Title: Economic impacts of frozen concentrated orange juice futures trading on the Florida orange industry
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Title: Economic impacts of frozen concentrated orange juice futures trading on the Florida orange industry
Physical Description: xi, 165 leaves : ill. ; 28 cm.
Language: English
Creator: Dasse, Frank A ( Frank Arthur ), 1933-
Copyright Date: 1975
 Subjects
Subject: Frozen concentrated orange juice   ( lcsh )
Oranges -- Marketing   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Frank Arthur Dasse.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 162-164.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00099262
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000355562
oclc - 02273892
notis - ABZ3803

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ECONOMIC IMPACTS OF FROZEN CONCENTRATED ORANGE JUICE
FUTURES TRADING ON THE FLORIDA ORANGE INDUSTRY

















By

FRANK ARTHUR DASSE






















A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
1975















































Copyright

1975

FRANK ARTHUR DASSE













ACKNOWLEDGEMENTS

The author wishes to express appreciation to his

graduate committee Drs. Lester Myers, Ronald Ward, James

Niles and Russel Fogler for their help and guidance through-

out the program of study and research. A most special measure

of thanks is due Dr. Ward for his patience and guidance during

the research period and documentation phase.

To Drs. Kenneth Tiefertiller, Leo Polopolous and Bernard

Lester goes an expression of gratitude for their help in sup-

plying financial aid throughout this graduate study program.

Thanks are expressed to Debbie Donahue, who suffered

through the many drafts of this dissertation and to Virginia

Walker for responding to the call for hurried final typing.

The author can not state adequately his appreciation for

the support and encouragement that his wife Jean provided

during this study period.

Also to his children thanks for the understanding given

an often absent-minded father.









TABLE OF CONTENTS
Page

ACKNOWLEDGEMENTS . . . . . . . . .. . iii

LIST OF TABLES . . . . . . . . ... .. . vi

LIST OF FIGURES . . . . . . . . . . vii

ABSTRACT . . . . . . . . ... . . . ix

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

Statement of the Problem . . . . . ... 1

Research Objectives ... . . . . . .. 4

Organization of the Study . . . . . . 4

CHAPTER II BRIEF BACKGROUND INFORMATION . . . . 6

Futures Markets . . . . . . . . 6

Futures Market in FCOJ .. . . . . . .. 8

CHAPTER III REASON AND IMPORTANCE OF THE STUDY ... . 12

On the Desirability of Price Stability . . .. 12

On the Theory of Hedging . . . . . .. 20

Summary . . . . . . . . ... . . 30

CHAPTER IV PRICE VARIATION ANALYSIS . . . . .. 32

Theoretical Discussions . . . . . . .. 32

Empirical Efforts . . . . . . . .. 43

Interpretation and Industry Application . . .. 60

Summary . . . . . . . . ... . . 65

CHAPTER V PRICE DIFFERENTIAL ANALYSIS . . . .. 67

Theoretical Model . . . . . . . ... 67

Empirical Model . . . . . . . ... 73

Interpretation and Industry Application . . .. 79

Summary . . . . . . . . ... . . 81








TABLE OF CONTENTS Continued

Page

CHAPTER VI BASIS MODEL . . . . . . . .. .82

Theoretical FCOJ Basis Model . . . . . .. .82

Basis Model Development . . . . . ... .89

Implications for Industry . . . . ... .120

CHAPTER VII SUMMARY AND CONCLUSIONS . . . .. .127

General Conclusions .... . . . . . . 127

Policy Implications . . . . . . .. 131

Suggestions for Further Research . . . .. .132

APPENDIX A INTRODUCTION TO THE FLORIDA ORANGE
INDUSTRY . . . . . . . .. 134

APPENDIX B MODEL DATA . . . . . . . .. 156

BIBLIOGRAPHY . . . . . . . . ... .. . 162

BIOGRAPHICAL SKETCH . . . . . . . . .. 165













LIST OF TABLES


Table Page
1 USDA crop estimates for Florida oranges,
1970-71 season. . . . . . . . .. .47

2 Typical inventory of industry during the season
(averages of 1958-59 season through 1973-74
season. . . . . . . ... . . .51

3 Results of initial least squares fit of basis
model . . . . . . . . ... . . 102

4 Correlation between various price series (data
from 1967-68 through 1973-74 seasons) and
price level observations. . . . . . .. .104

5 Transformations used for serial correlations
corrections . . . . . . . . ... 108

6 Results of fitting basis model with data
corrected for serial correlation . . . .. 110

7 Convenience yield influence on the September
basis . . . . . . . . ... . . 114

A-i World citrus production, oranges and tangerines,
se-qons 1970-71 through 1973-74 (production in
thousands of 90 lb. boxes). . . . . . 136

A-2 Florida orange production in thousand boxes . 138

A-3 Florida round orange production by counties in
1,000 boxes, 1973-74 season. . . . . ... 139

A-4 Analysis of "priced" fruit used for concentrate
(in boxes). . . . . . . . . ... 146

A-5 FCOJ pack in various form (in gallons of
450 Brix) . . . . . . . ... . 151

B-l Data matrix for the price variation model . . 156

B-2 Data matrix for the price differential model. . 157

B-3 Selected data and calculations for the basis
model (November contract) . . . . . .. .158














LIST OF FIGURES


Figure Page

1 Producers surplus with price stability . . .. .15

2 Producers surplus with a change in demand. ... .16

3 Geometric analysis of producers surplus with
price stabilization. .. . . . . . ... 18

4 Risk in two markets with low price correlation 20

5 Risk in two markets with high price correlation. 21

6 Optimum hedging ratios with varying price
deviation ratios and correlation coefficients. . 24

7 Simplified flow diagram of influences in pricing
Florida oranges. . . . . . . . .. .35

8 Possible inventory levels with a large crop
and nominal beginning inventories. . . . ... 41

9 Possible inventory levels with a nominal crop
and a large beginning inventory. . . . ... 41

10 Weather effect upon seasonal price variation . 45

11 Plot of typical inventory vs. weeks into season... 52

12 Observed hedging at specific points in the season. 63

13 Orange flow highlighting price differential
possibilities . . . . . . . . . 68

14 Availability influence upon relative prices. . 71

15 Observed mean seasonal price differential
(1956-57 season through 1973-74 season). ... .75

16 Freeze effect upon seasonal price differential .77

17 Supply curve of storage. . . . . . ... 84

18 Theorized freeze bias influence in FCOJ basis. . 93








List of Figures Continued


Figure Page

19 Freeze bias by contract month . . . ... .109

20 Typical risk payment for a January contract 112

A-i Flow of oranges from grower to consumption
outlets . . . . . . . . . . 144

A-2 Utilization by outlets of Florida oranges . . 149


viii












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

ECONOMIC IMPACTS OF FROZEN CONCENTRATED
ORANGE JUICE FUTURES TRADING ON THE
FLORIDA ORANGE INDUSTRY

by

Frank Arthur Dasse

June, 1975

Chairman: Lester H. Myers
Co-Chairman: Ronald W. Ward
Major Department: Food and Resource Economics

The Florida orange industry has had and continues to

have a major concern over how the futures market in frozen

concentrated orange juice (FCOJ) has affected the price

structure in this industry. The concern exists because a

number of growers and some processors sense, but cannot ob-

serve, that the pricing structure has been altered to their

detriment. Because the futures market has existed enough

years, because the structure of the industry has remained

relatively stable and because of this felt need by industry

participants, a relatively unique opportunity existed to

probe the economic impact of the FCOJ futures market.

A framework was established which showed the benefits

of stability of prices paid to the producers of oranges.

Thus, if it should be determined that the futures market in

FCOJ was a stabilizing influence, the market would be judged

as being beneficial. Also, a theoretical framework was es-

ix








tablished showing the benefits that could be gained if an

owner of product inventory could hedge risks of price varia-

tion in another market. Two models were indicated as guides

depending upon the certainty of an owner's stock.

An analysis of the seasonal variation of cash prices for

a number of years was the first economic impact studied. A

model was developed to measure the contributions that a number

of variables made to intraseasonal price variation. It was

established that the futures market had a stabilizing influence

upon price variation. As an adjunct to the price variation

analysis, an effort was made to assess the contributions of

the futures market to carrying inventory. Hedging behavior

was theorized and measured. An analytical framework for the

inventory carrying capabilities of hedging was established;

however, there were not enough data to accomplish any meaning-

ful statistical estimations.

There are different methods for growers to market their

fruit. These different marketing methods may generate differ-

ent values for a box of fruit. The second area of this study

analyzed these differential prices to determine if a futures

market impact could be measured. It was found that the fu-

tures market appeared to contribute to the lessening of dif-

ferential prices. The coefficient values of the model used

in this analysis were not statistically significant so the

opinions derived can not be defended with vigor. What may be

said more strongly than the above statement is that there is

no evidence to indicate that the futures market has caused








the cash fruit seller segment of the industry to suffer

relative to the pool fruit seller.

The last area of study covered the "basis" in FCOJ. A

basis represents the difference between a price in a futures

market and the cash price of a commodity. Existing basis

theory was abstracted and supplemented by some influences

unique to the Florida orange industry to develop a basis

model for FCOJ. The empirical results indicate that the FCOJ

futures market conforms to the developed theory. The futures

market acts rationally and appears to be a useful medium upon

which the Florida orange industry may hedge.

Finally, some policy suggestions were forwarded for in-

dividuals, industry associations or governmental bodies to

consider. Fundamentally, they suggested abandoning the

antagonist role and assuming a role of being a protagonist

for the futures market.













CHAPTER I
INTRODUCTION

Gray and Rutledge state:

The literature on futures trading owes more than
any similar body of literature to the fact that the
institution has been periodically attacked in the politi-
cal arena. These attacks have been based largely upon
misunderstanding, particularly the aforementioned mis-
conception that futures markets serve the whims of
speculators rather than the needs of hedgers. There have
been in consequence numerous efforts to legislate against
futures trading (successfully on occasion) and several
official investigations which have frequently contributed
significantly to better understanding. (11, Pg. 61)

Statement of the Problem

A recurring argument made against futures markets is that

they give rise to price instability by facilitating specula-

tion in a commodity. This recurring argument is certainly

prevalent in the Florida orange industry.

That this is true can be demonstrated in a recent letter

to the Florida Citrus Commission chairman from one of the

commission members:

April 9, 1974

Mr. Danforth K. Richardson
P. O. Box 370
Vero Beach, Florida 32960

Dear Dan:

I am very concerned about citrus futures and the way it
is influencing the price of FCOJ. I have recent, first-
hand experience that the price at which processors are
able to buy top-quality orange concentrate from the
futures market has lowered the price per lb. solids on
Valencia oranges.





2

Just as soon as possible, I would like the staff and/or
our legal counselor, and whatever or whoever else it
takes, to make a full and comprehensive investigation
as to the citrus futures' benefit to the Florida citrus
industry. This investigation should be so thorough that
we, as the Florida Citrus Commission, can help effect
whatever changes are necessary for the good of the
Florida citrus industry.

I think this should be on our agenda at the earliest date
possible.

The above sentiment is by no means an isolated incident.

This and similar comments can be elicited from other members

of the industry or have been recorded elsewhere.

The problem appears to be that certain elements of the

orange industry, principally growers, believe that the pricing

and, therefore, the profitability structure of the industry is

being detrimentally affected by futures trading.

Should the belief be true, then a problem clearly exists

for which remedial action should be taken to retrieve the

more equitable market and profit conditions. If this supposed

intrusion is not fact, then an education and/or extension pro-

gram is needed to relieve the rather extensive concern of

industry participants. Given that the futures market has not

been detrimental to the industry, it would further quiet the

trepidation against the frozen concentrated orange juice

(FCOJ) futures market to be able to explain the behavior of

the FCOJ futures prices in relation to the cash prices being

paid to members of the industry.

This project therefore focuses upon two areas. One area

is an analysis of the variation in prices per pound of orange








solids1 paid to a grower before and after the introduction of

FCOJ futures trading. The second area of emphasis will be a

definitional study of the relationship between prices in the

cash market and the futures market.

The relative newness of the FCOJ futures market offers

an opportunity to advance the hypothesis that the prices paid

to orange producers for a pound solid have become less varia-

ble since and because trading in FCOJ futures began. Eight

years of data are available to test this hypothesis, which

appears adequate.

Prices in the cash market represent an equilibrium price

between demand for oranges and the available supply at the

present time; whereas, a futures price is a collective judge-

ment between buyers, sellers, and speculators as to the value

of orange concentrate deliverable some time in the future. For

many reasons, therefore, including form and time dimension

changes, the prices in the two markets are and should be dif-

ferent. This difference is defined in the trade as "the basis."

The FCOJ basis will be the second area of inquiry in this study.

As a result of the empirical study of this portion of the pro-

ject, it is expected that the influences upon the FCOJ basis

will be defined. Knowledge of these influences, such as

strength and duration of influence, could aid in the formula-

tion of widespread, more efficient hedging programs.




A pound of orange solids describes what is left after
all water is removed from orange juice. It is composed of
soluble sugars, citric acid and vitamin D.








Research Objectives

To be able to help guide policy it is necessary that

there is an understanding of the subject matter upon which

the policy focuses. It is the general objective of this

study, therefore, to help with the understanding of the FCOJ

futures market. Whatever benefits the Florida orange indus-

try has derived from the futures market will become evident

and the future course of industry involvement in the futures

market will be suggested.

To fulfill these general objectives the following

specific objectives are formulated:

(1) To analyze the variation in prices paid to growers

for oranges before and after the introduction of

FCOJ futures trading with the purpose of isolating

the effect of futures trading on price stability.

(2) To develop an explanatory model of the FCOJ "basis"

for use in:

(A) Understanding the relationship and

(B) Developing strategies for futures market usage

by a larger segment of the industry.


Organization of the Study

There are seven chapters. Chapter 1 provides the gener-

al introduction. Chapter II provides a discussion of the his-

torical development of futures markets. It also presents

specific information pertaining to the development of futures

market for FCOJ. Chapter III probes the reason and importance








of this study to the Florida orange industry. It will deal

first with a study of price risk represented by price vari-

ation and what its implications are to the industry and second

with possible methods of risk avoidance through a hedging

program using a futures market. Chapter IV outlines the model

which will assess the contribution that the futures market

has made to the price variability of the cash commodity.

Chapter V will probe the changes which may have occurred in

the price relation of cash fruit compared to pool or participa-

tion fruit since the introduction of futures trading. Chapter

VI will describe a theoretical relationship between prices

in the cash market and prices in the futures market. Once

that goal has been accomplished, suggestions will be offered

to members of the industry regarding the advisability of

entering into hedging programs utilizing the futures market

for FCOJ. Finally, Chapter VII will summarize the study,

offer policy suggestions and suggest areas where further

research may be fruitful.














CHAPTER II
BRIEF BACKGROUND INFORMATION

Prior to formulating any sort of theoretical framework

or econometric models of the Florida orange industry and how

it may have been influenced by the introduction of a futures

market in FCOJ, some knowledge of the structure of the indus-

try is necessary. A discussion of the agricultural aspects

and the marketing methods is attached as Appendix A to fulfill

that need. It will be the purpose of this chapter to very

briefly introduce the concept of futures trading and discuss

briefly some specifics of the FCOJ futures market.

Futures Markets

Contracting for future delivery in many commodities has

for centuries been a normal, customary way of doing business.

The existence of future contracting developed over the cen-

turies as a method of forestalling to a degree the price swings

that many commodities were typically exposed to. The feature

of the development of this early future contracting was that

title or ownership of the commodity in question was expected

to change hands. As time progressed and as this method of

future contracting expanded, there developed also the concept

of buying or selling the rights and responsibilities of

these contracts to third parties. These actions were highly

informal, however legal and binding. It became apparent

in the midwest, particularly Chicago, that the developments







of standards, inspection, weights and measures, etc., were

necessary for orderly, lawful, and relatively simple transfer

of ownership rights of commodities. The Chicago Board of

Trade was organized in 1848 to facilitate the efficiency of

transferring ownership of various commodities typically

shipped from the midwest to the rest of the country by rail

and the rest of the world via the Great Lakes shipping routes.

One of the features of contracting through futures markets

was that specific quantities of a specific quality of a com-

modity could be traded for delivery in a specified time period

set openly in the future. The exchanges would, in a public

place and by open outcry, pass these transferable contracts

from buyer to seller with but a small fee for such a service

Anyone who met the financial responsibility required by the

exchanges could participate.

A participant in a futures contract always has two op-

tions. He can honor the terms of the contract during the

specified time period or he can sell his rights to another

through the exchanges. The futures markets typically ex-

perience relatively low delivery rates, usually less than 2

percent (17, pg. 17). This indicates that futures exchanges

Volume of physical commodity is but a small percentage of the

total contracts traded.

Futures trading has historically been justified for its

ability to cover all or a portion of the market or price risks

not covered by other means of doing business. Price risks or

uncertainty in agricultural commodities comes about due to








lags in time between production and consumption. The lags or

gaps are attributed to weather variability, seasonality,

processing times, shipping uncertainty or any other similar

problem which delays consumption. These delays cause un-

planned and often undesired fluctuations in the pricing of

the commodity. The practice of hedging therefore has developed

where individuals or firms having business risks in the cash

market may take offsetting risks in the futures markets.

Those engaged in the cash market of a commodity usually

deal in that commodity in some form. The price in the market-

place represents the collective judgement of those engaged in

the supply and demand of the cash commodity. Those engaged

in the futures markets may or may not be interested in the

physical commodity. The prices that exist in the futures mar-

ket represent during period t the traders expectations of the

conditions that will exist in period t + n. The tie between

the two markets is the ability to deliver or take delivery of

the commodity being traded. This option will usually cause

the two markets, cash and futures, to come into reasonable

consonance at or near delivery time.

It is the intent of this discussion to generally acquaint

the reader with some general background information regarding

futures trading. A more detailed exposure may be gotten from

Heironymus (13), Gold (7), or Tewles et al. (28). New terms

will be explained as they are introduced.

Futures Market in FCOJ

In 1966 the New York Cotton Exchange decided, after con-

sultation with members of the orange industry in Florida, that








a need for a futures contract in FCOJ did in fact exist. The

Citrus Associates was formed and trading was begun on October

26, 1966, with a total of 92 contracts being traded.

The following contract definition information is taken

from the By-Laws and Rules of the Citrus Associates of the

New York Cotton Exchange:

Contract Grade. "U.S. Grade A" with a Brix value
of not less than 51 having a Brix value to acid ratio
of not less than 13 to 1 nor more than 19.0 to 1, with
the factors of color and flavor each scoring 37 points
or higher and minimum defect score of 19 with total
score of not less than 94, is the quality of frozen
concentrated orange juice that is deliverable under Ex-
change contracts, provided that frozen concentrated
orange juice with a Brix value of more than 650 shall
be calculated as having 7.135 pounds of solids per
gallon delivered.

The United States Standards for Grades of concen-
trated orange juice for manufacturing effective Novem-
ber 17, 1964, shall be used as the Standards for the
grade and quality of all frozen concentrated orange
juice delivered on contract for future delivery. In
the event of an amendment to the official U.S. Standards
for Grades of concentrated orange juice for manufactur-
ing, such amended Standards shall become effective for
deliveries on and after the effective date of such
Standard. Frozen concentrated orange juice with pulp
wash solids is not deliverable on contract.

Contract Weight. The contract for Frozen Orange
Concentrate is a unit of 15,000 pounds of orange solids,
with an allowable variation of three percent more or less.
In addition, the lot must be uniform, and in this con-
nection, the Brix range of the delivery may not exceed
three degrees of Brix. Each Drum shall be numbered.
Also, as Juice is placed in a public licensed warehouse
approved by Stock Exchange, each lot receives a ware-
house lot number. Generally, the drums contain approxi-
mately 52 gallons of concentrate, however, this is not
a requirement of the contract and greater or less quan-
tities are acceptable on delivery.

A quantity of concentrate complying with the above re-

quirements may be certified for delivery by arranging for an

inspection by the USDA for a nominal fee. This inspection








must take place at the time the concentrate is placed or

while it is in a licensed warehouse. The Exchange certificate,

when issued, is good for one year from the date of inspection

or as long as the product remains in the licensed warehouse

whichever occurs first. There are presently 28 such delivery

warehouses located throughout the orange-producing section of

Florida. It has been calculated that the cost to deliver on

contract is about $75 above the cost of processing the concen-

trate into the bulk containers.1 This amounts to 0.5 cents

per pound solid of concentrate.

Trading is regularly conducted in the contract months

of January, March, May, July, September, and November. Con-

tracts can be traded as far away as 18 months from delivery

although most active trading occurs in the contracts maturing

in less than 12 months. The November contract is considered

the last contract of the old season. That means that the

November contract usually reflects conditions at the end of

the harvest and marketing period for that particular season.

It is also a transition contract in that the first supply es-

timates for the coming season are available prior to its matura-

tion so that it may also reflect some of the conditions for the

new season during its last few weeks of trading.

The background for the ensuing discussions has been




1This estimate was taken from a cost booklet compiled
by the Citrus Associates of the New York Cotton Exchange,
dated February, 1974.





11


covered briefly enough so that the objective of this study may

be pursued. For more detail on the FCOJ futures market the

reader may consult the USDA Commodity Exchange Authority book-

let "Futures Trading in Frozen Concentrated Orange Juice." (30)















CHAPTER III
REASON AND IMPORTANCE OF THE STUDY

The objectives of this study implicitly make some assump-

tions that will be the object of some theoretical review in

this chapter. Analysis of price variation is a task that is

not complete until some judgment is made on whether the

observed changes in price variation, if indeed there were

some, were good for the industry. The implicit assumption

in this case is that a decrease in price variability of orange

solids is both desirable and beneficial to the orange industry.

Therefore, the first portion of this chapter deals with that

assumption. The reason for the study of the relationship be-

tween prices paid to growers for orange solids and the prices

quoted on the FCOJ futures markets is to define an economic

link between the two markets. If a link between the two price

series can be established and some causality variables can be

identified, then a solid base exists to build a hedging pro-

gram that can be beneficial in reducing price risks within

the industry. The assumption here is that there exist methods

to hedge that will reduce risks and, therefore, will be bene-

ficial to the practitioners of such programs. The second part

of this chapter deals with the general concept of hedging and

explores some theory showing the benefits of proper programs.

On the Desirability of Price Stability

A persistent question in the literature on futures trading








is "What is its effect upon price variability?" The implicit

assumption is that price stability is desirable and that if

futures markets contribute to price instability then they are

bad.

That question is the first objective of this study. It is

expected that some statement will be capable of being made

regarding the FCOJ futures market contribution to orange

solids price stability. The contribution will be judged as

beneficial if it can be shown to be stabilizing in nature. It

will be judged as detrimental if it contributes to price in-

stability. A case needs to be made, in a theoretical sense,

that price stability is good for the orange industry to serve

as the substance behind these judgements.

One can argue the case against uncertainty with some ob-

servations. First of all, production and storage involve un-

certainty if for no other reason than mortals cannot foresee

and foretell the future with certainty. Recognizing this un-

certainty, producers and stores will need to spend consider-

able time and thought estimating future production and consump-

tion at the expense of their more normal activities. It can

be argued that uncertainty will result in restricted capital

usage either by internal decision or by external rationing.

With the opportunity to tie up purchases and/or sales well in

advance, the functions of price formation and uncertainty or

risk bearing can be transferred from the producer/seller to

the buyer. A forward market thus offers the transference of

these responsibilities to those willing and possibly more








capable of undertaking them. Having transferred uncertainty,

the capital rationing problem would be lessened and very

likely the availability of capital in such situations would

be larger than a situation with uncertainty. The transference

of price formation and risk also allows the producer to con-

centrate upon his main activity with the attendant increase in

efficiency.

The economic community is not by any means in agreement

on the benefits of price stability. Oi (21) developed an

argument that showed that producers would indeed benefit by

price instability, that benefit being producers' surplus or

profit. His assumptions however were that producers would

adjust their production immediately to the prices that exist

in the market.

Those assumptions do not fit well with the Florida orange

industry. The supply conditions are not altered by management

decision in the short run. Because of the nature of the mar-

keting of oranges, the prices received are only estimable so

that typically production plans are quite stable. The acreage

is slow to change. Thus the supply function for oranges can

be assumed to be price independent and in any specific season

the supply of oranges is a function of a number of exogenous

influences.

Under these conditions price stability can be shown to

be beneficial to an individual producer compared to a situa-

tion where prices vary. Consider a producer who produces with

two possible exogenous outputs Q1 and Q2 each having a proba-









ability of occurrence of 0.5. Assume a stable price exists:

say P His revenue would be in the long run represented by

Q1 + Q2
(3.1) E(R) = .5 Pn Q + .5 P Q, = Pn
n 1 n 2 n 2

or E(R) = Pn Qave

Now assume that there is a correlation between his output and

the output of the industry such that prices vary inversely

with his output. That can be depicted by Figure 1.



PRICE



P2

n
n \\\\\\ B
1





Q2 QAVE. Q1 QUANTITY
Figure 1. Producers surplus with price stability

When Q2 is being produced, the crop is short and P2 would or-

dinarily prevail. Revenue proportional to area A would be lost

in a situation where prices were to be held stable rather than

reaching an equilibrium price as the demand situation requires.

However, when Q1 is being produced, P1 would prevail. In this

situation there would be a revenue proportional to area B to

be gained by price stability. It is clear that area B is

larger than area A, such that in the long run a revenue gain

proportional to 1/2 (B A) would be the benefit to this pro-

ducer by a program of price stabilization.





16

The preceding argument may not necessarily be used for

the Florida orange industry because there has not been a buff-

er stock program for this industry. A buffer stock would need

to be maintained with inflow or outflow of goods to maintain

the hypothesized nominal or stable price.

The case will be considered where there has been a de-

crease in the price flexibility at the producer level resulting

in less price variation with the same range of outputs. Con-

sider Figure 2.

PRICE
S2


p _S1
2 A 1

P2

Pn

P,
1 B ]D'
1

D

Q2 AVE. Q1 QUANTITY

Figure 2. Producers surplus with a change in demand

Again the assumption can be made that output is an exog-

enous variable and varies to Q1 and Q2 with 0.5 probabilities.

With the demand curve changing from D to D' it can easily be

seen that the producers do in fact benefit from such a price-



Yeoh (37) in a recent study showed that if all supply
functions in the FCOJ markets were perfectly stabilized, all
market participants on the supply side would obtain an increase
in welfare. 81% of the increase in welfare would go to growers,
13% would go to retailers and the remaining 6% would go to
processors.









stabilizing influence and the benefit is calculable. The

losses from the stabilizing influence are Q2 (P2 P2') and

the gains are Q1(P1' P1). Letting AP represent the price

differential, the long-run gain to the industry is 1/2 (Ap Q -

AP Q2) or AP'Qave. Thus it seems that any measurable influ-

ence that affects the price flexibility affects price stability

and this can be translated into a change in revenue to the

benefit of the industry.

Massell(18) argues the case in a more general sense. He

assumes that the supply and demand curves each have an inter-

cept term that is a continuously distributed random variable.

They have the form:
(3.2) S = ap + x where a > 0

(3.3) D = -6p + y where B > 0

S represents the quantity supplied, D the quantity demanded,

p represents the price, and x and y are jointly distributed

random variables with means Vx and by, and variances xx and

a and covariance a = 0. The latter assumption means that
yy xy
the forces causing demand and supply to vary are independent.

The price prevailing in this competitive market would be

determined by equating (3.2) and (3.3) yielding:
e y x
(3.4) p = y-
a + B

The quantity moved in this market is determined by sub-

stitution of (3.4) into either (3.2)or (3.3) above, yielding:

(3.5) qe ay + Bx
a + +








Massell then evaluated the producers' surplus under con-

ditions of supply and demand variations compared to a condi-

tion of price stability. Consider Figure 3.



PRICE
S



S2


App
p Z------<



S S QUANTITY
P Up

Figure 3. Geometric analysis of producers surplus with
price stabilization


He suggests that the producers' gain from a price stabili-

zation program can be represented by areas A + B + C in the

illustration above. The areas can be represented by a rectangle

plus a triangle. By appropriate geometric representation the

gain can be mathematically stated as

(3.6) G m
(3.6) (p) (Pp )[S( p) + S(p)]

From (3.3) one can derive that

(3.7) i = y x

By substituting equations (3.2), (3.4) and (3.7) into

(3.6) and collecting terms one can derive that


(3.8) G(p) % x L + ay y + x)
(p) 2 L 2 a + +





19

The expected value of the gains to producers can be de-

rived from (3.8) above by properly integrating over x and y.

Subsequent to some mathematical operations the results

can be shown to be:

(a + 28) axx a o
(3.9) E(G ) = -
p 2( a+8)

Equation (3.9) represents the gain to producers by a price

stabilization program when they face variations in both supply

represented by xx and variations in demand represented by

a This general relationship can be applied to the Florida

orange industry with one assumption. That assumption is that

the supply of oranges is not sensitive to price but rather is

a perfectly inelastic function whose level is determined by a

number of exogenous influences. The assumption means that a is

zero. Therefore (3.9) may be rewritten as

exx
(3.10) E(Gp) =-

Equation (3.10) may be used to draw some conclusions about

the benefits of a price-stable situation for this industry.

The gains to producers by price stability is greater the

greater is the variation in supply.

Differentiating (3.10) with respect to yields


d E(G ) o
(3.11) d- xx
d 2

This can be interpreted as meaning that the gains to pro-

ducers from a price stabilization program will be reduced by

an increase in the elasticity of demand for oranges.

The purpose of this discussion has now been fulfilled.



___ __ -i








First by a simple diagramatical and mathematical exercise it

was deduced that price stability was desirable to producers.

Second, a more rigorous exercise led to substantially the same

conclusion, which is that producers can expect to gain by price

stabilization. Since the first objective of this study will

determine the contribution that the futures market has made to

price stability and since it has been determined that price

stability is desirable, should the futures market be shown to

be price stabilizing in nature, then it will be judged as

being beneficial to this industry.

On the Theory of Hedging

A repeat of the definition of hedging is in order. A

hedger is one who has exposure to risk in one market and off-

sets all or part of that risk by taking offsetting positions

in another market. This compares to a speculator who can be

defined as one who assumes risk where no risk existed before.

The concept of hedging may be motivated with a Venn

diagram as in Figure 4.


Figure 4. Risk in two markets with low price correlation








Let A represent the revenue risk represented by holding

inventory of the real commodity. Let B represent the revenue

risk by taking an opposite position in the futures market,

that is, selling for future delivery an equal position. In

this case the relation of the price series in the two markets

is so weak, that is non-correlated, that the risk after hedging

represented by the non-shaded portion of A and B is clearly

larger than if no hedge was taken.

Suppose however, that the correlation of prices in the

two markets was fairly close as depicted in Figure 5.




A B











Figure 5. Risk in two markets with high price correlation



In this case also, A represents the revenue risk in the cash

market while B represents the revenue risk in the futures mar-

ket. The non-shaded portions of A and B are smaller than A

alone so in this case hedging has reduced the risks compared

to the non-hedged condition. This is rather simplistic; how-

ever, it serves to visually stimulate the idea that should

there be relationships of prices for a commodity in differ-

ent markets, and if this relation is strong enough, then there








may be ways of taking appropriate positions in the two mar-

kets that can reduce the price risk that the inventory owner

must face.

The concept of Figures 4 and 5 can be expressed mathe-
2
matically. Let pA and oA represent the expected level of

profits and variation of profits in market A respectively.
2
Likewise, let pB and aB represent the expected level of pro-

fits and variation of profits in market B respectively. The

series are assumed to be related and the covariance between

the series is represented by oAB. The variance of the differ-

ence between the price series is represented by:

(3.12) Var (A B) = Var(A) + Var(B) 2Cov(AB)

where Cov(AB) = pAB aA B

Substituting these notations in (3.12) yields:

(3.13) Var(A-B) = oA2 + B2 2pAB A G

To explore the necessary closeness of the price series,

assume that it is desired that Var A > Var(A-B). The profit

risk after hedging, must be smaller than or equal to the origi-

nal non-hedged position. From (3.13) it follows that:

(3.14) A22 > _A2 + a 2 2pB A
A B AB A B

or:
2
(3.15) 2PAB A >B > aB
2 2
Since both aA and oB are positive roots of oA and B (3.15)

may be expressed as:

(3.16) PAB
AB 2a A









Therefore, depending upon the relative size of the variances

in the two markets, the necessary coefficient of correlation

can be determined that would facilitate a successful hedging

program. Should there be reasonable equality of variances in

the two markets the necessary correlation coefficient can be

as low as 0.5.

The above mathematical representations serve to give some

feel for the necessary relationship between the two series,

assuming equality of holdings of identical commodities in the

two markets.

To generate some relationships allowing the holdings in

each market to vary, equation (3.13) will be rewritten and

put in more general terminology. Let the return from storage

be represented by AP X. where AP. is the change in price and
1 1 1
X. represents the amount of holding of the cash commodity.

Let AP. X. represent the return from the futures markets. In

2
each case let ip and pj represent the expected returns, o.
2
and aj represent the price variation in the two markets and

2 2
let the variance in the returns be represented by X. o. and

X.2 .2 with covariance X. X.Cov... Then a formula for variance
3 3 1 3 13
of total return is:
2 2 2 2
(3.17) V(R) = X. o. + X. 2 2X. X. Cov .

Assume that it is desired to determine the position in

the futures market that will minimize this variation. That

value can be determined by differentiating (3.17) with respect

to X. and setting that expression equal to zero.
3




24

(3.13) V(R) 2X. 2 2X. Cov. = 0
ax. 3 J 11
3
From this the optimum level of holdings in the futures

market can be determined as:

X. Cov..
(3.19) X.* -= 1i
2 o
3
Remembering that Covj = Piji j, (3.19) can be restated

as
O.
(3.20) Xj* =Pijxi .


or
X. G.
(3.21) --_ = p. -
X. ij
i 3

These equations mean that the optimum hedge, Xj*, can be

determined by a simple mathematical manipulation of observable

parameters. Equation (3.21) is restated by graphical methods

in Figure 6 below.
X.*
3



p-X..


0.5 _, p =.3


0.5it / p =.3


0.5 1.0 1.5

Figure 6. Optimum hedging ratios with varying price
deviation ratios and correlation coefficients





25

Consider a situation where the price variation ratio is

1.5 and the correlation coefficient to be 0.7. Figure 6 would

indicate that the hedge ratio should be 1.05. This suggests

that positions should be taken in the futures markets which are

larger than one's ownership of the real commodity. This would

be classed as speculation plus hedging which is a position that

would be difficult to defend. Facing such market parameters,

full hedging would be the next best alternative.2

At optimum hedge levels, the optimum of variance in return

is determined by substituting (3.19) in (3.17) above yielding:


X. Cov. X. Cov.
(3.22) V(R)* = Xi2 O2 + o.2 2X i Covij
j20 0 2
which combines to L
2 2
X. Cov.
(3.23) V(R)* = X. 2 o. -_ 1


remembering that Covij = Pij i oa and substituting in (3.23)

yields:

(3.24) V(R)* = Xi2 oi2 (1 ij2)

It can be deduced from (3.24) above that the larger the

absolute value of the coefficient of correlation, the more re-



Ward and Fletcher (33) showed that producers and other
marketing agencies may take positions in the futures market
which represent less than complete hedging, 100% hedging, or
hedging plus speculation. Should there be extensive industry
policy that hedging must be limited to 100% of stocks, then an
inqeuality constraint must be introduced into the objective
function and optimal hedging positions established by programming
techniques.








duction in return variance that can be expected. As p becomes

1, that is when there is perfect correlation between prices

in market i and j, the risk can be reduced to zero. The

analysis indicates that the variance in return is dependent

upon the return variation of the real commodity and the coeffi-

cient of correlation of prices in the two markets.

This analysis would be sufficient for a holder of a

known amount of a commodity to determine the optimum level

of hedging to minimize risk if that is a goal for which he

is indeed striving. Given that he has observed enough data

to estimate oi, Uj and p then his hedging operation may become

a matter of counting his inventory and acting accordingly.

McKinnon (19) suggested that in a more real world situa-

tion a producer would not really know what amount of commodity

that he would have available for sale until the harvest period.

Earlier in the growing season his output would have to be con-

sidered a random variable. McKinnon also assumed that prices

were a random variable but that there is a correlation between

prices and output. In some commodities this correlation might

be small but such an assumption for the Florida orange industry

would be most valid. Due to the relatively close geographic

concentration of producers, if one grower is blessed with good

growing conditions or cursed with poor conditions the likelihood

is great that a substantial number of other growers in his

locality are likewise affected and thus will affect the aggre-

gate output of the industry. Given that industry output changes

measurably, prices will likely change also.






In this model let the following represent the return to

an individual producer.

(3.25) Y = PX + (Pf P)X

Here Y is a measure of total return from production of

a commodity represented by P (the price at harvest time) plus

the return from hedging in a futures market. X represents the

amount of planned production while Pf represents the futures

price at the time of the hedge and Xf represents the amount

actually hedged. X represents the only decision or controlled

variable in the model.

The assumptions in this model are:

(A) P and X are bivariate normal distributions with E(P)

= Pf, E(X) = pX' V(P) = ap2 and V(X) = X2 and

they are known to the producer along with a

correlation coefficient p X< 0 between them.

(B) That E(P) = Pf means that the prices at harvest

time are expected to be the futures price when

the hedge was taken.

(C) That there is no appreciable cost of hedging (an

assumption made to keep things manageable).

(D) That the producer is a risk minimizer.

Using these assumptions the expected return is pre-

sented by:

(3.26) E(Y) = E[P X + Xf (Pf P)] which yields

(3.27) E(Y) = E(P X) since E(Pf P) = 0

The variance of the return with this model is

(3.28) Var(Y) = E [Y E(Y)]2 = E(Y)2 E(Y)]2







Substituting (3.26) and (3.27) into (3.28) and expanding yields

(3.29) Var(Y) = E [P2 X2 2Xf PX(P Pf) + X 2 (P Pf)2]

[E(P.X)]2

carrying the expectation operator inside the first bracket

yields

(3.30) Var(Y) = E(P2 X2) 2Xf E [PX(P Pf)] + X 2

E(P Pf)2 E(PX) 2

This expression now is in the form that is differentiable

with respect to the amount of goods to hedge, Xf.

(3.31) DVar(Y) 2E [PX(P P) ] + 2X* E(P P )2 = 0
( 1 AXf f f f

There exists now an expression about the optimum hedge

position to take X* that will minimize the return risk. It

is minimum since the second order condition, the second partial

of Var(Y) with respect to Xf, is positive. These terms need

some manipulation to state them in more meaningful terms.

The second term is 2X* o2 by definition. Expanding the
f p
first term yields:

(3.32) -E [P-X(P Pf)] = -E[P Pf + Pf) (X PX + X)

(P Pf)]

= -E [(P Pf)2(X ) +((P p)2

x)+ Pf(P Pf)(X PX) + X Pf(P Pf)]

Carrying the expectation operator inside the brackets yields:

(3.33) = -E(P Pf) 2(X E(P Pf)2 -Pf E Pf)

(X X- Pf E(P Pf)







The first term is the third moment about the mean and with the

assumption of bivariate normal distribution becomes zero. The

last term is likewise zero since E(P Pf) = 0. Thus, the

remainder can be expressed as

(3.34) = -yX p2 Pf Cov(PX)

or

(3.35) = a P 2 p P a
f Xp p X

Substituting (3.35) into (3.31) yields

(3.36) 2X p 2 + 2 [-X p PXp Pf p UX]= 0

or finally

(3.37) X* = + pXp Pf

This can be rearranged into a more usable, understandable form

in the following fashion

cX
Xf* "X
(3.38) = 1 + P
PX Xp o
X g
Pf

These terms can be interpreted in the following fashion. X*/pX

represents the optimum ratio of hedging to expected output.

oX/X represents the coefficient of variation of output and

p/pf represents the coefficient of variation of prices. Since

PXp < 0, X*/pX < 1, therefore the hedge is always less than the
expected output. Only when output variability goes to zero can

the hedge be as large as expected output. Generally speaking

then, the larger the output variability the lower the optimal

hedge. Also, if pxp is zero, that is, if one producer's output








and market prices are uncorrelated, this says that he should

hedge his expected output. Thus, even though he has a short

crop and needs to go into the market to complete his commitment

he will pay average prices over time and thus will not increase

his income variance.

Should the coefficient of prices be zero, i.e., prices

are completely stable, equation (3.38) is valued at zero.

That is, under completely stable price conditions one would

not need to hedge.

Tools for the determination of optimum hedges have now

been presented. For the grower seeking to hedge his output,

McKinnon's model described above would prove to be a useful

guide. For those who can see for certain the level of inven-

tory or stocks, the model described by equation (3.20) or

(3.21) would prove to be the better guide.

Summary

The purpose of this chapter was to explore two theoreti-

cal areas. One area dealt with price stability and the bene-

fits that may be derived from such a price situation. The

other area dealt with hedging and its potential benefit to

producers or holders of inventory. That purpose has been ac-

complished.

Price stability was shown to be a state toward which

producers of a commodity should strive. From a rather simple

graphical analysis as well as a more rigorous mathematical

analysis it was shown that producers would gain additional

revenue from a program of price stabilization. Thus any in-








fluence that contributes to price stability should be con-

sidered a desirable influence.

The first specific objective of this study will deal with

the contribution that the futures market in FCOJ may have made

to price stability within the orange industry. If it can be

shown that the futures market has contributed to price stability

for orange solids, then the futures market will be judged as

being beneficial to the industry.

The last portion of the chapter probed the theoretical

benefits that could be expected from hedging. Two models

were developed for hedging depending upon the certainty of

one's inventory. It was shown that if an economic link be

established for prices of a commodity in two different markets,

then a hedging program can be established which will reduce

revenue risks for a business enterprise. It will therefore

be the purpose of the second specific objective of this study

to determine a relationship between prices for oranges in the

cash market and FCOJ in the futures market. Given that a re-

lationship can be shown, then hedging programs can be designed

for industry participants which will reduce price and revenue

risks that have at times plagued this industry.













CHAPTER IV
PRICE VARIATION ANALYSIS

This chapter deals with the first specific objective of

this study. The appropriate theoretical formulation for the

analysis will be presented followed by the empirical efforts

necessary to describe an econometric model. The last portion

of the chapter will deal with the results of the model and

the implications for the Florida orange industry.

Theoretical Discussions

Price Variation Model

There have been attempts to measure the influences of

futures markets upon price fluctuations in various markets.

The first published empirical investigation occurred in 1957

when Gray (8) forwarded evidence which indicated that the

seasonal price range in onion prices had been reduced subse-

quent to active trading in the onion futures market. Public

law 85-839 passed in 1959, legislated the onion futures market

out of existence. Gray (9) re-investigated the onion market

in 1963 and found that the onion price variation had gone

back to its original, higher seasonal price variation pattern.

Powers (24) studied the variation of live choice grade

cattle and pork bellies for a period before and after the in-

troduction of futures trading in these commodities. He attempt-
ed to partition the variance into a systematic component and a








stochastic component. He used Tintner's variate difference

method to isolate the stochastic component of price variation

and test the hypothesis that there was no change in price vari-

ation. He concluded that the random elements of the price

series had been reduced and that the differences in variances

were significant at the 5 percent level.

The price variation analysis that is proposed for this

study will follow a different methodology than that cited above.

It is the purpose of this analysis to assess the contribution

that futures trading has made to the variation in prices for

orange solids paid to growers.

A model will be developed to assess the various factors

that influence the variation in prices paid to producers

during the course of a harvesting season. The analysis will

focus upon the weekly average price paid to producers for

orange solids destined for use as FCOJ. Florida Canners

Association publishes price and other citrus data which are

distributed throughout the industry. These data are widely

used and watched as indications of the strength or weakness

existing in the FCOJ market.

These prices react to fundamental changes that occur

within the industry. Based upon recent data only about 20

percent of the oranges are priced at or near the time of de-

livery; thus the reported cash prices would represent more

nearly the worth of an added pound of orange solids during the

week they were delivered to the processors. If these data are

indeed marginal measures of worth, the variation would likely








be rapid and would be of significant levels enabling the iden-

tification and measurement of influences. The dependent vari-

able will be developed from the intraseasonal variations in

prices and will be normalized to mean yearly prices to

facilitate comparisons.

Figure 7 can be used to aid in selecting the likely con-

tributors to seasonal price variation. The supply, demand

and inventory need to be examined to determine factors that

potentially affect a stable price. The demand and changes in

demand for FCOJ develop slowly and take considerable time to

become recognized. Thus the demand side of equilibrium will

offer little explanation for the level of variation in price

levels. The major perturbation upon the equilibrium pricing

is the expected supply and it will be from the supply and in-

ventory conditions that explanatory variables will be chosen.

Crop size and its relation to previous production levels

and consumption are major contributors to price level and inter-

seasonal changes in that level. The crop size is estimated

with reasonable accuracy, barring freezes, about two months pri-

or to the beginning of the early variety orange harvest. The

price formation activities therefore have had considerable time

to establish a price level for a season prior to the commence-

ment of harvesting. Thus one explanatory variable that needs

not be included in an intraseasonal price variation model is the

estimated crop size or its relation to previous seasons.

The principal modifir to the supply and consequently the

seasonal price variation is cold weather. A freeze can modify














AGE OF NUMBER
TREES OF TREI


PEST & DISEASE
CONTROLS


S INSTITUTIONAL
RETAIL EXPORT


CONSUMER



Figure 7: Simplified flow diagram of influences in
pricing Florida oranges.





36

the crop size substantially, and depending upon the timing may

alter the seasonal price variation in a similar fashion. An

index of weather effect will be generated for each season which

will represent the contribution of a freeze to the seasonal

price variation. The index will be comprised of the severity

as well as the timing within the season.

An additional variable to be considered is the change in

expected supply. The total crop can not be estimated with

certainty until harvesting is completed. However, pricing de-

cisions continually need to be made as the harvest season pro-

gresses. The source of the estimated crop size is the USDA

estimate which is released beginning in October for the up-

coming season and then monthly (except November) throughout

the harvest season. In general the more variation which is

observed in the crop forecasts the more one would expect to see

prices change as the season progresses. Thus a variable which

reflects the changes in the crop forecasts will be developed

to assess this influence. In developing this variable, the

influence of freezes will be netted out to allow the other

changes in forecasts to be properly reflected.

Futures trading may influence the intraseasonal price

variation in two ways. The first influence is that of price

information transfer. By the mere fact that a futures market

exists and trading does take place, the dissemination of the

trading prices can be a means of transferring pricing informa-

tion more completely. A futures price may act as a datum upon

which the parties in a selling situation focus and negotiate.








People can use the futures prices, particularly the nearby

price, to judge if offering prices are reasonable. Thus it

will be hypothesized that a qualitative variable representing

the informational effect for futures trading will be necessary

in the price variation model. It is further hypothesized that

the effect should be stabilizing in nature.

The second effect of futures trading is felt through an

inventory variable. Theoretically inventory holding is facili-

tated by hedging in the futures market. If an inventory vari-

able is beneficial in decreasing price variability, then through

the inventory influence hedging is also influential in reduc-

ing price variation. This argument will be discussed in more

detail later in an inventory submodel.

In this, as in other commodity markets, pricing strategies

generally include price adjustments, holding inventories sta-

ble, inventory adjustments, holding prices stable, or adjust-

ments in both. The FCOJ industry exhibits a seasonal pattern

of holding inventory which is normal and desired. Inventories

may be allowed to build somewhat above the historical pattern

if the industry feels collectively that adjustments in market-

ing policies other than price adjustments can contribute to

revenue gains. Should that be the case, the marginal worth of

extra inputs would not be expected to change as much as if a

rigid inventory policy was maintained. Therefore, the develop-

ment of an explanatory variable which measures inventory in

relation to historic norms would be useful in helping to explain

seasonal price variation.








Over time many pervasive influences are present which

facilitate the orderly development of an industry. Better

technical production methods, better marketing activities,

more knowledge, better financing, easier, cheaper and more

available storage represent improvements that contribute to

a more orderly market. These influences are difficult to

observe and quantify; however, many are likely to be highly

colinear and be increasing over time. One way to represent

these aggregate influences would be to introduce time as an

explanatory variable. While this may not lead to a completely

specified model the interest in this model is not principally

directed towards having discrete knowledge of these effects,

but only to fairly represent them.

Incorporating the variables discussed above, an implicit

form of the price variation model follows as:

Annual measure of price variation = f(weather variable, fore-
cast deviation variable,
inventory variable, tech-
nological variable, fu-
tures trading variable)

Inventory Sub-models

Before addressing the empirical analysis for the price

variation model, a digression into the theoretical impact of

futures markets on inventory and inventory management will be

given.

As was discussed earlier, hedging can be useful in protect-

ing inventory from adverse price swings. Hedging, therefore,

represents the other method that futures markets may yield a

measurable influence.








Placing a hedge is a behavioral decision that can be

measured, using hedgeable goods as an explanatory variable.

Prior to or at the beginning of a season, inventories are usu-

ally at the lowest levels of the season and these inventories

are visible and certain. An estimate of the potential inven-

tory is evident from the reported expected crop size. Beginning

plus estimated inventories represent the hedgeable goods which

can be used to measure the behavior of the hedgers in the in-

dustry. If the futures market is being used by the industry,

one could hypothesize a rather simple model for this behavioral

response where:

Observed hedging = f(goods available to hedge)

It can be further hypothesized that if the behavior is normal

there will be a positive relation between potential inventory

and hedging.

The economic impact of hedging comes about after the hedg-

ing has taken place. The seasonal pattern of inventory suggests

strongly that inventory management is carefully planned and

effected. Should inventories be below normal the marketing

policies would be towards raising prices of the finished pro-

duct thereby reducing the amount demanded with the counsequent

raising of inventory levels. In such a condition there would

be no pressing reason to hedge for downward price protection

since the likelihood of prices dropping with a short crop and

inventory would be low.

Suppose that a condition of plenty exists. This may come

about due to a large crop forecast with nominal inventories or








a nominal crop and large beginning season inventories. These

suppositions mean that potential inventory levels could rise

to a level above normal patterns. Should such a condition oc-

cur, the industry could actively hedge, expecting to cover

carrying costs, thereby holding that inventory for a period

with considerably reduced risks. The industry could engage

in marketing activities designed to stimulate demand. These

marketing actions could result in an actual inventory pattern

different from and below potential levels. Figures 8 and 9

depict the two conditions.

The deviations of Iactual below Ipotentia could be a

result of marketing policies. Thus the size of the shaded area

in Figure 8, (Ipotential actual ), could be represented as

a dependent variable upon which the countervailing forces of

hedging and marketing activities could be regressed. The more

active and aggressive is the hedging program, the smaller would

be the area between the curves. The more aggressive the market-

ing activities the larger would be the area. Thus the model

could be depicted in general form as

potential actual) = f(hedging, marketingpolicies)
with the hedging carrying a positive relationship and marketing

activities a negative relationship.



Potential inventory is a level of inventory that may oc-
cur in a specific season. This can be derived by summing to
carryover inventory the assumed difference between the cumula-
tive harvest and the cumulative movement into consuming channels.








RATIO OF
INVENTORY
TO NORMAL
LEVELS Inv. Potential


Inv. Actual




1.0 Inv. Normal






TIME INTO SEASON

Figure 8. Possible Inventory levels with a large crop
and normal beginning inventories


RATIO OF
INVENTORY
TO NORMAL
LEVELS








1.0


Inv. Potential


" \ \ \ Inv.


Actual


Inv. Normal


TIME INTO SEASON

Figure 9. Possible inventory levels with a nominal
crop and a large beginning inventory





42

Prior to moving into the empirical development of these

models a review with specific attention to the futures trading

aspects will be made. The price variation model will assess

the contributions made by a number of influences toward intra-

seasonal price variation. Of specific interest in this model

is the coefficient associated with the futures trading variable,

FT.. The second model developed will measure the behavior of

hedgers towards apparent changes in their potential stock.

Finally the inventory model will assess the contribution that

hedging has made to carrying inventory.

The signs on each of these coefficients will cause re-

actions that may best be presented in tabular form. These

reactions will apply when the coefficient has been judged sig-

nificantly different from zero.

Futures Hedgeable Observed
trading goods hedging
variable variable variable


> 0





< 0


There is a temptation to draw conclusions when the coeffic-

ient is not significantly different from zero. Both the re-

searcher and the reader must realize that the chances of being

wrong are greater than the limits which were initially found

acceptable.


Cause for Expected Hedging is
and normal not helping
concern/ industry inventory
action behavior management



Benefit to Industry is Hedging is
wasting a
industry tool aiding









Empirical Efforts

Price Variation Model

The specific form of the price variation model in linear

additive form is postulated to be:

(4.1) PVIj = a0 + a Wj + a2 FTj + a3 j + a4 FDj

+ a5 T + uj

where PVI. = jth year's relative variance of prices,

W. = yearly weather (freeze) index,

FT. = futures trading qualitative variable,
3
I. = yearly mean deviation from historical

inventory patterns,

FD. = seasonal deviation in forecasted crop,

T = a time variable which is included

to account for the effects of

unspecified technological changes

which are assumed to occur uniformly

over time

u. = a stochastic error term
3
a. = the coefficients to be estimated


In order to compare price series from year to year in the

orange industry, the weekly price data need to be divided by

the mean price for the season to facilitate comparison between

seasons.









By reducing all weekly prices to a ratio of the mean

seasonal price, the data can be used directly with no concern

for deflating the price series as is often necessary and with

little concern for the heteroscedasticity between the mean and

the variance of prices in the different seasons.

Let P. represent the price in week i and P the mean

price for the season. The mean of Z. letting Z. = Pi/P is:


nP.
1 n
(4.2) E(Zi) = il n PZ= 1
n n i

The variation of Z. is by definition
1

(4.3) V(Z) = E (Z E(Z))2

or
1 n2
n 1=
V(Z) = n iJl (Zi i)

This is an expression for relative variance of the

seasonal price series. The PVI. then will represent the

level of V(Z) observed for each season. The data used to cal-

culate PVI. are the weighted weekly average prices of spot plus
3
contract fruit2 delivered-in reported by the Florida Canners

Association.

In developing the seasonal weather index W., consider

Figure 10 on the following page:





Spot fruit are brought to market with no prior price
negotiation whereas contract fruit comes to market with a
price prearranged up to four weeks in advance of delivery,
depending upon the specific terms of the contract.






PRICES





B

AAp








N WEEKS INTO SEASON

Figure 10. Weather effect upon seasonal price variation

Sunpose A represents the price before a freeze which

occurs N1 weeks into the season. Let B represent the price

after the freeze which will exist for the remaining (N N1)

weeks of the season. The price differences (B A)will be rep-

resented by a percentage of the crop being destroyed. This

relationship between crop reduction and price increase is

assumed to be linear.

Seasonal variation then is represented by
2 2
(4.4) Var(p) = (A p) + (N 1)(B P)

where
AN + (N N )B
(4.5) p N

Substituting for p in (4.4) gives:

(4.6) Var(p)= A- B N1(N N1)

which may be restated as

(4.7) Var(p) = ~2L +- N1





46

Thus by a combination of freeze severity represented by

percent of crop destroyed and by time into the harvest

season, the weather index vector, W., will be constructed.

Other weather influences are ignored as being small compared

to the freeze effect.

It will be assumed that the slope of the demand curve

stays constant throughout the season. Therefore there will be

a linear relationship between the change in the supply of

oranges and the change in the prices received for them. A

proxy for Ap will be the percentage change in the USDA esti-

mates of crop size from a prefreeze estimate to the next

"meaningful" post freeze estimate. A meaningful estimate is

one where the full impact of a freeze has been included.

Consider the data in Table 1 below which presents the

estimates for the 1970-71 season. In this example there was

a freeze on January 20-21. The estimate for February was held

relatively stable because the extent could not be properly

assessed. The March estimate, down 11 million boxes or 6.6

percent of the total crop estimated the previous month, was

the first estimate to reflect the freeze damage. To continue

with this example, the (N1/N) (N N1)/N) can be developed.

The length of the typical season N can be set at 210 days.

In this case, the freeze occurred on the 51st day of the sea-

son so the value of (N1/N) (N N1)/N) is equal to (51/210)

(159/210) = .1839. The weather index, W. for the 1970-71

season then would be 1.2137 which is the product of 6.6 (.1839)








Table 1

USDA crop estimates for Florida oranges, 1970-71 season


Early and
Month Midseason Valencia Total

- - - - -1,000 boxes - - - -
October 100,500 74,000 174,500

November 100,500 74,000 174,500

December 98,500 71,000 169,500

January 95,500 71,000 166,500

February 94,000 71,000 165,500

March 87,000 67,000 154,000

April 87,200 67,000 154,200

May 87,200 63,000 150,200

June 87,200 63,000 150,200

July 87,200 60,600 147,800

FINAL 87,100 60,200 147,300


Source: Florida Crop and Livestock Reporting Service.








The futures trading variable in the model, FT, is pro-

posed to be a qualitative variable set equal to 1 for all years

in which trading has taken place. In the first season of trad-

ing, the 1966-67 season, the value is scaled to be 0
This scaling reflects the developing awareness of futures

pricing information during this first season. This futures

trading variable will pick up the informational aspect of

futures trading and will be the principal focus of this model.

Attention will now be focused upon the inventory variable

for this model. As stated earlier in the chapter the industry

has two decision actions available when considering what to do

with the crop and the potential of moving it. With potential-

ly burdensome crops a useful method to help movements would

be to store the excess of production over consumption with the

anticipation that prices will become more favorable in the

future. The inventory would be stored if the holder expected

with reasonable certainty to recoup the storage costs.

Inventory maintenance, however, is an economic necessity

for processors. Typically, inventory must be built up for two

reasons. One is the usual agricultural problem of short pro-

duction seasons and the necessity to maintain inventory so

that the year-long demand can be met without major variations

in the product prices. The second reason stems from the indus-

try desire to produce a homogeneous product via the blending

of juices. Early and midseason juice is usually kept and blend-

ed with the late season Valencia juice and some Valencia juice

is maintained over the summer to blend with the early varieties

harvested in the fall months of the next season. There is a








seasonal pattern clearly established for inventory levels

which often serves as a guide for many within the industry to

help determine pricing policies. For the purposes of the

Price variation model a typical inventory pattern needs to be

established such that these data and deviations from the his-

torical pattern may be used as potential explanatory

variables.

To develop this pattern, a value was established for all

weeks of every season beginning with the recognized first week

for each season, usually the first week of December. With a

desire to normalize these data, the recognized goods on hand

for any specific week of a given season was divided by the

mean weekly movement for the past 52 weeks thereby creating

a datum that was free of absolute size problems.

Thus for week i in year j the datum would be represented

by:3


FGOH..
(4.8) 1 = (52)




An example of a calculation for I.. will be made using
the data for the first week of the 197311 74 season. The goods
on hand of FCOJ in all forms on 12/8/73, which represents the
end of the first week of the season, was 49,839,278 gallons
of 450 Brix. The actual inventory may have been stored at a
higher concentration level; however, the data were converted
into gallon equivalents of 45 o Brix. It was reported that
160,173,956 gallons of 450 Brix concentrate were moved in the
52 weeks preceding 12/8/73, thus
49,839,278
II' 74 160,173,956 x 52 = 16.180 weeks

represents an entry for the first week of the 1973 74 season.








where

ij represents the level of inventory in weeks at the end

of the ith week of the jth season,

GOHi represents the goods on hand at the end of the ith

week of the jth season,

YM.. represents the total movement of FCOJ for the 52

weeks preceding and including the ith week in the

jth season.

Summing these inventory levels across the k years and

dividing by k would represent a typical historical level for

the first week of a season. Represented mathematically

k
(4.9) T 1 I..
i. k j=l 13
where

i. represents the historic mean or average level

of inventory in the ith week of any given

season,

k represents the number of years in the study.

In this manner the data from the 1958-59 season through

the 1973-74 season were used to construct Table 2 and Figure

11, a graph of the typical inventories for the industry.

It is proposed that an inventory variable be developed

which shows the mean weekly deviation from historic norms

for the specific season, i.e.,

_01 nj
(4.10) 1 nj n (Ii T.)
.j n i=1 j 1.









Table 2

Typical inventory of industry during the season
(averages of 1958-59 season through 1973-74 season)


Weeks into Average Goods Weeks into Average Goods
Season on Hand Season on Hand


(Weeks)

10.424
10.374
10.919
11.463
12.397

13.378
14.509
15.796
17.241
18.567

20.025
21.222
22.089
22.567
22.686


(Weeks)

23.718
24.881
26.212
27.565
28.881

29.982
30.949
31.669
31.976
31.848

31.649
31.024
30.236
29.280
28.343


16 22.429
17 22.087
18 21.943
19 22.166
20 22.735


Source: Developed from Florida Canners Association data.













-- 0
r o0
4-4



H H0 tr 0
01 0
i -i +4J



0 0 1 0


O 0 O (N


H 0 I)

OO4O
0 -1 -I
f-: 4


O


0
>1












S 0
m 0

Z


































11
H

U)










4
n:j

cn O

0
42





0
,.





















41
-o












O4








where

I. represents the mean weekly deviation from

historic norms for the jth season,

nj represents the number of weeks in the jth

season,

I.. and I. are as before.

I., as developed, is assumed to be a measure of the in-

dustry's willingness to follow a strategy of holding prices

constant and allowing inventories to build. This willingness

to carry inventories higher than normal would likely translate

into less price variation within the industry.

The seasonal variation of crop forecasts, FD., will be

developed on an annual basis from the USDA forecasts. These

crop forecasts will be adjusted to allow for the estimated

loss should a freeze occur. The data from Table 1 would be

useful as an example. There was an 11 million box decline

in the crop forecast for March 1971 due to the freeze which

occurred on January 20-21. The March estimate and all sub-

sequent estimates would then be corrected for a freeze by

adding the 11 million boxes. This correction would separate

the influence of a freeze measured by another variable in the

model from the influence of changes for other reasons. To

compensate for the varying crop size the deviation will be nor-

malized by the mean forecast for the season to develop a

meaningful and comparable statistic. FDj, the index of crop

forecast deviation, then would be represented as:





54

1 n 2
(4.11) FD -= (CF. C .)
n CF 1
where CFij represents the crop forecast in the ith

month of the jth season compensated for a

freeze loss as necessary,

CF represents the mean crop forecast for

season j corrected for freeze losses,

n represents the number of forecasts in

season j.

Lastly, the time variable will be represented either as

time in linear form or as a log function to represent the

technological variables that could contribute to the price

variation.

The observations have been made over a period of 16 years

through the 1973-74 season. The number was chosen to insure

enough degrees of freedom to generate a reasonable estimate

of the covariance matrix. The number was also selected to

give an equal period of time before and after the introduction

of the futures market in FCOJ.

Making the assumptions of the classical linear model,

that is E(u) = 0, Var(u) = a2 and E(ut, ut-1) = 0, the price

variation model was subjected to an ordinary least squares (OLS)

fit using the RAPE program with the following estimates of




RAPE is an acronym for Regression Analysis Program for
Economists. Version 2.7 dated February 22, 1972, was the pro-
gram being used at the University of Florida's Northeastern
Regional Data Center during this investigation.








the structural form of the model. The figures in parentheses

are the standard errors developed by the program for each co-

efficient.
(4.12) PVI. = -6.601 + 65.282 W. + 2.485 FD. 0.689 T
3 2 3 *-
(-7.262) (6.796) (1.422) (-.940)

-33.029 FT. + 2.353 T + u.
3 3
(-15.856) (1.612)

with R = .9366, DW = 2.04

or

(4.13) PVI. = -4.827 + 66.290 W. + 1.867 FD. 0.401 T
3 3 3 .3
(-9.990) (7.033) (1.539) (- .921)

21.490 FT. + 7.808 LT + u.
(10.975) (7.079)

with R2 = .9315, DW = 2.05

The only difference in substance between the two equations

is in the presentation of time. Equation (4.12) has time in a

linear increase while equation (4.13) presents time in a natural

log form. From a technical sense both equations are reason-

able. The coefficient of determination is slightly higher in

equation (4.12) and both are absent of any autocorrelation.

The signs of the coefficients are identical so there is little

to suggest that one is better than the other. Equation (4.12)

will be used to discuss the coefficients and their implications

in the next section of this chapter.

During the early stages of this investigation another

variable had been contemplated for use in this model. That

variable was the ratio of priced fruit that entered the FCOJ

channel. The feeling was that possibly the size of this

priced fruit ratio might help explain the observed seasonal








price variation. It was dropped in the rudimentary stages of

the model development because its coefficient value and the t

ratio were both low. The extra degree of freedom gained by

discarding this variable was considered a desirable trade-

off.

If the reader will refer to Figure 7 it will be noted that

the major influences upon prices have been included in the price

variation model. The omitted influences upon supply are not

considered useful in determining intraseasonal price varia-

tion.

Inventory Sub-models

During the development of the inventory variable for the

price variation model, a second influence of futures trading

was discussed. Theroretically a futures market offers a hedg-

ing medium which facilitates the carrying of inventory. It

will be the purpose of this section to probe that second in-

fluence. It was discussed earlier in this chapter that hedg-

ing in FCOJ must involve two distinct activities. One is the

act of placing the hedge which is accomplished by selling con-

tracts on the futures market. The second act is removing the

hedge which is accomplished by either delivering the commodity

or by buying back the contracts in the futures market. The

act of placing the hedge is hypothesized to take place when

the size of the season's potential is known.

It is postulated that this behavioral response can be rep-

resented by

(4.14) OHA = 8 + 1 GH + v.
J J vj







A
where OH. = the observed hedging at time point A in

season j,

GH. = goods available to hedge at or near time

point A in season j.

The observed hedging will be represented by the level of

short hedges held by large traders whose accounts are classi-
5
fied as hedge accounts. The level of open interest in these

accounts reported by the Commodity Exchange Authority for

October 31 of each season (29).

At that time the hedging programs have had time to be

formulated and enacted, based upon goods readily visible in

freezers and the USDA October crop estimate for the upcoming

season. The observed hedging will be expressed in 1000 gallons

of 450 Brix by using the following conversion:

A1 (15,000)
(4.15) OH = .5122
4.5122
where OI = the level of open interest in hedge accounts

held by large traders,

15,000 = the pounds of solids in each contract,

4.5122 = the pounds of solids in a gallon of 450

Brix concentrate.



A large trader is one who has more than 25 contracts open
at any one time. This would represent about 70,000 gallons of
52 Brix concentrate. There may be some hedging done in lesser
amounts, however it is felt that the bulk of the hedging would
be represented by the large traders.








The large traders were not required to report their posi-

tions until January 20, 1969. For those periods not covered

by reporting an estimate of the hedging was generated by assum-

ing that 30 percent of the open interest would represent the

hedge accounts. This level was chosen because it reflected

the conditions for a number of months subsequent to the start

of reporting. This behavior was assumed to have been constant

up to the beginning of reporting.

To develop the variable, GHj, the stocks existing in in-

ventory as of October 15 were summed to the estimated gallon-

age available for concentrate from the new crop. Expressed

mathematically

(4.16) GHO = GOHO + (CF. U Y.)

where GOH. represents the goods on hand as of October 15
3
in season j,

CF. represents the October crop forecast for the
3
coming season in boxes,

Uj_l represents the percentage of the total crop

utilized for FCOJ in the previous season and

assumed to remain constant for the upcoming

season,

Y. represents the estimated yield in gallons of

concentrate per box from the USDA crop fore-

cast or the previous season's yield for years

prior to the USDA yield estimates.

The data from the 1966-67 season were not used since the








market had just been formed and the industry reaction was vir-

tually non-existent for a period of months thereafter. Thus

there are eight observations from which the following estimates

of October hedging behavior were derived.

(4.17) OHO = -1608 + .0415 GH0 + v.
2 2 3
(-2544) (.0137)

R = .6065, DW = 1.90.

Also the same model was used to observe the behavior for

July 31 of each season. At that time the harvest is complete

and GH. can be represented completely by GOH.. The OH. were

developed in precisely the same manner using July 31 data.

The estimate of the structure of the July hedge model was

(4.18) OH = -6803 + .1435 GHJ + vJ
(-5455) (.0617)

R2 = .4739 and DW = 2.45.

The effect of hedging upon the industry is that inventory

above traditional levels may be safely carried. The economic

effect of hedging can possibly be measured by a careful exami-

nation of possible and actual inventories. At the beginning of

each season an Ipotential(maximum possible inventory) curve may

be generated. The beginning level of stocks can be augmented

by expected harvest activity. Estimates of change in stock

level can be determined by estimating the movement, assuming

a constant demand. Should that stock level prove to be burden-

some, marketing actions can be taken to move the product thus

reducing sotcks nearer to the desired or normal levels. Stocks

may be successfully hedged and completely maintained above








normal levels (I normal Thus there exists a measurable in-

fluence on which explanatory variables can be regressed.

The dependent variable is a measure of (Ipot -
potential
Actual) as initially discussed on page 40. The area between
these values (see Figures 8 and 9) can be calculated by summing

the deviations observed weekly over the season. Thus the area

between these curves would represent the success of the hedg-

ing or marketing activities or a combination of these influences.

Since hedging inventories is most useful when stocks are above

levels that offer convenience yields, the data will not be use-

ful in developing a dependent variable when inventory levels

are at or below normal levels. An examination of the inventory

level in existence since the introduction of futures trading

shows only two seasons (1973-74 and 1969-70) when inventories

were substantially above the normal levels. Even though only

two explanatory variables are envisioned for the model, there

clearly are not enough data to facilitate estimation of the

structure of the model. A number of years of data with inven-

tory surpluses will be necessary to allow judgment on this as-

pect of the economic benefits of hedging.

Interpretation and Industry Application

Price Variation Model

Recall that the fitted price variation model was

(4.19) PVI. = -6.601 + 65.282 W. + 2.485 FD. 0.689 T
3 3 3 3
-33.029 FT. + 2.352 T

The dependent variable is a dimensionless measure of the








square of the deviation of cash prices expressed as a percent

of the yearly mean price. The coefficient on each explanatory

variable then shows the contribution to this yearly index. A

positive sign indicates that the variable has contributed to

price variation while a negative sign indicates a lessening of

price variation or said differently, a contribution towards

price stability.

The weather variable coefficient had a t ratio of 9.606

which is an indicator of its statistical significance as an

explanatory variable. The weather phenomenon is well recog-

nized with the industry. There is little that can be done to

soften the effects of freezes, given the industrial structure

and technology as it exists today. Development of better warn-

ing and better protection methods could possibly, over time,

mean that fewer oranges would be lost to a freeze of a given

severity. Development of mechanical harvesting means could

aid in salvage operations subsequent to a freeze. Presently

the salvage method is by hand picking as quickly as possible

and that must be limited by the size of the labor force and

the processing capacity. Should the industry decide to develop

a buffer stock program, the wide price swings that are some-

times evident subsequent to a freeze could be softened by the

sale of this buffer stock. Thus, while there are possible

means to mitigate the effects of freezes, they are not now

available and therefore the industry will continue to experi-

ence the problem of price variation as a result of a freeze.

The positive sign on the time coefficient indicates that








there is a time related destabilizing influence. This may

have occurred due to the introduction of new technology or

may have occurred due to the problems attendant with moving

ever larger orange crops into consuming channels.

The crop forecast deviation variable had a positive sign

and a relatively high t ratio. This indicates that changes

in the forecasts do contribute to price variation. The impli-

cation for the industry is that there should be attention paid

to the problems of errors of estimation. It might prove bene-

ficial to the industry if there were developed better estima-

tion methodology.

The second best coefficient in terms of the t ratio was

the futures trading variable. With the t ratio of -2.083 one

can test the hypothesis that the coefficient is equal to zero

against the hypothesis that it is less than zero. The null hy-

pothesis can be rejected in favor of the alternative that it is

less than zero at the 5 percent level. This means that the

futures trading has contributed to price stability for the

industry.

The inventory variable had a negative coefficient which

means that as the industry holds more inventory prices tend to

become more stable. Since hedging theoretically aids in hold-

ing inventory, the futures market appears to have made another

contribution to price stability.

The purpose of the price variation model was to isolate

the major contributors to variability of prices for orange

solids. Once accomplishing that the interest would be focused








upon the contribution that the futures trading may have made.

Those purposes have been fulfilled. The futures market in

FCOJ can be judged as being a beneficial influence for the in-

dustry. It was demonstrated in Chapter III that a tendency

toward price stability meant additional revenue to producers.

With the recognition of a number of influences that contribute

to price variability, the industry can consider itself fortunate

and financially stronger since and because of the introduction

of a futures market in FCOJ.

Inventory sub-model (Hedge Model)

The regression of large trader open interest of each sea-

son upon the goods available to be hedged yielded this rela-

tionship:

(4.20) OH. (in 1000 gallons) = -1608 + .0415 GH0 (in

1000 gallons)

(4.21) OH7 (in 1000 gallons) = -6803 + .1435 GH (in

1000 gallons)

These results will be presented in Figure 12 below.


20
OH
(in million JULY
gallons)

10


OCTOBER


50 100 150

Figure 12. Observed hedging at specific points in the
season








It can be deduced that there apparently has been a level

of inventories below which hedging is unnecessary. That point

is determined by dividing the constant term by the slope co-

efficient of GH.. This industry seems to consider that in the

vicinity of 40 million gallons, hedging is unnecessary. This

could be entirely reasonable if hedging is an activity which

is entered into to lower the risk of a price decline. When

goods available to hedge are low, the risk of price declines

is low and thus participants may accept that low risk, leave

their goods unhedged and wait for the more likely probability

that prices will rise.

The second deduction is that only a small percentage of

the goods available to be hedged are indeed hedged. The co-

efficient for the October model indicates that the typical re-

sponse of the industry to a rise in goods to hedge will be the

placement of hedges on only 4.2 percent of the increase. With

increases in hedgeable goods in the offing, there is an attend-

ant risk of price declines. When facing such prospects, reason-

able behavior would suggest the placement of substantial hedges;

thus it appears that this industry is not availing itself of

the opportunities to pass risk through the medium of hedging.

The same deductions may be made when observing the July

hedging except that the response to extra inventory is higher

at 14.3 percent. Perhaps the lack of uncertainty in the level

of inventory which exists at the end of the harvesting season

would account for the more positive response of hedging to

stock levels. A conclusion that can be drawn from both results








is that there is considerable inventory that does not carry a

protective hedge during a marketing season.

If inventories decline towards the 40 million gallon level,

present behavior would suggest that industry usage will decline

towards zero. This observation leads to two possible implica-

tions. First, should the reduction of hedging actually decline

towards zero, one of the beneficial effects of the futures mar-

ket on price variation would be considerably lessened. The

implication for the industry is that cash price variation

would be expected to increase. Second, should industry hedg-

ing actually drop to very low levels, there may be implications

for the health and continued vigor of the futures market for

FCOJ.

Summary

The futures market has contributed to price stability

within the Florida orange industry. Should price stability be

accepted as a desirable goal, then the futures markets have

clearly contributed to achieving that goal. The behavior of

industry participants towards hedging potential inventory has

the proper relationship; however, the reaction seems to be

relatively minimal.

One policy implication that can be suggested from the

analysis above is that as a minimum a policy of no intervention

would be in order. A more positive policy of endorsing an

educational program for industry participants would be suggest-

ed. Included in this educational program would be the attempt

to create a more positive image of the futures market in the





66


minds and actions of the industry members, as well as inform-

ing the participants to the intricacies of the act of hedging.













CHAPTER V
PRICE DIFFERENTIAL ANALYSIS

Oranges may enter the marketing channel and become valued

or priced at the time title to the fruit is passed to the

buyer. These oranges are classified as cash fruit. Also,

oranges may enter the marketing channel without a value being

established at the time possession and title change hands.

These oranges may be referred to as pool fruit. The ultimate

prices for pool fruit and the prices for cash fruit may be and

usually are different. These marketing methods (described in

Appendix A) have developed and have existed for many years. It

will be the purpose of this chapter to determine if the futures

market in FCOJ has become an influence which has changed the

relative returns for these two marketing methods.

Theoretical Model

To facilitate the discussions for this analysis, a slight-

ly different flow diagram from that presented earlier would be

necessary. Figure 13 below schematically highlights the price

differential potential. One can deduce from Figure 13 that

pool fruit flows from producers to processor without any direct

influence from the futures market. Cash fruit pricing, however,

may be influenced by the futures market. Since the price forma-

tion activities take place at or near the time of delivery both

the buyer (processor) and seller may use the data from the

futures market as indicators from which to make pricing decisions.




























































Figure 13. Orange flow highlighting price differential
possibilities







The price differential between pool and cash fruit which

existed before the development of the frozen orange concen-

trate product may have been affected by the advent of trading

in a FCOJ futures market. It can be hypothesized that with the

reporting of futures price information, the pricing of cash

fruit may well have been aided relative to pool fruit. This

occurs because there is an alternative market for the fruit,

that of custom processing and delivery through the futures mar-

ket. A model will be developed which will analyze the price

differential for a number of years with the intent of assess-

ing the contribution that the futures market may have made.

For this model one price series (cash fruit) is widely

published and easily available. The other price series, that

for pool fruit, is not available and must therefore be de-

rived. For the non-published price series, it is proposed that

a delivered-in price be derived from published FOB prices. The

FOB derived delivered-in price will be established by netting

from the current FOB prices the total costs of producing and

marketing concentrate. This is a practice normally used by

cooperatives and participation pools and is expected to serve

as a measure of what the "typical" grower might receive for

his product. The data which will be used to determine the pro-

duction and marketing costs are presented in the Spurlock

reports (27). The selected production costs will be those

for producing and selling a case of 48 six-ounce cans of

frozen orange concentrate, a typical retail size.








The largest influence contributing to the price differen-

tial is the new season's FCOJ availability.1 Participation

plans and cooperative membership once established tend to be

relatively stable over a number of seasons. Therefore, most

processors have known number of acres from which they receive

fruit. Also, most processors have usual sales outlets or an

assumed sales commitment. Cash fruit, in contrast, represents

an additional supply having a different marginal value to pro-

cessors. Suppose the processors' sales commitments can be made

from committed pool fruit. In that case, additional supplies

from cash fruit are not particularly desirable and therefore

it would command a price considerably less than the derived

price for pool fruit. Suppose, on the other hand, that committed

fruit will not fulfill expected needs. Then the marginal value

of the cash fruit may exceed that of the non-priced, pool fruit.

An explanatory variable which presents the relative change

in potential product availability would be a useful explana-

tory variable for this price differential model. Ward (32)

reported a secular growth in processed orange products that

would amount to an estimated increase in expenditures of about

6 percent annually. Given that the secular trend has been es-

tablished, one might expect that the availability influence upon




Availability is defined as FCOJ on hand in storage plus
estimated FCOJ production from new fruit.








relative prices for oranges could be represented as in Figure

14 below.

PRICES



CASH
PREMIUM



0 t--~-----'^ -


CASH
DISCOUNT




0 + % CHANGE IN AVAILABILITY

Figure 14. Availability influence upon relative prices



Figure 14 implies that a growth in availability may be

observed, but if the growth in availability just matches the

secular increase in demand for FCOJ then there will not be an

influence upon price differential. An increase in availability

less than the increase in demand would cause prices to move

in favor of cash fruit. There is an implicit assumption that

as availability increases, there will be a change in price dif-

ferential in favor of pool fruit.

As in the previous model a principal modifier to the avail-

ability is the effect of a freeze. The occurrence of a freeze

reduces the pool crop size. Given the crop commitments by pro-

cessors a reduction in members' supply increases the marginal








value of cash fruit. Hence the cash fruit may sell at a pre-

mium to the derived delivered-in prices. Since this model is

dealing with a price differential some function of time during

season and severity of a freeze will need to be included in

the price differential model.

Referring again to Figure 13 it can be deduced that there

are influences which in and of themselves should not contribute

to the differential price but which are multiplicative or inter-

active terms with the supply parameters discussed above. These

influences are hypothesized to be the cash fruit ratio and the

effect of futures trading.

Earlier it was discussed that because of supply and sales

commitments, processor would value an extra box of oranges be-

low the derived pool fruit price if it appears that the inflow

of fruit was ample compared to the demand. Conversely an extra

box of fruit may be valued well above pool fruit if sales com-

mitments could not be met from members' fruit. The amplitude

of the price variations would vary inversely with the size of

the cash fruit ratio. Thus the cash fruit ratio is hypothesized

to be an interaction term for both of the supply parameters dis-

cussed above.

The second interactive influence and the one of principal

interest for this model is the influence of futures trading.

The futures market would be of considerable interest to those



The cash fruit used for FCOJ is represented by spot fruit
and contract fruit. The size of this cash fruit in relation to
the total used for concentrating will be referred to as the
cash fruit ratio.









who are in the market to sell cash fruit. Given adequate

knowledge of processing costs, the cash seller can use the

futures market prices, particularly the near contracts, as data

to aid in the determination of fair and equitable prices for

his fruit. Thus because futures price data are widely pub-

lished and easily available to anyone interested, it is hypoth-

esized that the futures market has become an influence which

has dampened the amplitude of supply-induced price differen-

tial variations.

Referring once again to Figure 13, it will be noted that

the influences discussed above are the principal contributors

to the difference in prices between cash and pool fruit. The

price differential model in very general terms can be stated

as:

Price Differential = f(availability, freezes, cash fruit

ratio, futures trading)

A priori, any increase in the availability term would be

expected to affect the price differential with pool fruit

benefitting. The weather influence should affect the price

differential to the benefit of cash fruit. Each of the cross-

product terms should tend to soften the influences of these

two supply parameters, that is, have opposite signs.

Empirical Model

The linear form of the price differential model is postu-

lated to be:
(5.1) PDIj = YO + 1 AAj + y2 Fj + y3 AAj (PI ) + Y4

(PI%) + YAA. (FT.) + y Fj (FT.) + u.
.5 F 6





74

where PDI = mean seasonal differential between cash prices

and FOB derived delivered-in prices,

AAj = percentage change in availability from season

j-1 to j,

F = a freeze index to be developed below,

PI. = ratio of cash fruit to total fruit used for

concentrate in season j,

FTj = a qualitative variable representing the infor-

mational effects of futures trading.

The dependent variable for this price differential model,

PDIj, will be developed comparing what a cooperative or parti-

cipation plan member might expect to receive for his fruit to

the cash price actually paid to those who did not market their

fruit in this manner. What a participation plan member might

receive for his fruit can be approximated by the FOBDDI--the

FOB derived delivered-in price.3

It is calculated by subtracting processing and marketing

costs from the reported FOB price. The FOB price is usually

quoted on the basis of 12 six-ounce cans, thus some conversion

is necessary to derive an FOB price per pound solid. The pro-

cessing and marketing costs used are those costs for producing

a case of 48 six-ounce cans as reported in the Spurlock reports.

Again some conversions are necessary to determine a cost per

pound solid. The difference between the revenue and costs as

stated will be the FOBDDI. It will represent what a "typical"



Fairchild (4) outlined methods for deriving delivered in
prices from FOB quotations. The method used in this model is
similar to his "shortcut" method.









participation plan or pool member would receive for his orange

solids.

A seasonal mean price differential, PDI., may now be

established as:

n
(5.2) PDI. (CP.. FOBDDI .)
.3 n i ij

where CP. = cash prices during the ith week,


FOBDDIi = derived delivered-in prices for week i,


n = number of weeks in the season.

The calculations for PDI. are plotted below in Figure 15.
*3


PDI.
C/lb.
solid

20


16

12

8

4

0

-4

-8

-12


61-62 65-66 69-70 73-74
SEASONS

Figure 15. Observed mean seasonal price differential
(1957-58 season through 1973-74 season).







A positive level of PDI. indicates that over the season
-3
the cash prices netted out higher than the value that was

likely received by pool fruit sellers. A specific grower,

whether he be a pool fruit or a cash seller, might expect to

have enjoyed prices in excess of those used or fared worse than

indicated. However, this measure of differential prices is an

indicator of what likely happened in a specific season.

To develop an estimate of availability, fruit in concen-

trate form must be aggregated with on-tree fruit. The inventory,

in concentrate form, can be expressed in equivalent boxes by

dividing the gallons of 450 Brix concentrate by the previous

season's reported average yield. This can then be summed with

the new crop forecast to yield an expected availability. This

method was chosen because early forecasts were only in terms

of boxes and only recently have yield estimates been reported.

The change in availability, AA., can be expressed in percentage

terms as:
A. A.
(5.3) AA. = j-1
3 Aj-1

The freeze effect, F., will be calculated in a manner

similar to that used in developing the weather index for the

price variation model. Consider Figure 16.

It is assumed in Figure 16 that a freeze occurs N1 weeks

into the season or with N2 weeks left. The mean price differ-

ential for this model might be expressed as

(D A)N1 + (D B)N2
(5.4) PD =
.] N










PRICES



FOBDDI
D

B

A





1 N1 + N2
WEEKS INTO SEASON



Figure 16. Freeze effect upon seasonal price differential

which after necessary multiplications and rearrangements yields

N2
(5.5) PD. = (D A) (B A)

The availability term discussed above, AAj, will help

describe the initial levels of (D A). The second term on the

right-hand side of (5.5) will be the freeze effect, F., postu-

lated for use in the price differential model (5.1). Assuming

there is a linear relationship between changes in supply and

prices, (B A) will be represented by the percentage of the

crop destroyed. N2/N is simply the ratio of time remaining to

total time in the harvest season. Suppose a freeze destroyed

10 percent of a crop 70 days into a 210 day season. The freeze

effect, F., for that season would be represented by 10(140/210)

= 6.666.








As mentioned earlier, there are influences which in and

of themselves should not cause the price differential to widen

or narrow; however, because they are present at different lev-

els they may have a multiplicative or dampening effect upon the

price differential. These influences in the differential model

are the cash fruit ratio and the futures trading influence.

These influences will be introduced as cross-product terms.

PI will represent the ratio of cash fruit to total crop used

for concentrate during a specific season. The futures market

influence, FT., will be a qualitative variable set at a level

of one for all seasons since the introduction of futures trad-

ing except for the 1966-67 season where the value was set at

.25 and .50 for two fits presented below.

As was discussed in the price variation model, 16 years

of observations were used to generate estimates of the struc-

ture of the model. This number was chosen so that sufficient

degrees of freedom were available to estimate the covariance

matrix but not large enough to encompass significant structural

changes in the industry.

The model was fitted by OLS using the assumptions of the

classical linear model. The numbers in parentheses are the

standard errors. The estimates were:

(5.6) PDI. = 2.385 .467 AA. + 2.637 F. + .728 [AA

(1.501)(-.436) (7.214) (.924)

PI. 7.496 F.(PI.) + .088 AA. FT. .426 F. FT.
(25.884) (.184) (-.093)

with R2 = .6936 and DW = 1.27










(5.7) PDI = 2.462 .569 AA. + 2.451 F. + 1.012 AA.

(1.493)(-.372) (7.150) (1.125)

PIl 6.745 F. PI. + .144 AA. FT! .465 F. FT'
1 5 3 3 3 1
(-25.666) (.224) (-2.063)



with an R2 = .6997 and DW = 1.24.

From a technical sense (5.7) which has the futures variable,

FT! scaled to a level of 0.5 for the 1966-67 season would of-

fer slightly more in terms of R2. The Durbin-Watson statistic

deteriorates some; however, because of the low number of obser-

vations and the relatively high number of parameters, the in-

conclusive region is quite large in the test for autocorrela-

tion and the small amount of change is inconsequential. Equa-

tion (5.7) will be used as a basis in the following discussion.

Interpretation and Industry Application

It will be noted from an examination of the t ratios of

(5.7) that the coefficients of the variables used in the price

differential model have low statistical significance. There-

fore the following discussions must be interpreted with reason-

able caution.

A positive sign on a coefficient in the model will indi-

cate that a positive change in the associated variable will

cause a price differential change in favor of cash fruit

prices. A negative sign indicates that a positive change in a

variable will cause prices to move in favor of pool fruit sellers.








The coefficient with the highest t ratio was AAj, the

availability term. The theoretical discussions earlier hy-

pothesized that the influence would be negative and this was

realized. For every percent increase in seasonal availability

there is a change of approximately one-half cent per pound

solid in favor of pool fruit. It was also discussed in the

presentation of Figure 13 that there would be some positive

level of availability change that would not influence the price

differential. This would account for a secular increase in

the demand for processed orange products. By dividing the in-

tercept in (5.7) by the slope coefficient on AA it can be de-

termined that a 4.33 percent yearly increase in availability

did not affect the price differential prior to futures trading.

Subsequent to the introduction of futures trading the coeffi-

cient of AA. must be modified by the coefficient of AA. FT!
3 3 3
yielding a combined coefficient of -.425. The implication is

that the availability may now increase nearly 5.8 percent be-

fore there is an influence which will be to the detriment of

the cash fruit seller.

Cash fruit sellers do benefit from a freeze. A freeze in

early February destroying say 3 percent of the crop holding

all other terms constant can be evaluated by means of:

(5.8) PDI = 2.451 .4652 FT! 6.745 PI! AF.
L 3 31 3

Assume PIj equals 0.200. FT! is a qualitative variable equal

to one. Fj can be evaluated by the (B A)N2/N developed in

(5.5). (B A) will be represented by the 3 percent crop loss.

N2/N will equal about 140/210 or 2/3. Thus Fj = 3(2/3) = 2







therefore APDI for this example is 2(2.451 .465 -1.349)

or about 1.3 cents per pound solid and the change will be in

favor of the cash seller.

The negative sign on the coefficient of F. FT! indicates
J 3
that a given freeze severity will not produce as much positive

benefit to cash sellers due to the influence of futures. That

is the nature of an information variable. If information were

to aid in keeping prices from dropping too much it will also

aid in keeping prices from increasing too much. It can be de-

duced that the futures trading information effect has aided in

the reduction of the variability of differential prices, which

in the past were due to changes in supply.

Summary

While the futures market in FCOJ appears to have been

beneficial to price differentials for fruit, that position can

not be defended very rigorously. What can be stated empirical-

ly is that there is no evidence to indicate that the futures

market in FCOJ has been detrimental to the price structure

existing within the Florida orange industry.

The only policy implication that can be derived from the

preceding price differential analysis is that since there has

been no detrimental effect from the futures market upon the

industry, a policy of no action is clearly indicated.













CHAPTER VI
BASIS MODEL

The last specific objective of this study was to develop

an understanding of the relationship between prices in the

futures market for FCOJ and the cash market for orange solids.

Should an economic relationship be established, then,as re-

viewed in Chapter III, a means has been established to suc-

cessfully hedge some of the price risks of the industry.

This chapter will analyze the relationship existing be-

tween prices on the FCOJ futures market and the cash price for

oranges. The difference between the two market prices is known

as "the basis." A "Basis Model" will be developed to facili-

tate the study of the relationship.

It is expected that the knowledge gained in developing

the model will be useful in the generation of rules and in-

sights into hedging on the FCOJ market.

Theoretical FCOJ Basis Model

Existing Theory

Commodity basis refers to the difference between a commodity

futures price and a spot or cash price for that commodity in a

certain location. There has been considerable literature gener-

ated on basis and a number of articles will be cited as the

FCOJ basis model is developed.

Perhaps the first major contribution to the theory of basis

was developed by Keynes (16). He argued that "if supply and de-

mand are balanced, the spot price must exceed the forward price







by the amount which the producer is ready to sacrifice in

order to 'hedge' himself, i.e., to avoid the risk of price

fluctuations during the production periods."(16,Pg.143) In

a normal market, hedgers would be willing to sell forward con-

tracts at a discount to the cash price in order to reduce their

price risk. That discount would represent an insurance pre-

mium for the hedger. Keynes denoted this pricing phenomenon

as normal backwardation on the market.

Kaldor (15) later added to the basis theory the concept

of a convenience yield for holding goods. Generally, distant

futures will exceed the spot or nearby futures by the cost of

storage. Yet, if nearby reflects a shortage there is some

convenient yield for having at least a minimal stock. This

yield offsets at least part of the carrying cost. At times,

then the distant contract price may exceed the nearby by less

than the full storage cost.

Kaldor also theorized that interest cost must be summed

to carrying costs. He observed that by selling forward,

holders of stocks free themselves of any uncertainty (apart

from the risk, which we may treat as negligible, of contracts

not being fulfilled); hence the difference between forward

price and current price must be equal to the sum of interest

cost, carrying cost and convenience yield. The forward price

must always fall short of the expected price by the amount of

the marginal risk premium.

These statements can be expressed algebraically as

(6.1) EP CP = r + C + R Q







and

(6.2) FP CP = r + C Q.

Therefore

(6.3) FP = ER R

where EP = expected price,

CP = cash price,

FP = forward price,

r = interest cost,

C = carrying costs,

R = risk premium,

and Q = convenience yield.

Working (34, 35) attempted to synthesize a satisfactory

explanation for inverse carrying charges, that-is when the

cash price is higher than futures prices, and to mold the ex-

planation into a theoretical supply curve for storage, which

looks like:


FUTURES
PRICE LESS
CASH






0STO









STOCKS


Figure 17. Supply curve of storage








He draws upon Kaldor's concept of convenience yield to

rationalize why a great deal of storage does exist with a nega-

tive storage yield. He concludes the negative prices occur

when supplies are relatively scarce. They then impose pressure

on hedging merchandisers and processors to avoid holding un-

necessarily large quantities out of consumption in the form

of stocks which they can do without. Thus a negative price

of storage reduces storage and increases availability of pro-

duct for consumption in a year of shortage. Supplies would

otherwise remain in storage.

Brennan (1) developed an equilibrium model for storage

that used fundamentally the supply curves developed by Kaldor

and Working. He assumed the supply .curve was stable. He hy-

pothesized that the observed stocks could then be the equilib-

rium solutions of the varying demand for storage curves and

the fixed supply of storage curve. By calculating expected

prices and carrying costs, Brennan was able to empirically

measure a marginal risk premium and convenience yield related

to the level of stocks for a number of commodities.

Ward (31), applying theories of Gray (10) and Working (36),

developed a speculative index and attempted to explain price

distortions of the basis in the FCOJ futures market using this

index. He suggested that price distortion had a higher range

with too little speculative activity in the market than too

much. His data suggest that optimum speculative activity is

somewhere between three and five times the net hedging activity

in this FCOJ market. This is optimum because price distortion







is less than one cent, which typically is about 2 percent of

spot prices.

Additions to Basis Theory for FCOJ

The above influences can all be applied to the FCOJ basis.

In developing an empirical model for the basis, a synthesis

of the above theories together with some additional considera-

tions is necessary.

In almost all other agricultural commodities where there

exist futures markets, very little, if any, product transfor-

mation is necessary for the grower to maintain the capability

for delivering product. Sugar would be a notable exception

where the producers of cane or beets cannot deliver on contract

except by subjecting their product to a processing or ex-

tracting operation.

In FCOJ an orange grower needs to have the juice extract-

ed from his oranges and then processed into a concentrate level

that is typically used within the industry such as 580 Brix.

This concentrate is packaged in plastic liners, placed into

55-gallon drums and then frozen. Then and only then does the

grower have the potential to deliver against his futures con-

tract. Thus it can be expected that there will be a differen-

tial between cash solids and concentrate which will reflect

the transformation costs. The typical rule of thumb has been

a processing cost of 11 cents per pound solid. These data are

available in the Spurlock reports cited earlier. Processing

costs have risen slightly in the last few seasons. These costs

include selling expenses as well as certain fixed expenses which








a user of the futures market may not require. The typical manu-

facturing costs or variable expenses in producing concentrate

have been slightly less than 50 percent of the total cost based

upon the data from the 1966-67 season through the 1972-73

season. Further, these costs do not recognize the economic

value in the residual material. Cattle feed, molasses, and

essence oil are examples of the products which are derived out

of the residual from the concentrating operations. This may

have the effect of lowering the required differential price

between the cash and futures market to a level considerably

below full published transformation costs.

It can be hypothesized that the basis will reflect what

the industry considers a reasonable transformation cost. Fu-

tures prices lower than that which would cover such costs

would cause the supply of contracts from the industry sources

to dry up. Futures prices higher than reasonable costs would

cause an active supply of contracts from industry sources

causing prices to adjust back to a reasonable difference.

The futures markets react to expected prices according to

the theory discussed earlier. The cash price will react to

the same conditions after the expectations become fact. It is

anticipated that there exists a different response rate for the

two markets. Should this differential response exist, then the

basis, a differential price, will exhibit that behavior. An

expectation variable built upon crop estimates and reported

freeze conditions will be incorporated as an aid in explaining

the basis.








Lastly, the FCOJ basis appears to react to a "freeze

syndrome." The potential of a freeze which can destroy a signifi-

cant percentage of the crop exists until mid-February. This

has become ingrained in the behavior of participants of the

industry to the extent that prices of dealings in the future

usually include some expectation of a rise in value due to a

freeze-reduced crop. As the freeze season passes the expecta-

tion dissipates and the supply situation has very few "surpris-

es" left. By "surprises" is meant that unpredicted, exogenous

influences are largely dissipated and that the variance between

actual and predicted crop size drops considerably.

Speculators, knowing that the freeze potential exists, may

be willing to assume the risk of freezes by paying something

each year for the privilege of buying the occasional windfall

gain when a substantial freeze actually occurs. This action

would be in consonance with the desires of the producers in

that they would sell their rights to a windfall gain for a

smaller, more certain sum each season. This would be particu-

larly true for risk-averse individuals.

The influences have now been discussed. In general form

the basis model in FCOJ can be hypothesized as follows:

Basis = f(interest rate, carrying costs, convenience yield,
risk, transformation costs, futures trading dis-
tortions, weather premium, expectation)

The model will be derived explicitly below. There will be

basis models generated for the six contract months. In that

fashion participants with different and varying needs may make

use of the results.







Basis Model Development

As stated earlier the purpose of the "basis model" is to

develop an understanding of the relationship between the fu-

tures prices in FCOJ and the cash prices paid for fruit (pound

solids). An understanding of the basis is useful for determin-

ing if and to what extent this market will pay a risk premium

and to what extent price distortions resulting from trading

activities in the FCOJ futures market occur. Does the market

require a weather premium prior to and during the freeze sea-

son and does the market reflect a convenience yield. Finally,

does the basis model demonstrate the expectations influence

prices in the two marketsdifferently.

Explanatory Variable Development

Theroetically for a trader to hold inventory the market

will have to pay either the interest cost in carrying the

inventory or an opportunity cost of the inventory which is

held with capital generated in the business. Thus it seems

reasonable that futures prices should be high enough to pay

interest on the investment in inventory. Thus

(6.4) FP = (CP + TC)ert

where FP = Futures prices,

CP = cash prices,

TC = transformation costs,

r = market interest rates,

and t = time that inventory will be held.

Substituting (6.4) into the original basis definition where

B = FP CP yields




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