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 absentminded 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,
197071 season. . . . . . . . .. .47
2 Typical inventory of industry during the season
(averages of 195859 season through 197374
season. . . . . . . ... . . .51
3 Results of initial least squares fit of basis
model . . . . . . . . ... . . 102
4 Correlation between various price series (data
from 196768 through 197374 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
Ai World citrus production, oranges and tangerines,
seqons 197071 through 197374 (production in
thousands of 90 lb. boxes). . . . . . 136
A2 Florida orange production in thousand boxes . 138
A3 Florida round orange production by counties in
1,000 boxes, 197374 season. . . . . ... 139
A4 Analysis of "priced" fruit used for concentrate
(in boxes). . . . . . . . . ... 146
A5 FCOJ pack in various form (in gallons of
450 Brix) . . . . . . . ... . 151
Bl Data matrix for the price variation model . . 156
B2 Data matrix for the price differential model. . 157
B3 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
(195657 season through 197374 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
Ai Flow of oranges from grower to consumption
outlets . . . . . . . . . . 144
A2 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
CoChairman: 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 topquality 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 ByLaws 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 orangeproducing 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 longrun 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 pricestable 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 noncorrelated, that the risk after hedging
represented by the nonshaded 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 nonshaded portions of A and B are smaller than A
alone so in this case hedging has reduced the risks compared
to the nonhedged 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(AB) = oA2 + B2 2pAB A G
To explore the necessary closeness of the price series,
assume that it is desired that Var A > Var(AB). The profit
risk after hedging, must be smaller than or equal to the origi
nal nonhedged 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
pX..
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 [PX(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 85839 passed in 1959, legislated the onion futures market
out of existence. Gray (9) reinvestigated 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 Submodels
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 deliveredin 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 197071 season. In this example there was
a freeze on January 2021. 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 197071
season then would be 1.2137 which is the product of 6.6 (.1839)
Table 1
USDA crop estimates for Florida oranges, 197071 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 196667 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 yearlong 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 195859 season through
the 197374 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 195859 season through 197374 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
44
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 2021. 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 197374 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, ut1) = 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 Submodels
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 196667 season were not used since the
market had just been formed and the industry reaction was vir
tually nonexistent 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 (197374 and 196970) 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 submodel (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 nonpublished price series, it is proposed that
a deliveredin price be derived from published FOB prices. The
FOB derived deliveredin 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 sixounce 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 nonpriced, 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 deliveredin 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 supplyinduced 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 deliveredin prices,
AAj = percentage change in availability from season
j1 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 FOBDDIthe
FOB derived deliveredin 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 sixounce 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 sixounce 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 deliveredin 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
6162 6566 6970 7374
SEASONS
Figure 15. Observed mean seasonal price differential
(195758 season through 197374 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 ontree 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. = j1
3 Aj1
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
righthand 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 crossproduct 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 196667 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 196667 season would of
fer slightly more in terms of R2. The DurbinWatson 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 onehalf 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, thatis 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
55gallon 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 196667 season through the 197273
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 midFebruary. 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
freezereduced 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 riskaverse 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
