69

.52

.50

.56

.47

.51

1.30

.87


R2

.15

.04

.33

.08

.17

.08

.03

.01

.32

.34


F(yko=O'Ykl=1 )
7.52

7.48

18.33

4.81

3.15

.47

3.17

4.50

9.80

9.65


aCritical t1


Critical F121
.05;2,121


1.658


= 3.07












CHAPTER VI
SUMMARY AND CONCLUSION


VI. A A Summary of This Research

This dissertation has investigated whether portfolios composed of

default-free bills of various maturities and shares of common stocks

exist that will allow an investor to hedge against commodity price

inflation, without actually entering the futures markets. These hedging

portfolios, or "quasi-futures" contracts, for a particular commodity

were constructed such that they would have the same price and risk proper-

ties as the commodity itself, such as the expected price at delivery and

covariances with the stock market, all other commodities, and long-term

bills. The results indicate that an investor can create a stock-bill

portfolio which will serve as an unbiased hedge against commodity price

inflation. Thus, if markets are perfect and securities are traded cost-

lessly, futures markets may be unnecessary since they do not provide an

investor with a service that cannot already be duplicated in the existing

markets for common stocks and Treasury bills.

The techniques explored in this dissertation allow investors to

hedge against price inflation in any commodity. Previously, investors

could only obtain perfect hedges against price inflation in commodities

for which they could purchase a futures contract. Thus, hedging by means

of "quasi-futures" contracts will be especially appealing to investors who

wish to hedge against price inflation in commodities for which organized

futures trading does not exist.








Examination of the portfolio weights needed to maintain each month's

hedge indicated a need for frequent rebalancing. This extensive rebal-

ancing, which would be costly to an investor, indicated that futures

markets do provide a necessary service once the assumption of perfect

markets is relaxed. In addition to the value of their information con-

tent (see Black (1976)), organized commodity exchanges are economically

valuable since they provide a less expensive means for hedging against

commodity price inflation versus the use of "quasi-futures" contracts.

Explanations by various authors for the necessity of futures markets

were presented in Section I. B. Included among these were (1) the insurance

viewpoint of Keynes; (2) the gambling casino viewpoint of Hardy; (3) the

information content derived from the pattern of futures prices discussed

in Black; and (4) Stoll's rationale that farmers or privately held firms

are reluctant or unable to trade ownership claims on certain assets or

production techniques with which they are endowed. The literature,

however, contains little empirical analysis of the above viewpoints.

Dusak examined the returns to holders of futures contracts and found

evidence which was directly contrary to Keynes's viewpoint and only

partially supportive of Hardy's.

Long (1974), in his development of a multi-period capital asset

pricing model, uses an economy that not only includes a stock market,

as do the traditional single-period models, but also includes a market

for default-free bills of different maturities and many consumption goods

whose future prices are uncertain. Long relates the price of an asset to

not only the systematic market risk, but also to the risk due to changing

consumption opportunities (inflation risk) and changing investment oppor-

tunities (interest rate risk). Implementation of Long's pricing equation








(see equation (11-3)) requires the development of a specific stock-bill

portfolio. This stock-bill portfolio, which has a current ex-dividend

price of FkO, is constructed so as to have a time 1 "with-dividend" value

equal to the expected time 1 price of a particular good, 1k1, and also

to have the same covariances with the elements of (VMI1, nIl Bl) as does

11kl. This hedging portfolio is referred to as "quasi-futures" contract
for good k.

Chapter III presented a detailed methodology of how to create a

"quasi-futures" contract for a particular commodity. The steps to be

taken included: (1) performing time series regressions using historic

information on stock, commodity, and Treasury bill price data; (2) in-

verting a matrix containing the above regression coefficients, and inter-

preting the kth row as being the unit quantities of a stock-bill portfolio

that has the same covariances with the vector of prices (VMI1, i' B1) as

does the kth good; and (3) setting the expected value of each hedging

portfolio equal to the expected value of the kth good by adding a quan-

tity of short-term bills.

Section IV. A discussed the various assets used in the study for

which data were collected. The commodity data consisted of seven consump-

tion bundles used in constructing the Consumer Price Index and three

components from the Wholesale Price Index. The selected commodity indices

are listed in Table IV-1. Eleven various industry portfolios were

created since the risk parameters using portfolio data are more stable

than those of individual stocks. Table IV-3 lists the industries used

which were selected from the Compustat classifications. Finally,








Treasury bills, with maturities from one month up to six months, were

used to represent prices of default-free coupon-less debt obligations.

Estimation of the regression coefficients needed for the calculation

of the portfolio weights was discussed in Section IV. B. Each time

series regression consisted of observations on stock, good, and bill

price data taken from the sixty most recent months. Problems with

serial correlation in the residuals were encountered in the regressions.

This problem was alleviated by using the method of first differences.

The use of this technique was defended by showing that the values of

the first order serial coefficients of the regressions were close to

unity.

The "quasi-futures" contracts for each good were constructed to

serve as one month hedges. In order to properly maintain each hedge,

new portfolio weights were computed each month using the regression

coefficients that were estimated from the sixty most recent months of

price observations. Thus, every month from December 1965 through

February 1976, new "quasi-futures" contracts were constructed for each

good for delivery one month later.

The analysis of the composition of the portfolios indicated that

the bills served as a better hedge against commodity price inflation

than did common stocks. It was shown in Table IV-7 that the portfolios

were largely composed of Treasury bills with a short position in stocks

frequently observed. These results were similar to those of Fama and

Schwert (1977a),who found that bills served as a complete hedge against

expected inflation while the returns on common stock were negatively

related to the expected component of the inflation rate.








Section V. A presented tests of hypotheses concerning the actual

success of the "quasi-futures" contracts as hedging instruments. The

first test was to indicate if the subsequently observed value at delivery

of each "quasi-futures" contract was identical to the observed value of

the good. Although the hedge was not perfect, the portfolios did serve

as statistically unbiased hedges against commodity price inflation as

seen in Tables V-1 and V-2. The second test indicated that the risk

properties of the stock-bill portfolios were similar to that of the

goods. If each series of "quasi-futures" contracts had the same covari-

ance with the vector of prices (VM1' "1' B1) as did each good, then any

observed difference between the value of the portfolio and the good each

month should be non-systematically related to (VMIl, 1 B1). The results

in Tables V-3 through V-12 showed that these differences were insignifi-

cant, indicating the covariance properties of the hedging portfolios and

the goods were similar.

The tests were repeated for the period August 1971 through

December 1974 when the Nixon wage and price controls were in effect. The

results presented in Tables V-13 and V-14, and Tables V-15 through V-24

indicated that the controls had little or no effect on the success of the

portfolios as hedging instruments.

An attempt was made to reduce the costs of maintaining the proper

portfolio weights by reducing the frequency of the rebalancing. The

effect on the quality of each hedge was examined when the portfolios were

rebalanced at quarterly and semiannual intervals. A comparison of the

observed values of the portfolios and the goods for the quarterly

rebalancing case was presented in Table V-25. There was a significant

difference in the two values for two of the goods. More importantly,








all of the regressions exhibited positive serial correlation of the

residuals as indicated by the low Durbin-Watson statistics. The "quasi-

futures" contracts did not provide an unbiased hedge during the unrebal-

anced months. In addition, rebalancing would have incorporated any infor-

mation from the previous month's error. The results for the semiannual

case presented in Table V-26 indicated a further deterioration in the

success of the portfolios as hedging instruments. Thus, rebalancing at

quarterly or semiannual intervals in order to avoid costly brokerage

commissions is a poor strategy for an investor who wishes to maintain

an unbiased hedge. The realization of events each month appears to

significantly influence the portfolio weights.


V. B Suggestions for Further Research

This dissertation constructed portfolios which hedged against

various consumption bundles used in compiling the Consumer Price Index.

A logical step would next be to construct hedging portfolios using actual

commodities for which organized commodity exchanges exist. An investor

would then be able to compare the price of a "quasi-futures" contract

for a particular commodity with the actual price of a futures contract

for that commodity. If the price of the "quasi-futures" contract was

lower, then an investor could arbitrage the difference in prices by

selling the futures contract and purchasing the "quasi-futures" contract.

At the delivery date the investor would use the funds from the "quasi-

futures" contracts to settle his short position in the futures contract.

An alternate approach for hedging against commodity price inflation

might be taken from Manaster (1979). Manaster shows how all nominal

efficient portfolios can be made real efficient by the simple addition