Basis determination across commodity futures


Material Information

Basis determination across commodity futures
Physical Description:
vii, 202 leaves : ill. ; 28 cm.
Monson, Sandra Johnson, 1958-
Publication Date:


Subjects / Keywords:
Basis (Futures trading)   ( lcsh )
Farm produce -- Storage -- Prices   ( lcsh )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph. D.)--University of Florida, 1987.
Includes bibliographical references.
Statement of Responsibility:
by Sandra Johnson Monson.
General Note:
General Note:

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Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001102150
notis - AFJ8209
oclc - 19611641
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Full Text








I would like to give my sincerest and deepest thanks

to Dr. Ronald Ward for his enduring patience and

guidance throughout my graduate program. I want to say

in the strongest of terms that he is an extraordinary

researcher and teacher. I want to thank the many other

faculty members in the Food and Resource Economics

Department, too numerous to mention, that have made my

program fulfilling, as well as enjoyable. I would also

like to thank Dr. Richard Kilmer, Dr. James McClave and

particularly Dr. Mike Procter for their help with this


I want to thank my husband and more so my son

Jeffery, for putting up with me through this endeavor.

I especially want to thank Glenda Monson because I could

never have finished without her generous help. Finally,

I want to thank my friend Raleigh, who was the only one

who never asked me when I would finish.







Concepts of Storage . .
Functions of Forward Pricing Mechanisms.

Futures Markets .
Basis Concept. .
Problem Statement. .
Objectives .
Scope. .
Overview .


Basis Theory .
Theory of Storage. .
Previous Literature. .
Arbitrage. .
Summary. .


Time and Form Transformations.
Theoretical Model. .
Generalized Conclusions. .


Dependent Variable: A Measure of Basis
Performance ..........
General Model Specification.. .. ..
Data and Model Implementation. .


S. v

. 1

. 4
. 7





* .
* .

Model Specification. . 109
Summary. . . .. .116


Data Summary .............. 117
Empirical Results. . 119
Model Overview . 142

VARIANCE MODEL ............... 143

Arbitrage Response Functions . 143
Elasticity Measures. . 165
Summary. . . 176


APPENDIX. . . 195



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



Sandra Johnson Monson

December 1987

Chairman: Dr. Ronald W. Ward
Major Department: Food and Resource Economics

The basis between the cash and futures market is of

critical importance in determining the usefulness of

using the futures market as a method of reducing price

risk. The basis also provides an index for judging

market performance because a normal basis should reflect

any time, form or location differences. Basis

determination models have been developed for storable

commodities but there is a gap in the theory pertaining

to nonstorable commodities.

In this analysis, a basis determination model is

developed that is generalized enough to accommodate

storable and nonstorable commodities. Arbitrage is

identified as the competitive mechanism that integrates

the cash and futures markets. The basis is defined so

that it represents a value enhancing transformation,

either by time or form. The deviation of the basis from

the cost of transformation (basis residual) is a

function of the arbitrage potential. In turn, the

arbitrage potential is influenced by commodity and

market characteristics.

The empirical measure of basis performance is defined

as the normalized standard deviation of the basis

residual because the distributional properties of the

basis determine basis risk. Nine agricultural

commodities over a fifteen year period are included.

Basis models in which the time from contract maturity is

held constant are specified for two, four and six month


The empirical results indicate that an increase in

exports relative to production and an increase- in

futures market liquidity each significantly decrease

variability in the basis residual. An increase in the

hedging ratio beyond 50 percent improves basis

performance. The results indicate that integration

between the markets is strongest when stocks are

abundant, consistent with observed basis patterns. As

expected, the mean level of the normalized variability

in the basis residual is significantly higher for

nonstorable as compared to storable commodities.

Changes in the economic or political environment

would potentially be expected to influence exports,

market liquidity or the hedging ratio and in turn affect

basis performance. Changes in storability and the

seasonal pattern of stock levels, which require

technological advances, are less likely to occur.

However, ascertaining that these variables affect basis

performance is useful to understanding basis




An important area of analysis in agricultural

marketing has been directed to understanding forward

pricing mechanisms and how such pricing arrangements

affect producer risk, production decisions and the

temporal allocation of agricultural output. In the case

of the most institutionalized forward pricing

mechanisms, the futures market, the bulk of theoretical

and empirical investigation has been devoted to storable

commodities, where forward or futures prices have a

direct influence on the movement of commodities into and

out of storage. In particular, research has been

directed towards examining the economic advantages

arising from futures markets, identifying to whom these

advantages accrue and looking at the roles that traders

perform within the pricing system.

There is a noticeable gap in the theory pertaining to

agricultural commodities that do not meet

qualifications traditionally deemed necessary for

successful futures trading, such as storability.

However, agricultural commodities that lack this


characteristic comprise a significant share of total

agricultural output. One would expect that producers of

nonstorables could potentially benefit from forward

pricing mechanisms just as producers of storable

commodities do. Support for this reasoning is

suggested by the evidence of successful futures

contracts for nonstorable commodities such as live

cattle, feeder cattle, hogs and potatoes.

Accordingly, there is a perceived need for a

theoretical construct that can accommodate agricultural

commodities that do not fit into the existing

theoretical construct for storables. Without such a

theory, evaluation of market performance is hindered and

interpretation of any empirical analysis is limited to

each case study. Since generalization of results is not

justified in the absence of a unifying theory, progress

with the futures research for nonstorables has been


A generalized futures theory could offer a systematic

means of evaluating the efficiency of existing futures

contracts in terms of the benefits they generate to

producers, as well as provide a reference for judging

overall economic performance. Such a theory could be

used to identify potential benefits from creating new

contracts for commodities not currently traded.

Furthermore, a generalized theory for nonstorables would


provide a basis for developing various empirical models

useful for predictions. Finally, a guiding theoretical

construct is needed to fully analyze the basis since

successful hedging strategies depend on an understanding

of the relationship between the cash and futures


The purpose of this paper is to offer a theoretical

construct that is general enough to handle all types of

commodities, from those with a long storage life, such

as corn, to those which are highly perishable, such as

fresh beef. As in the case of storables, this theory

will be set forth in terms of the basis. In particular,

identifying and analyzing the relationship between

commodity characteristics and basis performance will

give insight into the functioning of forward pricing

mechanisms in the absence of perfect storability.

In order to begin this investigation, an orientation

towards the concept of storage will be useful, extended

by an examination of the similarities and differences

existing between storables and nonstorables. In

addition, a brief review of the functions of a forward

price mechanism, such as a futures contract, will set

the stage for developing a theoretical structure for all

types of agricultural commodities.


Concepts of Storage

The concept of storage can be viewed as an extension

of the purely competitive model. That is, incorporating

the time dimension into the traditional model yields a

temporal allocation model that is operationalized by the

potential for storage. Conceptually, the temporal

allocation model is analogous to the spatial equilibrium

model, but markets are separated by time periods rather

than by regions. In the purely competitive model,

market participants acting in their own self interest

generate the forces which bring about a competitive

price. Using the Pareto criterion, this price can be

shown to be optimal in conveying allocation signals

since the competitive price reflects the marginal value

of the product.

Theoretically, the prices arising out of the

competitive process in a temporal allocation model

reflect the commodity's marginal value in each time

period. Competitive forces insure that the prices among

time periods will differ only by those costs associated

with the various dimensions of storage; hence, it is

these costs that the basis reflects. The competitive

pricing system optimally allocates product across time,

just as a competitive system optimally allocates product

among regions in the spatial equilibrium model.


Both the temporal and spatial equilibrium models rely

on the potential for arbitrage to guarantee that the

competitive process operates properly. In the case of

storable commodities, deviations from the marginal

conditions are corrected since dealers can take

advantage of market distortions by moving the product

into and out of storage. Market participants have

expectations about supply and demand conditions for

future periods. Through the process of individuals

acting on these expectations within the competitive

market place, prices tend towards a competitive


A great deal has been written in this area of theory

concerning the temporal allocation of storable products.

An important topic deals with examining how pricing

institutions, such as forward prices and futures

contracts, aid in facilitating the movement of goods in

and out of storage. This same problem has been viewed

in terms of the supply and demand for storage. A

comprehensive discussion of the literature is included

in the next chapter.

A different perspective is needed when futures

contracts are considered for nonstorable commodities.

Conceptually, futures contracts exist for commodities

representing time or form transformations. For a

storable commodity going through a time transformation,

there is a clear relationship between the cash and

futures market that reflects the cost of storage. In

the case of a form transformation, such as feeding out

cattle, there is a relationship between the futures

price of the transformed product (slaughter weight

cattle) and the cash price of the untransformed product

(feeder cattle). Under competitive conditions, the

basis corresponding to a form transformation should

reflect the cost associated with completing the


Commodity allocation through time, form and space is

directed by prices in a competitive system. In a

temporal model, forward pricing mechanisms affect

allocation in two fundamental ways. First, forward

prices provide signals for product movement in and out

of storage. Secondly, these prices may also influence

production decisions. In the case of nonstorable

commodities, this second factor is of greater importance

because the ability to move a product through time may

be severely limited or even nonexistent for some

commodities. For example, fresh beef must be consumed

shortly after slaughter. A closer examination of the

functions and need for a forward pricing mechanism

follows in the next section.


Functions of Forward Pricing Mechanisms

Ideally, forward pricing mechanisms provide several

functions. Two functions of particular importance

discussed in this section are that it acts to provide

price signals to allocate products over time and that it

reduces producer's price risk. In addition, forward

pricing institutions provide producers with marketing

alternatives by offering an outlet for product delivery.

These pricing institutions assimilate market

information, thereby decreasing search costs and

increasing the effectiveness of the allocative


Forward prices give an indication of product value at

some future date. In terms of allocation, this type of

information influences the usage of current holdings of

stocks. Relatively high future prices quoted for a

forthcoming season for a storable commodity such as corn

may cause current corn supplies to be put into storage

until next season. For nonstorable commodities, these

price signals have a different impact. For instance, a

cattle producer may postpone a slaughter date by a few

days or weeks by slowing down the steers' rate of gain

or marketing at a heavier weight if relative prices

among time periods favor this strategy. However, the

cattle feeder's ability to manipulate the marketing date


is relatively limited when compared to a producer of a

storable commodity.

For commodities going through a form transformation,

price signals are more important in influencing

production decisions than allocating existing supplies.

Forward or futures prices have the greatest potential

impact before the production process has been initiated.

For example, if the futures price of fed steers six

months in the future is greater than the current feeder

cattle prices and the cost of feeding an animal out,

then a cattle producer may respond by increasing

production. However, supply response is limited by

other factors such as fixed inputs and biological

constraints. For instance, favorable future pork prices

may cause an increase in pork production, yet there is a

time lag in the increase since the hog reproduction

cycle is not instantaneous. In terms of financial

limitations, feedlot operators may not respond to low

future beef prices by reducing cattle on feed because

they want to spread their high fixed costs over as many

output units as possible.

From a broader perspective, a forward pricing

institution is beneficial in its allocative function

because it promotes an efficient distribution of output

over time periods. A forward pricing mechanism acts as

a market place in which market participants temporally


allocate product through time up to the point of highest

return. Ideally, this competitive process yields an

allocation in which the product's marginal value is

equalized across time. Therefore, the resulting

allocation is desirable in an economic sense.

A second function of a forward pricing mechanism is

that it helps producers reduce their price risk. The

agricultural sector is typically characterized by

substantial price fluctuations. While domestic demand

for many agricultural goods is relatively stable, export

demand may be significantly influenced by foreign policy

and exchange rates. Both of these factors can cause

appreciable price movements. From the supply side,

uncontrollable and unforeseeable factors such as weather

affect aggregate output and hence prices. Finally, the

relatively long production period associated with most

agricultural products increases price uncertainty for

the producer since the accuracy of predicting a future

price decreases with the length of time until marketing.

Accordingly, price risk arises from not knowing what

output price will prevail at the future date when the

production process is complete.

A reliable forward pricing mechanism can act to

decrease price risk by providing a mechanism for setting

prices for future delivery. One alternative is for the

producer to establish a forward contract with a buyer


specifying the price or formula for calculating the

price. By this means, a producer can lock in a price

for his output at some time prior to harvest. Another

alternative is for the producer to hedge his cash

position in the futures market. Thus, a forward pricing

mechanism is beneficial from a microeconomic perspective

because it can reduce the price risk component of a

farmer's operation. Furthermore, these cost reductions

eventually manifest themselves as lower output price at

the aggregate level and therefore the forward pricing

mechanism is also beneficial in a macroeconomic sense.

Several functions performed by forward pricing

mechanisms have been identified. In addition, there is

a great deal of interest in the process of price

discovery associated with these mechanisms. In the case

of futures markets--the most extensive and organized

forward pricing institution--the trading process

incorporates expectations from a wide range of

participants. These agents, including individual

producers, merchants, speculators, etc., use various

information sources to form expectations on future

demand and supply conditions. Through the market these

expectations are translated into futures price quotes.

The fundamental workings of futures markets are

described in the following section.


Futures Markets

A futures market is an organized market in which

contracts specified for some future delivery date are

traded on an open exchange. These contracts are

specified in terms of a commodity's quality, quantity

and delivery location. For instance, a corn futures

contract traded at the Chicago Board of Trade is 5,000

bushels of number 2 yellow corn. The purpose of

specifications is to facilitate trade by insuring

contract uniformity. Discounts or premiums from a

contract price can usually be arranged if a delivered

product deviates from the contract specifications within

defined limits.

Futures contracts are legally binding and traded by

qualified brokers that are members of the exchange. The

primary difference between a forward negotiated contract

and a futures contract is that the former usually

involves the actual delivery of the commodity. In

contrast, 98 percent of all futures contracts are

settled without delivery. Traders, acting through the

member brokers, buy or sell contracts and a clearing

house keeps a record of the brokers' net positions. To

enter the market, a trader can establish a long position

(contract to buy) or a short position (contract to

sell). A trader terminates his position by reversing

the initial futures commitment. For example, a trader


who buys three soybean contracts and then sells two

contracts has a net long position of one contract.

The basic purpose of a futures market is to provide

members with the facilities to trade contracts. The

trading activities are closely monitored to see that the

exchange's rules are adhered to. These rules are

intended to facilitate the trading process and specify

such things as the hours that trading will take place

and the daily price movement limits. In addition, the

extensive communication system associated with futures

exchanges promotes the trading process by quickly

disseminating market information to the public.

Those who trade commodity futures represent a wide

range of occupations, but can be classified into two

general categories according to their intent in trading.

One group is known as speculators since they speculate

on price movements. These traders take on the risk of

price fluctuations in hopes of a return. In percentage

terms, the potential return on their investment can be

phenomenal since only a small fraction of the contract's

value, i.e. the margin, must be put down in order to

trade. Of course, the speculator also subjects himself

to potentially significant losses in the event that

price moves against his favor. A speculator's position

may be long or short, or it may change from one to the

other. The second type of trader is known as a hedger


and he attempts to reduce the price risk that he is

subjected to in the cash market by hedging his position

in the futures market. The textbook example is for the

hedger to take an equal and opposite position in the

futures market than is held in the cash market. Since

prices in the cash and futures markets tend to move

together, losses in one market tend to be offset by

gains in the other market.

For example, consider an elevator operator who has

an inventory of corn which he is planning to sell at

some future date. To hedge, he would sell a.futures

contract so that his long position in the cash market is

offset by a short position in the futures market. A

price fall would decrease the value of his inventory,

but would also result in a gain in the futures market.

Alternatively, a price rise would cause a gain in the

cash market and a loss in the futures market. The

degree to which the gains and losses offset each

other--which measures the effectiveness of the hedge in

reducing risk--depends on the relationship between

prices in the cash and futures market. This

relationship, defined in terms of the futures price

minus the cash price, is called the basis and is

discussed in the following section.


Basis Concept

A basis can be broadly defined as the difference

between two prices. This difference reflects the

difference in a product's time, form or location

qualities. For instance, the basis for the corn price

in Chicago and Kansas City represents a location basis

and reflects the transfer cost between these two

locations. With respect to futures markets, the basis

is the futures price minus the cash price. There is a

basis corresponding to each delivery month, such as the

September or November soybean basis. In addition, the

term basis can be used to refer to the difference in the

cash price of one commodity and the futures price of

another. For instance, there is a basis for the cash

price of feeder cattle and the futures price for live


For a hedger, the basis is critical to successful use

of the market. It is this variable, rather than

absolute price levels that determine the returns to a

hedged position. Essentially, the hedger is averting

the price risk he would be subject to if he only held a

cash position by taking an offsetting position in the

futures market. There are underlying economic factors

which make futures and cash prices move jointly. If

basis variability is less than cash price variability, a

producer can reduce risk by placing a hedge.


From an economic standpoint, the basis is of primary

importance because it is an index for judging market

performance. A normal basis should reflect any time,

form or location differences. In other words, price

differences should reflect the value added by these

three dimensions. A basis that is too large or small

indicates a malfunction in a market that the competitive

process fails to correct. In order to identify

problems, it is first necessary to have expectations

about how the basis should perform.

Problem Statement

A great deal of research has been devoted to

analyzing how the time dimension affects the basis for

storable commodities. This work has led to a generally

accepted theory of basis determination. Lacking in the

literature is a comprehensive treatment of futures

markets for all types of commodities, beyond the case of

storables. There is a perceived need for a fundamental

theory of futures markets which can have a broad

application for commodities with different time and form



(1) Develop a theoretical framework for
classifying commodity futures according
to a) whether they represent time or
form transformations, and b) commodity
characteristics that limit arbitrage,
the market adjustment mechanism.


(2) Develop an analytical framework to
analyze the competitive adjustments that
relate the cash and futures markets.

(3) Identify factors that can limit
arbitrage and hypothesize their affect
on basis performance.

(4) Develop criteria for judging basis
performance based on economic
considerations and hedging

(5) Develop an empirical model using cross
commodity data in order to investigate
the relationship between basis
performance and commodity


In the present analysis a theoretical model of basis

determination is developed that is generalized enough to

include both storable and nonstorable commodities. The

emphasis is on relationships between cash and futures

markets that represent both time and form

transformations. The spatial dimension which influences

basis patterns is not explored. The entire analysis is

set forth in the context of arbitrage as the competitive

mechanism that integrates the cash and futures markets.

Neither the theoretical model nor its empirical

counterpart offer a means of determining price levels in

the cash or futures markets. Rather, the model is used

to investigate the basis levels between these markets.

While expectations are fundamental to price

determination, this basis model does not rely on the

formation of expectations to drive the model.


Alternatively, in the theoretical model potential

arbitrators trade on observed conditions between the two

markets. Two unobservable factors that make up the

basis, the convenience yield and the risk premium, are

recognized but not explicitly measured. In addition,

the model does not accommodate multiperiod storage


Nine agricultural commodities over a fifteen year

period are included in the empirical investigation.

Basis models representing two, four and six months from

contract maturity are examined. Market performance is

gauged by the variability in the basis since a reliable

measure of what a basis value should be can not be

accurately calculated. Furthermore, it is the

variability in the basis, or basis risk, that is

important to the returns to hedging. The empirical

model is useful to predicting how variability is

affected by commodity and market characteristics. Since

performance is viewed from a macroeconomic perspective,

alternative hedging strategies are not compared and the

returns to hedging are not empirically measured.


A summary of basis theory, the literature review and

discussion of arbitrage are set forth in Chapter II. In

Chapter III, where the theoretical model is developed,

an analytical framework that describes the adjustment


process between the cash and futures markets is

examined. In Chapter IV an empirical model is developed

in which a measure of basis performance is specified and

observable factors that influence arbitrage potential

are identified. Data and estimation procedures are also

discussed in length. Chapter V includes the results of

the empirical model. Chapter VI follows with further

investigation and simulation of the results while

conclusions are included in Chapter VII.


A summary of basis theory is presented at the

beginning of this section accompanied by a review of

pertinent literature. Specifically, the purely

competitive model of basis theory is set forth, extended

by the theory of storage and futures trading. Next, a

behavioral assumption is identified that acts to

integrate the cash and futures markets. By arbitrating,

market participants provide the economic forces

necessary to successful functioning of the market. It

is shown that limitations to this mechanism affect basis


Basis Theory

A thorough treatment of the theory of basis

determination for perfect markets can be found in

Bressler and King (1978). Under the competitive

assumptions of 1) perfect knowledge for buyers and

sellers, 2) free entry, and 3) rational behavior, the

fundamental basis theory is demonstrated for three broad

categories of product transformation, namely, space,

time and form. In Bressler and King, basis


determination for each dimension is first examined

separately, then the analysis is extended to models

which incorporate two or more of the transformations

simultaneously. A brief summary of fundamental basis

determination follows.

The spacial equilibrium model is simplified by

considering two regions with given supply and demand

conditions. First, market equilibrium is derived for

each market separately, yielding regional prices in the

absence of trade. Next, assuming unrestricted trade,

equilibrium is reached over both markets by product

movement from the area with a lower regional price to

the higher priced region. This product migration occurs

since arbitrators can buy in the lower priced region and

sell in the higher priced region, thereby profiting from

their actions. This process causes increased demand in

the exporting region and, hence, upward pressure on

price. Simultaneously, the influx of product into the

importing region causes downward pressure on price. The

process continues as long as there is a profitable

return to arbitrage. In the final outcome, price

between the two regions differs only by the transfer

cost between regions. That is, the basis between the

two regions will never exceed the transfer cost under

the above assumptions (Bressler and King, 1978).


Another important aspect of spacial equilibrium

concerns the allocation of supply points among competing

markets when production is dispersed. In this model,

the relevant basis is the difference between the market

price and the price received at the site of production.

Under competitive conditions, the site price, or net

price received by the producer, is equal to the market

price less transfer cost. Thus, the closer a supply

point is to the market, the higher its site price will

be. A market boundary is defined as points between

competing markets where the site price to either market

is equal. Therefore, a producer located on a market

boundary is indifferent to which market he supplies. By

acting to maximize net returns, producers provide the

forces which link prices within the competing regions.

A second dimension of market price involves

differences in commodity form. For instance, a raw

product such as milk can be transformed into a variety

of finished products like fluid milk, cheese or yogurt.

The allocation of raw product among competing uses is

governed by price relationships among alternative forms,

given the physical range of product characteristics. In

this instance, a basis can be defined as the difference

between the value of the raw product and the price of

the final product adjusted for raw product equivalence.

Just as the basis in the spatial model reflects transfer

costs, the basis in the form model reflects processing

costs. Under perfect market assumptions, the net value

of raw product is equal across all product uses. If

this were not the case, processors could profit by

shifting production patterns. For example, a basis

which exceeded processing costs would encourage entry up

until the point where excess profits were eliminated.

Therefore, processors' actions should insure a price

structure that is consistent with costs.

The above principles outlined for the space and form

dimensions can also be applied to markets which are

differentiated with respect to time. In this model, the

commodity is moved through time as opposed to space or

form. The analogy to transfer or processing costs is

storage costs in the temporal model. There are two

factors which complicate the analysis of temporally

separated markets. First, there is asymmetry in the

potential for product movement because future production

cannot be brought back to the present time period.

Secondly, uncertainty, or the absence of perfect

knowledge, enters the analysis since future supply and

demand conditions are unknown. A review of the

literature concerning the theory of storage is presented

in the next section.


Theory of Storage

The theory of storage can be analyzed in terms of

the demand and supply of storage. The equality of these

two functions yields an equilibrium storage price and

quantity. The demand for storage is a decreasing

function of price, that is, as the cost of storage

increases, the quantity of storage space demanded falls.

The storage supply function is discussed below.

Many economist have contributed to the supply of

storage theory, including Working (1948), Cootner

(1960), Kaldor (1939), Brennan (1958), and Telser

(1958). The supply curve is derived from the marginal

cost of storage. The total marginal cost is comprised

of several components, including physical outlay,

convenience yield and risk premium. Obviously, there is

a physical outlay required to carry inventories. The

physical outlay represents costs associated with the

physical care and handling of a commodity in storage and

include factors such as the cost of storage facilities

and damage insurance. This type of cost is relatively

straightforward to calculate.

Kaldor (1939) introduced a second component in the

total net marginal cost of storage known as the

convenience yield. The convenience yield is a negative

cost, or benefit, of carrying inventory. For example, a

processor benefits from maintaining some threshold of


inventory, even if prices are falling, so that he can

avoid interrupting the production process. Such

interruptions can be costly for plant operations and

customer relations. Therefore, when stocks are low, the

convenience yield can be used to explain an inverse

carrying charge, which is an empirically observed

situation where a spot or near futures price exceeds a

distant futures price. It is contended that when stocks

are low, the benefit from the convenience yield exceeds

the cost of the physical outlay, thereby resulting in an

inverse carrying charge. Thus, some storage will occur

even when the market price spreads do not fully cover

the cost of storage. Furthermore, the convenience yield

is a function of stock levels and is expected to

decrease rapidly as stocks increase.

Brennan (1958) extended the theory by adding a risk

premium to the other components of the cost of storage.

There is price risk inherent in carrying stocks.

Assuming risk aversion, holders of stocks must be

reimbursed with a premium for carrying inventory. Since

risk increases with the amount stored, the risk premium

is thought to be an increasing function of stocks.

Thus, in the Brennan model, the net marginal cost of

storage is equal to the physical outlay plus the risk

premium minus the convenience yield. Telser (1958)

utilizes the same construct in analyzing the storage of


cotton and wheat, while Weymar (1966) includes a

convenience yield and risk premium in an analysis of the

cocoa basis. Malick (1985) empirically estimates these

effects for frozen orange juice. However, since the

storage supply function cannot be empirically observed,

it is not surprising that controversy surrounds the

theory with respect to the risk premium (Gray, 1972).

The marginal return from holding stocks is the change

in price over the storage period. Since the future

price is not known a priori, inventory holders must make

price expectations, P*. The expected marginal return is

thus expected price minus current price, P* Pt. The

optimal holding of stocks is the inventory level where

net marginal cost equals expected marginal revenue,

assuming that costs are known.

The theory of storage outlined above is not

contingent on the existence of a futures market.

However, a futures market offers an organized exchange

for dealing in commitments that have deferred delivery.

Working (1948, p.2) discusses the theory of futures

markets emphasizing its "exceptional convenience and

economy of transaction." Other economists have analyzed

the theory of storage in terms of the equilibrium

between the cash and futures markets, as discussed



In "The Simultaneous Determination of Spot and

Futures Prices," Stein (1961) creates an equilibrium

model for spot and futures prices in the case of

storable commodities. He first develops a theory for

holding stocks to obtain the supply of hedged and

unhedged storage. He then derives a curve which gives

the combination of spot and futures prices that

equilibrates the demand and supply of storage. Next, he

derives a curve that equilibrates the demand and supply

of futures contracts. Together, these curves create a

simultaneous equilibrium system. With this model, one

can obtain qualitative results of how the basis adjusts

to variations in the demand and supply for current

production, and changes in expected prices. While

holding price expectations constant, Preston and Yamey

(1960) consider models based on alternative trader

compositions, such as hedgers, speculators, and

merchants, who respond differently to price changes.

They conclude that only the general direction of

equilibrium adjustment for stock and consumption levels

can be determined.

Previous Literature

In conjunction with the storage literature already

set forth, the research relevant to the present analysis

must include treatment of nonstorable commodities. Two

general areas in the nonstorable literature pertinent to


this analysis are price forecasting and market

efficiency; and hedging and basis relationships for


Because nonstorable commodities can not be carried

across seasons, they must be analyzed in a different

framework than storables such as grains. Commodities

that do not meet the qualifications of storability

include cattle, hogs, eggs, iced broilers, pork bellies

and potatoes. In the literature, these commodities are

referred to as nonstorables although the storage

potential among them varies. The bulk of nonstorable

research has been directed towards cattle and hogs since

these contracts have been traded in significant volume

for a relatively long period of time.

Price Forecasting and Efficiency

Much of the nonstorable research has been focused on

the futures market in its price forecasting or forward

pricing role. Tomek and Gray (1970) emphasize that the

primary function of futures markets for nonstorables is

establishing forward prices, as opposed to allocating

inventories. Many empirical studies have been conducted

to evaluate the pricing efficiency of futures markets

using different methods and criteria for judging

performance. The results of such research have

implications about how well futures markets function in

incorporating market information.


Leuthold and Hartmann (1979) appraise the efficiency

of the futures market as a price forecaster for hogs.

They compare futures prices to results from econometric

forecasting models. They find the econometric model to

be more efficient than futures prices at predicting

subsequent cash prices. Using a similar approach, Just

and Rausser (1981) compare futures market prices to

large scale econometrically based forecasts for both

storable and nonstorable commodities. While their

results are mixed, they find that on average, futures

prices perform relatively better than the econometric

forecasts. However, for livestock they find that some

econometric forecasts outperformed the futures market

for forecast accuracy.

Leuthold (1974) evaluates futures prices as

predictors for cattle prices using current cash prices

as the norm with which to base his comparison. He finds

that the cash price is a more accurate indicator of

subsequent cash price than is the futures price.

Marquant (1979) compares futures prices to various

governmental, university and commercial outlook reports

and finds futures prices to be superior forecasters of

cattle and hog prices in terms of timeliness and

accuracy. Martin and Garcia (1981) find live cattle

futures to have inadequate forecasting performance under

several alternative criterion, while they find that hog


futures perform better than cattle futures. They

conclude that "the analysis does not support the

contention that these futures markets are agencies for

rational price formation" (p. 209).

Market efficiency is closely related to price

forecasting since both of these dimensions relate to how

information affects price formation. Samuelson (1965)

demonstrates mathematically that prices generated in an

efficient market fluctuate randomly. In an efficient

futures market, prices should quickly reflect new

information. Assuming new information occurs randomly,

the sequence of futures prices should also be random.

Therefore, a test of the efficiency of the futures

market is whether or not futures prices follow a random

walk. This argument of unbiased price changes parallels

Muth's rational price formation model.

Many studies investigating the efficient market

hypothesis have included nonstorable commodities

(Cargill and Rausser, 1975; Mann and Heifner, 1976).

Helmuth (1981) develops a systematic trading technique

to predict price movements in live cattle futures. If

the futures market is truly efficient, that is, price

changes occur randomly, then no mechanical trading

method can be employed to increase trading returns.

Helmuth's (1981) results support Martin and Garcia's

(1981) ascertain that cattle futures defy the rational

price formation hypothesis. He concludes that

the live cattle futures market is not
operating as an efficient price discovery
mechanism and that this market is operating
with a consistent, systematic, downward bias.
(p. 356)

Palme and Graham (1981) contest Helmuth's findings

and argue that his results are based on poor analytical

techniques. In response to this controversy, Kolb and

Gay (1983) apply a different methodology to appraise the

efficiency of the cattle futures market. They find no

evidence of a systematic downward bias nor any reason to

suggest that the cattle futures market is inefficient.

Summarizing, the research concerning pricing

efficiency in nonstorable futures markets is

inconclusive. Research in this area has been directed

towards identifying whether or not inefficiencies exist,

rather than analyzing why they may exist. A rigorous

theoretical model has yet to be developed to explain

what may cause malperformance in the price determination


In addition to the work done in evaluating the

efficiency of nonstorable futures markets, others have

focused on the volatility of futures prices. Samuelson

(1965) hypothesized that futures price variability

increases as the maturity date approaches. Miller

(1979) investigates this hypothesis for live cattle and


her results support the hypothesis of increasing

variance over time.

Anderson (1985) tests Samuelson's hypothesis for a

variety to markets, including storable and nonstorable

commodities. He tests this maturity affect against what

he refers to as the state hypothesis. According to the

state hypothesis, futures price volatility is highest

when the greatest degree of demand and supply

uncertainty is resolved. In agriculture, these periods

when large amounts of uncertainty are resolved follow a

seasonal pattern. Using both parametric and

nonparametric testing procedures, Anderson finds that

both seasonality and time until maturity affect price

volatility, with seasonality being the dominant force.

Anderson's results influenced the empirical design of

this research, in particular, for decisions concerning

time aggregation and seasonal adjustments.

Hedging and Basis Relationships

Another area in the literature on nonstorables is

concerned with hedging and basis relationships. Topics

in this general area include determination of optimal

hedged positions, consequences associated with

alternative hedging strategies, basis risk and basis

determination. Some of the analytical techniques used

in this research are common in the investigation of both

storables and nonstorables. The relationship between


the cash and futures market is the fundamental element

underlying all research in this area.

Ward and Fletcher (1971) develop a generalized model

for determining optimal futures and cash market

positions in which the outcome depends on risk and

income trade-offs. The model is generalized enough to

handle short and long hedging, as well as speculation.

In the analysis, the transformation costs associated

with live cattle are treated the same as storage costs

for storable commodities. Using a similar portfolio

approach, Heifner (1972) determines the optimal hedging

levels for cattle feeding for five market locations. He

finds location, grade and sex of fed cattle to have

minimal influence on hedging effectiveness.

Studies pertaining to a wide variety of nonstorable

commodities have been used to evaluate hedging

effectiveness. Tomek and Gray (1970) consider the

consequences of production period hedging by examining

the variability of cash and futures prices. For

potatoes, they find the prices of distant futures to be

less variable than cash prices. Therefore, they suggest

that potato producers can hedge as a method of

stabilizing their incomes. Using a portfolio model,

Peck (1975) demonstrates that hedging can stabilize

revenues for egg producers. She considers hedging for

the period of time after the production decision is made


but before marketing. The results show that optimal

hedging can significantly decrease producer risk.

Brandt (1985) provides an example of hedging

effectiveness for the hog industry. He demonstrates

that information from forecasts can be combined with

hedging strategies to reduce risk to producers and first

handlers. Brandt compares results under alternative

forecasting methods and suggests that composite

forecasting may be preferred to a single forecast


Others have considered the effect of basis

variability on the returns to hedging. Bobst (1979)

examines the effect of location basis variability for

southern markets. He compares the variances of hedging

revenues for three Southern markets to that of Omaha.

Bobst finds significant differences for choice steers

but no significant differences for hogs in these

markets. He concludes that location basis variability

may be an important factor affecting hedging returns to

southern cattle producers. Carter and Loyns (1985)

consider basis risk for hedging Canadian cattle while

Ward and Schimkat (1979) look at the basis risk

associated with hedging Florida feeder cattle. Both of

these studies indicate that basis variability can make

hedging ineffective as a risk shifting device.


Vollink and Raikes (1977) examine the delivery period

basis for live cattle and find that frequently the basis

values exceed the estimated transaction costs of

arbitrating. They suggest that speculators' price

expectations account for a sizable percentage of this

basis variation. Garcia, Leuthold and Sarhan (1984)

analyze the basis risk for midwestern livestock markets

by decomposing the basis variation into systematic and

unsystematic components. They define basis risk as the

variance of the random component of the basis over time.

Their results show that this random variability in the

basis is influenced by factors related to the flow of

new information to the market. Furthermore, they do not

find strong evidence that basis risk changes over the

contract life.

In a similar vein, Castelino and Francis (1982)

analyze basis volatility over the life of commodity

futures contracts. They identify degree of storability,

volume of existing supplies and commodity

substitutability as factors having an important effect

on the structural relationship between spot and futures

prices. Castelino and Francis argue that since the

linkage between the spot and futures market strengthens

as maturity approaches, the volatility of change in the

basis declines as contract maturity approaches. The

authors empirically test this maturity effect using data


across four commodities and find volatility to decline

uniformly as contract maturity is approached.

Furthermore, when looking at a fixed time until maturity

across different commodities, they demonstrate that

storability, existing supplies and substitutability

affect the extent of basis variability. The present

analysis extends this research by examining a larger

cross section of commodities and including a broader

range of factors that influence basis behavior.

Leuthold (1977) analyzes basis determination for live

cattle. He examines the basis corresponding to the

current cash price of live cattle and the futures price

of live cattle. These prices reflect two different

supply and demand situations that can not be related by

storage. Therefore, only external factors common to the

beef industry relate prices in the two markets.

In his analysis, Leuthold assumes demand is constant

over the time interval considered and thus hypothesizes

that the basis is a function of factors that affect

supply, such as the beef-corn price ratio, cattle on

feed and feeder prices. In addition, he includes cash

price as an exogenous variable to adjust the basis to

the price level. Therefore, this variable appears on

both sides of the regression equation. Leuthold

recognizes, but does not pursue, the problems associated

with potential simultaneity (biased and inconsistent


estimates). This aspect of the model weakens the

reliability of the results. Based on his findings,

Leuthold concludes that for a time period of two or more

months until maturity, the basis reflects the expected

change in cash price from the current time until

contract maturity.

The present approach is similar to Leuthold's cattle

basis analysis in that factors affecting supply are

expected to influence the basis. One difference is that

a measure of basis performance rather than the basis per

se is used as the dependent variable. Secondly, the

basis in this analysis is defined as the futures price

minus the cash price of the input. Thus, in the case of

cattle, the basis is defined as the live cattle futures

price minus the cash price of feeder cattle.

In the present research, the choice of what basis to

consider takes precedent from the work of Paul and

Wesson, and Ehrich. Paul and Wesson (1967) examine the

basis between cattle futures and cash feeder prices.

They view this basis, minus the feed required to finish

the animal, as the competitively derived market value of

feedlot services. Ehrich (1969) analyzes the same

cash-futures price relationship and theorizes that

under purely competitive market conditions,
cash price of feeder cattle and futures prices for
fed cattle will bear a relationship which is
determined by costs of feeding and the level of
futures prices. (p. 38)


The present analysis is an extension along the theme of

this quote. In particular, the focus of this research

is to see how the futures-cash price relationship is

affected when purely competitive conditions are not


Garbade and Silber (1983) examine the relationship

between the cash and futures markets for storable

commodities. They demonstrate that the degree to which

the cash and futures markets are integrated depends on

arbitrage elasticity. Theoretically, when arbitrage

elasticity is infinite, then cash and futures prices are

perfectly correlated. The present study extends Garbade

and Silber's orientation towards arbitrage by

considering nonstorable commodities. Arbitrage

potential is recognized as the critical mechanism

linking the cash and futures markets. Thus, factors

that affect the potential to arbitrate ultimately affect

basis performance.

In order to analyze how competitive markets operate,

it is necessary to make certain assumptions concerning

the behavior of market participants. One such

presumption is that traders seek to maximize profit.

Given that those involved are knowledgeable about market

conditions, the above assumption implies that dealers

will arbitrate when potential returns from doing so


exist. Thus, arbitrage is the mechanism that brings

about adjustment in competitive markets when distortions

arise. Arbitrage is usually discussed in the context of

trading across market regions. Yet, the same concept

can be applied to trading across cash and futures


An arbitrator profits by buying in a low priced

market and selling in a higher priced market. This

function is not only performed by those who make a

profession of trading; others, who are actually involved

in producing, processing or marketing commodities, are

also in a position to take advantage of price

distortions. For example, assume that near futures

prices for oil and meal, adjusted for raw product

equivalence, exceed the price of soybeans and crushing

costs. A processor could sell oil and meal futures, buy

soybeans in the cash market and crush them, then deliver

on the futures contract. Thus, arbitrage can take on

many forms and this research is specifically concerned

with the arbitrator's role of integrating the cash and

futures markets, for storable and nonstorable


A number of conditions must exist for arbitrage to be

an effective adjustment mechanism. The most important

factor in relating the cash and futures market is that a

certain percentage of futures traders are hedgers.


Hedgers give substance to the futures market because

they have the potential to deliver against a futures

contract. Without hedgers, there is no reason for

futures prices to necessarily reflect demand and supply

conditions. Although very few contracts are fulfilled

by delivery, it is the potential for delivery that is


Limitations to the effectiveness of arbitrage can be

classified into two main categories, those which are

market oriented and those which arise from industry

characteristics. Several deterrents to effective

arbitrage that relate to the functioning of the futures

market may exist. One constraint is insufficient market

liquidity. The first step in addressing this issue is

to estimate the composition and relative share of those

trading a particular futures contract (Peck, 1980;

Rutledge, 1978; and Larson, 1961). Ward and Behr (1983b)

develop a simultaneous equation model of futures trading

in which a measure of market liquidity is shown to be

affected by market characteristics such as firm number,

industry concentration, price risk, government programs

and perishability. Price distortions may go uncorrected

in illiquid markets since a trader must incur higher

costs in order to establish or close out a futures



A second market related limitation to arbitrage is

lack of accurate price information. A basic premise of

an efficient market is perfect knowledge on the part of

buyers and sellers. Accordingly, the viability of the

competitive mechanism declines as information quality

decreases. In addition, industry structure has an

impact on the competitive mechanism. For instance, in a

concentrated industry with noncompetitive pricing,

prices no longer reflect demand and supply conditions

and the futures contract fails.

Another aspect of the futures market that may

interfere with the potential to arbitrate is contract

specification. If a hedger's product does not fulfill a

contract definition, then in some instances he may lack

the option to deliver. Ward and Schimkat (1979)

evaluate the basis risk associated with hedging Florida

feeder cattle with the Chicago contract that is tailored

for midwest feeder cattle. Dewbre (1977) examines the

potential for those in the Pacific Northwest to use

midwest wheat futures contracts. Carter and Loyns

(1985) find the U.S. live cattle futures to be an

ineffective hedging vehicle for Canadian fed cattle.

These studies emphasize that basis patterns, and hence

hedging effectiveness, can be greatly influenced by

contract specifications. Furthermore, the tradeoff


between a contracts fit and market liquidity must also

be considered.

The limitations discussed above are all related to

technical features that may be present for a futures

contract. In some instances, these problems can be

corrected through intervention. For example, contract

terms can be redefined in order to increase trading

volume and liquidity. In other circumstances, a

contract may simply fail because it lacks sufficient

commercial interest. For instance, if an industry

becomes highly concentrated and price volatility

diminishes, the economic need for hedging disappears.

The second major category of limits to arbitrage

involves industry characteristics that can not be

adjusted with market intervention. These

characteristics are inherent to production techniques

and biological processes and thus independent of the

institutional or market setting. One such limitation

involves capacity constraints. Many agricultural

industries are characterized by significant fixed

investment. Instead of smoothly rising cost curves,

total costs rise in stairstep fashion (Bressler and

King, 1978). Output can be increased at closely the

same per unit cost over a certain range, then, when full

plant capacity is utilized, substantial investment in

new plant or machinery is required to further increase


production. For example, by increasing the use of

variable inputs, a soybean producer can increase the

crushing rate at approximately a constant cost rate up

until the plant is used to full capacity. To increase

production beyond this level, a new plant must be built,

and accordingly, total per unit costs will rise


This type of cost structure causes inelastic supply

responses over at least some levels of output. These

supply inelasticities in turn influence the

effectiveness of arbitrage. Distortions can arise that

go uncorrected since the benefits from arbitrating are

not great enough to cover the costs necessary to

increase the fixed component of operations. For

instance, it is typical for crush margins to widen at

harvest time when plants are operating at or near full

capacity. The crush margin narrows during other times

of the year when competition among processors squeezes

profits to a minimum.

From an economic standpoint, it can be argued that

the differences in the pricing of processing services do

not necessarily indicate imperfect competition. If

opportunity costs are also considered, then the economic

cost of processing differs at various times of the year.

That is, total processing costs are highest at peak

demand periods because of the added opportunity cost


involved. Although capacity constraints definitely

limit the potential to arbitrate, one must use caution

in interpreting the implications of prices which are

above transformation costs.

A second industry characteristic that can limit

arbitrage originates from the biological nature of

production processes in agriculture. For many

commodities, time is a necessary ingredient for

completing a form transformation. This factor is

relatively unimportant in some transformations, such as

crushing soybeans into oil and meal. However, in many

commodity transformations, such as changing feeder

cattle into fed cattle, time is required to complete the

process. The necessity of time leads to production

inflexibilities that in turn restrict arbitrage. In

most instances, the potential for arbitrage does not

exist prior to completion of the transformation process,

for a particular producer. For instance, a farmer with

immature field corn cannot take advantage of a nearby

futures price that greatly exceeds his production costs

because he has nothing to deliver against the contract.

He can only act on futures contracts that mature

simultaneously or later than his harvest date. Ward

(1970) discusses the limitations imposed by the time

element in transformation process for cattle.


Two other commodity characteristics, seasonality of

production and perishability, also relate to the time

dimension. Frequent harvest periods and storability

both enhance marketing flexibility and hence aid in the

competitive adjustment process. In the aggregate, the

limitations imposed by the time input are much less

restrictive if a commodity is produced continuously

throughout the year. Such production processes yield a

flow of output to market, as in the case of broiler

production. At any given point in time, there is some

percentage of producers who are in a position to deliver

against a futures contract. Therefore, the potential

exists for correcting price distortions so that the cash

and futures markets are more closely linked.

Storability also adds flexibility to commodity

marketing. When storage is feasible, a producer or

handler has the option of when to dispose of the

product. Relative prices among time periods influence

current consumption and storage rates, while arbitrators

maintain price differences consistent with storage

costs. In contrast, the relationship between

transformation costs and prices is weaker for perishable

goods. For such commodities, current demand and supply

conditions are not linked by the storage function.

Because quality characteristics deteriorate rapidly for


perishable goods, market participants do not have the

option to buy and sell between time periods.

Another trait characteristic of agriculture that

reduces arbitrage potential is production uncertainty.

A significant portion of agricultural commodities relies

on uncontrollable inputs, such as weather, for the

production process. These uncontrollable--and

unpredictable--inputs lead to uncertainty about a

producer's final output. A producer's hedging strategy

may not be fulfilled if his output intentions are not

realized. For instance, assume a farmer places a short

hedge in the spring on an anticipated yield of 100

bushels of corn. Late summer drought conditions result

in an actual yield of 60 bushels of corn. This

producer's actual hedge differs substantially from what

he intended because his final output is significantly

less than anticipated. In essence, he has

unintentionally become a specutlator on the unrealized

production. If he had hedged 100 percent of expected

output, then his option to deliver his own crop against

the futures contract is mitigated. Therefore, the

potential for hedgers to arbitrate is reduced by

production uncertainty. Furthermore, production

uncertainty affects hedging strategies. A producer may

hedge much less than his optimal level since he must use

conservative yield estimates.



In the context of perfectly competitive conditions,

the fundamentals of basis determination were briefly

reviewed for the space, form and time models. The

temporal model was then elaborated with a summary of

major developments in the theory of storage. Literature

pertaining to basis determination for nonstorable

commodities was also discussed. Arbitrage was

identified as the force that integrates the cash and

futures markets. Factors that can potentially decrease

the effectiveness of arbitrage were explored and shown

to be related either to specific commodity

characteristics or technical features of the futures market.


In this chapter the theoretical model of basis

determination is developed. First, time and form

transformations are discussed and a measure of basis

performance is identified. Following, an analytical

framework is constructed that will be used to examine

the adjustment process in the cash and futures markets

corresponding to alternative basis levels. Finally, the

stringent assumptions underlying the perfectly

competitive market will be systematically relaxed and,

using the analytical framework, the affects on basis

performance can be theorized.

Time and Form Transformations

In marketing theory, three qualities are recognized

that can add to a product's value--namely, time, form

and space. In order to narrow the scope of study to

manageable proportions, the ongoing analysis will focus

on time and form transformations. The spatial dimension

will be accounted for in the empirical investigation,

however, no attempt will be made to evaluate or analyze

the level of transfer costs.


Conceptually, one can consider a product prior to a

time or form transformation as a principal input and the

resulting transformed product as output. For example, a

feeder steer is an input for a slaughter weight steer.

Alternatively, field corn put into storage at time t is

an input for corn consumed in period t+k. As discussed

in the preceding chapter, under theoretically ideal

competitive conditions, the price difference between

input and output should equal the cost of transforming

the product with respect to time and/or form.

Accordingly, the relevant basis to consider in

analyzing the futures-cash basis is the difference in

the cash price of the input and the futures price of the

output. It is this price difference that is important

because it reflects the value added by the

transformation. This value adding function may

represent a form transformation, in which case the

physical qualities of the input differ substantially

from the output, such as feeder pigs and live hogs, or

soybeans verses soybean oil and meal. In a form

transformation, the physical qualities of the output

represent the preferred or more useful form of the

commodity. In a time transformation, the physical

characteristics of the input and output are the same.

In this situation, the basis reflects a time value

generated by holding stocks for deferred consumption.


Table 3.1 shows examples of commodities going

through time or form transformations. The left hand

column symbolizes the cash price in the input market

while the right hand column designates the futures price

for the output. The center column shows the type of

transformation and some of the factors required to

complete the transformation process. Subscripts

designate time.

Essentially, the conventional theory of storage is

exemplified by the first commodity in Table 3.1, wheat,

that goes through a time transformation from period t to

t+m. The costs associated with this transformation

include physical outlay, convenience yield and the risk

premium. The basis, that is, the right hand column

minus the left hand column, should equal the total

storage costs under ideal competitive conditions. The

actual adjustment process leading to such an outcome

will be discussed in the analytical framework section.

Soybeans offer an example of a commodity that can be

transformed with respect to time or form. In the form

transformation of crushing soybeans into oil and

meal, there is no significant physical or biological

time requirement in performing the crush process.

Conversely, in the case of transforming a feeder steer

into a slaughter weight steer that meets the

specifications of a live cattle futures contract, time

Table 3.1. Time and Form Transformations.

Cash Price Transformation Futures Price
(t) (t+m)
of input of output

Time Transformation
Wheat storage cost: Wheat
(t) physical outlay (t+m)
convenience yield
risk premium

Time and Form Transformation
Soybeans storage (optional) Soybean Oil
(t) processing cost and Meal

Form Transformation
Soybeans processing cost Soybean Oil
(t) and Meal (t)

Form Transformation
Feeder cost of feeding out Live Cattle
Calves (t) to market weight (t+m)

Form Transformation
Seed Corn production costs Corn (t+m)
(t) (storage option)


is a necessary ingredient. However, in a form

transformation that requires time, the time dimension,

in and of itself, does not add to market value, as it

does in the case of a time transformation. The

distinction as to whether time enters the

transformation as a value adding function or a physical

requirement should be made clear.

The value added by time and form transformations can

be separated conceptually even though the opportunity to

perform the transformations simultaneously may exist.

For instance, soybeans in period t can be stored and

crushed in order to arrive at oil and meal in period

t+m. Therefore, in this example, the output in t+m

includes both form value and time value components.

Using this conceptual framework, transformations can be

categorized as shown in Table 3.2.

Returning to Table 3.1, the last row represents the

process of transforming corn seed stock into field corn.

This form transformation is conceptually the same as the

feeder-slaughter weight steer transformation, even

though corn is a storable commodity and fresh beef is

nonstorable. In the present study the

storab-le-nonstorable dichotomy emphasized in the

literature has minimal analytical usefulness. The

pertinent classification, as shown in Table 3.2 is based

on the type of transformation. Therefore, the

Table 3.2. Transformation


1) time transformation

2) form transformation

3) form transformation
requiring time

4) time and form



Physical characteristics are
constant over the time

Physical qualities of input
differ from that of output.

Time is a necessary factor
in completing the form
transformation but time does
not add market value per se.

Physical characteristics
change and time adds value.

~_ _


distinguishing characteristic between corn and cattle

in the present example is that the potential for time

transformation following the form transformation exists

for corn but not for fresh beef. That is, corn may be

stored after harvest whereas fresh beef must be consumed

shortly after slaughter. In addition, the issue of

whether or not a form transformation requires time is

important because this characteristic affects a

producer's ability to respond to prices.

The rationale for classifying commodities according

to the value enhancing transformation is that under the

assumptions of perfect competition, the marginal return

from transforming a product will equal the marginal cost

of transforming. If the marginal return is less than

the associated costs, then the transformation should not

be initiated. In the other direction, competition

drives the transformation margin (the basis) to a level

consistent with cost. The adjustment process between

the cash and futures markets will be discussed in length

subsequently, but first it is useful to theoretically

establish what level the basis should be and then

identify a meaningful measure of basis performance.

Returning to the purely competitive model of basis

determination set forth in Chapter II, it is shown how

competitive forces generate a price structure that is

consistent with costs. From a broad perspective, this


outcome, where the marginal cost equals the marginal

benefit of transformation, represents an efficient

allocation of resources in terms of Pareto criteria.

The same principal can be applied to the basis between

the cash price of the input and the futures price of the

output. Economic theory suggests that, ideally, the

basis should equal the economic cost. The economic cost

includes out of pocket expenses as well as costs that

are not directly observed, such as a risk premium, a

convenience yield or a return to fixed investment.

Given that we consider basis levels equal to cost to be

consistent with economic theory, one measure of basis

performance is deviation of actual basis values from the

ideal level.

Analytical Framework

In this section, an equilibrium approach is taken to

develop an analytical framework that will be used to

examine basis performance under various sets of

assumptions. While disequilibrium analysis has been

used to analyze futures markets, an equilibrium approach

is more useful in the present study because the focus is

on the relationship between the cash and futures

markets, rather than the performance of either market

separately. While equilibrium may never be reached

between the two markets, the equilibrium adjustment

process is useful in describing the direction of


adjustment. It becomes evident that hedgers are the

driving force in the adjustment process. The role of

speculators and expectations within the analytical

framework is also considered.

First, it is necessary to assume that potential

hedgers exist. Hedgers are of paramount importance in

linking the cash and futures markets because they are

the agents who can arbitrate. It is the potential to

arbitrate that dictates the relationship between the two

markets. Depending on their position in the cash

market, some hedgers sell futures while others buy

futures. In order to simplify the illustrations, only

short hedgers are discussed, but the analysis applies

equally well to long hedgers.

Given that there are potential hedgers, an

equilibrium approach can be used to identify economic

incentives that induce buying and selling in the cash

and futures markets. Consider Figure 3.1 that depicts

basis levels on the horizontal axis. The medial line is

a delimiter where the basis equals economic costs. The

basis is defined as the futures price (F) minus the cash

price (P). To the right of center the basis exceeds

cost and to the left of center the basis is less than


The forces that act to equilibrate the cash and

futures markets--to where the basis equals cost--are


Basis < Cost

Basis > Cost

cash market:
demand for cash input
falls causing P

futures market:
supply of futures
contracts falls
causing F '

result: F P
that is, basis widens

direction of adjustment:

----> ---> ---->

cash market:
demand for cash input
increases causing P f

futures market:
supply of futures
contracts increases
causing F /

result: F P
that is, basis narrows

direction of adjustment:

<---- <--- <--

(narrow basis) B = C (wide basis)

P = cash price
F = futures price
C = transformation cost
B = basis

Figure 3.1. Basis Adjustment Process.

described in each half of the figure. On the right

side where the basis exceeds cost, a producer has the

incentive to buy cash inputs and simultaneously sell

futures. As defined, a hedger has the potential to

deliver against the futures contract. Thus, the viable

hedger's return from transforming a product is at least

the basis, adjusted for transaction costs, such as

brokerage commissions and any transfer costs that would

be incurred in the event of delivery.

On the left hand side, where the basis is less than

the transformation cost, there is no incentive to place

a short hedge. In addition, for a producer who does not

want to initiate the transformation process unhedged,

there is no incentive to buy cash inputs.

The hedgers' buying and selling actions affect prices

in the cash and futures markets. On the right hand

side, which represents too wide a basis, the increased

demand in the cash market (Dp) causes upward pressure on

prices, assuming that the input supply elasticity is

less than perfectly elastic. The hedgers' selling

actions (Sf) in the futures market cause downward

pressure on price in the futures market, ceterus

paribus. The combined affect of these actions tends to

narrow the basis since the difference F P becomes

smaller as F decreases and P increases.


Accordingly, the direction of adjustment is towards

the basis at a level consistent with cost. The wider

the basis, the greater the potential returns from

executing a hedged transformation and thus, the greater

the corrective forces should be.

On the left hand side where the basis is less than

cost, the reduced supply of futures contracts, brought

on by the lack of a short hedging incentive, exerts

upward pressure on futures prices, ceterus paribus. For

those producers reluctant to initiate the transformation

process unhedged, the decreased input demand causes

downward pressure on price in the cash input market.

The combined action causes a widening force on the basis

since the difference F P increases. Once again, the

direction of adjustment is towards the basis level that

equals cost.

The above discussion relies on an individual's

hedging incentives or disincentives to drive the

adjustment process. How strong these adjustment forces

are at the aggregate level depends on what assumptions

are made about producers' behavior and industry

characteristics. As emphasized before, without

hedgers, there is no mechanism to integrate the cash and

futures markets. For this reason, the burden of

equilibrium adjustment between the two markets is

oriented towards the supply side where arbitrators


(hedgers) react to basis levels. If the potential to

arbitrate is very strong, then prices in the cash and

futures markets will be highly correlated and the

difference between prices should tend towards cost


Factors such as supply elasticity can limit the

potential to arbitrate. Therefore, these factors work

through the arbitrage potential to affect basis

performance. The focus of this research is to identify

such factors and analyze how they affect basis


In the present model of basis determination, the role

of expectations is not as critical as it would be in

analyzing price movements in either the cash or futures

market in isolation. The results would be relatively

insensitive to the choice of the behavioral assumption

regarding expectations. The analytical framework set

forth implies nothing about absolute price levels in

either market, rather, it defines an adjustment process

between the two markets. Changes in expectations affect

both markets if they are linked by the potential to

arbitrate. Therefore, the relationship between the two

markets is not directly contingent on how expectations

are formed.

Expectations enter the analysis indirectly by

influencing hedging decisions. For instance, if a

producer anticipates high output prices, he may choose

to speculate on prices and proceed with the

transformation process unhedged, even if the basis is

sufficiently wide to insure an economic return to a

hedged position. Alternatively, a producer may

initiate a transformation process even if the basis is

less than cost and speculate that the cash price of

output will cover his costs when he markets his output.

Such decisions may decrease the effectiveness of the

adjustment mechanism and this aspect will be dealt with


In the next section, alternative assumption sets are

applied to the theoretical model. First, assumptions

corresponding to pure competition are maintained in

order to examine basis performance under ideal

conditions. Then the assumptions are systematically

relaxed and important factors affecting basis

performance are identified. The outcomes of the various

models are then contrasted.

Theoretical Model
In the analysis, the term producer is used to refer

to anyone who has a position in the cash market, that

is, has the potential to control the physical commodity.

Thus, in the context of this research, producers include

processors, handlers, meat packers, elevator operators

and anyone who can actually make or accept delivery to

fulfill a futures contract. Before examining the

various models, a set of assumptions maintained

throughout the analysis are as follows:

(1) Producers act rationally and would make
decisions consistent with the marginal
conditions of equating price and
marginal cost, if price were known.

(2) Producers know costs, which are constant over
the transformation period or can be procured
before initiation of the transformation

Assumptions (1) and (2) imply that producers within

an industry do respond to price signals. Suboptimal

output levels arising from input price variability are

not considered. Assumption (2) is not overly

restrictive for storage costs, which are fairly

constant. In addition, livestock feeders may have the

option to forward contract their inputs, employ custom

feeding or place a long hedge for the primary inputs.

This assumption is less plausible for crop producers

where costs are more difficult to calculate and costs

vary with environmental conditions.

(3) There is perfect knowledge about current
market conditions.

This assumption is not overly restrictive given

contemporary communication systems where price and

market information is disseminated quickly and


(4) Producers are risk averse; that is, for
a constant income level, an activity
with lower price variability is
preferred to one with greater price

Assumption (4) identifies the impetus to hedge.

(5) Hedgers can meet margin calls if they


Assumption (5) protects against involuntary

liquidation of a hedged position. It implies that if a

producer sells a futures contract at time t that matures

at t+k, then he can ride out any adverse basis movements

between t and t+k, thus maintaining the option to

deliver at t+k.

(6) Any spatial basis is consistent with
transfer costs.

Analysis of the spatial dimension of a basis is

beyond the scope of this research endeavor. It differs

from the form and time transformations because the

uncertainty arising from the time dimension does not

directly affect spatial equilibrium. Therefore,

transfer costs will be accounted for when necessary, but

no attempt will be made to evaluate or analyze their


Version (1)

In this first version of the model, the assumption

set is defined such that the perfectly competitive

outcome with respect to time and form transformations

can be achieved. Specifically, the assumptions

fundamental to this outcome are as follows:

(1) Producers are willing and able to use
the futures market to hedge their cash

(2) There are no outside constraints to the
competitive functioning of the markets,
that is, no government programs,
monopolies, market manipulations, etc.

(3) Producers have complete supply
flexibility in getting into and out of
the market.

Decision rule: Producers will initiate a hedge if
the basis is greater than or equal to the
transformation cost. They will not initiate a
transformation process unless the hedge will cover

Given the above assumptions and applying the

analytical framework, the model results in a basis level

equal to cost, providing there is sufficient speculative

activity to operationalize the futures market. This

outcome can be shown by returning to Figure 3.1, where

the adjustment process is outlined. The basis level

consistent with cost is realized in this version

because, by assumption, there are no impediments to the

potential to arbitrate and producers do not initiate

transformations unhedged. Thus, under the heroic

assumptions of a perfect market the following holds:

(3.1) Bt = Ftt+k pt = Ctt+k where k >= T

For a form transformation:

Bt = input/output basis

Ftt+k = current price of futures contract (output)
specified for delivery in t+k
Pt = cash price of input

Ctt+k = total variable costs associated with
transforming over period t to t+k
T = time required to transform input to output

For a time transformation:

Ctt+k = total carrying costs from t to t+k

T =0
no physical change over t to t+k

Version (2)

In this second version of the model, the third

assumption regarding supply flexibility is relaxed and

the decision rule is modified to be more realistic.

(1) Producers are willing and able to use
the futures market to hedge their cash

(2) There are no outside constraints to the
competitive functioning of the markets.

Decision rule: Producers are willing to place a
hedge during the course of the transformation
process if the potential for a profitable hedge
arises. They will initiate a transformation
unhedged if basis conditions are not favorable at
that time.

The decision rule above implies asymmetry in the

basis adjustment process. For short hedging, the

adjustment described on the left hand side of Figure 3.1

is not as strong since, by assumption, producers will

initiate unhedged transformations. Therefore, the

demand in the cash market is not suppressed and P does

not fall. Under the new decision rule, the analytical

framework is shown in Figure 3.2. The basis levels on

B = C


Basis < Cost

Basis > Cost

futures market:
supply of futures
contracts falls
causing F t

result: basis does not
necessarily widen,
inverted basis may persis

cash market:
demand for cash input
increases causing P +

futures market:
supply of futures
contracts increases
causing F ,

result: F P 4
that is, basis narrows

direction of adjustment:

<---- <---- <--

(narrow basis) B = C (wide basis)

P = cash price
F = futures price
C = transformation cost
B = basis

Figure 3.2. Asymmetrical Basis Adjustment Process.


the left hand side are known as inverted since the basis

is less than cost.

There are two primary reasons why an inverted basis

may persist. The most pronounced reason is the

inability to bring future production into the present

time period. In this respect, temporal allocation

differs fundamentally from spatial allocation because of

asymmetry inherent in the time dimension. For instance,

with a seasonally produced storable commodity such as

corn, there is no theoretical limit to the magnitude of

the inverted basis. When current quantities are valued

higher than future supplies, then the inverted basis

signals inventory depletion and abatement of storing

into future periods. In such situations the cash price

reflects current relative shortages while the futures

price reflects anticipation of future supplies.

A second reason why an inverted basis can persist in

this model is because in many agricultural enterprises

there are few production alternatives, as a result of

climatic conditions or specialized capital inputs. In

the case of an inverted basis, many producers would

rather initiate the transformation and speculate on

prices than let their fixed investment lay

idle. As long as their price expectations are greater

than variable cost, producers are likely to operate.


Given the assumption set in Version (2), it is

possible to examine the impact of marketing and supply

inflexibilities on the basis adjustment process. The

potential to arbitrate insures basis levels that are

consistent with cost. Factors that decrease this

potential affect the arbitrage potential and therefore,

basis performance. Factors such as perishability,

production seasonality, fixed investment and time

requirements can affect a producer's marketing or supply

flexibility. Therefore, these characteristics are

expected to affect basis performance.

The tree diagram in Figure 3.3 allows classification

of commodities by various factors affecting flexibility.

Each branch divides into two segments that represent

opposite extremes of being flexible or inflexible. In

actuality, commodities lie somewhere between extremes

but double branching serves to illustrate the concept

without complicating the diagram unnecessarily.

All commodities can be located on the bottom lines in

the diagram. For instance, the production of fresh

fruit represents a form transformation, requiring time,

that is produced seasonally and is nonstorable.

Alternatively, storing wheat represents a time

that can be carried across seasons. The position of

commodities within the diagram indicates the degree of

marketing and supply flexibility. Hence, the position

Form Transformation

requires time


ex. fresh


ex. seed corn
into corn

time not
ex. soybeans
into oil/meal

ex. fresh

ex. frozen

Time Transformation

interseasonal intraseasonal
ex. potatoes ex. corn, wheat

Figure 3.3. Commodity Classification by Type of


also indicates whether or not a commodity

transformation will be suited for the futures market.

The model above can be expressed in a generalized

mathematical form.

(3.2) BD = f(A [e(PI,S,FC,T)] )

BD = basis deviation
BD = I B C | ; BD measures the difference between
the basis and the economic cost
A = potential to arbitrate
e = industry supply responsiveness
PI = perishability
S = seasonality of production
FC = level of fixed cost in relation to variable
T = time requirement for form transformation

Equation (3.2) shows how industry characteristics

work through the arbitrage potential to affect basis

performance. The industry supply responsiveness (e) can

be influenced by several factors. Both perishability

and seasonality affect supply responsiveness. In

addition, the ability to store and the ability to

produce frequently are partial substitutes if continuous

consumption is desired. The proportion of fixed cost to

variable cost, as measured by FC, indicates the degree

of input fixity in an industry. As before, T stands for

the time required to complete a form transformation.

Totally differentiating (3.2) yields

(3.3) dBD = (8f/8A)aA/ae [ae/aPI dPI + ae/as dS +

ae/aFC dFC + ae/aT dT].

The expected signs of the partial derivatives are as


aA/8e > 0
As an industry's supply response increases, the
potential to arbitrate increases since the options
to deliver against hedges increases.

aB/aPI > 0
The ability to store adds marketing flexibility. A
highly perishable commodity must be marketed
immediately whereas holders of storable products
have greater flexibility in timing their marketing.

ae/as < 0
As defined, supply responsiveness decreases as S
increases. The more often a commodity can be
produced within a season, the greater the marketing
flexibility is.

ae/aFC < 0
As the fixed investment component of total cost
increases, supply responsiveness falls because of
the high cost involved in switching to a different
production activity.

8e/aT < 0
When time is necessary for a form transformation,
an individual's ability to arbitrate is mitigated.
Whether or not this affect is manifested at the
aggregate level depends on regional production
patterns and what level of aggregation is

The primary implication of this model is that basis

performance is positively related to supply

responsiveness. For example, the attribute of

storability strengthens the link between the cash and

futures market, so much so that cash and futures prices

among different time periods have been described as a

constellation (Tomek and Robinson, 1972). For

nonstorable commodities such as iced broilers, frequent

production periods allow producers to respond to price

signals within the season, thereby potentially

increasing basis performance compared to strictly


seasonally produced commodities. Furthermore, from this

model one would expect capacity constraints to affect

basis levels for commodities characterized by high

fixed costs.

In addition, for an industry where short hedging

dominates, this model implies that the basis is more

likely to adjust towards the cost level if it is too

wide than if it is too narrow. This result arises from

the decision rule that allows producers to initiate

unhedged transformations. This decision rule also

implies that some price risk, but not all, is shifted to


Version (3)

In this version of the model assumption (1),

regarding producers' willingness to hedge, is relaxed

and the assumptions and decision rule are as follows:

(2) There are no outside constraints to the
competitive functioning of the market.

(3) Producers have complete supply
flexibility in getting into and out of
the market.

Decision rule: Producers will initiate the
transformation process for the quantity where
expected price equals marginal cost, when the
expected price is greater than average cost.

Given that assumption (1) is relaxed so that

producers or other agents are not willing to use the

futures market, the analytical framework in Figure 3.1

breaks down. This occurs because without potential


arbitrators, there is nothing to integrate the cash and

futures markets. This version of the model emphasizes

the importance of the first assumption, that producers

are willing to use the market. Hedgers rely on basis

performance while, simultaneously, the basis performance

depends on hedgers.

Version (4)

In this version, assumption (1) is modified, while

assumptions (2) and (3) remain intact.

(1)' Some producers are willing to use the
market but they are not adverse to
speculating on prices.

(2) There are no outside constraints to the
competitive functioning of the market.

(3) Producers have complete supply
flexibility in getting into and out of
the market.

Decision rule: The decision to hedge is based on;
(a) attitude about using the futures market, (b)
personal expectations about price, and (c) yield

The rationale behind assumption (1)' and the decision

rule is that in reality, only a small percentage of the

producers in most agricultural industries hedge. For

instance, in the cattle industry, only 2 percent of all

production is hedged. There are several reasons that

may explain the reluctance to use the futures market.

One primary reason is basis risk. Also very important

is the producers attitude towards the futures market.

Whether it is a result of ethical reasons, bias against

brokers and speculators, or ignorance, many producers do

not believe in using the market. For instance, they may

feel that speculators are taking advantage of hard

working farmers or think that brokers' fees are too


Another factor that influences the decision to hedge

is the individual's expectations about prices. Hedging

acts to moderate gains, as well as losses. Therefore, if

a person has high price expectations, he may prefer to

operate unhedged and speculate on a high return. In

addition, yield uncertainty can affect the hedging

decision because if actual production falls short of the

quantity hedged, then a producer's risk is increased.

This model can be expressed in the generalized form

(3.4) BD = f{ A(n[i,D(Z,X,U)])}.

A = arbitrage potential
n = industry supply elasticity of short futures
i = percent of industry already hedged
D = decision to hedge
Z = attitude towards using the futures market
X = price expectations
U = yield uncertainty

Totally differentiating (3.4) yields (3.5):

(3.5) dBD = (af/aA)aA/an { (n/ai di ) +

(an/aD[aD/aZ dZ + 8D/8a dX + aD/8U dU}

The expected signs are as follows:

aA/an > 0
Only hedgers have the potential to arbitrate. As
the industry's supply elasticity of short contracts
increases, the potential to arbitrate increases.

an/ai < o
As the percent of the industry already hedged
increases, the availability of new potential short
hedges declines.

an/8D > 0
As the likelihood that producers will decide to
place a hedge increases, the industry's supply of
short futures commitments becomes more elastic.

aD/aZ > 0
As a producer's attitude towards hedging becomes
more favorable, the likelihood that he will decide
to hedge increases.

aD/aX < 0
As price expectations increase, the desire to hedge

aD/8U < 0
As production uncertainty increases, the desire to
hedge falls. This occurs because if the quantity
hedged exceeds actual production, then the excess
amount becomes speculation in the futures markets.

Equation (3.4) shows that the potential to arbitrate

depends on the supply elasticity of short contracts, n.

That is, n reflects an industry's potential to come up

with short run marketable supplies that could be

delivered against short futures contracts. This measure

is important in analyzing basis performance because it

reflects the potential of the adjustment mechanism. The

industry's hedging elasticity arises from hedging

decisions made at the producer level. The decision to

hedge is in turn governed by preferences, expectations

and yield uncertainty.

The implication of this model version is that hedging

decisions at the producer level aggregate to ultimately

affect basis performance. Factors such as attitude and

expectations affect these marketing decisions.

Version (5)

In this version of the model, the assumptions

pertaining to Versions (2) and (4) are combined so that

the affect of supply inflexibilities and hedging

activity can be examined together. In addition, the

second assumption concerning the competitive functioning

of the market is partially relaxed. The assumptions and

decision rule are as follows.

(1) Some producers are willing to use the
market but they are not adverse to
speculating on prices.

(2) There are no outside constraints to the
competitive functioning of the markets
except within the technical aspects of
the futures market.

Decision rule: Producers are willing to place a hedge
if the potential for a profitable hedge arises. They
will initiate the transformation process unhedged if
basis conditions are not favorable at that time.

This model can be represented in the generalized form

as follows:

(3.6) BD = f(A [MI, U, n{i,D(Z,X,U)), e{PI,S,FC,T}] )

BD = basis deviation
A = arbitrage potential
MI = market index
U = production uncertainty
n = industry supply elasticity of short futures
i = percent of industry already hedged
D = decision to hedge
Z = attitude towards using the futures market
X = price expectations
e = industry supply responsiveness
PI = perishability

S = seasonality of production
FC = level of fixed cost in relation to variable
T = time requirement for a form transformation

As discussed previously, the industry's supply

elasticity of short contracts (n) and the industry's

supply responsiveness (e) affect the potential to

arbitrate and thus, basis performance. Production

uncertainty (U) represents yield uncertainty inherent in

the production process. For example, the yield

variability associated with growing corn is greater than

with feeding cattle. Production uncertainty enters the

equation in two places because if affects the arbitrage

potential both directly and indirectly. In one respect,

it affects the producer's willingness to hedge, aD/aU.

Secondly, yield uncertainty may affect a producer's

ability to deliver against short hedges. For instance,

if the quantity hedger is greater than actual

production, then delivery of the excess amount is

impossible. Therefore, the sign of dA/dU is negative.

That is, as production uncertainty increases, the

potential to arbitrate decreases.

The market index (MI) represents the technical

performance of the futures market. This variable is

affected by factors such as market liquidity and the

accuracy and timeliness of market information. In

addition, trader composition, or the relative share of

hedgers and speculators within the market, has been

shown to affect contract performance (Ward, 1974). As

discussed in Chapter II, contract specification also

affects contract performance. As a futures market

contract becomes more technically efficient, it

facilitates trading and arbitrage potential is

increased, that is, 8A/aMI is greater than zero. The

signs of the other partial derivatives in the total

differentiation of Equation 3.6 are as presented in

Versions (2) and (4).

Generalized Conclusions
The model versions discussed in this chapter imply

different outcomes with respect to basis performance.

The analytical framework, that specifies the adjustment

between the cash and futures markets, is applied to

various assumption sets ranging from perfectly

competitive conditions to less restrictive assumptions.

As these underlying assumptions are relaxed, the

adjustment mechanism, or arbitrage potential, is

altered. Consequently, basis performance differs among

the alternative versions.

The assumptions underlying the model pertain either

to industry characteristics or behavioral assumptions

about producers. In order to ascertain the impact that

industry characteristics have on basis performance, it

is useful to categorize commodities according to the

type of transformation as well as the characteristics

that affect the potential to arbitrate. This

classification indicates what factors influence the

degree of flexibility in the adjustment mechanism and

hence, basis performance.

The decision rule stated in each model version

represents a behavioral assumption about producers with

respect to their attitude towards price risk. For

instance, the decision rule stipulates whether producers

initiate transformations hedged or unhedged. In the

theoretical model, the alternative decision rules have

different implications for allocation and the burden of

price risk. In terms of allocative consequences, if

producers will not initiate unhedged transformations,

then production decisions are based on futures market

prices. For this theoretical extreme, speculators

formulate the allocative signals of when and what to

produce. In this case, the futures market must be

evaluated in terms of its price forecasting ability;

that is, does it represent an efficient method for

obtaining and assimilating market information.

With regards to the futures market in its risk

shifting capacity, the producer's decision rule is of

primary importance in determining where the price risk

falls. For producers who can deliver against a futures

contract, they can completely shift price risk to

speculators by hedging and thereby use the futures

market as a forward contracting mechanism. For those

producers who can not deliver, their ability to use the

futures market as a forward pricing mechanism is

mitigated. However, if the arbitrage potential is high

such that basis risk is low, then those unable to

deliver can use the futures market as a convenient

forward pricing mechanism. The usefulness of this

research is to identify factors that influence basis

variability so that we have theoretical grounds for

expecting how the basis for a particular commodity will

perform. The empirical analysis, as set forth in the

following chapter, is used to verify what commodity

characteristics are significant in influencing basis



In this chapter an empirical model of basis

determination is developed. Measures of basis

performance used in the analysis are discussed and

exogenous variables are defined. Data, estimation

procedures and treatment of technical problems are

described at length. Implications of modeling

assumptions are considered and testable hypotheses are

set forth.

Garbade and Silber (1983) find empirical support for

their contention that for storable commodities the

degree of integration between the cash and futures

markets depends on the elasticity of arbitrage. The

general hypothesis of the present analysis is that the

integration between the cash and futures markets is a

function of arbitrage potential for all types of

commodities, from storable to nonstorable. The

integration between the markets indicates how well the

competitive process is operating, and hence, reflects

basis performance. Basis performance is influenced by


an array of exogenous factors that differ across


The approach taken in this analysis involves

examining cross sectional and time series data so that

the relationship between commodity characteristics and

basis behavior can be estimated. Regression analysis is

used in order to establish an empirical linkage between

basis performance and those variables expected to

influence arbitrage potential.

For each model of basis performance, the interval of

time until contract maturity is held constant. That is,

all basis observations pertaining to a particular model

correspond to futures contracts maturing in the same

length of time, or as close as possible to the same

length of time. By holding this time dimension

constant, the integration between the cash and futures

markets is revealed as a function of commodity

characteristics, rather than a function of

time-until-maturity. These data will be referred to as

constant periods to maturity (CPM) series (see Malick

and Ward, 1987). This approach parallels Castelino and

Francis' (1982) method of examining basis variability at

fixed distances from maturity for different commodities

(see Chapter II).

The general objectives used to operationalize the

basis performance model are as follows:


(1) Develop an empirical measure of basis

(2) Identify observable factors that influence the
potential to arbitrate.

(3) Incorporate (1) and (2) in an applied
econometric model using cross sections of
futures markets with data recorded over time.

Dependent Variable: A Measure of Basis Performance

The properties that the dependent variable must have

are that first, it represents a theoretically consistent

measure of basis performance; and secondly, it can be

normalized for cross sectional analysis. As stated in

the theoretical chapter, under ideal competitive

conditions the basis should reflect the cost of

transformation that it represents. Therefore, how the

basis differs from the transformation cost indicates how

well the competitive process operates in appropriately

linking the cash and futures markets.

Figure depicts a distribution of basis

observations in relation to the reference line where the

basis is equal to the cost of transformation. The

distribution of the basis observations is the point of

interest since this distribution reflects competitive

adjustment or economic performance. For instance, using

economic criteria, the distribution shown in Figure

would be judged superior to the wider distribution of

Figure 4.1b. Conceptually, the distribution in Figure

4.1a represents strong integration between the cash and

Basis = Cost

4. b.


Figure 4.1. Alternative Basis Distributions.


futures markets where arbitrage activities keep the

basis consistent with transformation and/or storage


The distributional properties of the basis directly

affect the potential returns to hedging. The variance

of the basis describes the basis risk that a hedger

faces, assuming appropriately defined contract

specifications. Thus, the basis risk (or the variance

of expected returns) associated with Figure 4.1a is less

than that of Figure 4.1b. Several studies cited in this

research consider the effect of basis variability on

returns to hedging (Carter and Loyns, 1985; Ward and

Schimkat, 1979).

Another example of how the distributional qualities

of the basis affect expected returns can be illustrated

with Figure 4.1c. In both Figures 4.1a and 4.1b, basis

observations are distributed symmetrically around the

cost level. Alternatively, Figure 4.1c depicts a skewed

distribution that implies that the market adjusts

differently to a basis that is greater than cost

compared to a basis that is less than cost.1 The returns

to a hedged position are determined by the difference

1For theoretical reasons why this may be the case
see Version (2) in Chapter III.


between the beginning and ending basis.1 A widening

basis is profitable to a long hedger while a narrowing

basis is profitable to a short hedger. In Figure 4.1c,

the likelihood of a narrowing basis is greater than the

likelihood of a widening basis. Thus, for a given

beginning basis value, the distribution in Figure 4.1c

would favor a short hedger.

Arbitrage, in the form of hedging, integrates the

cash and futures markets. Since this integration is

reflected in the distribution of basis values, factors

that affect the arbitrage potential affect the

distributional properties of the basis. How the markets

are functioning, the time from contract maturity, the

institutional setting and commodity characteristics are

all factors that can affect the potential to arbitrate.

Therefore, theory suggests that the distributional

properties of the basis will differ according to

differences in these factors. Explicit identification

of the relevant factors and hypotheses concerning their

effect on basis distributions are set forth


Ivariability between these periods, while not
affecting the final outcome from trading, can create
considerable uncertainty and anxiety sometimes forcing
traders to deviate from normal trading plans. The
present analysis does not explicitly deal with this
dimension of hedging.


Other studies have focused on identifying factors

that influence basis variability. For instance, Garcia,

Leuthold and Sarhan (1984) found that the Consumer Price

Index had a significant effect on the random fluctuation

of daily basis values for Midwestern livestock.1

Castelino and Francis (1982) identified storability,

volume of existing supplies and extent of commodity

substitutability as factors that were important in

linking the spot and futures prices for four

agricultural commodities. The empirical component of

the present research includes nine agricultural

commodities and a variety of factors that potentially

affect basis performance.

General Model Specification

The basis residual (BR) can be defined as the

difference between the basis and the cost of


(4.1) BR = B C

C = cost of transformation
B = basis = F P
F = futures price across contracts having
common intervals until maturity (CPM)
P = cash price

The standard deviation of BR [SD(BR)] provides a

descriptive measure of distribution that is meaningful

IIn their analysis, the basis was defined as the
futures price of cattle minus the cash price of cattle.
The basis values in the present models are defined as
the futures price of cattle minus the cash price of
feeder cattle.


in the present analysis. Since the standard deviation

is not independent of scale, the SD(BR) is corrected for

scale differences in order to analyze variability across

commodities. That is, the SD(BR) for corn (in dollars

per bushel of corn) is not comparable to the SD(BR) for

soybeans (in dollars per bushel of soybeans) or to

SD(BR) for cattle (in dollars per hundred weight).

The SD(BR) is divided by the standard deviation of

the corresponding cash price so that the dependent

variable reflects the variability in the basis relative

to the variability in the cash price. That is, in the

absence of hedging, a producer is exposed to the risk of

cash price variability, whereas a hedged producer is

exposed to the risk of basis variability. Therefore,

the pertinent measure of basis variability should be

computed so that it is relative to the cash price


The integration between the cash and futures markets

should respond to changes in economic conditions that

affect arbitrage potential, such as rising or falling

stock levels. Accordingly, basis residuals are expected

to vary with economic conditions thereby reflecting

changing market conditions. In general, lower values of

the normalized SD(BR) are associated with better market

performance than higher values of the normalized SD(BR).

The normalized SD(BR) could be calculated for each

commodity and this method would yield one observation of

the dependent variable per commodity, in each constant

period from maturity (CPM) model. However, the model

specification can be improved by further grouping the

data by year and quarter. Thus, for each commodity, the

weekly data within a particular year of a particular

quarter are used to create SD(BR)ijk where i denotes the
ith commodity, j denotes the jth year and k denotes the

kth quarter. Technically, this partitioning is

desirable because it increases the number of

observations in each regression model and helps to

control for the changes in the price and cost levels

that occur over time.

There is also empirical evidence that basis

variability follows a seasonal pattern. Malick and Ward

(1987) examine the interaction of seasonality and stock

levels in the frozen concentrated orange juice (FCOJ)

basis. They estimate separate basis models each

representing a constant period from maturity. The

monthly dummy variables are found to be significant in

influencing the basis residual, which is the basis net

of storage costs. Using the empirical results, they

illustrate the effect of seasonality alone on the basis

residual, by holding stock levels constant at a normal

level. They conclude that the FCOJ market is not fully

correcting and attribute the persistence of seasonality

in the basis to the market structure prevailing in the

FCOJ industry.

Seasonality in the basis initially implies

inefficiencies within the pricing system. However,

seasonality often arises among agricultural commodities

because of seasonality in production, and hence,

seasonality in the flow of market information. For

instance, production forecasts and crop outlook reports

are seasonal. Futures markets should reflect

anticipations of the forecast where these anticipations

are based on limited information about market

conditions. Anderson (1985) empirically measures the

volatility of futures prices for eight agricultural

commodities. He concludes that "the principal

predictable factor in changes of variance is

seasonality" (p.345). He shows that the variance of

futures prices is highest when the greatest degree of

uncertainty (about supply and demand conditions) is

being resolved.

As discussed above, there is empirical evidence that

the FCOJ basis exhibits seasonality (Malick and Ward,

1987). Since Anderson found strong seasonal effects in

futures price variability for a variety of commodities

(including livestock), it is reasonable to expect that

basis values may also vary seasonally for the


commodities in the present research. That is, one would

expect to see greater variability in the basis during

seasons of the year when more uncertainty is resolved.

To account for this possibility, data are partitioned by

season within each commodity and year group.

The following equations summarize the general model

specification, where m = t + n:

(4.2) Bm = Fm Pt

(4.3) BRm = Bm Cm

(4.4) VAR(BR) = VAR(B C)
= VAR(B) + VAR(C) 2{COV(B,C)}

(4.5) VAR(B) = VAR(F) + VAR(P) 2{COV(F,P))

Substituting (4.5) into (4.4) and normalizing the

standard deviation of the basis residual SD(BR) with the

standard deviation of the cash price SD(P) yields

equation (4.6).

(4.6) SD(BR)ijk/SD(P)ijk =({VAR(F)+VAR(P)-


The SD(BR)ijk is calculated conditioned on commodity

(i), year(j) and season(k).

In equation (4.6) the SD(BR) for a particular

commodity in a particular quarter of a particular year

is divided by the standard deviation of the cash price

SD(BR) in the corresponding group. This denominator

serves to cancel units, adjust for changing price levels

and express the variability of the basis in terms

relative to the variability of the cash price. This


approach parallels Ward and Schmikat's (1979) method

ofusing a risk ratio in their analysis of basis risk in

Florida feeder cattle.

Let X and Z represent variables affecting arbitrage

potential, then:

(4.7) SD(BR)ijk = f(X,Z).

The independent variables in the model above are

represented in two categories; X and Z. Exogenous

variables in the first category (X) correspond to

factors that reflect the trading process in the futures

market, such as the market liquidity and the hedging to

speculative ratio, as well as variables that relate to

each commodity's physical or marketing characteristics.

For instance, indexes for storability and exports

relative to domestic production are included in type X

variables. The second category, Z, is comprised of the

seasonal dummy variables by which the data are


Data and Model Implementation

Selected Commodities

The commodities included in the present study are

listed in Table 4.1. This data set is more extensive

than those used in previous studies and includes nine

agricultural commodities recorded over approximately a

fifteen year period. The general objective was to

construct a data set with commodities that possessed a

Table 4.1. Agricultural Commodities Included in the
Empirical Model of Basis Perfomance.

Type of Commodity in Commodity in time
transformation futures mkt. cash mkt. series







form & time

form & time







pork bellies

Soybean oil

Soybean meal

Live cattle






pork bellies



Feeder cattle











wide variety of production and market characteristics.

Commodities such as cotton, sugar and coffee were

excluded from the analysis because of the extensive

market intervention associated with these commodities.

The first four commodities listed in Table 4.1

exemplify the grain group conventionally used in the

analysis of basis determination for storable

commodities. While the production patterns and degree

of storablility are very similar among these

commodities, they differ in other characteristics

expected to affect the potential to arbitrate. For

example, exports in relation to domestic production is

much higher for corn than for oats. Thus, even within

the grain group there is variability in the exogenous


Frozen concentrated orange juice is another storable

commodity that was selected because its production and

industry characteristics differ considerably from the

grain group. In addition, including FCOJ in the present

analysis allows comparison with the results of Malick

and Ward (1987). Frozen pork bellies were included in

the data set because they differ from the grain group in

two fundamental ways. First, the pork production

process is much less seasonal than grain. Secondly,

frozen pork bellies have an intermediate degree of