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This is to certify that the

dissertation entitled

Decision Support System Components for
Firm Level Risk Management Through Commodity Marketing

presented by

Richard Dwayne Alderfer

has been accepted towards fulfillment
of the requirements for

 

Ph.D. degree in Agricultural Economics

£an a gel/WA

Major professor

 

Date December 4, 1990

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DECISION SUPPORT SYSTEM COMPONENTS FOR
FIRM LEVEL RISK MANAGEMENT THROUGH

COMMODITY MARKETING

By
Richard Dwayne Alderfer
A DISSERTATION
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Agricultural Economics

1 990

--/‘7’~ 5/ 3L0

//

.1 .4.) '

ABSTRACT

DECISION SUPPORT SYSTEM COMPONENTS FOR FIRM LEVEL RISK
MANAGEMENT THROUGH COMMODITY MARKETING

By

Richard Dwayne Alderfer

Grain farmers can use several cash market and futures market instruments
prior to harvest to manage crop income risk. The farm problem is "Which pricing
alternatives to use and how many bushels to price, to manage income risk, when
production and ending period prices are uncertain?” The research problem was to
design and test a decision support system to assist with the farm problem, utilizing
the producer’s risk attitudes.

Farm Income Risk Management (FIRM) is a series of microcomputer models to
solve the farm problem above. FIRM is a single crop, stochastic, non-dynamic model.
An option pricing model is used to solve for the implied volatility of the ending period
futures distribution (using an efficient market assumption). Futures markets were
modeled as normally distributed. Basis and yield distributions were subjectively
elicited. These factors form the expected each market gross margin distribution. The
first two moments of the expected gross margin distribution seed an “equally likely
risky outcome" expert system called ELRISK, to give a subjectively elicited utility curve.
The result is a discrete 'Bernoullian' utility curve with 9 to 14 points that extends
across most of the gross margin distribution.

A non-linear 'Box’s Complex” subroutine seeks to maximize expected
subjective utility of the marketing simulation. The simulation includes all transaction
and opportunity costs. Bushels to forward contract, futures hedge, put hedge, and

basis contract are recommended for the individual producer and the particular crop.

 

Richard Dwayne Alderfer

Twenty-nine Michigan soybean producers tested FIRM at four
extension/research workshops. All 29 producers for the problem under consideration
were risk averse across the gross margin range elicited. Forward contracting was the
prevalent pricing alternative, while put options were seldom recommended. Producer
utility curves were fitted to four functional forms (linear, quadratic, semi-log and
negative exponential). The negative exponential function was judged to be superior
based upon R2 comparisons.

FIRM was judged to be successful in a workshop setting. The concepts used

in FIRM could be extended to other risk problems.

 

Dedicated to Lillian, Nathan, Kristen and our families.

 

ACKNOWLEDGMENTS

I wish to thank my major professor Dr. Stephen Harsh for the valuable input to
this research and manuscript. He, and dissertation committee member, Dr. Jim Hilker
helped present workshops and provided valuable feedback to the research and this
writing. Thanks also to the other two dissertation committee members. Dr. Larry
Connor kept a balance with a broad vision, while Dr. Steve Hanson examined the
details.

Several other professors also deserve recognition for their contributions. They
are Doctors Jack Meyer in Economics, Tom Manetsch in Systems Science, Lindon
Robison, Roy Black, Glenn Johnson, Jim Shaffer, Stan Thompson, John Ferris and
Bob Myers, all in Agricultural Economics at Michigan State University. Doctors Rob
King at the University of Minnesota and Jim Pease at Virginia Poly-technic Institute,
wrote dissertations at Michigan State University that were extremely important to this
research. Use of their material should be clearly indicated, but if somewhere it was
omitted it was certainly not purposeful.

I thank Department Chairmen Larry Connor and Les Manderscheid for
departmental and financial support. Most of the research funds came from the
Michigan State Agricultural Experiment Station.

The department secretaries and computer support persons were always

available to help. Daune Powell, Nicole Alderman, Nancy Creed, Linda Boster,

Eleanor Noonan, Ann Robinson, Chris Wolfe, Margaret Beaver and Jeff Wilson have
my sincere thanks.

Fellow students Larry Borton, Randy Harmon, Jim Phillips, Jim Lloyd and John
Mykrantz were good listeners, even when l was not. Student programmers Mark
Gandy and Carl Raymond helped with 'text graphics' subroutines for ELRISK

Midway through this two and a half year project, I underwent major surgery
and follow-up treatments. Related to this, there are many persons who helped me
finish this work. The staff at the Magnetic Resonance Imaging Lab at Michigan State
University uses a 'cutting edge' diagnostic technology that saves lives. Doctors Dela
Cruz, Rapson, and Spencer (and their excellent staffs) did the cutting and treatments,
and God did the healing.

Through this, the emotional support (and in some cases monetary support) of
the Alderfers, McCandlesses, Grangers, Franciscos, Bortons, Kelseys, Aliens,
University UMC, and countless others were sustaining. I would especially like to
thank my parents.

More than anyone else, I thank my best friend and wife, Lillian. She and

Nathan and Kristen provided love, like nobody but God could. Romans 5: 3-11.

vi

 

TABLE OF CONTENTS

LIST OF TABLES ................................................. x
LIST OF FIGURES ................................................ xi
LIST OF ABBREVIATIONS .......................................... xii
CHAPTER ONE - INTRODUCTION ..................................... 1
1. 1 Background .................................................. 2
1.2 The Problem ................................................. 5
1.3 Research Goal ............................................... 6
1.4 Research Objectives ............................................ 6
1.5 Research Benefits ............................................. 7
1.6 Research Methodology ....................................... 9
1.7 The Dissertation Framework ..................................... 12
1.8 Summary ................................................... 13
APPENDIX TO CHAPTER ONE- Terminology ........................... 14
1 .A Risk and Uncertainty .......................................... 14
1.8 Marketing Terminology ......................................... 17
1.0 Decision Support Systems ...................................... 19
CHAPTER TWO - HOW TO DESCRIBE AND DECIDE: A LITERATURE REVIEW . . 20
2.1 Risk Principles ............................................... 24
2.1.1 Probability Principles ...................................... 25
2.1.2 Expected Utility Theory (EUT) ................................ 26
2.1.3 Measures of Risk Aversion .................................. 30
2.1.4 Utility Functions .......................................... 34
2.2 Generating Yield Distributions ................................... 38
2.3 Representing Distributions ...................................... 42
2.4 Market Efficiency ............................................. 43
2.5 Generating Price Distributions .................................... 46
2.5.1 Futures Price Distributions .................................. 46
2.5.2 Basis Distributions ........................................ 50
2.6 Eliciting Risk Attitudes ......................................... 51
2.6.1 Methods ............................................... 51
2.6.2 Results of Risk Elicitation ................................... 61
2.6.3 Problems with Previous Research ............................. 63
2.7 Decision Rules and Efficiency Criteria .............................. 67
2.7.1 Maximize Expected Utility ................................... 68
2.7.2 Stochastic Dominance ..................................... 7O
vii

2.7.3 E-V, MOTAD, M-SD, and Semi-Variance ........................ 76

2.7.4 Target MOTAD and Lower Partial Moments ...................... 79

2.7.5 Safety First Decision Rules .................................. 83
2.8 Previous Efforts .............................................. 84

2.8.1 Risk Efficiency Studies - Research Oriented ...................... 85

2.8.2 Micro-Computer Based Simulations ........................... 89
2.9 Summary ................................................... 91
CHAPTER THREE - THE FIRM MODEL ................................ 93
3.1 FIRM Model Overview ........................................ 94
3.2 The Audience .............................................. 96
3.3 Generating Yield Distributions (ELICIT) ............................ 97
3.4 Generating Price Distributions ................................... 100
3.5 Adjusting Monte Carlo Observations .............................. 103
3.6 GENRINC ................................................. 104
3.7 Measuring Risk Attitudes (ELRISK) ............................... 106
3.8 Marketing Simulation - The Objective Function ...................... 114
3.9 Finding Superior Marketing Plans (MKTOPT) ........................ 121
3.10 Post-Optimal Solutions ...................................... 126
3.11 Issues ................................................... 128
3.12 Future Improvements to FIRM .................................. 131
3.13 Summary ................................................. 134
CHAPTER FOUR - MODEL VALIDATION .............................. 135
4.1 The Base Farm for Testing ..................................... 136
4.2 Test 1 - Effect of Utility Changes on Marketing Plans .................. 138
4.3 Test 2 - Effect of Utility Changes on Pricing Tools .................... 145
4.4 Test 3 - Changing Put Options Premiums and Utility .................. 148
4.5 Test 4 - Changing Price Distribution Forms ......................... 149
4.6 Summary .................................................. 152
CHAPTER FIVE - WORKSHOP RESULTS .............................. 154
5.1 Generating Price Distributions ................................... 155
5.2 The Workshop Format ........................................ 156
5.3 Getting Acquainted ........................................... 156
5.4 Yields and Probabilities ....................................... 158
5.5 Estimating Yield Distributions with ELICIT .......................... 158
5.6 Crop Costs and Effective Acreage ................................ 160
5.7 Running GENRINC ........................................... 161
5.8 Soybean Outlook and Volatility Forcasting .......................... 162
5.9 Estimating Utility Functions with ELRISK ........................... 162
5.10 Marketing Solutions ......................................... 168
5.11 Producer and Presenter Evaluation .............................. 171
5.12 Testing Other Utility Curves on a Case Farm ...................... 173
5.13 Changing Price Data for the Case Farm ......................... 179
5.14 Summary ................................................. 181

viii

 

CHAPTER SIX - SUMMARY AND CONCLUSION ........................ 183

6.1 The Problem ............................................... 184
6.2 The Research Objectives ...................................... 184
6.3 Research Findings and their Implications ........................... 185
6.4 Limitations of the Research ..................................... 188
6.5 Future Research ............................................ 189
APPEDICES ................................................... 192
A - Comments From Workshop Participants ........................... 192
B - Workshop Program .......................................... 193
C - Producer Curves ............................................ 196
D - Discrete Yield Data .......................................... 201
E - Discrete Price Distributions .................................... 204
F - Code for F&BDISTS.EXE ...................................... 208
G - Code for GENRINC .......................................... 215
H - Code for ELRISK ............................................ 217
I - Code for MKTOPT ........................................... 225
LIST OF REFERENCES ........................................... 236

 

 

LIST OF TABLES

Table m _P_a@
Table 2.1 Three Common Utility Functions. ............................ 35
Table 2.2 Interval Approach Choice Format ............................ 57
Table 2.3 Results of Previous Attitude Measurements .................... 62
Table 2.4 Previous studies in Marketing Risk Management for Farmers ....... 86
Table 3.1 Portion of ELICIT Output .................................. 99
Table 3.2 BUANDINC.DAT file created by GENRINC ..................... 106
Table 3.3 Static Input to MKT OPT ................................... 133
Table 4.1 Static Input to MKTOPT ................................... 137
Table 4.2 Marketing solutions for 5 Utility Functions. ..................... 142
Table 4.3 Pricing Solutions for 5 Utility Functions. ....................... 145
Table 4.4 Changing Put Premiums .................................. 149
Table 4.5 Comparing Price Distribution Functions ....................... 151
Table 5.1 Producer Data ......................................... 157
Table 5.2 Workshop Summary for GENRINC and ELICIT Results ............ 159
Table 5.3 Function Evaluation in CARA Order .......................... 164
Table 5.4 Summary of Producer MKTOPT Results ....................... 170
Table 5.5 Producer evaluations ..................................... 172
Table 5.6 Static Data for Producer CAL3 .............................. 174
Table 5.7 Utility Value Coordinates for Five Farms ....................... 176
Table 5.8 Comparisons of Utility Functions ............................ 178
Table 5.9 Testing Futures Price Biases ............................... 180
Table 5.10 Changing Biases in Basis ................................ 181

 

LIST OF FIGURES

Figure m Page
Figure 1.1 Components of a Modern DSS .............................. 19
Figure 2.1 Comparing Income Distributions ............................ 23
Figure 2.2 Basic Utility Concepts ................................... 29
Figure 2.3 Plotting Bernoullian Utility Curves ........................... 55
Figure 2.4 First Degree Stochastic Dominance (FSD) .................... 71
Figure 2.5 Second Degree Stochastic Dominance (SSD) .................. 73
Figure 3.1 Components of FIRM and their linkages ...................... 95
Figure 3.2 The Case Farm Yield Distribution (pdf) ....................... 98
Figure 3.3 Structure of Situations 1 and 2 in ELRISK ..................... 108
Figure 3.4 Case Farm ELRISK Situations 1 and 2 ....................... 111
Figure 3.5 Output from ELRISK .................................... 113
Figure 3.6 Schematic of Complex ................................... 123
Figure 3.7 Part of the Sample Farm Output ............................ 126
Figure 3.8 Additional MKTOPT Output ............................... 128
Figure 4.1 Case Farm Gross Margin Distribution ........................ 138
Figure 4.2 Five Negative Exponential Utility Functions .................... 139
Figure 4.3 Log-Normal versus Normal Prices ........................... 150
Figure 5.1 Negative Exponential Functions ............................ 165
Figure 5.2 Discrete and Fitted Utility Curves for FRA5 .................... 177
Figure 0.1 Utility Curves for all producers ............................. 196
xi

LIST OF ABBREVIATIONS

Abbreviations Page
ARMS Agricultural Risk Management Software ......................... 89
ASCII American Standard Code for Information Interchange ............... 40
ARA Absolute Risk Aversion a function - R(X) ......................... 32
ARIMA Autoregressive Integrated Moving Average ....................... 45
BASIC Beginner’s All-Purpose Symbolic Instruction Code ................. 47
BEAR Budgeting Enterprises and Analyzing Risk ....................... 90
BOPM Black’s (1976) Option Pricing Model ............................ 47
CARA Constant Absolute Risk Aversion .............................. 36
CBOT Chicago Board of Trade ..................................... 45
CV Coefficient of variation ..................................... 48
CDF Cumulative Distribution Function ........................... 22, 25
DARA Decreasing Absolute Risk Aversion ............................ 36
DEU Direct Elicitation of Utility .................................... 51
D88 Decision Support Systems ................................... 19
DY/dX derivative of the function Y with respect to X ...................... 34
ELRO Equally Likely Risky Outcome ................................ 56
EUT Expected Utility Theory ..................................... 26
E-SD Mean-standard deviation .................................... 76
E-SV Expected value - SemiVariance ............................... 79
E-V Expected value - Variance ................................... 76
E[X] Expected value operator .................................... 28
FIRM Farm Income Risk Management ................................ 6
FSD First degree stochastic dominance ............................. 70
IV Implied Volatility .......................................... 47
IARA Increasing Absolute Risk Aversion ............................. 36
LPM Lower Partial Moment ...................................... 79
MOTAD Minimization Of Total Absolute Deviations ........................ 78
OEB Observed Economic Behavior ................................ 51
pdf Probability density function .................................. 25
GP Quadratic programming ..................................... 77
r2 Correlation coefficient ...................................... 37
R()() - U”(X)/U’(X) called ARA ................................... 31
RP Risk premium ............................................ 29
880 Second degree stochastic dominance .......................... 72
SDWRF Stochastic Dominance With Respect to a Function" (SDWRF) ......... 59
T80 Third degree stochastic dominance ............................ 74
U()() Utility of income .......................................... 28

xii

Abbreviations Page

VAR Vector Auto Regression ..................................... 45
vN-M Von Neumann-Morgenstern (1944), ............................ 54
WFRRM Whole Farm Risk Rating Model ............................... 90
Xce Certainty equivalent ........................................ 29

xiii

 

CHAPTER ONE

INTRODUCTION
1.1 Background ............................................ 2
1.2 The Problem ............................................ 5
1.3 Research Goal .......................................... 6
1.4 Research Objectives ...................................... 6
1.5 Research Benefits ........................................ 7
1.6 Research Methodology .................................... 9
1.7 The Dissertation Framework ................................ 12
1.8 Summary ............................................. 13
APPENDIX TO CHAPTER ONE - Terminology ...................... 14
1.A Risk and Uncertainty .................................... 14
1.8 Marketing Terminology .................................. 16
1.0 Decision Support Systems (DSS) .......................... 18
1

 

1.1 Background

Commercial grain farmers can use several cash market and futures market
instruments prior to harvest to manage crop income risk. The farm problem is "Which
pricing alternatives to use and how many bushels to price, to manage income risk,
(for a particular grain commodity) when production and ending period prices are
uncertain?" Commercial grain farmers face production, futures, and basis uncertainty
resulting in substantial income risks.

Newbery and Stiglitz (1981) noted in their assessment of price stabilization
schemes that: "If the riskiness of agriculture is reduced, it may allow more powerful
incentives to increase output. Price stabilization may therefore generate additional
efficiency gains which are very desirable".1 In an effort to create more ways to
manage income risks, the Commodity Futures Trading Commission has subsequently
approved trading of options on several agricultural commodity futures contracts
(CBOT; 1985, Cox and Rubinstein; 1985). Buying put options2 provides "price
insurance“ for producers that lead to more efficient risk contingency markets. This
means that farmers and elevators can get price insurance, but how much insurance
should they buy, or should they just hedge or sell some of the expected production?

A 1988 survey indicated that less than 5 percent of the producers and less than
half of the commercial elevators were using options on futures contracts in pricing
grains in Illinois (Whitacre and Olmstead, 1988). The survey focused on minimum

pricing contracts which are a cash market instrument based upon options on futures.

 

1p.169

2 Marketing and risk terminology are described in a special appendix to this chapter.

 

3

Sixty-nine percent of the elevator managers surveyed indicated that the major reason
for low use of minimum pricing contracts by producers was a lack of knowledge
about their mechanics and application (an information gap). Several other surveys
showed a minority of United States farms use futures and options directly (Helmuth,
1977; Patrick et al., 1985; Harwood et al., 1987; and Shapiro and Brorsen, 1988).

Patrick et al. (1985) found that acquiring market information was the most
important management response for reducing farm income risk of the 149 farmers
they surveyed (in 12 states). They also found that the farmers surveyed felt product
prices were the most important source of farm income risk. Branch and Olson (1987)
found similar results in a study of Wyoming ranchers.

Arthur Anderson and Company (1982), in conjunction with the University of
Illinois, surveyed 535 commercial Illinois producers. Ninety percent of those surveyed
felt management assistance in marketing would be important in the future. Most felt
present marketing services were inadequate, and nine out of ten felt that marketing
consultants would also be important in five years.

Brown and Collins (1978) surveyed 782 farmers from 10 states, and found that
marketing was the number one informational need. Other survey efforts were
summarized by Hughes et al. (1981) leading to similar conclusions that farmers need
and want improved marketing information.

Batte et al. (1988) surveyed 215 Ohio grain farmers. Sixty-nine percent of the
respondents said marketing information needs were adequately met. One possible
reason for this difference is that respondents were not instructed on the difference
between data and information. Davis and Olson (1985) and Hodge et al. (1984) noted

that data and information are quite dissimilar. Data needs to be processed before it

 

4
can become useful information. The Ohio survey asked for rankings of marketing
"information" sources, where some alternatives suggested were data oriented (e.g.
local newspapers) and other alternatives information oriented (e.g. marketing
consultants) .

Perhaps farmers receive enough marketing data, but desire more marketing
information. If the conflicting findings of Batte et al. (1988) are reconciled as farmer’s
lack of desire for additional marketing data, then there is consensus. In fact, Batte
(1985) suggested "that a new area of emphasis in risk management research be to
improve information quality and quantity. This involves a shift of emphasis from
measuring risk to improving information available to farmers so as to reduce the
uncertainty in the decision environment".3

Surveyed producers and agricultural economists have generally concluded that
farmers need more marketing information in order to manage risk. The introduction of
new pricing alternatives (Le. hedging with options and minimum pricing contracts)
have accentuated this need, especially since these new pricing alternatives involve
"price insurance," and do not set a price for the commodity.

Pre-harvest marketing implies that total production is not known. This is a
much different (and more difficult) problem than postoharvest. After harvest, marketing
becomes a storage and pricing problem, since the quantity produced is known. If
output is known with certainty, the entire crop can be sold and there is no more
income risk due to price. There may remain some small storage risk, if a forward

contract is used to price grain later in the marketing year.

 

3 p. 197

 

1.2 The Problem

Commercial grain farmers can use several cash and futures market instruments
prior to harvest to manage their crop income risk. The producer problem is, "Which
pricing alternatives should I use and how many bushels to price for a particular grain
commodity, when production and ending period prices are uncertain?" This type of
market information is not currently available to individual farmers, except perhaps
through marketing consultants. Furthermore, this question, "How to sell and how
much?" needs to be frequently re-examined during the growing season, as new
market data emerges and growing conditions change. Answers to the "How and how
much?” question, are influenced by the risk attitudes of the producer.

Producers presented with improved market information should be able to more
easily appraise market conditions and more fully comprehend the income risks. With
this knowledge, managers can make more rational decisions related to income risks.
be better able to understand income risks, and through the selection of appropriate
pricing alternatives, manage income risks. Agricultural economists have contributed
substantially to literature on risk theory, decision analysis, pricing alternatives, and
farm records systems, but have yet to combine these efforts into a set of decision
tools to provide farmers with improved farm marketing information. The research
problem is to improve marketing information by developing and testing
microcomputer tools that help farmers consider their risks and decide how many

bushels to price, with each pricing method.

 

1.3 Research Goal

The goal of this research is to design, construct and evaluate microcomputer-
based software components that help farmers evaluate grain market conditions,
production and pricing risks and to evaluate preharvest pricing instruments. Grains
were chosen for their seasonal characteristics, strong market structure and substantial
yield and price uncertainty. This microcomputer decision software is designed to
manage risk through selection of commodity marketing alternatives for a single grain

commodity.

1.4 Research Objectives

Several objectives must be accomplished in order to meet the research goal

These objectives are:

1. To review and summarize relevant portions of systems science methods,
probability theory, risk theory, decision analysis, commodity marketing,
decision support systems, and management literature related to the farmer's
marketing problem. This will help in the selection of methods used to address

the problem.

2. To develop a marketing model, "Farm Income Risk Management" (FIRM)
that will provide improved information to commercial grain producers regarding
income risks related to commodity marketing. This model addresses the farm
problem; "Which pricing alternatives to use and how many bushels to price,

when production, futures and basis are uncertain (for a particular grain

 

7

commodity)?" FIRM will be developed for use in a workshop setting and as a

research tool.

3. To test the usefulness, "workability“ (effectiveness), and whether the
recommendations of the model correspond to previous experiences and

marketing thumb rules.

4. To identify those areas of theory and knowledge that this research has

contributed and discuss research areas that need further exploration.

1.5 Research Benefits

Disciplinary and subject matter work is verified, not only by other related
research efforts, but also by the application of those theories to actual problems. This
research. Problem solving research has a responsibility, to point out disciplinary and
subject matter research areas that need further studying. Subject matter and
disciplinary researchers should benefit from the identification of those economic
issues where further understanding and insight are needed.

Since FIRM will be tested for workability by grain producers, it should improve
their understanding of the risks they face in producing and pricing grain and their
ability to manage those risks. If an "end-user" product Is ultimately developed as an
extension of this research, FIRM users will be able to evaluate grain marketing
decisions more frequently and thoroughly, and manage their income risk more

efficiently.

 

‘ Johnson (1986) further defines workability.

8

FIRM will be a package in the Decision Support System (see Chapter 1
Appendix). As such, its components or modules could be adapted by problem
solving researchers for solving related problems. FIRM could be adapted to other
commodities, livestock, other marketing strategies, non-commodity products and
government commodity program benefits.

FIRM could serve as a teaching tool for farm management, commodity
marketing, applied risk management and/or systems science, by showing the subject
matter components as well as the modeling methods. Appropriate audiences could
be upper level undergraduates and graduate students, as well as extension workshop
participants. Efforts in this area are not explicitly part of the research objectives, but
are realistic possibilities.

FIRM will not be designed to My increase aggregate or individual producer
income over time. If FIRM is successful for individual producers, It will allow them to
manage expected grain income/risk tradeoffs consistent with their desired risk
attitudes. As Newbery and Stiglitz (1981) noted earlier this may bring indirect gains in
efficiency over time. Regarding evaluation of decisions rules, von Winterfeldt and
Edwards (1986) noted:

..rules for decision making should never be evaluated on the basis of their

results (p. 2). the quality of decisions really means the quality of the process

by which they are made, and that can be evaluated only on the basis of
information available before their outcomes occur or become certain. Rational
decisions are made and must be evaluated with foresight, not hindsight.5

If farmers are not currently operating in the area of their desired income/risk

preferences, and/or they are choosing marketing alternatives that are inefficient by

 

 

9

income/risk standards, then successful use of FIRM should bring improved farm
performance. This improved farm performance must be measured by the same
income/risk criteria. If bankers see that a producer is managing risk more efficiently,
cost of capital could be lower and/or increase borrowing capacity might be possible
bringing potential indirect profit improvements in the long run.

Agricultural futures and option markets have been under-utilized by producers,
if agricultural economists are correct in assessing their risk reducing benefits and
costs (see Holt and Brandt, 1985 for a review). FIRM will be able to more completely
evaluate grain pricing mechanisms, such as futures and options (from a risk
standpoint), allowing producers who have not used a particular pricing tool, to easily
consider them. A farmer with little or no understanding of futures and options will
have impetus for learning about futures and options, if these marketing mechanisms
are suggested to him or her by FIRM. Marketing and management consultants, farm
lenders, extension personnel and elevator service personnel could benefit from their
own analysis and use of FIRM, as well as perform analyses for farm clientele.

Testing FIRM on a group of producers will generate empirical information
regarding risk behavior and the efficiency of various commodity marketing alternatives
for the test group. To the extent that the evaluated farmers (and their risky
environments) are similar to farmers in general, these findings may be helpful to other

problem solving and subject matter researchers.

1.6 Research Methodology

Research Methodology is not to be confused with research methods. Machlup

(1978) defined methodology as:

10

The study of the principles that guide students of any field of knowledge, and

especially of any branch of higher learning (science) in deciding whether to

accept or reject certain propositions as a part of the body of ordered

knowledge in general or of their own discipline (science).6
Webster's New World Dictionary (Guralnik, 1972) defined methodology as "the science
of method, or orderly arrangement; specifically, the branch of logic concerned with the
application of the principles of reasoning to scientific and philosophical inquiry."
Researchers may use different methods, but hold similar methodological views, or
hold different methodological perspectives and use similar research methods.
Remaining chapters will discuss research methods, but discussion of the researcher’s
methodology is an important prerequisite to thorough research.

The research methodology employed is predominantly pragmatism and Is an
important reference point for the reader. Many efforts in risk literature are positivistic
or conditionally normative. Baysian approaches to statistics are in fact a cornerstone
of risk theory, and are perhaps best described as conditionally normative. Johnson
(1986) noted that "conditional normativism has the distinct merit of permitting a
positivistically inclined economist to engage in problem-solving and subject-matter
research".7

This research will employ tools common to positivistic or conditionally
normative research, but its pragmatic nucleus is still asserted. Problem-solving
research, particularly involving system science methods and structure, is by nature
pragmatic. Knowledge about values is called normative and descriptive or largely

value free knowledge is called positivistic. While normative and positivistic knowledge

 

6p. 54

7p.86

11

might exist separately, the pragmatist views them as interdependent in the problem
context. Conditional normativists view both types of knowledge, but discount their
interdependence.

Problem-solving results in prescriptive knowledge. The pragmatist relies largely
on the test of workability of the consequences in addition to tests of correspondence,
coherence and clarity when validating his or her research. With those tests in mind,
the product of this research should correspond to related previous knowledge, be
logically consistent, lack ambiguity, but most importantly, work well enough to solve
the problem of risk management described earlier.

Pragmatism has its strengths and weaknesses. Its strengths include ability to
address real problems and the capacity to merge the value and value free sides of the
problem. This somewhat holistic approach also breeds complexity. It is not as well-
suited to problems that are chiefly value free (e.g. physical science research) or
heavily value laden (e.g. social science research). Further weaknesses are that truth
is conditional to the particular problem. In response to these weaknesses, firm level
risk management will necessarily involve both value and value-free information. The
prescriptive knowledge generated for a particular decision-maker will be unique or
conditional to the problem situation. For some research this is a weakness, but in
decision support systems it is a vital characteristic.

Positivists perform tests to accept or reject hypotheses at some specified
confidence level. The test of workability, which is a cornerstone of pragmatism, is not
usually easy to measure. "How well must the decision support system work, and
what percentage of the time must it work well?" are important questions. The

pragmatist must resolve these questions with the same experience, knowledge and

12

intuition that the positivist uses in selecting the appropriate confidence level. For
FIRM the test of workability will be aided by a series of producer workshops that will

include formal and informal surveys of the participants.

1.7 The Dissertation Framework

Chapter one defines the goals and objectives of this research. An appendix to
Chapter one discusses important terminology that is used in the remainder of the
research. The appendix contains three sections of terms. The first section is risk and
uncertainty, the second is commodity marketing, and the third is Decision Support
Systems.

Chapter two examines literature on procedures used to describe the problem
and methods employed in deciding which solutions to the problem are preferred.
Chapter two also contains an extensive review of risk-related literature, followed by a
review of pertinent research efforts. This review will identify advantages and
disadvantages for decision methods to be considered for FIRM, as well as
characteristics of the problem set, that impact the decision methods.

Chapter three presents a more complete description of the problem
environment, the target audience, state and control variables. Chapter three also
presents the FIRM model. A case farm and results of that farm are used to illustrate
how the model operates. Chapter four is model validation. Tests of hypothetical
producers are designed to validate the FIRM model and see if results correspond to
what is already known about risk reduction and commodity marketing.

Chapter five summarizes information about producer participation in the four

extension/research workshops. Risk attitudes of the workshop participants and the

13

marketing recommendations of FIRM are summarized. The later part of Chapter five
presents workability tests, to examine how well FIRM operates with farmer/managers.
Chapter six is a summary and conclusion chapter. Chapter six also presents
the research findings and opportunities for further research.
The computer code for FIRM components is included in the appendix, along

with workshop evaluation forms, workshop data, and utility functions of the producers.

1.8 Summary

Improving the quality of marketing information is an important factor in
reducing farm income risks, according previous research efforts. This research will
formulate, document and test decision support system (DSS) modules for grain
producers to manage farm income risks through selection of pre-harvest commodity

marketing alternatives. Research goals and objectives were presented in this chapter.

14
APPENDIX TO CHAPTER ONE - Terminology

The following subsections describe fundamental terminology of the important
subject matter areas. These brief subsections are included here rather than with the

remainder of the appendices at the end of the dissertation, to encourage their reading.

1.A Risk and Uncertainty Terminology

Any work involving decision-making in conditions of risk and uncertainty would
be incomplete without clarifying the author’s use of terms "risk" and “uncertainty."
Knight (1921) made an early attempt to differentiate between risk and uncertainty. He
felt risky situations were those where the decision-maker had empirical information
available to develop more objective probabilities. Uncertainty involved less familiarity
with the situation leading to subjective probabilities. See Debertin (1986) for parallel
ideas.

To Knight, a coin toss or roll of the die would be viewed as risky, not uncertain.
Consider the event of whether a particular person will be rained on one week from
today. If that person were a meteorologist, such an expectation would likely be based
on a greater deal of familiarity and therefore characterized as risky. Using Knight’s
terminology, for most persons the event of rain one week hence is uncertain.

Robison and Barry (1987) argued that whether the decision-maker has
familiarity or empirical evidence regarding the situation, he or she must still form
personal probabilities regarding the possible outcomes and form a decision (See also
Anderson et al., 1977). With this argument, the distinction that Knight (1921) used

becomes less useful. Robison and Barry (1987) found it more valuable to consider

 

15
risky events as a subset of uncertain events. Uncertain events are those which result
in two (or more) possible outcomes or states. According to Robison and Barry (1987)
risky events are "those uncertain events whose outcomes alter the decision-maker's

n8

well being By this distinction, a mere coin toss is an uncertain event that becomes
risky to the person(s) involved when differing rewards or punishments are determined
by the outcome of the toss.

Both attempts to differentiate risk and uncertainty have intuitive appeal as well
as limitations. Robison and Barry (1987) left little room for economists use of the
word uncertainty, except where "risky" would more accurately describe the situation.
Uncertain events which are not risky would be trivial to the economist and the
decision-maker. Using this more recent distinction only risky events have utility for
economists.

In this dissertation, the terms risk and uncertainty will be used interchangeably.
This does not mean the terms are perfect synonymous. By intuition, risk implies
potential for welfare change more so than uncertainty. Throughout this text, few
uncertain events will be discussed that hold no welfare consequences for the decision-
maker. This is not an admission that the difference between risk and uncertainty is
insignificant or does not exist. Stronger conclusions were reached by Sonka and
Patrick (1984) when they state that "the distinction between risk and uncertainty is
unimportant".9

Foregoing Knight’s (1921) distinction between risk and uncertainty, creates the

need for terms to delineate situations where probabilities are formed with greater or

 

8p. 13

9p. 94

 

16

lesser confidence. With limited meteorological data, the chance of next year’s April
showers exceeding seven inches in Washington DC. could be elicited from most
persons, with very little confidence. Making odds on a coin toss coming up heads is
likely done with much greater confidence. This author will use the terms objective
probability to represent the coin toss type situations and subjective probability to
describe cases like the April showers example.

Of course, decision-makers almost never face probabilities that are purely
objective or subjective, but rather on a continuum between the extremes. Knight
(1921) faced this same difficulty with the terminologies he chose, and there seems
little way to clearly describe all of the situations between the extremes. The practical
solution is to describe situations that are largely “risky" in Knight’s (1921) terms as
objective, and those he would have classified "uncertain" as subjective probabilities.
This same nomenclature and similar arguments were also presented in Bessler (1984
and 1985). Decision-makers often integrate objective and subjective probabilities in

decision analysis. Thus the two terms become useful, but are not independent.

1.8 Marketing Terminology

Agricultural Economists have used the term "marketing" to include every item
passing in and out the farm gate, and on to the consumers' table or textile mill.
Subtopics of marketing include, transportation, distribution, processing, standards and
grading, wholesale and retail sales pertaining to food, fiber and other agricultural
products and inputs. There is little doubt that the subject of marketing covers vast
territory. Only a small portion of this broad topic is addressed in this particular

research. This segment involves farm-level marketing of grain commodities such as

 

17
com, soybeans and wheat. The decision support system (DSS) to be developed will
deal primarily with pricing these commodities, through standard pricing alternatives
(e.g. futures hedging and cash forward contracting).

Pricing will be used in terms such as pricing tools, pricing alternatives or
pricing commitments, to indicate the process of establishing a price (or portion of the
price) for some number of bushels, through a contractual agreement, for a specified
delivery or contract period. Marketing, as used by this author, is a superset of pricing
that could include different time periods, as well as a combination or portfolio of
several pricing alternatives. A database of previous pricing commitments for the farm
would best be described as a marketing database, since the portfolio of commitments
could involve various time periods, several pricing alternatives and more than one
crop.

Several commodity marketing terms have local meanings, and may be
understood differently in different parts of the country. In this document the
terminology used in the Chicago Board of Trade (1985) Commodity Trading Manual
will be used where possible. Some critical terms are summarized and boldface in the
remainder of this section.

There are two major markets, the cash market and the futures and options
markets. The cash market involves delivery of the physical commodity, either now or
at some date in the future to a specified location. Any two individuals can make an
exchange in the cash market. An exchange made now is called a gm sale. There
are cash contracts for future delivery. Such contracts may include the entire price or

value (called a forward contract) of the commodity or some agreed upon portion of

 

 

18

the price (such as a basis contract). Forward contracts and spot sales can take
place in any volume and location agreed upon by both the buyer and seller.

Futures markets are highly structured forward markets for standardized
commodities, at specified months, uniform quantities and federally supervised
locations. Futures contracts are bought and sold on the futures markets. The buyer
[seller] of a futures contract must sell [buy] the contract back before It expires, or
upon contract expiration pay the futures contract price and take possession [receive
the contract price and make delivery] of the same quantity and quality of the
commodity at a terminal location.

Options can be purchased [alternatively sold first] on the underlying futures

contract for a specified strike price at a negotiated premium. A put option [fl

 

option) gives the buyer the right, but not the obligation, to sell [buy] the underlying
contract in the futures market at the strike price. Options are traded on an underlying
futures contract. They serve as futures market’s price insurance.

The basis (in this research) is defined as the cash market price minus the

 

appropriate futures market price, at a specific location and time. The basis for spot
sales today is the spot price minus the nearest futures contract price. The basis for
January soybeans is the January forward contract price minus the January soybean
futures price. The soybean, corn and wheat basis is usually a negative number in the

major grain producing states.

1.C Decision Support Systems (DSS)

Sprague and Carlson (1982) described DSS as computer-based systems that

help decision-makers confront ill-structured problems through direct interaction with

 

19

data and analysis models. More specifically, Sprague and Watson (1983) outlined the
conceptual design of a DSS and its components as shown in Figure 1.1. The three
principle components of a DSS are the data base, model base and decision-maker.
The integration of data and models into a DSS reduces data entry, since production

and financial records are available to the model base.

 

 

 

 

 

 

 

 

 

 

 

 

     
      

 

 

 

 

 

 

 

 

 

 

T STRATEGIC
R FINANCE INTERNAL MODELS
A DATA BASE MODEL BASE
N DATA —— —— TACTICAL
S PRODUCTION MANAGE- MANAGE- MODELS
A MENT MENT
C OPERATIONAL
T MARKETING SYSTEMS SYSTEMS MODELS
I
0 MODEL
N PERSONNEL BUILDING
EXTERNAL BLOCKS AND
D SUBROUTINES
A RESEARCH DATA
T MODEL BASE
A OTHER DECISION-
MAKER
DATA BASE

Sprague & Watson (in House;1983, p. 22)

Figure 1.1 Components of a Modern DSS

House (1983) is a good source for further DSS concepts and examples. Harsh
(1987A and 19878) detailed DSS in the context of agriculture, including a description
of the Integrated Decision Support System project at Michigan State University. FIRM
is part of this larger DSS project which is being designed to operate on powerful

micro-computers (Intel 80286 and 80386 based machines).

 

CHAPTER TWO
HOW TO DESCRIBE AND DECIDE:
A LITERATURE REVIEW

2.1 Risk Principles .......................................... 24
2.1.1 Probability Principles .................................... 25
2.1.2 Expected Utility Theory (EUT) ............................. 26
2.1.3 Measures of Risk Aversion ............................... 30
2.1.4 Utility Functions ....................................... 34
2.2 Generating Yield Distributions .............................. 38
2.3 Representing Distributions ................................. 42
2.4 Market Efficiency ........................................ 43
2.5 Generating Price Distributions .............................. 46
2.5.1 Futures Price Distributions ................................ 46
2.5.2 Basis Distributions ..................................... 50
2.6 Eliciting Risk Attitudes .................................... 51
2.6.1 Methods ............................................. 51
2.6.2 Results of Risk Elicitation ................................ 61
2.6.3 Problems with Previous Research .......................... 63
2.7 Decision Rules and Efficiency Criteria ........................ 67
2.7.1 Maximize Expected Utility ................................ 68
2.7.2 Stochastic Dominance .................................. 70
2.7.3 E-V, MOTAD, M-SD, and Semi-Variance ..................... 76
2.7.4 Target MOTAD and Lower Partial Moments ................... 79
2.7.5 Safety First Decision Rules ............................... 83
2.8 Previous Efforts ......................................... 84
2.8.1 Risk Efficiency Studies - Research Oriented ................... 85
2.8.2 Micro-Computer Based Simulations ......................... 89
2.9 Summary ............................................. 91
20

 

.n

21

Recall from section 1.2 that the farmer's problem is 'Which pricing alternatives
to use and how many bushels to price, (for a particular grain commodity) when
production is uncertain?‘ Such a problem implies uncertain futures price, basis, yield
and total costs.

The purpose of this chapter is to review literature to help find 0(2); where, x is
uncertain crop income for a single crop, and DO is a decision rule or efficiency criteria,
or some method to measure of the desire for income (x) from the crop (under the
related marketing problem).

For the case of deciding pre-harvest marketing...

D(x) = g(f,6,y,C(a),c(y,a),a,S,m,n,Cov(i,6,y)) (2.1)

where: 00 decision method - may depend on more than 2
2 income distribution
9 the marketing function
5 basis distribution
i futures distribution
yield distribution
(1 ..m) subscripts for the particular pricing methods
n(1..m) the number of bushels to market in each of the m methods
C direct costs per acre (seed, chemicals, fuel, not land)
c yield dependant variable costs (on a per bushel basis)
a acreage (cash and owned plus portions of share crop)
Cov(f,6,y) covariance matrix between distributions
8 static market information. Static information involves interest rates,
today's cash market quotes, option premiums, time until option
expiration and more. The control variables are n(1..m).

For this decision domain, the direct costs (C) do not vary with yield, but would
vary if a different crop were grown or a different yield target. Often direct costs for

crops are allocated on a per acre basis. Per bushel costs for the problem described

include harvesting, trucking, drying and other handling expenses.

 

 

22

Equation 2.1 is a general form because selection of a particular DO will affect a
more specific formation of the problem. It is possible that other factors should be
considered besides uncertain income. These factors could include, but certainly are
not limited to, the decision-maker’s desire for income, leisure, debt, financial
constraints and understanding of pricing methods. Without an intrapersonally-valid
common denominator between these other factors, no unique solution may exist.
Multiple criteria decision making is possible (if other criteria are deemed important),
but cannot guarantee a solution exists, and if one exists, that it is unique (Manetsch
and Park;1988). For the marketing problem uncertain income was deemed the
important decision factor, because most other factors would not be affected from one
marketing plan to another. While financial constraints may be very real, the best or
acceptable D0 should have ways of working with such constraints. Depending on the
decision methods chosen, it may be important to know the attitudes the producer has
about income/ risk tradeoffs.

This chapter begins with overviews in risk principles, probability principles, and
expected utility theory. In a later section the right hand side of equation 2.1 will be
discussed further, with special focus on how uncertain variables can be evaluated and
represented. The chapter continues with decision rules or ways to decide, followed
by previous related research, and finally a summary.

Uncertain crop income can be represented by a 'Cumulative Distribution
Function' (CDF) in Figure 2.1. A CDF shows the probability of getting equal or less
income at every income level. Changing the number of bushels to be priced in each
of the pricing alternatives considered in the 90 function (above), could give different

income distributions, like those in Figure 2.1. Any of the three distributions shown in

 

23
Figure 2.1 could be the 'best' depending on how they are evaluated. Some
evaluation methods or decision criteria offer analysis for large classes of producers

and others are very specific for the individual producer and their attitudes about risk.

 

 

0.9‘
0.8-
0.74

Y

F’

0')
1

0.5“

ProbabflH

.0 9
u p
l l

0.2‘
0.1"

 

 

 

 

0 10 20 30 43 :30 sin 76 80 90 100
Income (x)

 

 

 

Figure 2.1 Comparing Income Distributions

Before constructing “Decision Support System' (DSS) tools to manage income
risk through commodity marketing, there are a number of background areas that need
examining. Exploring these areas will hopefully lead to a more objective selection of
decision methods (the 'D()'). This should help develop a common understanding of

numerous terms in risk and decision theory, as well as introductory probability theory.

24
In addition, this research will certainly benefit from a review of methods previously
developed, even if many of them are not used.

Decision theory, with special attention to decision rules, risk efficiency and risk
preference elicitation will be a critical part of the research foundation. An
understanding of commodity markets and price behavior, with particular attention to
market efficiency, futures price volatility and how to estimate and represent uncertain
variables are prerequisites to the research.

In this chapter there are a number of technical terms which are used to
describe risk, but which should pp; be used with farmers or decision makers.
Decision theorists create games, gambles or lotteries with probabilities of payoffs or
outcomes. The word 'games' may accurately describe the situation for a theorist, but
perhaps not for the manager or decision-maker. Managers make plans and
selections based on the situations they face. They may get good results or bad, but
they don’t 'play games.‘ (See Musser and Musser;1984 for more) In this chapter the
theory terms will be used, giving way in later chapters to terms that represent

management activities.

2.1 Risk Principles

Daniel Bernoulli (1731) proposed the idea that people act as if they make risky
decisions by adding up the utilities times the probabilities of each possible outcome.
The Latin term he used for this process translates to “mean utility.‘ In his collection of
letters and papers he demonstrated this particular view with several examples.

Except for Bernoulli’s early work, risk is a relatively new topic in economics,

with much of the research progress being made after World War II. The subjects of

 

25
risk and decision-making are shared across several disciplines including (but not
limited to) management science, economies, medicine, psychology, and statistics. In
this section the focus on risk is largely from the prospective of economics,
management science, and statistics. Previous efforts and terminology related to risk

form an important foundation for the development of the DSS components to follow.

2.1.1 Probability Principles

Two terms critical to probability and risky decision-making must be defined.
The 'probability density function' (pdf), denoted by f(x) (where x is the uncertain value,
of a variable X), is f(x) = p[X=x]. Where x = x,, x2..., and the sum of the probabilities
for all x| under consideration is one. Lowercase p indicates the probability of the
event in the subsequent bracket. A related function called the 'Cumulative Distribution
Function' (CDF), and denoted by F(x) is simply, F(x) = p[X< =x]. Where x = x,, x,,..
For continuous random variables, the pdf is a function whose probability at a
particular value x is infinitely small, since X is continuously divisible. However, a
common practice with continuous variables is to form histograms of equal interval.
The CDF for continuous random variables is expressed as an integral of its related pdf
function, taken from minus infinity to some value of the variable X. The value of the
CDF probability is bounded by zero and one.

With continuous random variables only the CDF can be graphed with
numerical values on both axes. The p[X = x] for a continuous variable is infinitely
small, but pdf's are often sketched for continuous variables with no values on the
probability axis. For most persons, probabilities (values of the pdf) are more easily

understood than the CDF (von Winterfeldt and Edwards, 1986). For this reason,

 

26
empirical work with continuous random variables usually involves converting the
distribution to a discrete one and eliciting probabilities of intervals. An alternative is to
elicit percentiles, where the 20th percentile is the value of X for which F(x) = .20, and
the 50th percentile is the median of the distribution. With enough elicitations a
discrete CDF is formed which may then be smoothed if the underlying variable is
continuous.

The kth moment of a probability distribution about the origin is E[X"]. Thus,
when k=1, the first moment of a distribution about the origin is the mean of the
distribution. Higher moments about the origin are seldom discussed. More useful
measures are higher moments about the mean. The kth moment of a probability
distribution about its mean is M" = E[ X - E()() 1". Where M" is the kth moment of a
distribution about its mean, X is a random variable and E represents the expected
value of the bracketed expression. The second moment of a distribution about its
mean (M2) is the variance. M“ is a measure of symmetry or skewness. If M3 = 0, the
distribution is symmetric (e.g. Normal distribution) and M‘ is kurtosis. Kurtosis
modifies the normal distribution to give it a thinner higher peak and thicker longer
tails. Skewness and kurtosis are used in testing normality of futures price movements

(Gordon, 1985; Gordon and Heifner, 1985; Mann and Heifner, 1976).

2.1.2 Expected Utility Theory (EUT)

'Expected Utility Theory' (EUT) is the cornerstone for most risk research in
economics. In fact, while Bernoulli did not name his concepts EUT, he easily could

have. A number of authors have referred to risk related utility functions as Bernoullian

 

27

utility functions (Lin and Chang;1978, Buccola and French;1978, Ramaratnam et
al.;1986).
Numerous authors, (von Neumann and Morgenstern, 1944; Friedman and Savage,
1948; Luce and Raffia, 1957; and Machine, 1983), have contributed to the theory
through fundamental axioms and deductions that result. Summaries of EUT primary
axioms and implications can be found in Robison and Barry (1987), Anderson et al.
(1977), Machine (1983a, 1983b), and Copeland (1983). The following is a brief
overview.

Using Machina’s (1983a) nomenclature, the three primary axioms of EUT are
(1) completeness, (2) transitivity and (3) independence. Completeness (by some
authors called 'ordering of choices') simply means that any two choices (of all
available choices) can be compared; and the decision-maker will either prefer one of
the two choices or be indifferent between the two choices. Decision makers may
weakly prefer or strongly prefer one item over another. Weak preferences indicate
either preference or indifference, while strong preferences indicate no indifference and
only preference.

The transitivity axiom says, 'if a decision-maker weakly prefers choice A to B,
and weakly prefers choice B to C (with at least one strong preference), then choice A
must be strongly preferred to choice C. This axiom indicates that decision-makers
have the ability to ordinally rank preferences.

The first two axioms deal with preferences for choices under certainty, although
they imply individual’s preferences may be represented by a “preference functional"
defined over a probability distributions. In other words, the decision-maker’s choices

could be between gamble A and gamble B. The most critical and often questioned

28
axiom is that of independence. To quote Machina (1983a), the independence axiom
is: 'a risky prospect A is weakly preferred (preferred or indifferent) to a risky prospect
B if and only if a p:(1 - p) chance of A or C respectively is weakly preferred to a
p:(1 - p) chance of B or C, for arbitrary positive probability p and risky prospects A, B,
and C'.‘ This standard independence axiom implies that person’s preferences are
linear in the probabilities. Machina (1983a and 1983b) details a more general and
recent form of the independence axiom which extends the breadth of the EUT.

From these three axioms come simple, but important theorems. The theorems
are proven in most of the risk literature previously cited, as well as in Varian (1984). If
a decision-maker obeys the axioms, then the utility of a gamble is equal to the sum of
the utility of individual outcomes times the probabilities of their occurrences. This
implies a Bernoullian utility function representing decision-maker preferences and
subjective probabilities formed by the decision-maker who has accepted some
gamble from a set of possible gambles (the results of Theorem #1).

A related theorem (#2), is that 'for any gamble there exists some certain
outcome (called a certainty equivalent), such that the expected utility of the gamble
and the utility of the certain outcome will be equal, and the decision-maker will be
indifferent between the gamble and the certain outcome (measured in the income
units).'

The idea of a certainty equivalent for a gamble was described in Robison and
Barry (1987) and is shown graphically in Figure 2.2. The horizontal axis is the income
(or lottery payoffs or just X), the utility of income (U()()) is plotted on the vertical axis.

E[X] is the expected gamble income and is proportionally distanced between the two

 

p.2

 

29
lottery payoffs according to their respective probabilities. In Figure 2.2 the gamble is
a .5 probability of an $80,000 income and a .5 probability of $40,000. With a utility
curve (A-B) in Figure 2.1, the E[U] for the gamble is 200. This is simply
.5 U(80,000) + .5 U(40,000). The "certainty equivalent" (Xce) is the amount of certain
income whose utility would equal the utility of the gamble. In Figure 2.1 the Xce is
$50,000. There is a $10,000 difference between the Xce and the E[X] due to the
degree of risk aversion (bend) in the utility curve. This $10,000 difference is called the

"Risk Premium" (RP).

 

 

700
500 - D
500 -
400 ~
300 ~
200 — r
100 -

 

 

UUUTY

 

-100“
-200-

300 A Xce E[X]
-40 0 | I I I I
30 40 50 60 70 80 90 100 110 120

INCOME
(Thousands)

 

 

 

 

 

 

 

 

 

Figure 2.2 Basic Utility Concepts

 

30

A decision-maker with a concave utility function like that shown in Figure 2.2
would be willing to accept some certain income less than E[X] rather than accept the
gamble. This behavior is called risk averse since E[X], the expected income of the
gamble (measured in X), exceeds the Xce of the gamble.

Persons with utility functions that are globally (locally) concave in income
would be globally (locally) risk averse. Utility function convexity if global (local) would
show a global (local) preference for risk. Similar arguments hold for linearity of the
utility function implying risk neutrality.

A utility function like Figure 2.2 is called a Bernoullian or sometimes von
Neumann-Morgenstern (1944) (vN-M) utility function. Bernoullian utility functions are
not equivalent to utility functions in traditional consumer demand theory because the
former involve uncertainty and risk preferences, where the latter do not. In addition,
Bernoullian utility functions are cardinal, since they are unique up to a linear
transformation of the utility measurement. Utility functions in modern consumer theory
are ordinal and, therefore, unique up to any monotonic transformation. Risk theory
seldom involves ordinal utility functions of consumer theory, but relies heavily on the
Bernoullian utility function. As a result, all references to utility in this document will be
to Bernoullian utility, unless it is specifically stated that the utility is of an "ordinal"

nature.

2.1.3 Measures of Risk Aversion

Utility is measured on an arbitrary scale. As Varian (1984) mathematically
showed, changing the location and/or scale of utility (a linear transformation of the y

axis) results in an identical expected utility function (expected risk behavior). Robison

 

 

31
and Barry (1987) showed this graphically by shifting each point on the utility function
in Figure 2.2 some equal distance upward (a change in location). When this is done
the certain equivalent for the two utility functions (persons) remains identical. Similar
graphical evidence can be made for changes in the utility scale. This lack of
appropriate units with which to measure utility means that cardinal measure of utility is
not an important characteristic for measuring risk preferences, but rather the bending
rate of the utility function.

Using Figure 2.2, it is easy to see that as the utility function bends more
sharply, the certainty equivalent of the gamble is farther from the expected outcome of
the gamble (both measured in X). The second derivative of the utility function plays
an important part in measuring the rate of bending and, therefore, risk aversion. Most
decision-makers operate in a range where more is preferred to less; thus U'()() > 0
(the first derivative of income utility, is positive). The utility function is upward sl0ping
when income (X) is plotted on the horizontal axis and U(X) on the vertical axis.
Knowing U’(X) > 0 says nothing about whether the decision-maker is even risk averse
or preferring, since the utility function could be concave or convex.

When the second derivative of income utility, U"(X), is negative (positive, zero)
the decision-maker is risk averse (preferring, neutral) as previously discussed, and the
utility function is concave (convex, linear). The size of U"(X) indicates the degree of
bending in the utility function, but because utility is unitless, U"(X) needs to be
"normalized." Pratt (1964) set R(X) = - U"(X)/U(X) called an "absolute risk aversion"
(ARA) function. R(X) can be useful for measuring degrees of risk aversion /preference

when the decision-maker conforms to the realistic axioms of EUT.

 

 

32

The value of the ARA function, R(X), evaluated at a particular income is called
the ARA coefficient. The ARA function is not affected by linear transformations of the
underlying utility functions, allowing some comparison of risk behavior across
individuals. However, the ARA coefficient is a local measure of risk aversion that is
dependant upon the income level at which it is being measured (Raskin and Cochran;
1986). This is true for all reasonable utility functions, except the negative exponential
utility function and linear functions of risk (risk neutral).

ARA coefficients for two different individuals (different utility functions) allow
comparison of risk attitudes, provided that X is measured in common units, the values
of X at which the ARA is calculated and interpretation of X are equivalent for the two
persons. The larger the value of the ARA coefficient the greater the degree of risk
aversion, and the expected income from a gamble will be greater than the certainty
equivalent (for positive R(X)). The equation is RP = E[X] - Xce, where RP is the risk
premium, E[X] is the expected income from the gamble, and Xce is the certainty
equivalent of the gamble (all measured in units of X). The more positive (negative) the
value of the ARA coefficient the more risk averse (preferring) the decision-maker is,
and the larger (smaller) the risk premium. When the ARA coefficient is zero, the
decision-maker is locally risk neutral and the risk premium is zero. Such a person is
locally a profit maximizer.

R(X) is a local measure of risk aversion, but RP can be applied at any income
level. In fact, if a person is offered a discrete lottery of winning or losing $10,000
based on a fair coin toss, the value of U’(X) evaluated at the mean (zero) may be zero
leaving R(X) undefined, but the RP will always be defined. If a subject indicated he or

she would pay $50 to avoid such a gamble, then the Xce = -$50, the E[X] = 0 and

33

RP = $0 - ($50) or $50. Thus, in some situations RP is more useful as a risk
measure than R(X). This issue is useful in designing risk analysis software, since RP
has units that producers should understand. Lin and Chang (1978) outline many
reasonable utility functions, most of which have R(X) values that become undefined
when evaluated at certain income levels.

To this point utility has been a function of net income. It is possible to rewrite
utility to make it a function of wealth. The inclusion of wealth into utility results in the
same value of the ARA coefficient when the starting wealth or endowment is constant
(see Raskin and Cochran; 1986, theorem 2). If W = X + k, where W is wealth, X is
uncertain income, and k is the endowment (a constant regardless of the gamble),
then R(W) = R(X). This is true because dU(W(k + X)dx) is U’()() and k, being
constant, drops out. Thus U’(X) = W’(X+k) when k is constant. The second
derivatives follow from the first and the R(X) = R(W). When k is allowed to change, as
in examining a decision-maker at two different wealth levels, or when X has some
correlation to k during the uncertainty period, then R(VV) will not equal R(X), (since k
can’t drop out). If the beginning endowment changes due to uncertain income from
the crop under consideration, before the crop is sold, then the utility should perhaps
be called Enterprise Utility. Other factors such as excellent income from wheat, might
alter mid-season risk attitudes for corn and soybeans. These same arguments apply
to gross margins, where some static variable representing fixed costs such as land, is

no longer needed, just like the fixed endowment (k).

 

 

2.1.4 Utility Functions

Table 2.1 shows three commonly used utility functions; their related absolute
risk aversions; R(X), and the derivative of the absolute risk aversions with respect to X,
where R’(X) = dR(X)/dX. A lower case d is used for partial derivatives, so that dY/dX
is the derivative of the function Y with respect to X.

The quadratic, semi-logarithmic, and negative exponential are often used in
analytical risk research as approximations for decision-maker utility functions. The
semi-logarithmic is the least common of the three, owing to its inability to deal with
negative incomes. It was proposed by Bernoulli (1738) in one of the first discussions
of utility functions. In the problem Bernoulli presented (called the St. Petersburg
paradox), all of the income possibilities are positive so the semi-logarithmic provides a
reasonable solution to that problem.

The quadratic utility function is commonly used in expected value-variance
models (E-V models) for the following mathematical properties. If U = X - b*(X2),

then from statistic principles we know:

E[U] = E[X] - mew] (2.2)

and, E[X2] = V[X] + (E[X])Z, where V[X] is the variance of X. Subbing this into

equation 2.1 gives:

E[U] = E[X] - b"(E[X])“ - b*V[X] (23)

Using equation 2.2, dE[U]/dV[U] (change in expected utility with respect to variance,
holding expected outcome constant) is negative if b > 0. This implies that expected

utility will be increased if the variance of income is reduced. Also, if b is sufficiently

 

35

small (1 /[2b] > E[X]), increasing E[X] will increase E[U], if V[X] is held constant. That

is dE[U]/dE[X] will be positive. The conclusion is that if utility is quadratic then utility

can be increased by increasing expected outcome and decreasing variance, which

are the criteria for E-V efficiency. However, there are also problems with quadratic

ufiMy.

Table 2.1 Three Common Utility Functions.

 

UTILITY FUNCTIONS ARA function
(b,c > 0, and constant)
X = income R(X) = - U"/U’

SEMI - LOG

U = b*In X 1/X
st. X > 0

QUADRATIC

u = bx - cx2

2c/(b-2cX)
NEGATIVE EXPONENTIAL

U = - ce(-bx)

2

 

A positive value of b Implies risk aversion, which is a common behavior in

applied risk research. For the EV criteria not to contradict EUT, income must remain

sufficiently small for quadratic utility. At high expected income levels dE[U]/dE[X] will

be negative so further increases in income, will decrease utility. For nonsatiable

36
goods like income, this would seem to be an unreasonable conclusion. With R'(X)
always positive, quadratic utility implies 'Increasing Absolute Risk Aversion (IARA)
behavior. It is more commonly believed that most decision makers exhibit
"Decreasing Absolute Risk Aversion" (DARA). This later behavior indicates that as the
income is increased, willingness to take risks decreases. Robison and Barry (1987)
contains a more extensive presentation of IARA, CARA and DARA.

Quadratic utility is often used in applied risk research in spite of the problems
mentioned (see Miller;1986, and Alexander et al.; 1986). This is largely due to the
analytical simplicity of the function. Its users also point out that, by Taylor series
expansion about a point, any function can be approximated by a quadratic (Chang;
1984). The E-V model applies under other conditions besides quadratic utility. A
more complete review of the EV model appears in section 2.7.3.

The negative exponential function has two strong features that make it
common in risk research. The first feature is its "Constant Absolute Risk Aversion
(CARA)." If a decision-maker has a negative exponential utility function (or a linear
transformation of one) and behaves according to the EUT axioms, then the value of
the ARA coefficient will be globally constant regardless of the decision-maker’s wealth
level, or the scale of the gamble. There is only one other CARA function available,
and that function is the special case of perfect risk neutrality (a linear function). If two
decision-makers are both CARA, then it is simple to compare their risk behaviors by
simply comparing their ARA coefficients. These comparisons can only be made for
the special case of CARA, when the income under consideration is measured in the

same way.

37

The second reason the negative exponential utility and its CARA properties are
commonly used is that they are reasonably supported by empirical research.
Ramaratnam et al. (1986) elicited risk preferences from 26 producers and fit the utility
observations to four different utility functions for each producer. The negative
exponential gave a better fit (higher r3, correlation coefficient) than the quadratic and
semi-log functions previously mentioned, and was also superior to the log-linear
function.

Two properties of CARA utility should be noted. Several surveys have shown
that as producers move to higher wealth, risk aversion is not constant but usually
declines (DARA). Examples are Binswanger (1980), Dillon and Scandizzo (1978),
Patrick et al. (1981), and Moscardi and de Janvry (1977). Secondly, as gambles
approach large negative values, the slope of the negative exponential utility function
(dU(X)/dX) approaches infinity. Kahneman and Tversky (1979) felt that dU(X)/dX
should approach zero at large income losses. Such rational indicates that if there is a
possibility of losing a $100,000 then what is another $1,000. To demonstrate suppose
a person must face Game 1 below. How much would the person be willing to bid to
avoid lottery A and play the better B? Most decision-makers will have a very different
risk premium (bid to choose lotteries) regarding Game 1 and 2.

Play this... lottery A: .5(A=$0) ~ .5(A=$-102,000)

or pay to

Game 1 play this
better game. lottery B: .5(B=$0) ~.5(B=$-101,000)

How much will you pay to avoid lottery A and buy the safer B ?

 

38
Play this... lottery A: .5(A=$0) ~ .5(A=$—2,000)
or pay to
Game 2 play this
better game... lottery B: .5(B=$0) ~.5(B=$-1,000)

How much will you pay to avoid lottery A and buy the safer B ?

Lottery outcomes are separated by "~', with payoffs in parenthesis, preceded
by their probabilities. In both games above, lottery B has an expected value of $500
more than lottery A. Intuition suggests decision-makers might be risk neutral when
faced with two possible large losses like game 1. If so, they would only pay some
small amount for the only slightly safer B. The same decision-maker could be
substantially more risk averse (compared to game 1) when faced with the possibility of
breaking even, versus moderate losses in game 2. Bids for the safer B in game two
will likely be higher than for game 1.

Lin and Chang (1978) have detailed and summarized methods for estimating
several additional functional forms for utility. Buccola and French (1978)

demonstrated a method for estimating negative exponential utility functions.
2.2 Generating Yield Distributions

Having reviewed the theory necessary for the remainder of this chapter, it is
time to begin a study of how the right hand side (descriptive) of the marketing model
can be represented for problem solving. Recall that the marketing model was:

(it) = g(f,6,y,C,c(y,a),a,S,m,n,Cov(f,6,1]))

To solve for x, the uncertain 1,6 and 9, must be forecasted or estimated. In

this section, uncertain yield (9) is examined. In the following section, ways to

represent uncertain variables are discussed.

 

39

The decision model should be designed to run several times through the
growing season. Yield uncertainty could be quite high at planting time. As the
season progresses, more information is revealed, and the yield becomes more
certain. A mid-season forecast should include all the crop development to date, plus
the uncertainties related to the remainder of the season. To capture this process with
historical data like USDA yields or farm records would be nearly impossible. The only
reasonable sources in this situation are objective professionals or farmers.

One method to assist producers in giving mid-season personal probabilities
would be the incorporation of a plant growth model and a weather simulator. With
such an addition, it would be possible to enter the weather to date (retrieve it from the
database) and Monte Carlo the remaining weather for the crop year. By simulating
enough such "years of remaining weather", it would be possible to form probability
distributions that are conditional upon the weather to date. Such a model would need
to consider the soil type, previous weather, date of planting, the time to maturity of the
variety and the latitude of the growing area. There are also many other factors that
might also be important. These include the manager’s skill, soil fertility, and
supplemental drainage and irrigation. This alternative seemed impractical to employ
directly, but research with crop growth models (like Ritchie; 1986) could be helpful in
this area by providing guidelines for changes in mid-season yield uncertainty.

Previous research and software development on eliciting yield probabilities has
already been carried out. Pease and Black(1988) designed a software program called
ELICIT to collect discrete pdf’s from farmers. ELICIT is used in the Agricultural Risk
Management Simulator (ARMS) Version 3.x. as one method of establishing yield pdf’s

for analysis of Federal All-Risk Crop Insurance.

 

 

40

The "conviction scoring" method used in ELICIT involves first selecting yield
intervals, such as five bushels per acre for soybeans. Next, the user selects the yield
interval he or she expects to most likely receive. Suppose the user chose the interval
30-35 bushels per acre, as the most likely to occur. In this interval the user enters a
score of 100. From there, the user moves to adjacent intervals and asks, "if the
"anchor" interval occurred 100 times, how often would each of the other intervals
occur?" Other intervals are evaluated in a similar manner. These numbers are re-
indexed to give a discrete pdf that is graphed for the user. Users may then go back
and re-examine their conviction scores. ELICIT stores the discrete pdf, CDF, mean,
and standard deviation in an "American Standard Code for Information Interchange"
(ASCII) text file named by the user.

Pease et al. (1990) described the conviction scores method of elicitation in
greater detail. They concluded growers were very interested in this activity.
Producers with very little understanding of probabilities, could use the conviction
scores quite successfully. The following equations show how ELICIT works. Suppose
a decision-maker indicated the following values (in brackets) for the five bushel
increments in soybean yield: 15-19.9bu [5], 20-24.9bu [10], 25-29.9bu [20],
30-34.9bu [40], 35-39.9bu [1001, 4044.960 [40], 4549.960 [20], 50-54.9bu [5]. The
numbers in brackets are summed. An adjustment ratio is calculated as the desired
total value of 1 divided by the summed amount. For this example the bracketed
terms sum to 230. Multiplying each bracketed number by 1 /230 and rounding to the
nearest hundredth, the discrete pdf is:15~19.9bu [.02], 20-24.9bu [.04], 25-.29.9bu

[.08], 30-34.9bu [.17], 35-39.9bu [.42], 4044.960 [.17], 4549.960 [.08], 50-54.9bu

 

41
[.02], 55-59.9bu [2.5]. These values are displayed in a histogram by the ELICIT

software. Users are permitted numerous revisions.

Unfortunately there are very few other methods of what Pease et al. (1990)
called "measuring alternative events." Detrended local yield distributions would be
useful, but are subject to detrending method error, aggregation error, possible
measurement error, perhaps limited observations, but more important, potential
problems of availability.

Another way of representing yield uncertainty is through parametric
distributions, rather than the discrete pdfs and CDF’s formed by ELICIT. Parametric
distributions could be triangular, normal or log-normal, since these three functions are
easier to represent than most others. These functional forms could be fit to discrete
data or perhaps elicited directly from producers. The advantage of the triangular
function is it’s flexibility, and the simple data to describe it (high, low, and mode). The
disadvantage is that much error can occur in the tails of the distribution, when
continuous distributions are represented by a triangular distribution. Anderson et al.
(1977) demonstrated use of triangular distributions.

The biggest advantage of subjective yield elicitation is that farmers can do it.
Producers may have errors, but they can make the data available. Conditional
normativists would say that whether their opinions are close to the "truth", they
represent what the decision-maker feels is truth, and they make decisions based on
these subjective probabilities (see Anderson et al.;1977)’. In time they will likely get
better at evaluating probabilities, (as learning takes place). However, conclusive

evidence to this regard was not discovered.

 

2 p. ix (Preface)

42

2.3 Representing Distributions

There are two basic methods for representing uncertain variables
(distributions). The first is the direct method, using the functional form of "well
behaved" (parametric) distribution(s). In this method, basic principles of probability
theory are used to add, subtract or multiply the equations to get a CDF for the
performance (it for this research). Often, normal distributions are used to represent
these functions, because normals are common in nature and they are easy to work
with from a statistical standpoint. Unfortunately, with two or three Important
distributions and their relationships (correlations), the process of using functions
directly becomes very difficult. Anderson et al. (1977) gave an example of calculating
the variance of gross revenue resulting from uncertain quantity times uncertain price.
When non-parametric distributions are part of the problem, the direct method can not
be used. Since individual producer yields are not expected to be well-behaved or
parametric, the direct method is only useful for more simple problems.

The second way of representing uncertain variables is to create a large number
of observations on each distribution in the problem, in such a manner that the CDF of
the large number of observations is like the CDF of the discrete or continuous
functional form. These observations are constructed using a zero-one random
number generator and the CDF of each uncertain variable. Each continuous zero-one
random number maps into a unique value of the CDF, since the CDF is a non-
decreasing function. That is pI = CDF( x,) for all i, and 0 s pl 5 1. These
observations can then be used in computations to find the CDF of the performance
distribution. This second method is called Monte Carlo representation. Non-

parametric distributions such as those created by ELICIT, can be represented by

 

43

Monte Carlo methods and the CDF transformation method, as well (Manetsch and
Park;1988).

King(1979) presents methods for dealing with correlations among uncertain
variables (distributions). Fackler and King (1988) made further improvements on this
process by suggesting use of fractile correlations rather than typical "mean-based"
correlations. Distributions that are uncorrelated to all the others can be generated
independently. If there are non-zero elements in correlation matrix between the
uncertain variables, then the variables are multivariate and each distribution is referred

to as a marginal distribution.

2.4 Market Efficiency

Forecasts of price distributions (fend 5) are necessary, when developing a
pre-harvest risk management commodity marketing program. There is a simple way
to forecast prices, if the item is traded in an efficient forward market. A forward
market is one where price can be set today for a good to be delivered at a specified
future time. The item to be traded could be stocks, bonds, stock options,
commodities, futures on commodities and options on futures. Any item that is traded
in a public market, with grades and standards, with many traders and highly visible
prices is a candidate for being efficient. If a market is efficient, the unbiased forecast
of the price of an item in the future period, is its current market price.

The Dictionary of Modern Economics (Pearce, 1983) summarized the Efficient Market

Hypothesis as:

 

44
The title given to a view about the stock market that the prices of shares are
good, or, the best available estimates of their real value because of the highly
efficient pricing mechanism inherent in the stock market. There are three
levels of efficiency. First, the market is held to be "weak-form efficient" if share
price changes are independent of past price changes. Second, semi-strong
form efficiency is present if share prices fully reflect all publicly available
information. Third, strong-form efficiency will imply share prices will have taken
full account of all information whether publicly available or not.

Leuthold et al. (1989) discussed each form of efficiency and appropriate tests.

These same efficiencies can be applied to commodity futures markets, as well as a

stock market. The three efficiency classes were first described by Fama (1953).

Leuthold et al. (1989) concluded that "none of these developments (research) have

shown an alternative marketing mechanism that provides prices of any less biased

nature than the futures market. No one has devised a more efficient marketing
alternative."3

Semi-strong market efficiency implies that today’s futures price for November
soybeans is the best predictor (currently available) of the closing price of that contract
on the day it will expire. Market efficiency also implies that speculative attempts to
arbitrage the market cannot result in long-run profits. This latter position is particularly
true for farmers, since their transactions costs and information costs (per bushel) are
higher than large commercial firms that trade futures. The efficient market also means
that necessary data is minimal; only the currently traded price is important.

The principle of the efficient market, is that numerous persons are processing
market information, and "voting" with dollars if they believe an arbitrage exists. Such

opportunities might be across time or distance. The standards involved with a futures

contract make this process easier. While some market participants are exposed

 

3p. 116.

 

45
(taking risks), others use tactics of selling one product and buying a slightly different
product, with a belief that the spread between the two is misopriced. With enough
market liquidity, the current price for November Soybeans at the "Chicago Board of
Trade" (CBOT) is a composite forecast of all of the market participants. Note that
persons who do not participate in the market, by abstention, signal that the price is
too low (if they hold grain to be sold), or too high if they will need grain in the future.
In this way, even producers and commercial buyers who are not currently trading in
the market, are helping form the price.

Thompson et al.(1988) surveyed farmers and grain merchandisers regarding
subjective mean and standard deviation of harvest-time commodity prices. The
individuals seemed to use closing futures price for expected price, but underestimated
volatility implied by the BOPM. Producers also failed to adjust prices for transactions
cost. This implies that letting producers subjectively enter price distributions for
analysis might be an inferior method.

The antithesis of the efficient market is the idea that the market is mis-priced or
biased. If this case were true, some system or formula or person, should be able to
profit from such a situation. Tinker et al.(1989) outlined seven different forecasting
methods including VAR, ARIMA, and technical trading systems, for the soybean
complex (beans, oil and meal), for three and six month periods. They concluded that
"No model exhibited significant market timing value for soybean oil prices", and only
one of seven were significant for soybeans (a six month ARIMA model). Their
research excluded execution costs which Greer and Brorsen (1989) summarize as
significant and variable across commodities. In addition, brokerage costs were

excluded in the Tinker et al. (1989) research. These are understandable omissions

46

since Tinker et al. (1989) were trying to find efficiency in the way Fama (1953) had
defined it. Unfortunately, producers and users of futures must pay brokerage and
execution costs, which likely void most opportunities for arbitrage, making the futures

market at least weakly efficient (especially from the producer’s viewpoint).
2.5 Generating Price Distributions

The next two subsections further discuss sources and measurement for the
marginal distributions of futures (I) and basis (6). These are presented separately
because futures prices are centrally determined in large markets and represent a large
portion of the total price. Basis is a local indication of demand, as well as distance to
major terminals where futures are delivered and received. Only a small portion of
futures contracts are ever delivered upon, or delivered from these major terminals, but

they serve as reference points to the cash market.
2.5.1 Futures Price Distributions

Black (1976) developed a model relating market volatility to the premium on an
options contract. Cox et al. (1979) expanded on this model with their own binomial
pricing model. Under continuous market assumptions the models converge, as
shown by Cox et al. (1979). In either case, computer programs like the one
Labuszewski (1983) developed, can be used to solve for the implied market volatility.
Such programs are used by traders in options pits, as well as other speculators,
spreaders and traders. These general equilibrium models have basically two
unknowns, (1) the premium of the option and (2) the futures market volatility. By

fixing one of the two variables it is possible to solve for the other. For forecasting

 

47
price distributions, the current premium is assumed to be efficiently formed in the
market and the model is solved for the "Implied Volatility (IV).' There is a third
unknown to the equation; a functional form of the distribution Is usually assumed in
the model.

Fackler and lfing (1988) developed a non-parametric approach to building the
CDF for futures prices. Their approach involved a conversion of put option premiums
at all of the actively traded strike prices, into a discrete pdf. There are assumptions
about tails of the distribution that must be made, but their method makes no
assumptions about a functional form for the price distribution. One disadvantage of
their model is that distant trading months have thinly traded options at only a few
strike prices. When option contracts are in distant months only a few of the strike
prices will be traded. With only a few strike prices trading, assumptions about the
tails of a distribution become more critical. Their model does incorporate non-
parametric factors such as commodity loans, to the extent that the market has already
considered them. This is a big advantage in the Fackler and King (1988) approach.

"Black’s (1976) Option Pricing Model" (BOPM) is a general equilibrium model
based upon the capital asset pricing model. Development of the BOPM is fully
detailed in Black (1976), Cox and Rubenstein (1985), lngersoll (1987), Elton and
Gruber (1987) and Labuszewski (1983). Labuszewski proceeds to show a program
written in BASIC. Using his notation and article, the BOPM value for a call premium
is:

c = e“-[UN(d,) - EN(d,)]

 

43

Where: d, = [In(U/E) + (62t)/2]/a(t"’) (2.4)
d2 = [In(U/E) -(a’t)/21/a(t"’)

And:

C = Fair value call premium ($/bu.)

U = Current underlying commodity price ($/bu.)

E = Exercise price ($/bu.)

r = short term annual interest rates (with continuous compounding)

t = years until option expiration

a = standard deviation of annualized returns

N = normal cumulative probability distribution

a = the base of natural logarithms, approx. 2.71828

ln= the natural logarithm

The expected price ratio of U/E is 1.0, with some standard deviation for the
distribution. Both of these measures are unitless since the ratio of prices removes
units. If the options market is efficient, option premiums (especially those close to the
money) can be inserted into the BOPM to solve for a. The c (implied volatility) or IV
that results is an indicator of potential price movement. More precisely a is the
annualized standard deviation in percent of the expected price ratio.

If the IV is .12 or 12 percent, it implies that annualized returns over the period
will vary and 67 percent or the time the price ratio will be within 12 percent of the
expected price ratio (1.0), (95% of the time within 24%). If we assume that prices are
normally distributed, the IV is equivalent to the 'Coefficient of Variation" (CV). The CV
is the ratio of the standard deviation of a distribution divided by its mean. The CV is
very much like the IV, except for important distributional assumptions. Both are
unitless.

The issue of a "best" functional form for ending period marginal distributions for

futures is not simple. Black (1976), assumed log-normally distributed price changes,

implying that the underlying futures price distribution would be log normal. His

 

49
assumptions, allowed cleaner analytical solutions than normally distributed futures
prices. Originally, he and Scholes had worked on a stock option pricing model
published in 1973. Since that time other researchers have re-examined normally
distributed futures. Hudson et al. (1986) examined soybeans, wheat and live cattle
and concluded "the results of the study suggest that options pricing formulae which
rely on the assumptions of normality will do an accurate job in predicting true option
premiums.“

Forecasting price distributions under the efficient market assumptions, really
means selection of a distributional form and forecasting the variance. Another method
of measuring futures price variance, is to believe that percentage changes in historical
prices from today's date to the ending date, will be the same this year, as in some
previous year(s). The CV’s could be compiled for weeks or months (prior to harvest).
This method would be especially useful if there was strong evidence to believe that
this year is like some other year or group of years. One disadvantage of this method
is the requirement that a very large database be maintained. On the other hand, this
historical data could be compiled and summarized. No previous research on this
historical method or the next method has been located to date.

A final method for forecasting futures price distributions is to use today’s
futures price as the expected futures price in the ending period, and the market’s
historical volatility for the past few days or weeks. The assumption with this method is
that the market volatility will continue as it has. Naturally, this is a rather naive
assumption. However, such a simple model could also be used in conjunction with

other forecasts. In addition, the IV and the historical variance follow one another very

 

p.2

so
closely, but neither are stationery when examining CBOT charts for 1990 corn,

soybeans, and wheat.
2.5.2 Basis Distributions

Like the previous two distributions, basis could be represented as parametric,
(e.g. normal) or it could be entered in a discrete manner similar to the ELICIT program
used earlier for subjective yield distributions. Since there is no way to arbitrage basis
volatility, small error in the volatility of the basis distribution should minimally affect
marketing strategies. Bias in the expected value of the basis, however, could be
arbitraged and is critical. In either case, error in estimating the basis distribution will
probably have a small effect on the marketing equation, compared to errors in
forecasting the futures price distribution, since futures are the major portion of price.

If basis records have been kept, they should be helpful in forming subjective
basis distributions. If there are no records, grain elevators or possibly commodity
brokers might have them.

Miller and Kahl (1987) used an E-V framework to compare forward contracting
to futures hedging. The difference between these methods in a non-dynamic analysis
is the basis. They concluded from their research: (1) Basis uncertainty does not
explain why producers prefer forward contracting. (2) The use of aggregated data to
represent individual decision-makers is not advised. (3) The effects of basis on

hedging decisions is very small.

51
2.6 Eliciting Risk Attitudes

The preceding sections discussed the uncertain distributions on the right hand
side of the marketing function. In the next several sections, the topics focus on how
to decide (left side of the equation).

If accurate utility curves can be gleaned from producers, then they could be
used to find solutions in the manner that Bernoulli (1738) suggested. There are two
key words in the previous sentence that make this section necessary. They are
"accurate" and "gleaned." The easiest part is gleaned. We can discuss hypothetical
situations, present real opportunities, or observe producer behavior. Each of these
are discussed in the sections that follow. The more difficult part is, how do you know
when you have subjective attitudes measured most accurately? There is lack of

consensus in the literature.

2.6.1 Methods

Employing "Expected Utility Theory" (EUT), researchers are able to study
decision-maker preferences in risky situations to determine the nature of their risk
utility functions. The three general methods for accomplishing this are known as (1)
"Observed Economic Behavior" (OEB), (2) "Direct Elicitation of Utility" (DEU) and (3)
experimental methods. Regardless of the general method, the researcher has little
a priori knowledge of the functional form of utility or which moments of a risky
decision are important to the decision-maker. Only with repeated decisions at known
probabilities and known income levels, is it possible to solve for risk preferences and

approximate a utility function in the neighborhood of the problem.

 

52

Using Observed Economic Behavior (OEB), such as actual farm plans for
farmers, assumes the researcher knows all constraints affecting this decision and the
decision-maker has formed subjective probabilities similar to the more objective ones
the researcher might use. Linear programming methods like MOTAD (discussed later)
are used to find risk efficient farm plans, and then measures of the difference between
efficient farm plans and the current farm plan are made (not in terms of R(X), but
changes in allocation). The difference between the two farm plans (allocations) is
attributed to risk. Of course all error from each of the plans are contained in each of
the solution, along with risk affects. Musser et al. (1986) showed that incomplete
constraint sets may overstate the benefits of risk aversion in firm decisions. Many
researchers refrain from using OEB and instead rely on direct elicitation, because of
difficulties in measuring expected probabilities and assuring a complete constraint set.

Brink and McCarl (1978), and Moscardi and de Janvry (1977) are examples of
research that utilized OEB. Brink and McCarl noted difficulties in their model and
concluded in the summary that, "although it appears desirable that risk studies be
done using actual farmer behavior rather than hypothetical behavior, the difficulties
encountered here with price expectations, for example, may indicate why gaming
approaches have been preferred?5

Binswanger (1980) used experimental methods with real payoffs for 240
peasant farmers in India. Gambles were simple with the lowest payoff being zero.
Local income rates and high currency exchange rates (dollars to rupees) helped make
the project affordable while evaluating payoffs that were at times greater than the

monthly income of the subjects. He also repeated these gambles without payoffs

 

5 p. 262

53
(direct elicitation) to examine the difference in the two methods. He found that direct
elicitation was inconsistent with the experimental methods of elicitation (using actual
payoffs). One criticism of experimental methods is that some persons may have
moral objections or preferences to the act of gambling. Such biases might be
accentuated by the fact that the gamble is carried out and transactions are actually
made. With hypothetical gambles (no payoff), the moral objection or preference might
be diminished by describing the gamble as a realistic business decision.

An additional problem is that with actual and sizable lotteries, the wealth of the
individual is not held constant over the observations. One would expect if decision-
makers are not CARA, then their ARA coefficient would change throughout the
elicitation process, even if the set of lotteries remained the same.

The conclusion of Binswanger (1980) regarding the superiority of experimental
methods is disturbing; because, while they may be more accurate, they have extreme
limitations. It would be difficult to find willing subjects for an experiment in which
several of the outcomes might be losses of the size that decision-makers often
encounter. Each person will have unique risk attitudes (see 2.6.2), so results of one
experiment could not be applied to another set of decision-makers. If Binswanger is
correct, aiding a decision-maker through a risky decision (using experimental
methods) requires them to first make an equivalent risky decision with an actual
payoff.

For helping decision-makers through more complex risky decisions there is no
practical choice but to interview them to establish their risk preferences, prior to the
"real-world" decision. Young (1979), in his summary of empirical risk measurement

methods, called this "direct elicitation of utility (DEU)." Unlike experimental methods,

 

54

the DEU involves no real payoffs, and therein lies its biggest criticism. Without real
risks, decision-makers behave differently than with the experimental and/or observed
economic behavior methods. For this reason Musser and Musser (1984) noted that
"In contrast to standard procedure, the attitude literature suggests that utility functions
for analysis of specific management decisions should be elicited in the context of the
particular decision".°

In experimental methods and DEU, there are several ways that gambles can
be presented. The von Neumann-Morgenstern (1944), (vN-M) method requires the
decision-maker to choose certainty outcomes which are equivalent to specified

gambles. So that.

U(A) = P*U(B) + (l-P)*U(C) (25)

where A, B, and C are outcomes, and p is the probability (0 2 p 2 1) of outcome B.
The decision-maker chooses a value for A to satisfy the equality. Outcomes B and C
remain fixed while the researcher varies the value of p. The monetary value of A is the
certainty equivalent for the decision-maker, and can be plotted in income-utility space,
as shown in Figure 2.3. The values for U(B) and U(C) are arbitrarily valued on the
utility scale. If U(B) = 0 and U(C) = 1, then the coordinates on the utility curve are
(A,, E[p,*0 + (1-p,)*1]), with the i subscript denoting the i‘“ observations. The resulting
coordinates are data for a utility regression, with a functional form for utility provided
by the researcher.

One weakness of the vN-M method is evidence that decision-makers have

more difficulty dealing with changing probabilities than with changing outcomes (see

 

8p. 85

 

55

Officer and Halter, 1968; Anderson et al., 1977).7 Further, persons may systematically
underbid the problem due to the bidding process. Since any bid would be accepted
they enter a low bid. Other persons may systematically overbid in a desire to get rid

of all risk, regardless of lottery values.

 

 

 

 

 

U U(C)-- *
T *
I *
L *
I «- «A»
T *
y *
*
U(B)* Hi i l l l l
B A4 A6 A7 A8 C
Income (in same units as entered)

 

Figure 2.3 Plotting Bernoullian Utility Curves

The second method of DEU is the modified vN-M method which involves the
same equality of equation 2.5, but p is fixed (usually 0.5) and values of B and C are
varied. This method allows decision-makers to analyze situations with familiar (and
constant) probabilities, overcoming one of the objections to the vN-M method. Biases

from moral objections to gambling are still present. Methods for approximating the

 

7p. 69

56

utility function are an adaptation of the vN-M method described above. Systematic
over or under bidding could still occur.

The Ramsey (1931) method of DEU involved the following equation..

P*U(A) + (1-P)*U(B) = P*U(C) + (1-P)*U('?') (2-6)

The value of p is fixed by the researcher (often 0.5) and A > B > C are outcomes,
also set by the researcher. If the value of p is set to .5 the method is usually referred
to as an 'Equally Likely Risky Outcome' (ELRO) method. The value of "?' to satisfy
the equality is provided by the respondent, or alternatively, varied by the researcher
until the respondent is indifferent between the gamble on the left of the equation and
the one on the right. Officer and Halter (1968) presented a method for establishing
new values for A, B, and C for the purpose of subsequent elicitations. For each value
of '?" which makes the decision-maker indifferent between the two sides of equation
2.6, then U(B) - U(A) = U("?") - U(C). Repeated tests provide additional interval
values on the utility scale.

Proponents of the Ramsey (1931) method point out that because the
respondent is choosing between two risky situations, biases due to morality of
gambling are diminished. This should especially be true if the choices are described
as business decisions rather than monetary lotteries. Like other DEU methods, the
Ramsey (1931) method involves a game with only hypothetical gains or losses.
Because of this important abstraction, Binswanger (1980), as well as Newbery and
Stiglitz; 1985) have faulted its realism.

King (1979) and King and Robison (1981) developed an elicitation procedure

called an “interval approach“ to risk measurement. King felt that other elicitation

57

procedures over-simplified the decision domain by presenting simple gambles and

solving for precise risk preferences and utility functions. Skeptics of EUT also point

out that decision-makers may be indifferent about some range of risky alternatives. If

this is true, then maximizing expected utility and presenting the decision-maker with

only one optimal solution would be an over-simplification of his or her preferences.

As the name implies, the interval approach finds interval values of local risk

preferences. The decision-maker is asked to choose between two hypothetical risky

alternatives, each with similar mean income values. Each alternative has six possible

outcomes and each outcome has equal probability (1 /6). The example in Table 2.2 is

from King (1979).“

Table 2.2 Interval Approach Choice Format

Compare distributions 5 and 20 and indicate which one you prefer.

Dist 5
9400
9850
9900
9900

10050

101 50

Ave. 9875
St.Dv. 258

Dist 20
9250

9300

9600
10300
10400
10600

9909
595

Outcomes under each distrib-
ution have equal (1 /6) chance
of occurrence.

These bottom four values are
are for summary and are not
shown to the decision-maker.

 

° p. 219

58

If the decision-maker chooses the riskier distribution (20), he must prefer more
risk than the 'safer' distribution (5) offers. Alternatively, if 5 is chosen, the decision-
maker must prefer less risk, than distribution 20. If the decision-maker chooses
distribution 5, elicitation would proceed with two new distributions, both located about
the same expected income and less risky than distribution 20. If the decision-maker
chooses 20, elicitation would continue with two different distributions that would be
more risky than Distribution 5. The elicitation proceeds though one more branch of
choices, until risk attitudes are narrowed down to a small interval.

Comparing three such pairs of distributions is all that is needed to solve for
one of 8 interval values of the ARA coefficient at a single expected income level.
Since the ARA coefficient is local and the form of the global utility function is
unknown, the process must be repeated at other income levels that are likely to be

experienced by the decision-maker. Locally the ARA is solved by assuming utility is

as follows.
U(X) = -e('RX) if R(X) > o
U(X) = x if R(X) = o (2.7)
U(X) = emx) if R(X) < o

The risky distributions offered to the respondent are closely clustered about similar
means resulting in small variances. The coefficient of variation (standard deviation as
a percent of the mean) for the distributions used in lGng’s (1979) work were in the

range of .024 to .085 percent (for non zero expected income levels).

 

59

Thomas (1987) used the interval approach to measure risk attitudes in a survey
of Kansas farmers. He noted that surveyed farmers often commented that they really
did not see much difference in the two distributions offered to them.

The interval approach to risk measurement is extremely flexible. The
researcher or decision analyst can choose several income levels to be elicited, as well
as the size of the intervals. Once elicitation is complete, the decision analyst has
observations of risk preference at various income levels without any assumption of a
particular functional form for utility. income levels can be negative and positive. It is
relatively simple to check consistency of responses by incorporating one or two
additional pairs of risk alternatives at each income level. (\Mlson and Eidman, 1983;
and Tauer, 1986).

The interval approach is not without some limitations. The fact that a utility
function is not solved gives added flexibility and increases computational problems.
Meyer (1977a) developed a method of using interval approach measurements called
”Stochastic Dominance With Respect to a Function' (SDWRF). SDWRF uses optimal
control techniques to find efficient alternatives that reflect the decision-maker’s interval
preferences for risk, but are independent of a particular utility function. SDWRF is
usually more selective than a decision criteria called second order stochastic
dominance (defined in section 2.7.2) since individual risk preferences are
incorporated. King (1979) demonstrated the selectiveness of SDWRF compared to
other criteria. The stochastic dominance methods he examined (first and second
order), are not usually very discriminatory, while utility maximization finds the single
optimal solution. SDWRF has intermediate discriminatory power that varies according

to the income distributions and the individual's interval measures.

 

60

The decision analyst can determine how narrow or wide the risk intervals will
be, the number of possible outcomes in each gamble presented, how many income
levels will be tested and the number of consistency checks to be made at each
income level, all of which will alter the results of elicitation and the SDWRF efficient
set. In addition, the researcher can choose to keep skewness at zero for all
distributions offered to the decision-maker or may vary skewness either systematically
or randomly. Skewness is likely an important part of risk preferences that is not fixed
by the other DEU methods described (Alderfer and Bierman; 1970).

The flexibility of the interval approach makes it important for the researcher to
perform consistency checks. King (1979), Love (1982) and Thomas (1987) pretested
their interval surveys, but did not perform consistency checks at each income level for
all respondents. Wilson and Eidman (1983) and Tauer (1986) did performed
consistency checks on each person surveyed, with differing success. In the case of
Tauer’s work, less than half of the respondents were consistent enough that their
results could be used in analysis. Tauer (1986) did show that as a group, choices
between the intervals presented were far from being random, indicating that
substantial consistency existed compared to random selection. Wilson and Eidman
(1983) showed fewer inconsistencies, perhaps due to a different set of intervals and a
different method of consistency checking than Tauer (1986).

In addition to interval measures of risk aversion, there is magnitude estimation.
Patrick et al. (1981) reviewed elicitation methods and described magnitude estimation.
Magnitude estimation, like interval measurement, does not result in a utility function.
Instead, it gives an ordinal measure of attitudes based on the importance of risk

related goals of the respondent. Magnitude estimation is similar to attitude indices

61
developed in social sciences. For example, Hughes (1971) describes the Likert (date
unknown) scale of attitudes.

The attitudes expressed regarding risk related goals were not stated as a
function of some income level in the Patrick et al. (1981) research. Magnitude
estimation may be useful for correlation of risk attitudes to socio-economic variables,
but Patrick et al.(1981) had low r1 values (correlation coefficient) and concluded that
risk attitudes are quite varied across subgroups. Since the measured preferences are
not a function of an income level, magnitude estimation cannot give a utility function,

nor an ARA coefficient; making its use for decision assistance very limited.

2.6.2 Results of Risk Elicitation

Officer and Halter (1968) tested all three DEU methods described, and found
the vN-M method inferior to the modified vN-M and ELRO methods. Ramaratnam et
al. (1986) and Lin et al. (1974) used the ELRO method with the respondent choosing
a value of '?' to balance equation 2.6. Ramaratnam et al. (1986) also tested four
functional forms of utility for goodness of fit, and for their sample, found that the
negative exponential had the best 14, and the most desirable economic properties.
Dillon and Scandizzo (1978) used the modified vN-M method, to find that most
Brazilian farmers and land-owners were risk averse. Reviews of other efforts to survey
decision-maker’s preferences can be found in Young (1979), Robison et al. (1984),

and Love (1982).

62

Table 2.3 Results of Previous Attitude Measurements

Percent of Risk Attitudes Sample
Averse Neutral Prefer Size
United States

 

Brink & McCarl * 66 34 0 38
Love (1984) ** 35 15 50 23
Tauer (1986) + 34 39 26 72
Thomas (1987) ++ 73 DNA 27 30
Wilson & Eidman (1983)+ 44 34 22 47

* Observed Economic Behavior

** Average of 2 years elicitation at group mean income. + Each
producer attitude measured near expected income. ++ Average of
all income levels (group mean income not given)

Most surveys show that farmers are in general risk averse or risk neutral, with a
minority of individuals showing preferences for risk at high positive levels of income,
and also at very low income levels. Young (1979) summarizes earlier work in risk
preferences. Table 2.3 focuses on more recent work concerning U.S. farmers.

Many of the researchers combined risk elicitation with cross-sectional analysis
of producer characteristics such as age, education, financial measures, and other
factors. These have often been regressed on the ARA coefficients to examine their
associations and related statistical significance. For examples of these efforts, see
Love (1982), Tauer(1986), Wilson and Eidman (1983), Patrick et al. (1985) and Branch
and Olson (1987). In nearly all cases, the r’ values were low (often less than .20).
Because each research group regresses a different set of independent variables, it is
difficult to summarize their findings on related socioeconomic characteristics. There
does seem to be positive correlation between the ARA coefficient and both the age

(or farming tenure) of the operator and financial debt of the operation. This generally

63

indicates that older farmers are more risk averse (ceteris paribus). As expected, farms
with higher (but probably manageable) debt levels were also more risk averse. When
debt is burdensome some managers will likely become risk preferring, much like the

long 'bomb' at the end of a football game (see Robison, 1986).

2.6.3 Problems with Previous Research

Anderson et al. (1977) felt the realism of hypothetical losses or gains is
increased when elicitation is couched in terms of net worth rather than income. This
directly contradicts the findings of von Winterfeldt and Edwards (1986). They argued
convincingly that decision-makers do not often know their asset position and are more
comfortable dealing with cash flows (Income). They also obsen/ed that decision-
makers learn to write off the sunk costs. Other supporters of this later view are
Newbery and Stiglitz (1985). Previous elicitation research has involved gross income,
net income, after-tax net income and net worth. As noted by Raskin and Cochran,
these changes in units of measure for X (income), affect the R(X) (the ARA function)
and diminish the comparability of the research results, except when the negative
exponential utility function is used.

Regardless of how preferences are queried, there will always be critics of EUT
and the methods of elicitation. Simon (1986) and others have argued decision-
makers exhibit "satisfycing' rather than utility optimizing behavior. King and Robison
(1981) felt the decisions faced in DEU 'games' are too simplistic and not
representative of the choices decision-makers face. G. A. Miller (1956) found that
human cognition is limited to simultaneous analysis of "seven, plus or minus two"

factors. Most interval approach work has been performed with two columns of six

54

numbers each, thus giving the producer no summary information and twelve data
points to consider.

Solving for a utility function requires some assumption of the functional form.
With limited data points and reasonable responses, several different forms may have r2
values exceeding .95 (see Officer and Halter, 1968; Ramaratnam et al., 1986 for
examples). Individual decision-makers can be expected to vary in both form and
coefficients, of their utility functions. Management prescriptions (or suggestions)
arising from errors in fitting a utility function could themselves be in error.

Another error not mentioned in the literature is related to wealth effects of the
gambles presented. Was the survey respondent to view the gambles being offered in
elicitation as supplements to their 'real-world' next period income distributions, or as
replacements of such distributions? In decision assistance the analyst is usually trying
to seek attitudes about a 'real-world' situation and would like the decision-maker to
replace that situation with the hypothetical ones presented. The research presented
has indicated that preferences can be elicited and that some response consistency
beyond random selection is present (T auer;1986 and others). What is not clear, is
whether the survey respondents always understood the wealth effects of the
hypothetical gambles. Even if respondents fully understood these wealth effects,
could they mentally substitute hypothetical income distributions for real ones?

There are limitations with the interval approach to elicitation. The interval
approach asks for responses with various expected income levels and small
'coefficient(s) of variation'(CV’s). As a result, producers must indicate preferences at
income levels other than the expected, which exclude any possibility of realizing the

expected level of income. This diminishes the realism of the gambles and could

 

 

65
contribute to respondent misunderstanding. An example of this misunderstanding is
reported by Love (1982). He stated:

Farmers may have been willing to take added risk at the $0 income level due

to the relatively small magnitude of the absolute dollar amounts and variability

of the paired distributions. it was noted from farmer comments that while they

make decisions involving a wide range of dollar values, many put little time and

effort into decisions involving dollar amounts in the $0 - $50 range.“
Statements like those from Love indicate added potential misunderstanding. The
survey dollars were suppose to represent whole farm annual income. The frequency
with which farmers make $50 decisions should have almost no bearing on their desire
for $25 or $50 of annual income. This means that the respondents (and possibly
researcher) may have forgotten that annual income preferences were being measured.

Another possible misunderstanding of most approaches is that respondents
may forget that survey games are to be 'played' at the same frequency as the real
decision. That is, annual problems need values that are understood to be annual.
Farmers may spend little time on real-world small gambles, because they are played
quite often compared to gambles of $30,000 or more (annual).

The variance of the total outcome of a gamble is diminished as the activity is
increasingly subdivided (if each sub activity is independent). An example is the adage
of not putting all the eggs in one basket, or not betting all of your money on a single
horse in a single race. Of course with some activities, splitting them creates two

perfectly correlated activities, and no loss in variance occurs, due to a covariance

term. An example of this later situation is dividing a corn field into two equal parts

 

°p.91

66
and growing an identical corn crop in each half of the field. In this case, no risk
reduction can occur, because both parts of the subdivision are perfectly correlated.

The point is, if a risk attitude survey is to represent annual income, then the
respondent must keep in mind that the hypothetical gamble will be played only once
per year. This would surely be aided by keeping the variance of elicitation in the
neighborhood of realistic annual income variance.

The above discussion points out a difficulty of comparing results of the interval
method of elicitation to other methods. ELRO methods examine U(X) in the
neighborhood of the problem considered. The interval method looks at very small
intervals of income and does not attempt to build a utility curve. One expects that
these safer subdivisions or intervals of the problem would understate the variance of
the problem allowing producers to be more risk averse over a small domain. This
does not indicate errors in the interval method, especially since it uses stochastic
dominance with respect to a function (rather than form a utility function). It does
mean that the interval method local ARA coefficients should not be averaged to imply
a global ARA coefficient.

Finding the answers to questions of wealth effects and other potential
misunderstandings are not easy. An initial reaction is that if decision-makers are
unable to consider risky synthetic gambles as substitutes for real distributions, then
decision analysts have no way to assist decision-makers except through static
analysis. There is little doubt that decision-makers mast be presented with realistic
gambles and that the wealth effect of the gambles is fully understood before elicitation

takes place.

67

Throughout the discussion, utility has been a non-decreasing function of
money (dollars, net income, gross margin, wealth, or some financial measure). Other
factors besides measures of income affect utility, or at the very least, decisions.
People take vacations, serve on civic committees, attend church, and spend time with
the children and grandchildren. Decision-makers have knowledge constraints, time
constraints, and financial limitations. These factors have not been included in an
examination of utility and maximizing expected utility. This is also true of decision

rules and criteria, portfolio analysis, E-V analysis (see section 2.7.3).

2.7 Decision Rules and Efficiency Criteria

There are several methods for analyzing risky situations and helping decision-
makers reach workable solutions. What follows in this section is an overview of the
more commonly used decision rule concepts and efficiency criteria from decision
theory, examples of research using the methods described, and a discussion of the
strengths and weaknesses of the various methods.

A decision rule is a framework for analyzing alternative actions in a risky
environment. Decision rules reflect the decision-maker’s risk attitude by establishing
procedures for analyzing alternatives. Decision rules make strong assumptions about
utility functions and generally result in the selection of only one optimum course of
action. Examples of decision rules are safety first rules, maximize expected outcome,
maximize the minimum outcome, and maximize expected utility.

Risk efficient criteria are a more general tool in decision theory . A risk efficient
criteria is a method or standard for dividing decision-maker alternatives into efficient

and non-efficient classes, with only general assumptions placed on decision-maker

68

utility functions and/or the pdf’s they face. An example of a risk efficient criteria is the
EV model, where producers maximize expected income while minimizing income
variance. Risk efficient criteria can be adapted for individual use when more specific
risk preferences of the decision-maker are known. Because risk efficient criteria make
few assumptions regarding the preferences of individuals, the efficient or dominant set

of solutions can be quite large.
2.7.1 Maximize Expected Utility

Previous sections discussed methods for measuring decision-maker utility
functions. If such functions can be accurately measured, then optimal decisions will
be those that maximize expected utility. In the case of risky decisions, optimal
solutions will also depend on probabilities of the various outcomes (either subjective

or subjectively modified from objective information). Mathematically this is simply

052": (I),l ... U (xu) st. 2 pm =1 (for all i) (28)

l-1 l-1

where j indicates the number of possible outcomes for each i decision alternative. if
probability is continuous, the probability density function must be known, or for
numerical solutions the process can be made discrete by choosing small intervals in
probability.

When maximizing expected utility, the underlying performance criteria (i.e., net
income, wealth) must be of the same form and unit of measure as was used in utility

elicitation (see section 2.3.2).

69

Utility elicitation and the subsequent fitting of the utility function, took place in
some definite interval of X. Maximization of expected utility can involve decision
alternatives that result in outcomes outside the elicited range. The extent that this
occurs should be minimized. This could be done by designing the elicitation around
the context of the problem, and its related alternatives. Assuming the functional form
and coefficients of the utility function elicited over a definite interval, will hold globally,
further adds to errors in decision assistance.

Maximizing expected utility is the most flexible decision rule, since it is possible
to deal with decision-makers having any type of utility function, regardless of whether
they are risk averse, neutral or preferring. Not only is the method flexible, but if the
utility function can be accurately formulated, and probabilities are known with
confidence, then it is possible to solve for a single decision alternative. The price for
such flexibility and power is moderately high.

The big criticism of maximizing expected utility is that errors in forming vN-M
utility functions and subjective probability are likely sizable, not often measurable and
usually ignored in the final optimal solution (see King and Robison, 1984). A second
shortcoming is efficient programming algorithms. Most cases of directly solving
expected utility involve optimization of a non-linear problem, requiring numerical
search algorithms. Exceptions to this are when assumptions regarding utility and/or
probabilities are made.

Two proponents of maximizing expected utility are decision analysts von
Winterfeldt and Edwards (1986). They felt that persons can not only express

preferences, but also strength of preferences. They pointed out that while persons are

70

sometimes inconsistent in preferences (cognitive illusions), persons are seldom

indifferent to two alternatives. Perhaps their most pointed statement was as follows ..
We find the preceding argument so convincing a demonstration that you can
indeed judge strengths of preference, and we are so well aware of the
simplifications that such judgments produce in obtaining measures of utility,
that we are compelled to ask why many deeply respected theorists either deny

the possibility of such judgments or refuse to use them in decision analytic
procedures.‘o

2.7.2 Stochastic Dominance

”First degree stochastic dominance' (FSD) is the simplest risk efficient criteria
and requires minimal assumptions of decision-maker preferences. If income (X) is a
continuous random variable with values x, and if there are two different CDF’s called
F(x) and G(x), then F (x) is first degree stochastic dominant (FSD) over G(x) if
everywhere F(x) is less than or equal to G(x), and for at least one x, F(x) is absolutely
less than G(x). More simply, the graph for F(x) will never cross the graph of G(x), and
must never lie to the left of G(x) (see Figure 2.3). FSD (and stochastic dominance of
any degree) also applies to discrete distributions. For discussion of discrete stochastic
dominance see Robison and Barry (1987), Anderson et al. (1977), or Elton and Gruber
(1987). The principles are the same for the discrete case as the continuous, except

that summations replace integrals (F00 and 600).

 

‘° p. 210

71

 

 

(L9*
(L8'

Y
<3
by

robobmf
c»
tn

0. 0.4a G(x)
(L3‘
(L2‘
0.1 - F(X)

 

 

 

o 10 20 3'0 40 so so 70 8b 9b 100

 

 

 

Figure 2.4 First Degree Stochastic Dominance (FSD)

FSD applies to all decision-makers who prefer more to less (U’(X) > 0). They
may be risk averse or risk preferring. With such broad application, it should seem
little surprise that FSD eliminates few decision alternatives in a practical setting (King
and Robison, 1984; Anderson et al., 1977). Alternatives that are not dominated by
any other decision alternative are said to be first degree stochastic efficient, or
members of the FSD efficient set. Transitivity is a property of FSD (and higher order
stochastic dominance) so that if F(x) is FSD over G(x), and G(x) is FSD over H(x),
then F(x) is FSD over H(x).

FSD and stochastic dominance of any degree have a strength that is often

overlooked. No restriction is placed on the types of probability distributions the

72

decision-maker faces. F(x) and G(x) may be parametric or non parametric, skewed or
symmetric, discrete or continuous.

“Second degree stochastic dominance” (SSD) requires added assumptions on
decision-maker utility, but not on the type of probability distributions to which it can be
applied. SSD compares the area under two CDF’s taken from minus infinity to values

of x. Using subscripts to denote integrals, so that

x,
f f(x)dx a F(x) 2 F1(x) a d(F2(x))ldx (2-9)

The CDF is F, (x), but the CDF subscript will usually be omitted (as are the constants
of integration).

With two different CDF’s called F(x) and H(x), then F(x) is SSD over H(x) if
everywhere F2(x) is less than or equal to H2(x) for all possible values of x,
with at least one value of x having a strict inequality. in other words, the area under
F(x) is less than the area under H(x) at every point. The two CDF’s may cross as in
Figure 2.4 creating differences indicated by the letters A and B. In essence, SSD says
we prefer F(x) to H(x) because more of F(x) lies to the right of H(x). In Figure 2.4 this
condition is true if the area of A is greater than B. If F(x) and H(x) are normally

distributed then SSD is equivalent to mean-variance analysis.

 

73

 

 

(L9‘

(L81

9 p p
u! at \l
l 1 l

roboblllfy

 

 

 

 

100

income (x)

 

 

 

Figure 2.5 Second Degree Stochastic Dominance (SSD)

SSD assumes that decision-makers prefer more to less, as with FSD
(U’()() > 0), and that they are risk averse in the area of the values of X being
evaluated (U”(X) < 0). This later assumption is a reasonable one for many, but not all
decision-makers. Evidence of individual producers showing preference for risks (that
is, the ARA coefficient is negative) can be found in Thomas (1987) and Love (1982).
King (1979) indicated that most (14 of 17) farmers exhibited local preferences for risk
in at least one of four queried income levels. All of these researchers were using the
interval method of risk elicitation, however. Often such preferences for risks occur at
negative income levels. Broader findings previously discussed in section 2.4.2

showed that in general, producers are risk averse.

74

SSD involves narrower assumptions regarding decision-maker behavior and its
discriminatory powers are larger than FSD (Anderson et al., 1977), but for some
decision domains, may not be selective enough (IGng, 1979; King and Robison, 1981).
If the distributions being faced by the decision-maker are normal, then the means and
variances sufficiently describe the opportunity set. In this situation, the SSD set, will
also be the mean-variance efficient set (further discussed in the next section).

"Third degree stochastic dominance' (T SD) begins with the same decision-
maker utility assumptions as SSD, and also assumes that U”’(X) > 0. This implies
that R’()() is negative, or that decision-makers are DARA. This assumption is usually
considered empirically reasonable. Findings discussed in 2.6.2 support the
assumption for surveyed decision-makers in aggregate, but should be questioned for
prescriptive work with individual decision-makers.

The definition of TSD is a logical extension of SSD involving integrals of the
SSD cumulative function. Anderson et al. (1977) presented a more complete
discussion of TSD. With increased decision-maker assumptions and computational
complexity, TSD is not as commonly used as SSD. In addition, when distributions are
symmetric, SSD sets and TSD sets should be identical.

Asymmetry is measured by skewness. Rational producers should prefer
negatively skewed distributions over alternatives that are symmetric, but with the same
mean and variance. Negative [positive] skewness implies the median is above
[below] the mean, and a thinner tail appears on the left [right] of the pdf. Work by
Alderfer and Bierman (1970) suggested that skewness is important in decision-

making. For situations where distributions are clearly not symmetric, TSD should

75

have increased discriminatory power over SSD. An example of such a situation would
be an insurance scheme.

Stochastic dominance is an important benchmark in risk analysis. While its
assumptions may not hold for certain individuals, decision analysts should seek
prescriptions which are part of the stochastic efficient set, using a level of stochastic
dominance appropriate for the individual. If an individual is known to be risk averse
(through elicitation or behavior), then prescriptions sought through other decision
criteria should be a subset of the SSD set.

Stochastic dominance is not without weakness. Because no restrictions or
assumptions are made regarding the probability distributions, computation can be
quite intensive. Anderson et al. (1977) developed a Fortran program for stochastic
dominance. The program makes pairwise comparisons of CDF’s (or for appropriate
orders of stochastic dominance the related integrals of the CDF), beginning at the
bottom of the distribution. The routine requires all distributions to be bounded, uses
numerical integration and represents continuous distributions as uniformly divided into
small discrete sections. The authors admitted that because the algorithm begins at
the lower part of the distribution, it is particularly sensitive to errors in the lower tail of
the pdf. Anderson et al. (1977) presented a comparison of TSD results to an E-V
efficient set, for a case problem. Because of asymmetry in the pdf of the problem,
TSD rejects several alternatives which were E-V efficient. This demonstrates a
problem with E-V efficiency when used with asymmetric distributions, more than a
weakness of TSD. TSD is never less selective than SSD, but when distributions are

symmetric, TSD offers little added selectivity. The decision to use SSD vs. TSD can

76
also be justified by knowledge of pdf symmetry or asymmetry. Anderson (1975)

further discussed risk efficient Monte Carlo programming and TSD.

2.7.3 E-V, MOTAD, M-SD, and Semi-Variance

So far in section 2.7, no assumptions have been made about the probability
distributions that decision-makers confront, except that the decision-maker (and
analyst) can represent the entire distribution with a known continuous functional form,
and/or the distribution can be approximated by converting it to small discrete
segments. With the mean-variance efficiency criteria, also called 'Expected value -
Variance" (E-V), the subject is assumed to examine only the mean and variance of
each pdf in evaluating alternatives. This simplifies data requirements as well as
analytical solutions, thereby explaining the popularity of E-V models.

Probably no single risk efficiency criteria is more widely used and documented
in risk research than the EV model. Elton and Gruber (1987), lngersoll (1987),
Robison and Barry (1987), Barry (1984), and numerous other texts and articles in the
last 30 years, have presented extensive discussion of E-V and its application.

E-V is consistent with EUT when decision-maker utility is quadratic or when
decision-makers are CARA and the distributions they face are normal (Fishburn, 1977;
Selley, 1984; King and Robison, 1984 and others). More generally, the income
distributions need not be normal, but they must be identical except with respect to
location and scale (Meyer, 1987; Robison and Meyer, 1988). This broader criteria
expands the applicability of E-V.

Meyer (1987) made use of 'mean-standard deviation' (E-SD), because the

convex preference set requirement applies to a larger number of utility functions and

77

distributions than when variance is used as a measure of risk. E-SD also allows the
units of measure to be retained in an understandable manner. If decision-makers
exhibit constant absolute risk aversion CARA and distributions are identical except
with respect to location and scale, than E—V and E-SD are equivalent (and consistent
with EUT).

The E-V decision rule has a number of advantages in addition to those
previously mentioned. Many investment pdf's can be approximated by normal
distributions, especially investments whose daily price movement can be characterized
as a random walk. This is the expected result of the central limit theorem. With some
income distributions this may not be the case. Pre-harvest crop income is a function
of three stochastic income factors: basis price, yield, and futures price. Each of the
marginal distributions that make up uncertain crop income may or may not be
normally distributed for the individual producer. Day (1965) and Gallagher (1986)
make cases for non-normal yield distributions in cotton and corn respectively. Even if
the individual pdf’s (marginal distributions) are not normal, it is still possible to
estimate the mean and variance of the resulting crop income distribution (Anderson et
al., 1977).

A second disadvantage of E-V is that solutions are often sensitive to changes
in values of the variance/covariance matrix of all the marginals. This data is not
available in many cases, especially for individual farmers. Even if historical
correlations were available, they may not include effects of commodity programs and
insurance payments.

'Ouadratic Programming" (OP) is often used in applied risk analysis to solve

for E-V efficiency when proper conditions are satisfied (or assumed to be). OP is

78
computationally efficient relative to many risk programming alternatives, and requires
the analyst to input the vector of means for decision alternatives available, as well as
the related variance/covariance matrix. Section 2.8.2 documents several efforts in
analyzing marketing alternatives through E-V criteria. Quadratic programming is
documented in Hazell and Norton (1986) and in Taha (1987). Algorithms for quadratic
programming are presented in Kuester and Mize (1973) and Scales (1985). To solve
for the entire E-V efficient set using OP, requires repeated analysis with varied levels of
expected income (a OP constraint).

Hazell and Norton (1986) presented a method called ”Minimization Of Total
Absolute Deviations“ (MOTAD), which is related to E-V analysis. MOTAD is a linear
programming algorithm that maximizes expected returns from various alternatives,
while minimizing the absolute deviations from the mean. To solve for the entire
efficient set using MOTAD requires several successive runs, with changing values of
the expected income parameter (similar to the changing OP expected income con-
straint for E-V). MOTAD implicitly handles covariances between decision alternatives.
Tauer (1983) showed that MOTAD results are not necessarily SSD.

The biggest disadvantage of E-V, E-SD and MOTAD is that good outcomes
(above the mean) are weighed the same as bad outcomes (below the mean) if their
distances to the mean are the same. Thus skewness and preference for skewness
are ignored by these decision rule concepts. Holthausen (1981) and Fishburn (1977)
argued that decision-makers more likely view risk as deviations from some common
point across all distributions, rather than as deviations from the various means. The

alternatives they proposed are later presented.

79

In response to some criticisms, it is possible to use semivariance. The
semivariance is measured like the variance, except only deviations below the mean
are squared. The result is a measure of risk involving only bad outcomes (those
below the mean), and ignoring favorable ones. If the pdf’s the decision-maker faces
are normal (or more generally symmetric), the EV solution is equivalent to the
'Expected value - SemiVariance“ (E-SV). This is because with symmetric distributions
the minimization of deviations below the mean also minimizes those deviations above
the mean (since the two are equal). E-SV has strong intuitive appeal for skewed
distributions (see Markowitz, 1959)." it has not been extensively used in applied
efforts, probably owing to lack of a mathematical programming method, the difficulty
of calculating semivariance, and the complexities of using it in analytical models. If
decision-makers view risk as deviations from some common target or threshold, then
E-SV would be inappropriate, just as E-V, E-SD and MOTAD. The commonality that
these four efficiency criteria possess are that (1) all of them measure risk as deviations
from the mean of each pdf and (2) they are only consistent with SSD under specific

conditions.
2.7.4 Target MOTAD and Lower Partial Moments

Section 2.1.1 discussed moments of probability distributions taken about the
origin and the mean. The “Lower Partial Moment“ (LPM) is a probability distribution
measurement that quantifies outcomes below some level. The semi-variance is a
special case of a lower partial moment for a probability distribution. More generally

lower partial moments are noted as.

 

" See page 200.

 

80

t
LPM(a,t) = f (t-x)‘ f(x)dx (2.10)

where a 2 0 (and constant), t is some target or reference level of income, and f(x) is
the pdf. LPM(2,E[X]) is the semi-variance. LPM(1,E[X]) is equivalent to the absolute
value of deviations below the mean. Porter (1974) proposed the use of LPM(2,t)
where t is a constant level of income across all decision-maker pdf’s. He called this
the fixed reference point semi-variance. Fishburn (1977) generalized Porter’s more
special case to give the definition of equation 2.11. Fishburn (1977) also proved that if
a 2 1, then examining alternatives in a mean-LPM(a,t) framework, would give efficient
solutions that were a SSD subset.

Tauer (1983) presented a linear programming method for analyzing mean-
LPM(1,t < mean) that he called Target MOTAD. While all Target MOTAD solutions
are members of the SSD set, Target MOTAD may not find all members of the SSD
set. Tauer believed that by repeated analysis using different values of t, it should be
possible to find all members of the SSD set. At a given target, numerous levels of the
risk parameter (allowable deviations below the target) must be analyzed to find the
efficient mean-LPM(1,t < mean) set for the given t. Thus to find as many members of
the SSD set as possible, requires N*M Target-MOTAD solutions, where N is the
number of target level values and M the number of risk parameter values to be con-
sidered.

Target-MOTAD strengths are the ability to model using linear programming
algorithms and its relation to SSD. Where MOTAD has a single parameter that needs

changing, Target-MOTAD has two. The first Target-MOTAD disadvantage is additional

 

81
computation. The extent of this added effort is likely problem dependant. It is also a
disadvantage that most Target-MOTAD proponents discount. In some situations, it
may be more expedient to use numerical methods for SSD (Anderson et al, 1977)
rather than Target-MOTAD. This suggestion is not addressed in the Target-MOTAD
literature.

A second disadvantage is that, like SSD, Target-MOTAD may not provide
enough discriminatory power for some problem situations. The exception would be
when the decision-maker knows what target level is most important and is only
interested in solutions related to that target. This would reduce the computations, and
the solution set. It would also eliminate some SSD solutions, possibly including those
in the neighborhood of the decision-maker’s optima.

Atwood (1985) utilized LPM’s to improve Tchebyshev-type inequalities for
safety first criteria. Previously, these inequalities were too conservative when the
mean and variance were used to solve the inequality. This usually resulted in
selection of overly conservative management alternatives. Atwood et al.(1988) and
Berbel (1988) developed math programming methods for solution of other LPM-type
analyses which are useful in safety-first analysis (see section 2.3.5).

In addition to Target-MOTAD and mean-LPM efficiency, Holthausen (1981)
proposed replacing mean as a measure of desirable outcomes. Instead of the mean,
he proposed an upper partial moment (UPM). The UPM is similar to LPM, but taken
from the same target to positive infinity. Holthausen (1981 ) labeled the LPM 'risk"

and the UPM “return.“ The two criteria model from Holthausen (1981) is ..

82

LPM(a,t) = f(t—x)‘ f(x)dx (2-11)

UPM(a,t) = ] (x—t)” f(x)dx (2-12)
I

a,b > 0, and independent
The two measures can be used to solve related efficient alternatives as done in
Hauser and Eales (1987a, 1987b).

With the Fishburn (1977) mean-LPM model, decision-maker utility is linear or
risk neutral for outcomes above the target, since they are not part of the risk measure.
With the Holthausen model the decision-maker is risk averse, (risk neutral) (risk
preferring) below the target if a > 1 (a = 1) (0 < a < 1). The value of b is
independent of a, so a decision-maker can be risk averse above the target and risk
preferring below. When t=0, such behavior is observed in much empirical work and
supported by Kahneman and Tversky (1979). For values above t, the decision-maker
is risk averse (risk neutral) (risk preferring) if 0 < b < 1 (b = 0) (b > 1).

Holthausen (1981) showed how to solve the utility function described by his
model using the standard vN-M elicitation method (section 2.6.1). As previously
discussed, the standard vN-M method involves selection of probabilities which lead to
indifference between a certain gamble and an uncertain one. Section 2.6.1
documents the shortcomings of this method. The Ramsey (1931) method of DEU
does not incorporate utility functions like the ones proposed by Holthausen (1981),

but could easily be modified toward that effort.

83
One advantage of Holthausen’s (1981) utility function is its flexibility to

represent nearly any decision-maker preferences. It is consistent with FSD, SSD, and
TSD for particular values of a, b, and t. The flexibility becomes a disadvantage in
estimating the function because additional parameters reduce the degrees of freedom.

Also, ordinary least squares cannot be used to estimate the non-linear function.
2.7.5 Safety First Decision Rules

There are three types of "Safety First Rules" (SFR) that may be used for
decision analysis. The first rule, developed by Telser (1955-56), assumed that a
decision-maker maximizes expected returns E[X] subject to the constraint that the
probability of a return, less than or equal to a specific amount (EMIN), does not
exceed a stipulated probability (SP). Telser’s SFR is to maximize E[X] subject to p( X
< = EMIN ) < = SP. Each SFR is well illustrated in Elton and Gruber (1987).12

The decision-maker first determines a threshold level of income (EMIN) and the
probability with which incomes must exceed this level (SP). These values are the key
indicators of risk attitudes under Telser’s SFR. This same decision rule is outlined in
Elton and Gruber (1987).

The second safety first decision rule was developed by Kataoka (1963).
Kataoka’s SFR chooses a plan that maximizes the lower confidence ”level of income"
(INCL) subject to the constraint that the probability of income (X) being less than or
equal to the lower limit, does not exceed a specified value, 'Plimit.' in effect, this rule
maximizes the return along a fixed lower confidence Plimit.

Kataoka’s SFR is: maximize INCL subject to p(X<lNCL) < = Plimit.

 

‘2 Chapter Nine

84

Roy's (1952) SFR is the third-and final rule. Roy's (1952) SFR chooses the
plan with the smallest probability of yielding a return (X) below some specified income
level (INCL). The objective function is: Minimize p( X < INCL).

If a solution exists, and income is normally distributed, then all SFR's return
solutions on the E-SD frontier (Elton and Gruber;1987). SFR’s can be incorporated
into linear programming methods (e.g. see Atwood et al., 1988). The Tchebyshev
inequality can be used to approximate the probabilities in the SFR’s regardless of the
form of the pdf for income. Unfortunately, the Tchebyshev inequality gives
conservative probabilities that result in 'overIy-safe' solutions. Atwood et al. (1988)
used linear LPM's of the pdf to solve for Telser’s and Kataoka’s SFR in a linear
programming framework. These methods resulted in less conservative solutions than
mean-absolute deviation methods like those presented in Anderson et al. (1977).

These expansions of SFR's through LPM's extend the usefulness of linear
programming in risk analysis. Previously, the decision-maker’s action could not alter
the income distributions. This stipulation was satisfied for only simple problems such
as selecting pricing alternatives for a known (deterministic) number of bushels. These
new developments help apply SFR’s to chance-constrained programming problems,

as well as problems where the events are stochastic.

2.8 Previous Efforts

Early computer applications in risk management and analysis were written for
university mini-computers and mainframes. Generally, these efforts were aimed at a
group of producers typical of the area. The most common application has been

selection of risk efficient enterprise mixes, where efficiency was either E-V, MOTAD or

85
mean-LPM (e.g. Target-MOTAD). In nearly all of these early studies individual
producer behavior was assumed to be globally risk averse (R(X) > 0) and constant
(R()()’ = 0). These computer models were not intended for direct use by individual
producers and are, therefore, termed 'research-orlented efficiency studies.‘

With the advent of more powerful micro-computers, some risk management
analysis can be done by the producer without use of large computers. This category
of micro-computer risk management applications Is in early development stages, as
witnessed by the small number of completed applications. The following sections
discuss in more detail, research-oriented efficiency studies and micro-computer based

simulation efforts.
2.8.1 Risk Efficiency Studies - Research Oriented

Barry (1984), Anderson et al. (1977), Tauer (1983) and Hazell (1971) developed
models for risk analysis and management through enterprise selection. This section
overlooks efforts similar to those in order to more closely focus on efficiency studies
which include risk management through alternative marketing strategies. Table 2.4
summarizes research efforts to find risk efficient producer alternatives for marketing.
The efforts by Musser et al. (1986) and Watts et al. (1984) are included because they
compared two types of efficiency criteria across the same problem set.

Research models employing static yield assumptions might be appropriate for
post-harvest risk management, or production enterprises where output uncertainty is
minimal. These models restrict pre-harvest marketing commitments to some
percentage of the expected crop. Curtis et al. (1987a, 1987b) limited pre-harvest

contracts to 60 percent of expected production. For many Midwestern producers, this

86

Table 2.4 Previous studiesiin Marketing Risk Management for Farmers

RISK EFFICIENT MANAGEMENT STUDIES

# of # of Option Perf.
Price Fara hedge Vari-

Author Method Prices Yields Tools Entpr. Avail. able Other
Alexander, E-V St.Ave St.Ave 3 2 Mo Gross B,E,PY
et al. (1986) Month An. Revenue
Anaman & SDURF 1970- Crop 4 4 Yes Met 8,5,2
Bogess (1986) 84 Model income
Curtis, Target St.Ave Static 4 1 No S/bu 8,1
et al. (1985) MOTAD Month soybeans
Hauser & Risk/ Futures Static 3 1 Yes S/cwt F,H
Eales (1987) Return Only beef
Hudson, SDURF St.Ave Static 5 1 Yes Slcwt B,PY
et al. (1985) & E-V wkly 0 beef
Mapp, MOTAD St.Ave AES 2 8 Mo Gross 8,!
et al. (1979) 3 Sim. An. 0 Plots 0 Margin
Musser, MOTAD An.Ave Multi-Co 1 6 Mo Gross I,N
et al. (1986) & OP Cash 0 An.Av 0 (cash) Margin
Rowsell & Target Terminal Static 4 1 Yes Gross 8,1
Kenyon (1988) MOTAD Prices swine Margin
watts, T-MOT& Co.Ave Co.Ave 1 5 No Gross I,N
et al. (1984) MOTAD An. 0 An. 0 (cash) Margin

8 - Basis was historical & included 0
E - Enterprise covariances were used F
l - Covariances are implicit in MOTAD M
PY - Cov(Price,Yield) were incorporated 2

Discounted prices or Detrended yield
Fixed basis assured zero (cash 8 futures)
Mo futures prices were included
CovtPrice, Yield) = Zero

Prices are indicated as annual (An.), monthly (Month), weekly (Ukly) averages (Av or Ave).
Prices usually refer to futures and cash. Yields were state (St.), county (00.) or regional
(Reg.) averages. Gross margin is gross revenue'minus variable production costs. Net income
is gross margin minus fixed costs. All performance variables were net after marketing
costs.

simplification for a drought year could result in over-contracting. When price is the
only income risk (yield is static), there is no danger of "over-contracting" Clearly,
these assumptions simplify the model, but lead producers to pre-harvest prescriptions

that ignore unlikely, but not inconsequential outcomes.

 

87

Sources of yield, futures, and basis data are important for the usefulness of the
individual research effort and its applicability to producers. in examining prescriptions
from the research models, those that use highly aggregated yields and prices have
likely understated the variances and overstated covariances of yield and price (in
absolute terms), compared to an individual producer. if one is considering adapting a
research model to use as individual decision support software, the data used in the
research model must be replaced by individual data. Producers could substitute data
relevant for their own farms, providing such data is available.

The use of SDWRF in research models (Anaman and Bogess, 1986; Hudson et
al., 1985) is an effort to apply a newer portion of risk theory to a group of producers.
Unfortunately, SDWRF cannot easily be applied to groups without some assumption
of the underlying forms of the utility function. Anaman and Bogess (1986), as well as
Hudson et al. (1985), implicitly assume producer utility functions are negative
exponential (CARA) by using only one interval of R(X) to describe each producer
group. In Meyer (1977a), R(X) is a function rather than a constant. Replacement of
the function with constant numerical values of R(X) implicitly requires the utility
function to be CARA for all producers. The SDWRF research models may be more
suited to adaptation for individual producers than for use to characterize risk attitudes
of groups of producers.

Research models using MOTAD and Target-MOTAD require observations of
historical yields and prices to be recomputed into deviations and entered into the
linear programming matrix as they jointly occurred. Alternatively, Monte Carlo
methods and simulation solutions, could be converted to observations in the MOTAD

matrix. In either case numerous solutions to the matrix, with changing values of

88

lambda (the right hand side constraint for income) are needed to identify an efficient
set of marketing plans. Producers might have no way of knowing where they should
be on the efficient set.

Chance-constrained programming is a safety first linear programming model
which has seldom been used in solve marketing problems. Taylor and Zuhair (1986)
solved a simple peanut contracting problem with chance-constrained programming.
Adapting the Taylor and Zuhair model to incorporate several marketing alternatives
with stochastic yields and prices would be very difficult. Linear programming models
such as chance-constrained programming, MOTAD and target-MOTAD, must be
carefully constructed when building decision support components for use by
producers. \Mthout care, the user may receive a message regarding an unbounded
solution, or an infeasible one.

Research models have several distinct advantages compared to software
decision aids developed for individual producers. One advantage is that researchers
have access to historical prices, yields, variances and covariances that producers may
not have available and may not understand. A second advantage is that research
models can be run on larger and faster computers, not easily accessed by farmers.
Some research models may exceed the capacity of farm micro-computers, or may
utilize software development tools not readily available for micro-computers. A final
advantage is that researchers control the program assumptions and interpretation of
the output. This reduces programming and development time and guarantees data

quality. The disadvantages of research models will be discussed in the next section.

89

2.8.2 Micro-Computer Based Simulations

Unlike the research-oriented efficiency studies, micro-computer efforts at farm
risk management are difficult to generalize, except that all have been simulation
based. None have attempted to search for risk efficient solutions. This leaves the
task of finding superior alternatives for risk management to the producer, who then
must use trial and error to find efficient solutions. Experienced simulation users may
be able to form heuristics to more quickly locate 'good" solutions.

Knight et al. (1987) and Alderfer (1988) reviewed extension oriented risk
management software in some detail. What follows is a brief overview of four of the
software packages reviewed by Alderfer. Not summarized are a crop insurance
evaluation program developed at Virginia Polytechnic institute and a package
regarding the government feed grain program developed at Texas A. and M. Both of
these were reviewed by Knight et al. (1987).

Agricultural Risk Management Software (ARMS) was developed by King,
Benson and Black (1987). ARMS allows yields and/or prices to be entered non-
parametrically, or as normal distributions. ARMS was primarily developed to look at
the question of participation in federal all-risk crop insurance. ARMS can look at
forward contracting versus fall cash sales, but does not incorporate basis uncertainty,
futures hedging or options hedging. Three risk scenarios can be analyzed side-by-
side (with both graphics and table output) for comparison. Correlation coefficients are
entered for yields and prices within and across enterprises. ARMS uses Monte Carlo
techniques for simulation. ARMS is a stand-alone program available for MS-DOSTM

computers.

90
The ”Whole Farm Risk Rating Model' (WFRRM) was developed by Anderson

and Ikerd (1984, 1985). All pdf’s are entered using triangular distributions (low, mode,
high). The "entered“ mode is used to approximate the mean. The distance between
the high and low possible outcomes is assumed to be twice the standard deviation of
the distribution. Elicited yield distributions are assumed to be normal and price
distributions log normal. The product of yield times price distributions is
approximated as a normal distribution of expected income for each enterprise.
Calculations employ the use of appropriate correlation coefficients. Up to nine farm
enterprises may be modeled for a single farm.

WFRRM incorporates stochastic yield, basis and futures. Crop production
costs are not stochastic, but some livestock production costs are. WFRRM was
developed in BASIC for the MS-DOSTM and TBS-80'” micro-computers. The output to
the producer is expected income, optimistic (expected plus one standard deviation)
and pessimistic (expected minus one standard deviation) income for any combination
of enterprises, or for the entire farm. The four marketing alternatives available include
futures hedging, basis contract, forward contract and cash sales.

Budgeting Enterprises and Analyzing Risk (BEAR) is a Lotus template
developed at Guelph University (see Bates et al., 1987). BEAR followed the pattern
established by its predecessor, WFRRM. BEAR allows no analysis of pricing
alternatives, variances within enterprises are fixed, and covariances between
enterprises were forced to be zero. These factors may have been updated in a more
recent version. BEAR requires the user to own LOTUS, and the manual suggested

larger more powerful micro-computers to speed computations.

91

Baldwin and Dayton (1988) developed a Lotus spreadsheet template similar to
BEAR but theirs focuses on grain marketing. The template, called ”Grain Marketing
Risk Management“ (GMRM) uses a fixed coefficient of variation on all crop yields of 20
percent. GMRM incorporates price variance, but those variances are entered by
extension specialists, and are not intended to be varied by the producer.

The micro-computer based simulation software discussed are quite different.
WFRRM and BEAR are concerned with trying to analyze all farm enterprises, whereas
ARMS and GMRM are more concerned with crop enterprises. All of the simulation
models, except for ARMS, make very restrictive assumptions about the pdf’s for yields
and prices. All of the packages require numerous runs to analyze different
alternatives, and contain no incorporation of decision rules or efficiency criteria to

assist the user.

2.9 Summary

This chapter began with principles in risk, probability, and utility theory that
established a foundation for the remainder of the chapter. A marketing decision
model was presented to show how the problem could be described (the right hand
side). Of particular emphasis was representing distributions for the stochastic factors
of basis, futures, and yield.

Methods of describing the probability distributions on the right hand side
included historical data, option pricing models for futures, and subjective probability
elicitation. Candidates for representing uncertainty include triangular functions,

discrete functions, and smooth parametric functions like the normal and Iognormal.

92

Subsequent to the right hand side discussion of how to describe or represent
the problem, the focus became how to decide the problem. Decision Rules and other
supportive methods that are candidates for use as Decision Support System Tools, for
problems with significant economic risks were reviewed. The list of methods was not
exhaustive, but rather an attempt to identify and briefly describe appropriate
alternatives. The later portion of the chapter focused on risk efficient research models
versus micro-computer based simulation software.

The risk efficient research models are quite different than the micro-computer
based simulation software. The research models tend to make restrictive
assumptions about risk behavior. For producers whose risk attitudes are accurately
represented, the risk efficient research models could be adapted for individual use for
decision support. This would eliminate repeated simulations that would be needed to
find similar results using micro-computer based software. Unfortunately, producer risk
attitudes are not simple (see section 2.6.2), and are probably not stable over time,
due to changes in wealth, age, and other factors.

To increase the value of information to the producer regarding marketing and
risk management, more processing is needed than what is provided in the micro-
computer based simulation models discussed. The mainframe research models
provide some help in this area, but are not designed as DSS components for
individual users. The method selected, was to elicit risk attitudes of producers
(Bernoullian utility) and incorporate those attitudes into the DSS. The utility curves will
be used along with simulation and optimization to find superior marketing alternatives
in the neighborhood of the optimum.

In Chapter 3 this proposed solution will be further defined.

CHAPTER THREE
THE FIRM MODEL

3.1 FIRM Model Overview .................................... 94
3.2 The Audience .......................................... 96
3.3 Generating Yield Distributions (ELICIT) ........................ 97
3.4 Generating Price Distributions ............................. 100
3.5 Adjusting Monte Carlo Observations ......................... 103
3.6 GENRINC ............................................ 104
3.7 Measuring Risk Attitudes (ELRISK) ......................... -. 106
3.8 Marketing Simulation - The Objective Function ................. 114
3.9 Finding Superior Marketing Plans (MKTOPT) .................. 121
3.10 Post-Optimal Solutions .................................. 126
3.11 Issues .............................................. 128
3.12 Future improvements to FIRM ............................. 131
3.13 Summary ............................................ 134

93

94

Farm Income Risk Management (FIRM) is detailed in this chapter. Several
topics related to FIRM have been presented in Chapter 2, but their relationship to the
model should be more completely understood following this chapter. A research
model of FIRM was developed, as opposed to a finished end-user package. A
hypothetical producer of 250 acres is used to demonstrate FIRM. The producer
should not be misunderstood to be representative, average or typical, but instead
merely a case farm.

The chapter begins with a brief overview of the FIRM model, followed by a
description of the appropriate target audience for the research. Beyond this are major
sections that discuss each of the FIRM components. The chapter concludes with a
short discussion of FIRM’s strengths and weaknesses, a section for future

improvements, and a summary section.
3.1 FIRM Model Overview

FIRM is a set of DSS components that allow a commercial grain producer to
analyze pre-harvest risk management through commodity marketing. FIRM requires
input on market prices, and distributions of prices and yields expected in the future.
FIRM measures farmer yield predications and risk attitudes and finds a portfolio of
pricing alternatives that maximize expected utility. Other portfolios near the optimal
one are also outputted for comparisons. Following optimization, the manager can
enter custom marketing plans and compare them to the best plan.

FIRM uses option premiums to generate an ending period 'Cumulative
Distribution Function' (CDF) for futures prices. CDF’s are also formed for basis and

yield using historical values (if they exist) and subjective modification. Monte Carlo

95

 

 

 

PRICE
DISTRIBUTION ELICIT
PROGRAM

l l

Price Distribution Yield Distribution
Data Data

 

 

 

 

 

 

 

 

 

 

 

 

IL GENRINC II
ll
1
Gross Margin
Distribution Data

 

 

 

 

l
ELRISK

 

 

 

 

Market I

Data Utility Distribu-
tion Data

—-ll mm ll

1 I

Optimal Solutions, Near Optimal,
and User Entered Marketing Solutions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.1 Components of FIRM and their linkages

observations on the distributions are generated. FIRM first simulates the 'all cash'
marketing plan to determine the expected gross margin for a single commodity and
its standard deviation. These two values are inputs to seed an expert system that
measures producer risk attitudes for the gross margin distribution of the crop. Next,

non-linear optimization searches for mixtures of pricing alternatives that maximize

96

expected utility. FIRM is a single crop, non-dynamic, stochastic simulation and non-
linear optimization program. Figure 3.1 shows how FIRM is organized.

There may be important correlations between crop yields, futures, and basis
for the crops produced on a farm. This would especially be true if more than one
crop were examined simultaneously. It was decided early in development to focus on
a single crop marketing model (particularly soybeans). If a single crop model could
be developed, then perhaps a two crop model could follow.

The following sections examine each of the major components of FIRM.

3.2 The Audience

The target audience for this research is commercial grain producers with
above-average understanding of marketing and management. Farm size is not a
selection criteria for the target audience and neither is financial condition, age,
education, or computer experience. These later factors were not considered
important because of the heterogeneous characteristics of farmers. The farm factors
just mentioned might indirectly affect solutions, but many types of farmers are
welcome in this 'target-audience.‘

Above-average management skills and marketing knowledge are needed to
complete the input data and interpret the solutions. It is possible that marketing
consultants and advisors could use the model to provide a service for producers with

a weaker understanding of commodity pricing tools.

97
3.3 Generating Yield Distributions (ELICIT)

FIRM was designed to be run at any time through the growing season. Yield
uncertainty can be quite high at planting time. As the season progresses, more
information is revealed and the yield typically becomes more certain. A mid-season
forecast of a yield distribution should include all the crop development to date, plus
the uncertainties related to the remainder of the season. To capture this process with
historical data would be nearly impossible, since farm records on mid-season yield
forecasts have probably not been kept. Plant growth models were a possibility
mentioned in Chapter two, but a suitable candidate was not available. The only
reasonable sources in this situation are objective professionals or farmers themselves.

As discussed in Chapter 2, ELICIT was used with the conviction scoring
method. ELICIT is used in the Agricultural Risk Management Simulator (ARMS)
Version 3.x. as one method of establishing yield pdf‘s for analysis of Federal All-Risk
Crop Insurance.

ELICIT results in a discrete pdf like the one in Figure 3.2. for the case farm.
ELICIT stores values for pdf, CDF, sample mean, and sample standard deviation in an
ASCII text file named by the user. The file is automatically given a '.PRB" extension.
A portion of this file is shown in Table 3.1 for the case farm pdf in Figure 3.2.

In FIRM, yields are elicited in this manner and a list of the CDF paired values
are formed. One vector in the table is the CDF(x) and the other is x; where x is the

upper end of a range of equal interval yields. The CDF(x) is bounded by zero and

 

. HELD r;gg,.g.[LlilEE BF ;-'-:-:.‘Exeans I/HCFE} __ ‘ ___

 

toe“ .
variation:
19

 

 

 

 

 

 

 

 

 

 

 

“ RUEMGE : 37

WW%AQN%W

PDF '4) 2 9 0 t7 0
- 2 _c It; 31 _ 73_ so r so
F1=Help F2=Prev. Screen F7=Print F9=llherefinl? F10=llenu

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0

 

 

 

Figure 3.2 The Case Farm Yield Distribution (pdf)

one. Numerous UNIFORM(0,1)‘ observations are created with a random number
generator (FIRM uses a default number of 200 Monte Carlo observations). The default
can be increased or decreased. The random numbers are some proportion between
two CDF values. To demonstrate, the mode (.5 CDF) for the case farm, falls between
.3125 and .7292 in the CDF values that correspond to 34.99 bu/ac. and 39.99 bu/ac,
respectfully. One half (.5) is 55 percent of the distance between the two CDF values
(above .3125). Fifty-five percent of the way from 34.99to 39.99 is 37.74 bushels per

acre.

 

‘ A specific uniform distribution is usually denoted by its name, followed by the two
boundaries.

Table 3.1 Portion of ELICIT Output

 

A Portion of an Output File from
ELICIT for the case farm

0.00 4.99
5.00 9.99
10.00 14.99
15.00 19.99
20.00 24.99
25.00 29.99
30.00 34.99
35.00 39.99
40.00 44.99
45.00 49.99
50.00 54.99
55.00 59.99
60.00 64.99
65.00 69.99
70.00 74.99
E[yld.] =
St.Dev. =

40.00
100.00
40.00
20.00
5.00
0.00
0.00
0.00
0.00

36.77 bu/ac
6.85 bu/ac

0.17
0.42

0.08
0.02
0.00
0.00
0.00
0.00

CDF*100

31.25
72.92

97.92
100.00
100.00
100.00
100.00
100.00

 

This linear mapping between the CDF and its values changes 200 random

numbers into observations of yield whose PDF and CDF, look like the ones the farmer

suggested in ELICIT. The net result is that a discrete yield distribution has been

converted to 200 samples of the yield distribution.

Pease et al. (1990) concluded from their experience in using ELICIT, that

"The authors have not figured out good methods for elicitation in the absence of a

‘professional' performing the elicitation. The interaction between the grower and the

100

individual performing the elicitation has been important in our studies and in Extension
meetings.‘ (draft, unnumbered)

This is to be expected with any user of new software. Computer software
learners naturally learn well with 'hands-on' training of new software. The student -
teacher interaction is also expected to be valuable. However, it should be possible to
train in a workshop setting and expect the producer to later be able to use the
knowledge and software on his or her own farm.

Justifying the selection of ELICIT to be part of the FIRM model is not difficult,
since there was almost no other available method to measure mid-season yield
distributions. A distant second choice would have been to elicit a triangular yield
distribution directly from the producer. This second choice would have been a shorter
subjective procedure, but errors in the distribution tails might have been substantial.
Empirical research comparing the elicitation of triangular distributions to output from

ELICIT was not available.

3.4 Generating Price Distributions

FIRM used manual entry of the mean and standard deviation of both futures
and basis, and assumed that both were normally distributed and uncorrelated. The
correlation is actually a user input, but all analysis in this research were run with the
correlation set to zero. The current futures price and basis levels implied the
expectation of the ending period distribution, if markets are efficient. Thus, today's
futures price is equal to the mean of the ending period futures price distribution. For
example: the case farmer called the elevator for fall soybean prices. CBOT November

soybean futures were trading at $61825 per bushel, and the forward contract for

101
delivery in mid-October was $6.08, with $-.1025 equal to the basis (ignoring
transactions costs on futures). The $61825 and $-.1025 are the desired means for
the ending distribution of futures and basis, if markets are efficient.

With normal distribution and a mean, only the volatility is needed to completely
describe a futures or basis distribution. Hilker and Black developed software to
examine two different option pricing models. They examine the "Black Option Pricing
Model“ (BOPM) with a conversion to normality. They also examined a model like the
one used in ARMS 3.0 (King, Black and Benson;1987). Values from their software
generated futures price volatility estimates that were entered by hand into the file
called PRICE.DAT. Fackler and King (1990) have continued research in this area.
They support evidence found in other research (Mann and Heifer;1976, Hudson et
al.;1986) rejecting the hypothesis that futures prices should be log normally
distributed. Hudson et al. (1986) summarized:

These results have implications for option pricing. Black’s option pricing

formula assumes log-normality and constant variance. The recent move

toward normality in commodity price changes suggest that such formulas may
adequately represent the actual value of the commodity traded on option
markets. Also, hedgers who rely on the portfolio theory of hedging typically
maximize revenue given risk (variance). These results suggest that the
variance exists and Is finite, allowing portfolio models to be used optimally?

The choice of a particular "Options Pricing Model' (OPM) has not taken place
for an end-user version of FIRM. The availability of a reasonably good OPM facilitated
testing FIRM. Further research in this area is needed. it should be noted that using

the BOPM or other no-arbitrage based models should still be better than eliciting

subjective price distributions from farmers (as done for yield). Thompson et al. (1988)

 

2p.14

 

102

found in their survey that farmers underestimated market variance compared to the
variance implied by BOPM.

An improved version of the Fackler and King (1988) non-parametric model
discussed in section 2.5.1 does exist, has been viewed, but was not available for
evaluation. An added alternative is the coupling of two or three OPM's into a
composite forecast. Such a model could use volatility measures that are historical
(e.g. prior 20 trading days volatility) or implied by one or more of the OPM’s. As new
research makes improvements in volatility forecasting, this portion of FIRM should be
updated.

With efficient markets (see section 2.4), the futures market provides an
unbiased forecast of the ending period mean price. Additionally, if options markets
are efficient, they give the best estimate of the volatility being implied by the market
through’option pricing models such as Black (1976) (also Cox and Rubinstein;1985).
Occasionally during a trading day a particular option premium will have both a BID
and ASK price. This evidence of illiquidity and non-existence of a risk neutral value,
violates assumptions of the BOPM as well as Cox and Rubinstein (1985) model. The
OPM by King and Fackler (1985) assumes no particular distribution, but depends on
thinly traded option premiums and assumptions about the tails of the distribution.
OPM's are the best currently available tool for forecasting the futures distribution. The
OPM’s are surely an improvement on subjective price elicitation, but are they good
enough? An answer is not expected, but may come through extensive future
research.

An added concern is the distribution functional form for the probability density

function. If it is "properly defined", the result is the market's implied pdf for futures

 

103
contracts. Of course a major research issue is the best functional form (normal, log
normal, other) to best describe the total pdf implied by the options markets. This

issue is addressed in Chapter Five.

3.5 Adjusting Monte Carlo Observations

With efficient markets, the price generator needed to generate prices with
average values the same as expected price. Otherwise, false arbitrage opportunities
could have existed in the data. If the ending period price distribution has an average
value of $6.01 /bushel, but today's forward contract price for that period is only
$6.00/bushel, there is opportunity to make (on average) one cent per bushel. Monte
Carlo methods have difficulty creating distributions with means precisely equal to the
desired value, except with extremely large samples which increase computational
costs and time. One vector of 200 prices may have a mean slightly below the desired
mean, and the next vector computed may be above the mean.

Adjusting the mean of the Monte Carlo vector for prices is a simple matter of
moving all observations by a distance of E/n, where E Is the error in the two means
and n is the number of elements in the vector (200). Suppose the market price for
futures is $6.18, but the 200 observations on ending period futures have a mean price
of $6.17. The error of $.01 is divided by 200 observations, and all elements of the
vector are increased by $.01/200.

A similar process is used to adjust observations of symmetric distributions to
give exact desired sample standard deviations. These later changes are based on a
ratio of 'desired total sum of squared deviations” (DSSD), divided by the 'sample sum

of squared deviations“ (SSSD) for the 200 Monte Carlo observations. X, is each

104

sample observation and l is all integers from 1 to 200, denoting elements in the
vector. XBAR is the desired mean, and each X, was compared to XBAR (see equation

3.1)..

if the x, > XBAR then:

XI = XBAR + SOR(((X,-XBAR)’- (DSSD/SSSD)) (3.1)
If the X, < XBAR then:

x, = XBAR - son(((x, - XBAR)’- (osso/ssso»

Of course if X, = XBAR it doesn’t need to be adjusted.

3.6 GENRINC

The purpose of GENRINC is to compute a mean and variance, of the ending
period gross margin distribution, when the Monte Carlo production (yield times acres)
is sold on the uncertain cash market (futures (1) plus basis (6), using the notation in
Chapter two). They are used as measures of the magnitude and range of gross
margin.

GENRINC is listed in Appendix G; its output file "BUANDINC.DAT' is in Table
3.2.' It requires the producer to enter the number of acres of the crop (soybeans), the
variable costs per acre for production, as well as the remaining variable costs that are
yield dependant. Examples of these later expenses include harvesting, trucking,
drying etc., and are not to be double counted with the per-acre costs. Producer crop
acreage is calculated according to rental arrangements. Acres that are owned and

cash rented for the crop in question are added to the producer’s proportion of share-

 

105

rented acres for that crop. Summing these gives the effective production acreage.
The producer must also enter the name of the data file from ELICIT.

GENRINC reads the data file from ELICIT to capture the CDF values for yield.
GENRINC also opens the 'F&BDIST2'.DAT file, where 200 independent observations
of futures price and basis are stored. Zero-one uniform random variables are created
using the Microsoft OuickBASlCTM function, RND. These values are converted into
200 observations of yields as discussed in section 3.3.

All of the Monte Carlo values are stored to disk and summarized with sample means

and standard deviations.

GMi =(f, + b1 - c)-a-yi - C-a (fori = 1 to n) Where: (3.2)
GMi = the ith observation on gross margin (all cash sales)

fi = the ith observation on futures prices

b1 = the ith observation on basis

y, = the ith observation on yield

a = effective acreage

C = per acre costs (seed, chem, fuel etc.)

o = per bu. costs (harvesting, drying, trucking)

n = number of Monte Carlo observations (usually 200)

GENRINC was used to compute an expected gross margin, standard deviation of
gross margin, total costs, and gross income. All of the gross margin Monte Carlo
values were stored on a disk and summarized. The output file for GENRINC is called
BUANDINC.DAT. That file consisted of a brief heading, four columns of numbers, and
a footer. The BUANDINC.DAT file for the case farm is shown in Table 3.3.

The top line of the file shows the number of Monte Carlo observations to be
listed, the number of acres of production (250), variable costs per acre ($57/ac.), and

variable costs related to yield ($.3/bu) (from left to right, respectively). The remainder

106
Table 3.2 BUANDINC.DAT file created by GENRINC

200, 250, 57, .3, footer has moments

Total bu. Gross inc. Total costs Net inc.
8923.971, 45425.75, 16927.19, 28498.56
11984.88, 73775.27, 17845.46, 55929.81
7211.078, 47274.95, 16413.32, 30861.63

(195 more lines here)

9175.797, 65904.46, 17002.74, 48901.72
7158.459, 50047.78, 16397.54, 33650.24

Var . Average St . Dev . Skewness Kurtosis
Bum Prod. 9081.563, 1748.188, 5.691607E-04, -3.000179
Net Inc 38122.09, 11280.13, 8.820823E-05, -3.000014

 

of Table 3.3 is labeled. As GENRINC is run it also presents a screen image of the
summary information, for the user to view.

The important results from GENRINC are the expected or mean gross margin
($38,122.09) and the standard deviation of gross margin ($11,280.13). These two
numbers are entered into the next program to give a starting place for eliciting risk

aufludes.

3.7 Measuring Risk Attitudes (ELRISK)

At this point, it might help to re-examine Figure 3.1 (diagram of FIRM) to
examine what has been covered in FIRM, and what remains. All of the distributions
have been created, and all of the static information has been entered into the model.
The first simulation (GENRINC) has been done to compute the mean and standard

deviation of the gross margin, if the producer sells all grain at the spot price in the fall.

 

 

107

Software presented in this section will measure producer’s risk attitudes in the
neighborhood of the gross margin distribution that the producer will confront.

ELRISK is an expert system based on an "Equally Likely Risky Outcome"
model. Expected gross margin and the standard deviation (values from GENRINC)
seed elicitation values in ELRISK. Using the values of mean and standard deviation is
not an admission that gross margins are normal, nor that producers only consider the
first two moments. Instead, they are starting values that ensure the utility curve
elicited is in the neighborhood of the income distribution.

As suggested by Musser and Musser (1984), the elicited preferences are
described in the context of the problem the producer actually faces. For this reason,
ELRISK uses terms like “situation“ rather than 'game“ and “marketing plan“ rather than
“lottery.“ ELRISK also stresses that marketing plans presented in each situation that
they face (not 'play"), are based upon their individual gross margin distribution.

ELRISK sequentially presents the producer with two marketing plans to be
analyzed. Each plan has two possible outcomes of equal probability. The producer
is reminded that these outcomes should be considered gross margins for the crop
analyzed, and for the same time period (annual). Three of the four possible outcomes
in the first two plans are a function of the mean and standard deviation of gross
margin. A risk-neutral value for the fourth outcome, giving equal expected outcomes
for the two plans, is suggested to the user for revision. ELRISK seeks a revised fourth
outcome, which makes the user indifferent between plan A and B. Expert system
rules ensure that one plan does not dominate the other, and they establish new
situations. Elicitation continues until utilities have been elicited for incomes that are

approximately two standard deviations above and below the expected income. The

108.

logic and expert system rules of ELRISK have been written in a standard programming
language (FORTRAN) for added flexibility.

Halter and Mason (1978) used a similar method for establishing only five points
on a utility function. ELRISK uses a modification of the Halter and Mason (1978)
method to elicit 10 to 14 points. The expert system logic in ELRISK rounds the
distribution mean and standard deviation input, establishes new situations and checks

for errors and consistency. No specific form of the utility function is assumed.

 

 

 

 

 

Situation 1 Situation 2
Marketing Plans Marketing Plans
PROB A 8 PROS A B
.5 Mean - .5 7 from
Bad Year Stand. 7 Bad Year Game 1 7?
Dev.
.5 Mean + Mean + .5 Mean + Mean +
Good Year Stand. 1/2 * Good Year Stand. 1/2 *
Dev. StDev. Dev. StDev.

 

 

 

 

 

 

 

 

 

 

 

Figure 3.3 Structure of Situations 1 and 2 in ELRISK

Figure 3.3 shows an example of situations one and two. Every situation is
shown to the producer on a separate computer screen in ELRISK. In Figure 3.5 this is
not the case because we are focusing on the theory of the game. In situation one,
the decision maker must enter an income level in the quadrant marketed by “?", that
makes him or her indifferent between marketing plans A and B. in subsequent
situations, the values of the other quadrants are varied and a new indifference level is

sought

 

109

Halter and Mason showed that if the response to the second situation
(indicated by “??") is arbitrarily given a utility of 200, and the mean minus one
standard deviation is given a utility of zero, then the response to situation one
(indicated by “?“) must have a utility of 100. To demonstrate why:

Game 1: .5(0) +.5U(k,) = .5U(?) + .5U(k,) (3.3)
Game 2: .5U(?)+.5U(k,) = .5(200) + .5U(k,)

Since all probabilities are equal in Equation 3.3..

Game 1. 0 + U(k,) = U(?) + U(k,) (3.4)
Game 2. U(?) + U(k,) = 200 + U(k,)

Solving for U(k,) in game 2 of equation 3.4,

U(k,) = 200 + U(k,) - U(?) subbing this into U(k,) of game 1 equation 3.3

0 + 200 + U(k2) - U(?) = U(?) + U(k,) combining terms gives...
200 = 2U(?) { ? = response to first game in S}
U(?) = 100

The previous condition holds, if the respondent’s behavior satisfies the
principle axioms of expected utility theory. After the first 2 games there are dollar
values for three utility levels. These three levels 0, 100, 200, can be used to
sequentially build the remaining situations. If plan A is a choice between U($) = 100
and U($) =200, while plan B is a choice between U($) =0 and a response field, the
user response, in dollars will be the dollar value for U($) =300. This is true to satisfy
principal EUT axioms. This process continues upward until the last point surpasses
the mean plus two standard deviations. The process can be reversed with the dollars
for U=(0,100) in plan A, and plan B is U=(?,200). The user response to ? in this case

is U=(-100).

110

The risk attitudes generated are specific for an individual, at a particular wealth
level, regarding a particular commodity to be produced and marketed. ELRISK can
be used in other contexts besides commodity marketing, but it is still sensitive to the
context in which it was elicited. Context dependence makes the situations presented
more “real“ to the decision maker, but limits any other contexts in which the utility
function could be applied.

Previous risk attitude measurement research (summarized by Young, 1979)
has included (1) experimental games with real payoffs, (2) games with no payoff, and
(3) observed economic behavior (OEB). Each of these three classes of risk
measurement have disadvantages (see section 2.6.1).

ELRISK is similar to direct elicitation of utility methods with no payoffs, except
producers are reminded that income levels used in ELRISK are theirs. Also, their risk
attitudes reflected from ELRISK will affect marketing recommendations that are found
in the utility optimization model following ELRISK. Thus, ELRISK is context sensitive,
so that producers and users have strong incentives to carefully consider their
response, if they know it will impact their solution.

The first choice when operating ELRISK, is to choose between using the mean
and standard deviation, or a triangular distribution to describe the probability density
function (pdf) of the gross margin. Recalling the mean and standard deviation were
$38,122.09 and $11280.13, respectively, these numbers were entered by the manager
of the case farm. ELRISK uses a complex set of rules to round the input values.
These rules can be found in the code for ELRISK in Appendix H. The case farm input

values were rounded to $40,000 and $12,000 for the mean and standard deviation.

111

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Situation 1 Situation 2
Marketing Plans Marketing Plans
PROB A B PROB A B
.5 .5 ? from $35 K
Bad Year $28,000 ? Bad Year Game 1 ??
($34K) $31K ($37K)
.5 .5
Good Year $52,000 $46,000 Good Year $52,000 $46,000
Average $40,000 $40,000 Average $41,500 $41,500
Values in parenthesis are risk neutral computer suggestions.

 

Figure 3.4 Case Farm ELRISK Situations 1 and 2

Figure 3.4 shows the basic method for seeding the risk elicitation. The case
farm manager was asked in Situation 1 which marketing plan (gross margin for
soybeans) was preferred (A or B) when the $34,000 was inserted for the “7“ value. in
this situation both plans had the same mean return, but a substantial difference in
variability. The farmer said that marketing plan B was his choice (because it is less
risky). ELRISK responded with a message that “if plan B was preferred, the manager
must lower the value in the cell marked “?“ until he or she became indifferent between
plan A and the revised plan B.“ The case farm entered the value of $31,000 in the
upper right corner of situation 1 (marked by the single question mark in Figure 3.4).
Oueried amounts can be revised numerous times. Each time they are revised, a new
average for Plan B is recalculated and the screen is updated. When the producer is
satisfied with a situation, function key 10, <F-10> is pressed and ELRISK moves to

the next screen and a new situation.

 

112

Situation 2 depends upon the “?“ response given by the producer in situation
1. In Situation 2 the bottom values were unchanged. Risk neutral values (equal
average incomes) were suggested, and the producer was asked whether he preferred
A or B. Again, plan B was safer, he preferred it, and the computer reminded him to
lower the value in the upper right-hand comer of Situation 2. The case farm manager
entered $35,000.

During the development of ELRISK, it was discovered that many decision
makers wanted to find the risk neutral situation if it was not given to them. This is
called anchoring (von Winterfeldt and Edwards;1986)°. From this reference point or
anchor, they would proceed to revise. For this reason, ELRISK starts the producer
with plan A and plan B each having the same average gross margin. After deciding
which plan they prefer (A or B), the software rules suggest whether the value to be
elicited should be moved up or down.

Using Figure 3.4 and the expected utility, theory in Chapter 2 the case farm
has identified the following preferences U($35,000) = 200, U($31,000) = 100 and
U($28,000) = 0. The process continues using the known values. If plan A is
U(.5(U= 100) /.5(U=200)), and plan B is U(.5(U=0)/.5(???)), then the producer
response for U(???) = 300. This process is repeated both upward, and downward,
according to stopping rules. The slashes are used here to represent differing
outcomes, and probabilities proceed the known dollar values.

There is a consistency check for U($) = 200. If the dollar values for
U($) = 200 differ by more than 5 percent, the user can (1) back up and replay that

situations, (2) average the two dollar values, or (3) take the previous dollar value and

 

3p. 541

113

 

 

 

1000+
RISK PREFERENCES UTILITY [HOME
800-

* 700 68,000
600- * 600 59,000
, * 500 52,000
U 4004- 1' 400 45,500
T * 300 40,000
I 200» * 200 35,000
L " 100 31,000
1 0-- * 0 28,000
T * -100 25,000
Y -200- * -200 22,000
* -300 20,000
-400<- * 400 19,000
* -500 18,000

-mn l i l I

"V l l I fl

16000 29000 42000 55000 68000
Income (in same mits as entered)

 

 

 

Figure 3.5 Output from ELRISK

proceed. The first alternative (to back up) is best when the answers differ
substantially. The second alternative (averaging) is fine when the two values are
moderately close, and the third (use previous value) is used when the two values are
very close, but not within 5 percent. For example of the third case, suppose a gross
margin distribution goes from $ 0 to $ 10,000 and U($150) = 200 and the consistency
check shows U($140) = 200. In this situation the percentage differences are more
than 5 percent, but not really significant because of the comparative size of the
distribution.

Figure 3.5 shows the ELRISK results for the case farm. The values of utility on
the Y axis are cardinal; like the measure of temperature. Any linear transformation of
the scale results in new utility values, but the same shape of curve and the same
optimal risk solutions. Curvature is more important than the absolute value of utility.

if a producer has two marketing plans with expected utilities of 200 and 201,

how much is that difference in tangible terms? The answer is to convert the U($) =

 

114

201 and U($) = 200. These dollar values are called certainty equivalents. Subtracting
one certainty equivalent from the other gives a risk premium between the two utility
values. The risk premium is in dollars and for FIRM the dollars are gross margin.

The ELRISK utility function is used in a table-lockup function like the one
described to ELICIT yields. ELICIT uses probability on one axis of the CDF(x) and
yield (X) on the horizontal axis, while ELRISK examines income (x) versus its utility.
Both result in paired vectors of non-decreasing elements. One difference, between
them is that the CDF of yield is bounded by zero and one, while utility and income for
the marketing problem are not bounded. Both paired vectors are evaluated with the
same table look-up subroutine that extrapolates linearly between two elements, and
beyond ending elements if necessary.

From previous research (Love, 1982; Ramaratnam et el._ .1986), it was
demonstrated that utility functions for farmers were quite varied. Rational producers
could be risk preferring at some income levels and risk averse at others. Measuring
utility with DEU offered behavioral flexibility not offered by most decision criteria.
Maximizing utility is not only flexible, but offers higher levels of discrimination than
decision criteria. Naturally, if utility is measured inaccurately, the solution will be

erroneous.

3.8 Marketing Simulation - The Objective Function

To find optimal marketing strategies that maximize expected utility...

115

 

n m
E[U(>'<)] = 2 U, [ 2 N,-G,,j -(C-a) - c-(aoyj) ]

max j=1 i=1 (3.5)

n
m
st. 2 N1 5 E[y]-a-3 and 0 s N, 5 z1
i=1
Where:
E[ ] = the Expectations operator
n = number of Monte Carlo (MC) observations (usually 200)
y,- = MC observations on yield
G1, j = marketing revenue or marketing method (i = 1 to 6)
N1 = Number of bu. marketed in the Gi way
C = direct costs per acre (vary only with intended yield)
c = costs which vary according to actual production (i.e. trucking, drying etc.)
U[] = utility function or table lookup values for utility conversion
21 = default for z is (3/2)-a-E[y]) for cash market contracts (i=1,4),
otherwise default for z is (2-a-E[y]) (i=2,3,5)

m = the number of marketing alternatives available (including spot sales)

For FIRM, n (the number of Monte Carlo observations) is usually 200 and m
(the number of marketing methods) is 6. Spot harvest sales are one marketing
method, but the No for spot sales is a residual, since production is stochastic. The y
vector is created from the producers subjective yield distribution. The research model
has independent yield, basis, and futures. Bivariate basis and futures were possible,
but that correlation was kept at zero throughout the research for consistency. The
correlations for yield to basis and futures vectors were also zero. This allowed the
researchers to set up all the price data and the distributions on the evening before,
resulting in a shorter workshop on the following day and common price distribution for
all producers at a particular workshop. While some producers may have significant
non-zero correlations between the three stochastic variables, the logical base plan for

research is independence.

116
FUNKSHUN is the marketing simulation that is being optimized in MKTOPT.

The entire FUNKSHUN subroutine is listed in Appendix l. The value returned by
FUNKSHUN is expected utility of a particular marketing plan. FUNKSHUN calculates
the like equations which follow.

The marketing simulation can be subdivided into each of its 6 ways of
marketing (each G,, J) for i = (1 to 6). The six ways are ordered in the same
sequence that MKTOPT outputs them to the screen or printer, with forward contract
(the left most column) being G1, J. Production and transportation costs are considered
elsewhere in the marketing functions, so the only costs in this section are pricing

costs. GM. represents gross revenue for forward contracting as shown below.

G1. J. = N1. FCPo for all j Monte Carlo observations (3.6)
Where: G1.J = gross revenue from forward contracting (non-stochastic)

N1 = bushels fonivard contracted (control variable)

FCPO = forward contract price in time 0

The other cash market contract is a basis contract in column four of the
MKTOPT output. Gm is stochastic basis contracting income, and N, is number of
bushels to basis contract. Bushels yet to sell in the cash market (NW) are reduced
by N, and N,. G6,, is remaining cash bushels to sell (or buy if over-contracted). Ned.
is bushels to sell in the uncertain cash market, and is a residual variable (not a control
variable). Gross revenue from basis contracting and cash sales are equations 3.7 -
3.10.

cm = N,- (13c0 + £3) . (3.7)

Q,- : (3“Y3) ' Na ‘ N1 = No.3 (3-8)

IF Q, 2 0 THEN G6,,- = 03- (fj+b,) .sueilingtheresidual. (3.9)

117

IF Q, < 0 THEN Gs”, = Q,» (fa-+1354» ASK-BID) ...buying grain (3.10)

Where:
N6, j = Quantity remaining to be sold in the ith Monte Carlo
(a- y,) = acreage times the ith Monte Carlo of yield (production)
ASK-BID = elevator “spread“ if buying grain to meet contracts (can be zero)
G... J = a stochastic revenue from basis contracting
G6, , = a stochastic revenue from cash sales (could be negative)
BC, = basis contract level in time zero

The ASK-BID is a cash spread or any type of penalty for not delivering all the
bushels in a cash contract. The ASK-BID is a user input and can be set to zero, if
there are no penalties for not filling a contract. If equation 3.10 is true, then the
revenue for cash sales (Gm) is negative, since N5“, is negative. At this point, all cash
grain in the simulation is disposed. Hedging does not require offsetting by a precise
number of bushels. The remaining marketing functions are futures hedge (Gm), put

hedge (G3, J) and a speculative call position (Gm). For futures hedging:

G2,j z N2.[(fo"f3) " I't’ (AMf + TCz) “ TCz) ] Where... (3.11)

AMf

average margin deposit per bushel (for futures)
time in months that margin money remains on account

o-b
ll

f, = the futures quote at the time the hedge was initiated
TC2 = round trip per bushel brokerage commission

N2 = number of bushels to futures hedge

G2, 3 = a stochastic revenue from futures hedging

Annual interest/ 1200
ending period futures price (stochastic)

The formula for G2,J uses a constant margin requirement (AMf) and interest
rate. Persons who routinely hedge may use U.S.Treasury Bills as security in their
margin account so that the opportunity cost (interest) is zero, since the Treasury Bills

still grows in value while in the account. Persons who fear margin calls while hedging

 

 

118

can commit extra margin deposits at the start. This makes futures hedging more
costly and less attractive than the cash market instruments.

The two remaining plans involve options, but a few new variables are needed.
The “Put Premium“ (PP,) is a function of the ending period futures price (1,). PP, is
the beginning premium at the time of purchase, and the “Call Premium“ is CP,; with
CP0 equal to the purchased call in time zero. The “Strike Price of a Put“ option (SPP),
and the “Strike Price of a Call“ option (SPC), are set at purchase time and remain a
constant number of dollars per bushel. TC1 is one-way per bushel transactions costs
for options, and t is the number of months from the time options are purchased until a
few days before they expire. The ending time period is chosen to eliminate most of
the time value of an option, leaving only intrinsic value. Also, the last day that an
option trades can be more volatile than normal. This is due in part to the dwindling
liquidity as more traders move to the next contract month.

The formula for returns from put hedging (33,3) is ..

PP,- = the larger of (0, SPP - f,) (3.12)
IF PP, 5 Tc, THEN
(:3,J = N3-[PP3 -(1+Iot) (PPo + TC, + AMo) + A140] (3.13)
IF PP, > TC, THEN
33,, = N3-[PP, -(1+I-t) (PPo + Tc, + AMo) + AMo - TC,] (3.14)
Where:
I = (Annual interest) /1200
t = time in months that margin money remains on account
AMo = average margin deposit per bushel (for options)
PP, = the put premium at the time the hedge was initiated
TC, = one-way, per bushel brokerage commission for options
N, = number of bushels to put hedge
G3, ,- = a stochastic revenue from put hedging
SPP = the strike price of the put
PP, = ending period put premium

119

subscript for Monte Carlo observations
ending period futures price (stochastic)

-o.
9.
II II

The speculative call position is exactly as it sounds. Almost like the

calculations for puts, the one for calls (Gm) is

CP, = the larger of (0, f, - SPC) (3.15)

IF CP, 5 TC, THEN

IF CP, > TC, THEN
‘55.: = N5o[CP, -(1+ Iot) (CPo + TC, + 11140) + AMo - TC,] (3.17)

Where:
I = (Annual interest) /1200
t = time in months that margin money remains on account

AMo = average margin deposit per bushel (for options in $/bu)
CPo = the call premium at the time the call was initiated

TC, = one-way per bushel brokerage commission for options
N5 = number of bushels to speculative call position

G5, , = a stochastic revenue from speculative calls

SPC = the strike price of the call

CP, = ending period call premium

1, = ending period futures price (stochastic)

Combining the previous 6 portions into the larger objective function gives...

 

n r m
E[U($’()] = z U,| 2 N,-G,',(y,,f,,b,,t,S)-C-a -c-(a-y,) ]
j=1 Li=1 (3.18)
n
to
st. 2 N, s E[y]-a-3
i=1

st. a user adjustable constraint 2,, so that 0 s N, s (z,)

the Expectations operator
number of Monte Carlo (MC) observations

El]

3
1| 1|

120

y, = MC observations on yield

G,,J = marketing revenue or marketing method (i = 1 to 6)

N, = Number of bu. marketed in the G, way

S = Static market data such as interest rates, costs ,’today 3 bids,
option premiums and strikes, transactions costs, time and more

1, =Stochastic futures

b, = Stochastic basis

a = effective acreage (portions share rented plus all cash rent and owned)

C = direct costs per acre (vary only with intended yield)

c = costs which vary according to actual production (i.e. trucking, drying etc.)

U[] = utility function or table lookup values for utility conversion

2 = default for z is (3/2)aE[y]) for cash market contracts (i=1,4),
otherwise default for z is (2-a-E[y]) (i=2,3,5)

t = time (in portions of a year) from beginning period to ending

m = the number of marketing alternatives available (including spot sales)

By examining equations 3.4 through 3.17 it is easy to observe that the strength
of simulation is its ability to completely represent the problem. This strength is directly
related to its biggest weakness. With even a modest problem, the situation may
become complex enough that the modeling process is not tractable, and becomes a
black box to the reader. Error trapping is an added concern with simulation.
Programming errors can go undetected causing incorrect results. There is also a
problem that user input could create a run-time error (e.g. dividing by zero). In spite
of all the possible problems, when simulation works correctly, the analyst has an
opportunity to examine factors like transactions costs that simpler models may not
incorporate. Simulation can also be used to handle government commodity
programs.

Using simulation creates a need for optimization, but methods needed may
exceed the limitations of linear programming. With non-parametric utility functions.
Non-parametric yields, quadratic programming, and many math programming
methods might be less efficient than using the simulation directly in a search

algorithm. This is unfortunate since these methods are relatively fast, and if Kuhn-

121
Tucker conditions are met they will have a single global optima. As previously
mentioned, a disadvantage of most math programming methods for risk is that one or
more parameters, must be varied to solve for an efficient set. Such an efficient set for
a marketing problem with extremely divisible solutions would do little to help
producers, and requiring numerous program runs, would reduce the speed
advantage.

Producers need more than an efficient set. The reason for this, is that they
might not know where in the efficient set they should operate. They need some small
number of reasonable solutions near an optima based on their individual risk attitudes.
They also need post-optimality analysis to measure the tradeoffs of other potential
solutions. The most discriminatory method available is to elicit producer utility
functions, use those functions in a simulation model to measure uncertain income
with various marketing plans, and seek a marketing plan that maximizes expected
utility. No other method allows for such high degree of selectivity, and a highly

representative marketing model.
3.9 Finding Superior Marketing Plans (MKTOPT)

Kuester and Mize (1973) presented a simple version of Box's Complex in
FORTRAN. Complex operates by evaluating the objective function at a best guess,
and K-1 other randomly chosen vertices in the solution space. K is the number of
vertices to simulate in the solution space. The number of vertices is usually 2 to 3
times the number of search (control) variables (N). The notation for Complex follows
the notation of Kuester and Mize (1973). The objective function is inserted into a

subroutine. Values of the control variables (a vertex) are passed to the objective

122

function subroutine and the value of the objective function at the vertex is returned to
Complex.

Complex can handle explicit constraints on the control variables, as well as
implicit constraints. An example of an implicit constraint is when the sum of all control
variables must be less than some fixed value. If a vertex in the search space violates
any of the explicit constraints, it is moved a small distance (delta) inside the constraint
and re-evaluated for feasibility. Feasibility not only involves meeting the explicit
constraints, but also the implicit ones. If the objective function values of all vertices
are within “Beta“ of one another, the search stops and results are printed. “Beta“ is a
convergence parameter with the same units of measure as the objective function.

Until convergence is reached, the vertex with the lowest objective function
value is selected, and a centroid of the other vertices is computed. The “worst“ vertex
is moved toward the centroid of the other vertices a distance of “Alpha“ times the
distance of the vertex to the centroid (on a straight line when the solution space is 2
or 3 dimensions). Alpha is usually 1.3 so that some intentional “overshooting“ of the
centroid occurs. Larger alpha (1.6) increases robustness and computing time, while
smaller alpha are less robust in finding the true optimum, but are less likely to get
“stuck“ in the search process. Smaller alpha lead to an averaging process.

Figure 3.6 shows principle components of Box’s Complex with 2 control
variables. A is the lowest valued vertex in the solution space. The large C is the
centroid of all the other points. A is moved in the direction of the centroid by a factor
Alpha times the centroid to A distance. If the new point (the black square named B)
is still the “worst“ it is moved half way back toward the centroid. If it violates any

explicit constraints, the new point is moved “delta“ (a very small distance) inside of the

 

lNPUT B
W)

 

 

 

° BOX'S COMPLEX INPUT ><<1>

 

 

 

 

 

Figure 3.6 Schematic of Complex

constraints to satisfy the constraints. If the new box (b) is not the “worst“ point, a new
“worst“ point (lowest objective function value of all vertices) is selected, a new centroid
is computed, and (in the same way) the new worst point is moved toward the new
centroid. As mentioned, convergence occurs when all objective function values for all
the vertices are within “Beta“ of one another.

The routine used to optimize expected utility for FIRM is a modified version of
Box's Complex. Some of the modifications are from Manetsch and Park (1988) and
many from the author. Manetsch and Park wrote an M-OPTSIM (1986) version in
BASIC that included a variable value of Alpha. Early in the convergence process

Alpha is 1.6 to increase robustness, and as convergence proceeds Alpha is reduced

124

to 1.3 and progressively to lower values. This gives all the robustness of a large
alpha, followed by the desirable faster convergence of a smaller alpha.

Other improvements for FIRM (to Complex), were to completely rewrite the
code in a structured format using a compiled version of BASIC (MicroSoft's
OuickBASlC‘“. The version of Complex used in FIRM differs also because the 15 best
vertices (marketing plans) are printed as part of the solution. Rather than choosing a
single best guess for a vertex to seed the search, MKTOPT (the FIRM version of
Complex) uses 5 “best guesses“ (vertices 15). Best guesses in MKTOPT use only
one of the five marketing methods at a level of half the expected production, (while

the other four marketing methods are set to a level of zero. Thus..

Vertex N, N2 N3 N, N5

- k - _-_._ ___... ---_ ---_ __-_

1 = z,1 o o o o

2 = o z“ o o o

3 = o o z,3 o o

4 = o o o z,,, o

5 = o o o o 25,,

6‘15 = r11: 1 rk,2 rk,3 rk,4 rk,5
3.1.05 rk,, 5 UC, for all i= 1,2. . .6

and for all k = 1,2,...15

st. 05 Z,_, s the lesser of (UC,, .5E[y-a])

Where:
N, = number of bushels to forward contract
N2 = number of bushels to futures hedge
N, = number of bushels to put hedge
N, = number of bushels to basis contract
N5 = number of bushels for speculative call
rkl, = random number of bushels

E[y-a] = expected production

UC, = upper constraint (user adjustable)
k = the number of vertices
Z, , = best guess marketings

125
The objective function for FIRM is
Max E[U,(G,,,(N,...)] (3.20)
s.t.0 s N, 5 UC, i=(1,2,3,4,5,6)

N,,=N,+N,+N3+N,+N5

Where:
G,, , = Previous marketing functions (see section 3.8)
E[ ] = Expectations operator
N, = Bushels to sell the ith way (fori = 1,2,3,4,5)
N,5 = Total marketings (UC,5 = 3-E[production]
UC, = Upper Constraints (defaults are user adjustable)
U, = Utility of gross margin for a marketing plan

The numbers for each pricing alternatives relate directly to the subscript i in the
marketing function. Remaining production is also sold, but is not a control variable.
In fact, if negative bushels remain, the producer may have to buy back the cash
commodity at a potential premium.

Utility (U,) is computed from H, ,where H, = 2 6,“, (i = 1,2,3,4,5,6),
based upon the Monte Carlo observations of yield, basis, and futures. All U, are
summed and divided by the number of Monte Carlo observations to get expected '
utility. Each set of gross margins at a particular Monte Carlo obsen/ation (numerator
in equation 3.18) is converted into utility through a table-lockup function from ELRISK
data. From ELRISK each producer had a utility curve where the rounded expected
gross margin minus the rounded standard deviation of gross margin was equal to a
utility of 0. This is true because of the way that ELRISK was seeded. This means that
large farms and small farms are indexing their gross margin distributions via their
utility functions. This conversion into utility doesn’t precisely standardize the expected
utility (the performance criteria), but it does bring all producer's answers into a relative

neighborhood. This is a big advantage for non-linear optimization, since the beta

126
convergence parameter can be set in advance. Most producers who run ELRISK will
have expected utilities of 100 to 400 regardless of farm size. Beta is set at a default of
1.00 internally, but the default can be changed by the producer.
Penalties on undesirable outcomes can also be incorporated in Complex, but
were not utilized if FIRM. MKTOPT source code in MicroSoft OuickBASlC’" is listed in

Appendix I.
3.10 Post-Optimal Solutions

Figure 3.7 is the output from MKTOPT. The last three lines are custom plans
entered by the producer following the first 15 provided in optimization. Custom plans

allow exploration by the producer, and overcome the difficulties of contract lumpiness.

 

------- BUSNELS TO- - - - - - -
Forw. Futures Put Basis Spec Expect Exp. Risk
Plan Cont. Hedge Hedge Cont. Call SpotBu Util Prem
1 4541 0 0 0 0 4542 205.1 0.0
2 3324 52 0 420 38 5338 204.9 11.2
3 3949 0 30 950 125 4188 204.8 14.9
4 3724 23 44 188 65 5170 204.8 15.7
5 3388 0 88 0 2 5693 204.7 17.9
6 4355 0 39 0 110 4727 204.7 19.7
7 3327 28 44 225 63 5529 204.6 22.8
8 5204 16 39 391 92 3511 204.5 28.2
9 3622 0 156 0 52 5459 204.5 31.0
10 3100 156 0 0 68 5982 204.5 31.3
11 3170 15 23 162 89 5749 204.4 31.8
12 3166 46 19 0 84 5916 204.4 32.4
13 5247 12 74 159 85 3691 204.4 32.6
14 2888 0 51 0 0 6194 204 4 35.7
15 3013 0 11 0 75 6069 204 3 36.7
16 0 0 0 0 0 9082 197.0 372.6
17 5000 0 0 0 4088 205.0 4.8
18 5000 2000 0 0 O 4088 201.4 186.0

 

 

 

Figure 3.7 Part of the Sample Farm Output

The value in the expected utility column has little meaning to producers, since

it is unitless. This is much like the idea that a temperature of 38 degrees could be

127

Celsius, Fahrenheit, or Kelvin. Note that the 15 alternatives have been sorted from
highest to lowest expected utility. On the far right of the output is a column called risk
premium. Suppose each expected utility value in Figure 3.7 was converted to dollars
via the producers utility graph in Figure 3.5. The result is called a “certainty
equivalent.“ These values were not listed in the output, but if they were, the certainty
equivalent could be thought of as a selling price for the risky proposition of the
expected utility it represents. The difference between the certainty equivalent of one
plan, and that of another, is the risk premium. in ELRISK, the risk premium listed is
the difference between the certainty equivalent of the best plan listed (plan 1), and the
certainty equivalent of each of the rest of the plans. Plan 16 shows that if the
producer does no marketing between now and harvest, then by his or her risk
preferences this is $372.60 worse than the best plan in “certain“ terms. in other
words, doing no advanced marketing has a risk “cost“ of $372.60 compared to plan 1
for the sample producer. This $372.60 risk cost is referred to as the “Risk Premium
Above Doing No Marketing“ (RPANM) in the remaining chapters.

Users of FIRM (e.g. researchers, farmers, extension agents) may enter up to
five post-optimal plans to compare to the above 15. These plans can address
problems of “lumpy contract values“, where futures and options are only available in
fixed contract sizes. Post-optimal testing allows the elimination of some marketing
alternatives by setting the quantities to zero.

Figure 3.8 shows additional output from MKTOPT for analysis of means,
standard deviations, and four different percentiles. This data was computed from
FUNK2 a subroutine in MKTOPT that works just like the objective function (marketing

simulation), except that the 200 observations are sorted to give percentiles of the

128

 

 

Expected SDev. ------- PERLENIILES ---------

Plan Util. $Rev. $Rev. 5th 10th 20th 80th
1 205.1 38112 10328 17864 24016 30298 45347
204.9 38108 10487 17631 23156 30491 45705

3 204.8 38093 10401 17736 23404 30272 45493
4 204.8 38099 10427 17668 23384 30309 45556
5 204.7 38102 10475 17601 23239 30452 45751
6 204.7 38093 10349 17772 23796 30254 45305
7 204.6 38100 10488 17591 23151 30508 45687
8 204.5 38092 10265 17970 23718 30245 45226
9 204.5 38086 10435 17604 23406 30330 45594
10 204.5 38101 10510 17556 23144 30421 45655
11 204.4 38100 10521 17548 23130 30464 45670
12 204.4 38100 10517 17544 23145 30437 45670
13 204.4 38088 10259 17957 23692 30262 45238
14 204.4 38109 10565 17692 23259 30422 45816
15 204.3 38104 10552 17641 23219 30434 45773
16 197.0 38122 11280 18431 21783 29203 47126
17 205.0 38111 10283 17958 23937 30244 45322
18 201.4 38037 10209 18169 23507 30600 44471

 

 

 

Figure 3.8 Additional MKTOPT output

gross margins. This additional data in Figure 3.8 is occasionally needed to help
understand the differences in two distributions listed on the previous screen (Figure
3.7). Note that Plan 16 offers the highest expected income, but its standard deviation
is substantially higher than the best plan. Since distributions are non-parametric, it

may be necessary to examine percentiles when comparing two close distributions.

3.1 1 issues

Choosing the appropriate mix of pricing alternatives and the number of bushels
to commit to each alternative is an ill-structured task during the pre-harvest time
period. The decision-maker must consider the uncertainties of yield, basis, and
futures, plus factors related to the producer’s ability (or desire) to accept risk. It is not

yet clear whether producers can accurately do this. Some would argue that they

 

129
already implicitly do this in marketing, but how accurately can producer risk attitudes
and subjective yields be “known“ by producers and elicited? Such a question could
be studied by behavioral analysts, but the process of extracting information from
humans will always contain some misunderstanding and mis-information (error),
however small.

There are numerous pricing alternatives available for producers, but only six
basic methods were considered in the research. This is several more pricing methods
than most research projects have handled simultaneously. Other pricing strategies
were not considered in the research because they are extremely close substitutes for
the six pricing alternatives listed above. One example of these is the hedge-to-arrive
contract. In this contract the grain elevator is a “substitute“ for a broker, and offers a
cash contract covering only the futures portion of the price, for specified quantity,
location, and time. Non-linear optimization is very difficult when nearly perfect
substitutes are available. In such situations there is usually not a single optima, but a
“ridge“ formed between the two substitutes. One answer Is to reduce substitutes in
the model, but realize they might exist at the time the grain is priced. There may be
“non-pricing“ reasons to use hedge-to arrive contracts rather than futures hedging
(e.g. margin calls).

Time is an additional consideration for the problem environment, but it affects
the problem in two ways:

1. Marketing is a stochastic, dynamic process, since decisions can be made
numerous times during the season. The problem was reduced to a two period (non-
dynamic) stochastic one. Period one is any pre-harvest time when acreage ls known

or intended, but yield is not. Period one is also the day the model is run. Period two

130
is a post-harvest date when residual cash sales will take place. For convenience in
calculating options premium values, period two is a day or two before option
expiration. At that point, the time value of the option is minimal, and only the intrinsic
value remains (if the premium has value at all). The problem here is that dynamic
strategies could be superior. The difficulty of dynamic analysis is one of data
(conditional distributions), and computing power at the farm level.
2. The second effect of time is that yield pdf’s and static market data will change
throughout the growing year as weather and crop information is updated. Although
the model is not dynamic, it is expected that producers should be able to market in
several different time periods. Producers should be able to price some grain at
planting time for harvest delivery, and later in the season, with the help of the model,
make commitments on additional sales (perhaps in January for tax purposes).
Changes in the yield distribution and static market data affect subsequent marketing
decisions. The'need for mid-season yield pdf’s dictated that yields be subjectively
formed from the producer. Mid-season elicitations of yields would likely have a shift in
the mean from a planting time elicitation, and would usually be less volatile.

Income in FIRM is measured in terms of gross margins (total income minus
direct costs). Two kinds of direct costs are considered. There are “per acre“
expenses such as seed and fertilizer, and “per bushel“ expenses such as drying and
trucking. Some risk research is based on wealth (Robison;1987), some on per bushel
income (Rister and Skees;1982), and nearly every measure in between. Raskin and

Cochran noted that most studies used net farm after-tax income. von Winterfeldt and

131
Edwards argue that people do not know their wealth. They also argued that "investors
and poker players alike must learn to write off sunk costs.“

Most decision theory and management texts would encourage decision
makers to examine only the relevant information. Enterprise analysis and partial
budgeting are perfect examples of tools to produce useful information for decision
making. Risk theory has incorporated wealth into the utility function as an explanatory
variable on why wealthier persons seemed to behave differently than less wealthy.

The same principles of utility can be used for enterprise risks as well as the whole
farm. Doing this, implies that farm wealth does not change during the risky period

due to the enterprise risk.

3.12 Future Improvements to FIRM

Quality records are the foundation for sound decision analysis. FIRM needs to
know what previous commitments have been made for the crop in question and the
amount of deterministic gains or losses to date (if any). Ferris (1985) designed a
marketing record system to be kept on paper. This system is the outline for a
computerized grain marketing database. The database will record marketing
transactions and will contain information about brokerage commissions, storage costs
on grain, and other needed price data. The database will employ a dBase IV file
format, but entry forms will be supplied to the producer, thereby eliminating the need
to purchase and learn Dbase. Database tools are under development in the AIMS
project at Michigan State University, Department of Agricultural Economics that will

help facilitate building a marketing database.

 

‘p. 377

132

The most important portion of the marketing database for FIRM is the open
position report. The open position report is a summary of marketing commitments yet
to be delivered (contracts in the cash market) or offset (futures and options markets).

The format for the open position report is shown in Figure 3.9.

 

 

Contract Mktg # of Price Strike Tran Margi
Date Crop Month Method Bu. S/Bu. S/Bu. ¢/Bu. ¢/Bu.

 

2-16 Soy 11—89 For.Con. 1000 6.83 0.00 0.0 0.0 I

 

 

 

3-19 Soy 1-90 Buy Put 5000 .49 6.75 3.0 15.0 I

 

 

 

 

 

 

 

 

Figure 3.9 Report From the Marketing Database

When FIRM is executed, the first action would be to read the open position
report and retrieve entries related to the selected crop. FIRM will also need current
pricing data and data from the production portion of the database. Important data
also includes historical yields for the selected crop, acreage, and leasing
arrangements for crop land. This data will come from the field records section of the
farm database.

The research model of FIRM has no marketing database. However, needed
static default data (e.g. interest rates, current cash, and futures market bids) are
stored in ASCII files. All of the default values can be changed when the program is
run. Some database material for the research model is entered manually, such as
direct costs, per bushel, variable costs, and acreage. Table 3.1 is a listing of

database static marketing data for a case farm.

Table 3.3 Static Input to MKTOPT

 

PARAMETER VALUES FOR THIS RUN
NS= 5 NC= 6 NV= 15 ITMAX= 100
ALPHA= 1.35 BETA: 1 GAMMA= 5 DELTA= .0001

The upper constraints for
Forward Contracting = 9081.563
Futures Hedging = 18163.13
Put Hedging = 18163.13

Basis Contract = 9081.563
Speculative Call = 18163.13

Today’s month is 1

The contract month is 11

The unbiased Futures price is ($/bu) 6.1825

The forward contract price is ($/bu) 6.08

The Price of a basis contract is ($/bu) -.1

The Call premium is ($/bu) .44

The Strike for the Call is ($/bu) 6

The Put premium is ($/bu) .28

The Strike for the Put is ($/bu) 6

Round trip trans. costs for futures (cents/bu) = 1.5
ONE-WAY trans. costs for options (cents/bu) = 1.5
Margin costs per bushel on futures ($/bu) .3
Margin costs per bushel on options ($/bu) 0

The ANNUAL interest rate is 10.000

The cash elevator spread for ASK - BID is ($/bu) .05

 

The ASCII file data includes option premiums, strike prices, the closing futures
price for November soybeans, current contract prices, interest rates, and other
transactions costs. This data is stored in a file named PRICE.DAT and is read into the
FIRM model. The workshop coordinator is able to update the PRICE.DAT file.
PRICE.DAT provides default values in the MKTOPT program, which can also be

changed by the user when running MKT OPT. (MKTOPT is described later)

 

134

The generation of futures and basis required that the Monte Carlo sample
mean for futures, had to equal the static futures price in the PRICE.DAT file. All price
distributions (futures and basis) were adjusted following their creation. This was not
necessary with the yield distribution, since it was not parametric.

In addition to a database, there are improvements needed to the user interface
with help messages, screen editing, documentation and more. An end-user version of
FIRM should also include an interface to electronically available market data, further

reducing data entry.

3.13 Summary

This chapter presented the Farm Income Risk Management (FIRM) model.
FIRM is a commodity marketing tool that maximizes decision-specific subjective
expected utility, thereby matching pre-harvest price risk with producer's desire or
ability to bear risk. FIRM can be operated on a IBM compatible microcomputer. A
case farm was presented to improve understanding of the research version of FIRM.
Chapter 4 presents two major groups of tests; the first set of tests are validation.
Chapter 5 presents a group of tests for correspondence and workability. The final

chapter is a summary and presents challenges to further research.

CHAPTER FOUR

MODEL VALIDATION
4.1 The Base Farm for Testing ..................................... 136
4.2 Test 1 - Effect of Utility Changes on Marketing Plans .................. 138
4.3 Test 2 - Effect of Utility Changes on Pricing Tools .................... 145
4.4 Test 3 - Changing Put Options Premiums and Utility .................. 148
4.5 Test 4 - Changing Price Distribution Forms ......................... 149
4.6 Summary .................................................. 152

135

136

Chapter 4 contains tests of FIRM. Most of these tests are performed on a
feasible or reasonable situation, with marginal changes in model inputs. Several
degrees of risk attitudes are explored, especially negative exponential ones, since they
are common in other research (Ramaratnam et al.;1986) and are easily summarized.
The tests in this chapter are part of the validation process before field testing.

The number of inputs and parameters to FIRM exceeds 20. If each is tested at
3 levels (high, low, and medium) the total number of combinations would be 320 or
more than 3.4 Billion. Fortunately, not all combinations are needed, in order to
validate the model. There are, however, several systematic value changes that should

be considered and evaluated. The process used, is to formulate a reasonable base

situation and begin changing important inputs (one at a time).
4.1 The Base Farm for Testing

The base farm in this chapter is different than the one used to illustrate the
model in Chapter 3, although several factors of the base farm are the same. In the
previous chapter ELICIT was used to create a non-parametric yield for 250 soybean
acres. This distribution is unchanged, as are production costs. In some of the tests
in this chapter, transactions costs will be reduced to zero. The reason for no pricing
(brokerage) costs was so that E[basis] = E[cash price] - E[futures]. Although
someone must pay brokerage fees and interest on margin, it is not clear where those
costs should enter in the traditional equation of futures + basis = cash price.

Upper constraints in MKTOPT were increased on forward contracting and basis
contracting in order that any pricing alternative could be done at up to twice the

expected production level. Twice the expected production should be high enough

137
that only speculative positions would be constrained. Options retained their interest
on premiums for time “t“ (from purchase to just before expiration). Table 4.1 lists

static data for this farm.

Table 4.1 Static Input to MKT OPT

 

PARAMETER VALUES FOR THIS RUN

The upper constraints for
Forward Contracting = 18163.13
Futures Hedging = 18163.13
Put Hedging = 18163.13

Basis Contract = 18163.13
Speculative Call = 18163.13

Today’s month is 1

The contract month is 11

The unbiased Futures price is ($/bu) 6.1825

The forward contract price is ($/bu) 6.08

The Price of a basis contract is ($/ bu) -.1

The Call premium is ($/bu) .44

The Strike for the Call is ($/bu) 6

The Put premium is ($/bu) .28

The Strike for the Put is ($/bu) 6

Round trip trans. costs for futures (cents/bu) = 0
ONE-WAY trans. costs for options (cents/bu) = 0
Margin costs per bushel on futures ($/bu) = 0
Margin costs per bushel on options ($/bu) = 0
The ANNUAL interest rate is 10.000

The cash elevator spread for ASK - BID is ($/bu) .05

 

Figure 4.1 is a “Cumulative Distribution Function“ (CDF) that represents the
income distribution with no advanced marketing. This distribution is a function of non-
parametric yields, costs, and normally distributed futures and basis. Costs include

both per acre costs, as well as, costs that vary with yield. Table 4.1 data also affect

 

1.0

0.9
5.013
§0.7
g 0.5
0..

E 0.5

(503
0.2

0.1

 

0.0
10 20 30 40 50 60 70

Cum Margin (thomands 3)

 

 

Figure 4.1 Case Farm Gross Margin Distribution

the gross margin distribution in Figure 4.1. Very few gross margin observations occur

below $18,000 and above $68,000.
4.2 Test 1 - Effect of Utility Changes on Marketing Plans

Figure 4.2 shows 5 negative exponential utility functions. The span which they
covered includes roughly 95% of the gross margin observations in Figure 4.1. The
utility functions were created with the aid of Borland’s Ouattro Prom. A negative
exponential function of the form U(X) = k - a-(EXP(-b-X)) where k and a are location

and scale parameters and b is the CARA coefficient. There are no “curves“ in Figure

 

139
4.2, as each “curve“ is actually 12 line segments. One point here, is that 13 data

points can very closely approximate a curve, even a moderately risky one. Of course,

this presumes the points are reasonably well fitted.

 

800

600

400

200

Utility

-2 00

-400
68

-600
18 26.3 34.7 51.3 59.7
Dollm of Gms Margin (thousamb)

 

43

 

 

 

Figure 4.2 Five Negative Exponential Utility Functions

140

The linear (risk neutral) risk attitude in Figure 4.2 behaves like a profit maximizer. If
offered a gamble with a half chance of winning $18,000 and a half chance of $68,000,
the expected income would be $43,000, resulting in a utility of 100 for the risk neutral
producer. This producer would equally prefer the gamble to its expected outcome.
This same situation presented to the producer with .00005 CARA coefficient would bid
only $30,317. The producer with .0001 CARA coefficient would pay $24,852 (or less).
These values are available in Figure 4.2 at the utility level of 100 for various producers.
Each of the dollar values are called “certainty equivalents,“ and the difference between
them and the expected outcome ($43,000) is the “risk premium.“

The reason for these values is not due to the utility of 100, but because
$43,000 is the expected value, midway on the line between $18,000 and $68,000. The
straight line represents not only the risk neutral producer, but a linear gamble set
between the two endpoints. The midpoint of the line represents a 50/50 gamble of
the two endpoints. This is also where the risk neutral producer has a utility of 100 for
$43,000. The risk neutral producer is willing to pay the expected outcome of the
gamble, ($43,000), and the risk prefering producer will pay extra, above the expected
outcome, to play the this 50/50 gamble.

The real issue is not how much producers with different risk preferences would
bid for some extremely high variance gamble, but how they would market the grain
from a farm that has identical production and common prices. Just as with the
gamble above, more risk averse producers should have higher risk premiums
(compared to doing no pricing). They should prefer hedging or forward contracting
over basis contracting, because basis contracting protects a much smaller portion of

the total price. Risk neutral producers are profit maximizers and are indifferent to

141

variance, they will seek any chance to increase expected income through marketing
regardless of the variance. Risk neutral persons help identify arbitrage opportunities.
When the best price is the ending period cash price, risk neutral producers will do no
advanced marketing. Persons who prefer risk, prefer income and variance, such a
person might like to speculate by selling much more that expected production and
increasing the variance of gross margins.

The first test in this chapter is to let the five CARA attitudes analyze the same
marketing problem. This test also examines behavior of the pricing instruments under
different risk attitudes. All of the five utility curves in Figure 4.2 extend over most of
the income distribution in Figure 4.1.

In the MKTOPT output 14 other plans are listed with the best plan to give
sensitivity analysis in the area of the optima. Boiling down these answers to a single
marketing plan results in lost information, since there is no information about tradeoffs
near the optima. For many tests in this chapter and the next, it is not possible to list
or easily summarize the neighboring solutions. Since this is the case, it is more
important that the optimal solution be more tightly converged. All of the optimal
marketing plans in this test (and all other tests except where noted) were the result of
two passes with MKT OPT. The first pass with MKTOPT was to get in the area of the
optimum. The best 15 solutions were examined, the constraints were tightened
around the best 15 plans, the convergence parameter to MKTOPT (beta) was further
reduced, and MKTOPT was rerun.

Table 4.2 shows the best marketing plan for each of the five negative
exponential utility functions. Table 4.2 gives expected results for the three risk

averters. Expected utility rises across these producers, as anticipated from looking at

142
the graph (Figure 4.2). Also “Risk Premiums Above doing No Marketing“ (RPANM)

increases as the CARA coefficient increases. To compute the RPANM, the optimal
plan is compared to a plan with no advanced marketing (just ending period spot
sales). Since the optimal plan has a Risk Premium of zero,‘ it is useful to find out
how much better the optimal plan is compared to a “do nothing“ plan (only spot
sales). The higher the RPANM the larger the risk aversion, especially when the “do
nothing“ plan is the same for all producers (the CDF in Figure 4.1 is the CDF of the

“no advanced marketing plan).

Table 4.2 Marketing solutions for 5 Utility Functions.

_ _ BUSHELS_ _
CARA Forw. Futures Put Basia Spec Exp. Exp. *
Coef. Cont. Hedge Hedge Cont. Call Spot Util RPANM

 

 

 

 

 

 

 

-.00001 9000 18154 0 0 0 82 -58.2 557.5
Neutral 0 0 0 3913 0 5169 -17.1 0.1
.00001 1963 5237 0 2524 0 4595 43.4 95.4
.00005 370 5601 0 2988 0 5724 257.2 436.7
.0001 2585 3012 0 1327 0 5170 421.4 740.4

Risk Premium Above doing NO Marketing

A perfect risk neutral decision-maker (profit-maximizer) would be indifferent
between doing nothing and some marketing activity with the same mean (regardless
of variance). This is different than the risk preferrer who seeks higher variance. Table
4.2 indicates the risk neutral person would basis contract 3913 bushels and that this

person would be happier by 10 cents versus doing no advanced pricing (all spot

 

1

MKTOPT always give the best plan a risk premium of zero since it is the base for
comparison to the other plans on the output.

143

sales). This indicates that the ending period basis distribution had a mean that was
slightly lower (in fact 10 cents in 3913 bushels or $.000025/bu) than the current basis
contract offer. Basis contracting improved profits slightly for the risk neutral producer,
but if production ever fell below 3913 bu (15.6 bu/ac) the $.05 ASK-BID spread would
affect each bushel below 3913. Since the risk neutral producer did not use futures or
fonivard contracting, today's futures price must be below the expected fall futures
price.

in Table 4.2 the risk preferrer was suggested to sell all but 82 bushels of
expected production by forward contracting, then sell twice his expected production in
futures contracts. Total sales by all pricing methods were limited to three times
expected production (an implicit constraint on N, discussed in Chapter 3). Each
individual pricing method was limited to twice the expected prodicution (upper explicit
constraint). No long futures positions, or option granting (writing) was allowed (lower
explicit constraints were zero bushels).

Before leaving Table 4.2 there are other observations to be made. Options
failed to enter any of the optimal solutions. One possible reason is that the assumed
interest of 10 percent is higher than risk-free short-term interest rates used in the
option pricing models that generated the futures price variance. At low enough
interest rates and/or lower premiums, options would be expected to come into
solution. A second observation from Table 4.2 concerns the difference in the neutral
versus .00001 behaviors. if the two curves are considered to be possible
measurement error of each other, important conclusions result. The risk premium
above doing no marketing (RPANM) only changed by $95 from risk neutral to the

.00001 CARA producer. This infers that measurement errors in elicitation will have

144

more impact in the neighborhood of a linear function (in terms of marketing solutions,
but not in terms of risk premiums)."’ On the other hand, going from CARA .00001 to
the producer with CARA of .00005 is a factor of five and involves a greater visual
change on the Figure 4.1 graph. But examining Table 4.2, the change between these
two utility curves (.00001 and .00005) is much greater in terms of utility and risk
premium, but much less in terms of the marketing plan (compared to the differences
in risk neutral versus .00001, that were just discussed).

With no transactions costs and no dynamic factors (across time), forward
contracts and futures hedging are nearly perfect substitutes. If forward contract and
futures hedging are added together, each of the risk averters had similar levels of
forward pricing, but increasing utility and RPANM.

To summarize, increasing the risk aversion (the CARA coefficient), increased
the expected utility of the best marketing plan and the Risk Premium Above No
Marketing (RPANM). Global risk preference was shown to behave in an unusual
manner that can be summarized as a preference for higher variance. It appears that
measurement error (perhaps in elicitation) in the neighborhood of risk neutral behavior
would result in greater changes in activity levels and less in terms of RPANM when
compared to changes in more risk averse utility curves. One important note is that
the analysis seemed consistent with expectations. These findings are based upon

well defined utility curves (CARA) and the specific pricing circumstances.

 

2 Except for the unusual case of global risk preference. Global risk preference is logical
behavior for persons in dire straights. One rule here would be to maximize the maximum
outcome. This would lead to unusual behavior as happened in Table 4.2.

145
4.3 Test 2 - Effect of Utility Changes on Pricing Tools

In this test the base farm remains the same, the brokerage fee is still zero, but
each producer will individually examine enly ene prieing alternative at a time (plus
cash sales in the final period). Spot (cash) sales are always available and cannot be
turned off. The expectation here is that producers might use a poorer performing
pricing alternative, if they have no other choices except all cash sales. Expect the risk
averters to price more grain in each individual risk reducing pricing alternative, than
when they could choose from all five simultaneously. Basis contracting is not likely to

change utility or the risk premium much, since it is a small part of price.

Table 4.3 Pricing Solutions for 5 Utility Functions.
—

 

 

ONLY ONLY ONLY ONLY ONLY

CARA Forw. Futures Put Basis Spec
Coef. Unite Cont. Hedge Hedge Cont. Call

Bu. 0 18163 0 0 0

$ RPANM 0 75.3 0 0 0
Bu. 0 O 0 0 0

Neutral Util. -17.1 -17.1 -17.1 -17.1 -17.1
$ RPANM 0 0 0 0 0
Bu. 5536 7079 0 4541 0

.00001 Util. 43.3 43.4 41.0 41.1 41.1
$ RPANM 91.3 93.6 0 2.3 0
Bu. 6227 6617 0 4541 0

.00005 Util. 257.1 257.1 245.1 245.1 245.1
s RPANM 433.4 433.6 0 10.3 0
Bu. 5641 5858 2888 4723 0

.0001 Util. 421.4 421.0 403.7 403.2 402.5
5 RPANM 738. 724.8 48.5 25.6 0

146

The risk neutral producer did no pricing in any of the five alternatives, when
each were examined individually. When no pricing is done all sales are spot cash at
harvest. This indicates the ending distributions for basis and futures had expectations
no higher than current bids. The very small arbitrage using basis contracts (10 cents
on 3913 bushels), was discovered earlier in the related search in Table 4.2., but was
not found in this test. The slight risk preferrer sold twice his expected production on
the futures market. This is a very predictable behavior. Without system constraints it
is probable the solution would have been unbounded. Using futures to speculate
(beyond production), increases the maximum possible outcome, with almost no
change in mean of the price distribution and the fonivard contract price. Reasons for
this are that transactions costs are zero, and market means were fairly unbiased.)
Thus, variance could be increased and the mean preserved, by speculating in added
short positions in futures.

The three risk averters can be discussed as a group since several patterns
appeared. Producers with these attitudes gained most from either forward contracting
or futures hedging. None of these persons overhedged in any instrument (more than
expected production). Basis contracting did little for risk reduction as indicated by its
with very low RPANMs compared to the other instruments.

When no other marketing alternatives were available, the very risk averse
producer, did use the nearest out-of-the-money put hedge. The put hedge purchase
involves, not just paying the premium, but interest on the premium until expiration. If
farmers have higher interest rates than the “risk arbitragers“ in the market, then the
shift in expected gross margins with options may overshadow its risk reducing

benefits. This could explain why options did not come into solution for the less risk

147
averse producers. Note that the Put hedge for the .0001 risk averter has a RPANM of

$48, while fonivard contracting and futures hedging had RPANMs of more than $700
for the same risk averter.

In Table 4.2 the risk neutral producer “basis contracted“ 3931 bushels for a
$.10 benefit on an expected $38,000 in gross margins. This explains why the same
solution was not reached between Table 4.2 and 4.3 regarding the risk neutral farmer.
In fact, the non-linear search algorithm usually converges before such small
differences could be detected. With a risk neutral producer, totally unbiased prices
and distributions, then the producer will get the same utility from any plan chosen
(including doing nothing). This creates a “flat“ optimal area where many equal-utility
solutions exist. This is what is seen in Table 4.2 and Table 4.3. The risk neutral
behavior (profit maximizer) is very useful for finding arbitrage opportunities.

RPANMs among the risk averters increased, as the risk aversion coefficient
increased. The recommendation that the .00001 producer market 4541 bushel when
basis contracting was the only pricing alternative, is weakened by its meager RPANM
of $2.3. Users of FIRM should understand that the solution is important, but that the
RPANM is like a confidence or conviction factor. The RPANM rises (for risk averters)
as the amount of risk reduction increases.

At the begining of this section it was observed that the tests would also reflect
the risk averting strengths of the pricing alternatives. Since speculative calls do not
reduce risk they were not selected by any of the producers. Even the slight risk
preferrer, chose not to use them. The reason for this is that although the speculative
call position could increase variance, the cost of the premiums and interest on them,

reduced expected gross margins.

148

Futures and forward contracting are very similar in their risk reducing capacity.
Their pricing levels, utilities and risk premiums were very similar to each other for the
three risk averters. Options and basis contracting were less effective in risk reduction
as indicated by smaller risk premiums (and smaller utility) than forward contracting
and futures hedging. These judgements are based on examining utility values as well
as RPANMs across the table for each of the risk averse utility functions.

In this section, 5 CARA utility curves were matched with 5 individual pricing
instruments for 25 situations and twice that many runs of MKTOPT. Futures hedging
and fonNard contracting functioned almost identically, since transactions costs are
zero. RPANMs and utility increased as risk aversion increased. The basis contract
does little to reduce risk for this group of producers. Speculative Calls were not used
by any producer. Only the most risk averse producer used put-hedging. This
occurred when put hedging and cash sales were the only pricing alternatives available

for the .0001 CARA producer.

4.4 Test 3 - Changing Put Options Premiums and Utility

With Put options priced at $.28, (10 months from harvest) the implied volatility
of futures prices from the Hilker and Black OPM was 11.5%, or roughly $.69 standard
deviation, with $6.18 soybeans. This is the same distribution and volatility used
previously in this chapter. In Table 4.4 Put premiums were lowered further to examine
their acceptance at different risk attitude levels.

Table 4.4 shows that more risk averse producers should be first to Put hedge.
With $.24 put premiums the .00001 CARA attitude, still did not purchase options.

Lower put premiums bring increased purchasing, increased utility, and increased risk

149

reduction as measured by the RPANM. In Table 4.4 all other pricing alternatives were
eliminated (except cash sales), in order to focus on option hedging. Table 4.4 and
Table 4.3 are similar in the way they were computed; both examined one pricing

alternative at a time.

Table 4.4 Changing Put Premiums

CARA Put * Bushels

Coef. Prem Put Hdg Utility RPANM
.00001 $.24 0 41.0 0
.00005 .24 1623 245.0 $2.1
.0001 .24 5843 408.5 232.8
.00001 $.20 0 41.0 0
.00005 .20 7696 250.2 182.5
.0001 .20 8649 416.9 561.0
.00001 $.16 18163 48.8 310.8
.00005 .16 14098 262.5 628.3
.0001 .16 11591 427.7 983.3

Put premiums were $.28 originally. No brokerage fee in these
calculations. Annual interest rate on premiums from purchase to
liquidation was 10 percent.

When put premiums were lowered to $.16 they became profitable, and the
.00001 risk aversion attitude bought all the Put options possible (2 times expected
production). The other more risk averse producers each bought more Puts than
expected production, but less the .00001 attitude. This indicates that for the price
distribution used, a $.16 put premium is too inexpensive. Also shown here, is the fact
that the decision-makers risk attitude determines whether he or she believes options

are fairly priced.

150

 

log -nor moi

Futures Price (S/Bu)

normal

3
0.0 0.1 0.2

 

0.3

 

0.4 0.5 0.6 0.7
Cumulative Probability

Anhverted CDF for Futures Prices

log—normal

normal

0.8 0.9 1.0

 

Figure 4.3 Log-Normal versus Normal Prices

4.5 Test 4 - Changing Price Distribution Forms

Fisher Black (1976) developed an “Option Pricing Model“ (BOPM) based upon
log-normally distributed prices. This research used normal distributions for futures
and basis, since some empirical work indicates they are appropriate. This section
examines results when prices have three different representations; (1) normal, (2) log-

normal, and (3) randomly chosen prices from a normal distribution. information on

how each of these were developed are in Appendix E.

 

151

Figure 4.3 shows two distributions of normal and log-normal prices. Values of
the two distributions are listed in Appendix E along with the values randomly drawn
from a normal distribution. All three distributions are very similar in appearance, but
howdo they compare in FIRM?

Table 4.5 shows results of tests with transactions costs (i.e. brokerage fees
and interest on margin) both included and excluded. In this analysis none of the

optimal solutions included option hedging or speculative call positions. The same

Table 4.5 Comparing Price Distribution Functions

 

BUSHELS PR Above
Distri- Trans ARA Forward Futures Basis No Mrktg
bution Cost* Coef. Contract Hedge Contract Utility (RPANM)

 

 

Normal None 0 0 O O -11.2 0
Normal None 1E-05 2068 6334 1108 49.9 184.5
Normal None SE-Os 1809 6798 3450 266.4 859.7
Normal None .0001 3576 8341 1179 430.6 1404.5
LnNorm None 0 O 0 O -11.2 0
LnNorm None lE-OS 1639 6564 3251 50.0 184.0
LnNorm None 5E—05 3790 4791 1147 266.6 842.6
LnNorm None .0001 619 7957 4129 431.1 1368.8
MCNorm None 0 0 0 O —10.0 0
MCNorm None lE-OS 1648 7747 2998 50.5 205.5
MCNorm None 5E-05 2301 6460 2664 263.1 796.8
MCNorm None .0001 2021 5357 2707 422.5 1045.8
Normal IMSB O O O O -11.2 0
Normal IM&B lE-OS 6982 O 0 49.6 173.0
Normal IM&B SE—OS 8068 0 0 265.7 833.4
Normal IM&8 .0001 7673 0 0 429.5 1362.5
LnNorm IM&B O 0 O 0 -11.2 0
LnNorm IM&B 1E—05 7000 0 0 49.7 172.7
LnNorm IM&B SE-OS 8221 0 0 265.9 815.7
LnNorm IM&B .0001 8040 0 0 429.9 1325.1
MCNorm IM&B 0 0 O O -10.0 0
MCNorm IM&B lE-OS 7443 0 0 50.0 185.3
MCNorm IM&B SE-OS 8201 0 0 262.3 769.6
MCNorm IM&B .0001 6736 0 0 422.0 1027.1

* "Interest on Margin and Brokerage" were included or not (None).
LnNorm is log normal and MCNorm is Monte Carlo Normal Prices.

 

152

CARA risk functions were used, as previously described in this chapter. The basis
vector of 200 observations and the yield vectors were unchanged from one price
distribution to another. All three futures distributions had means of $6.1825.

It is easy to see that transactions costs make a bigger change in optimal plans
than do changes in the form of the price distributions. With transactions costs
included for futures, all optimal plans involve only forward contracting. When
transactions costs are excluded futures and forward contracting are similar, except
that forward contracting also looks in a basis level and retains a small penalty for over-
contracting. Of course these conclusions are based on the pricing relationships used
in this test. It should be noted, that from a risk management standpoint, the inclusion
or exclusion of transaction costs had minor effects on the utility and the RPANM.
Examining Figure 4.4 and Table 4.5 leads to the conclusion that the differences in
normal and log-normal price distributions with equal mean (6.1825) and standard
deviation (.6983) is very small, and creates only minor differences in optimal solutions

in FIRM.

4.6 Summary

In this chapter four tests were performed using different CARA utility functions.
Firm performed as expected by showing higher utility and risk premiums for more risk
averse utility curves. Tests covered changing price distributions, inclusion and
exclusion of transactions costs, changing put premiums, examining all five pricing
alternatives as well as each one individually. All tests were done across changing

utility functions.

153

It was shown that the global risk preferrer can be represented by the FIRM
model, but that such behavior is not likely to occur. FIRM has nearly 20 data inputs
that could be altered to change the model. With the values used in this chapter: (1)
more risk averse producers had higher risk premiums above doing no marketing, 2)
indicating increased benefit of using FIRM (for more risk averse utility) compared to
less risk averse producers. 3) log-normal and normal price distributions gave very
similar results as did randomly chosen prices from a normal distribution. All pricing
functions worked as expected. Put options came into solution for all producers when
premium prices were lowered. When put options and spot sales were the only pricing
methods, put options were used by the most risk averse producer. When other
pricing methods were available, futures hedging and fonivard contracting reduced the
use of options. This was probably because futures hedging and forward contracting
protect the producer from low prices without reducing exepted income, as much as
options do. Basis contracts offered very little risk reduction compared to futures
hedging and forward contracting. This latter observation was expected since basis is
such a small part of the total price.

FIRM performed well with well-behaved utility curves. In the next chapter,

workshops with soybean producers are summarized and tests are performed with less

well behaved utility functions.

CHAPTER FIVE

WORKSHOP RESULTS

5.1 Generating Price Distributions ............................. 155
5.2 The Workshop Format ................................... 156
5.3 Getting Acquainted ..................................... 156
5.4 Yields and Probabilities .................................. 158
5.5 Estimating Yield Distributions with ELICIT ..................... 158
5.6 Crop Costs and Effective Acreage .......................... 160
5.7 Running GENRINC ..................................... 161
5.8 Soybean Outlook and Volatility Forcasting .................... 162
5.9 Estimating Utility Functions with ELRISK ...................... 162
5.10 Marketing Solutions .................................... 168
5.11 Producer and Presenter Evaluation ......................... 171
5.12 Testing Other Utility Curves on a Case Farm ................. 173
5.13 Changing Price Data for the Case Farm .................... 179
5.14 Summary ........................................... 181

154

155

A small group of Michigan Extension Agents, in conjunction with their District
Farm Management Agents, were asked to coordinate a local workshop for marketing
“new-crop“ soybeans. Agents were informed that the workshop was research related
and that workshop participants were needed to test microcomputer risk management,
marketing software. The target audience of Chapter 3 was described to agents, for
agents who wanted to select the audience. At least one of the workshops was open
to the general public, because the agent did not want to exclude anyone. Another
agent made personal. contacts by mail and phone. One workshop was held in August
1989 to examine October 1989 sales, and the other three workshops were held in
January and February of 1990 to examine October 1990 pricing alternatives. The title
of the workshops was “How to Price Pre-Harvest Soybeans and How Many Bushels to

Price In Order to Manage Risk.“
5.1 Generating Price Distributions

On the night before each workshop, the coordinators created the random price
distributions. The Hilker and Black (1988) Option Pricing Model (OPM) was used to
solve for implied volatility of the futures price distribution, and the closing futures price
was the expected value of the distribution. November CBOT Option Premiums on the
strike closest to being “at-the-money“, were assumed to be efficiently priced. The best
basis in the area of the workshop was set to the expected value of the basis
distribution, and the standard deviation was subjectively estimated to be 10 cents per
bushel

The means and standard deviations were entered into a program called

F&BDISTEXE, that is capable of making bivariate normal distributions for basis and

156

futures. Correlations for all four workshops were set to zero for consistency. This

made basis and futures independent.

Futures and basis prices were created and copied onto each workshop

computer. Based on market information and closing prices, the PRICE.DAT file was

also updated on the evening before each workshop. PRICE.DAT contains option

premiums, strike prices, the closing futures price for November soybeans, current

contract prices, interest rates, transactions costs, and other default inputs to the FIRM

model. Each of the values in PRICE.DAT can be revised by the workshop

participants.

5.2 The Workshop Format

9:00
9:15
9:30

10:30
10:40
1 1 :00

Noon
1:30
3:00
3:15

WORKSHOP SCHEDULE

Coffee and Donuts (get acquainted)

A Brief Overview of the Program - Steve and Rich
Presentation on Yields and Probabilities - Rich

Run ELICIT Software for Soybeans Yields - Jim

Fill Out Crop Costs Worksheet - Steve

Generate Income Distributions - Rich

Ten Minute Break

Soybean Outlook and Volatility Forecast (including basis forecast) - Jim
Risk Attitudes (based upon income distributions) - Rich
Run ELRISK Software

LUNCH

Solve Individual Marketing Plans Under Base Assumptions
Discussion and Evaluation

Adjourn

5.3 Getting Acquainted

Workshops were advertised to start at 9:00, but attendees did not know that a

special “get acquainted“ period would begin the meeting. To get acquainted with the

29 workshop attendees, it will be helpful to study Table 5.1. These Michigan

 

157

producers were from seven different counties and represented a spectrum of ages,
farm types, education levels, and soybean acreage. The 29 farms produced over
10,000 acres of soybeans. The largest soybean acreage was 810 acres and 77 was

the smallest.

Table 5.1 Producer Data

Descriptive Descriptive

Farm Data Soys Farm Data Soys
Yrs Soy as 8 Yrs Soy as %

Code Age farm Ac. Inc. Code Age farm Ac. Inc.

 

FRAl 47 21 810 40 MONS 37 10 98 20
FRAZ 40 22 420 30 MONG 50 30 500 50
FRA3 45 45 85 MON7 36 18 630 35
FRA4 46 26 77 10 MONS 37 19 300 5
FRA5 50 31 300 30 MON9 50 34 S75 30
FRA6 52 30 350 20 MONll 49 30 120 18
FRA7 40 18 420 30 MON12 42 20 225

FRAB 49 27 700 33 MON13 32 20 500 50
CAL2 34 17 320 MON14 26 S 347 45
CAL3 25 6 250 40 SHI1 35 17 629 55
CAL4 44 22 160 45 SHIZ 46 28 187 38
MONl 40 18 400 20 $813 65 40 162 30
MON2 38 18 480 25 $816 63 45 190 40
MON3 38 19 605 29 8817 80+ 200

MON4 29 20 350 20

It should be noted that two of the producers listed in Table 5.1 were actually
family teams. Also, one farm couple chose to make their analyses separately and
thus represent two producer observations. Acreage and percent of income from
soybeans varied substantially among the attendees, as shown in Table 5.1.

Following the “get acquainted“ time was an overview of the program and the

schedule. The schedule was printed at the start of the three page program. The

158

entire program is reprinted in Appendix B. The three page program was the outline

for the presentation of the overview.

5.4 Yields and Probabilities

Following the overview, was a presentation on yields and probabilities with a
very basic introduction to probability density functions (pdf's). All distributions that
producers examined were discrete pdf’s. It was explained that yields and yield
uncertainty were important factors in preharvest marketing. The example of “over-
contracting“ due to a drought was discussed. There was short discussion of how an
uncertain futures, plus and uncertain basis formed an uncertain price, and that the
uncertain price could be multiplied by an uncertain yield to give an uncertain income
per acre.

Producers were asked to consider that no other marketing had taken place,
and that all farmers would be considering harvest-time delivery. This helped place all
farms in a more comparable situation. It also reduced the data and calculation

requirements for prices commitments in other ending time periods.

5.5 Estimating Yield Distributions with ELICIT

Table 5.2 shows the mean and standard deviations of yield for each producer,
as they entered beliefs into ELICIT. Producers were asked to consider a planting time
yield forecast, so that all distributions would reflect a similar time period. Producers
seemed to understand this. There were few sources to prove any inaccuracy on the

part of the producers. Pease (1987) pointed out that using an anchoring method for

159

elicitation leads to an over-confidence in the mean, and less dispersion than what
“really“ exists. Workshop attendees were encouraged to examine their graphical pdf
solutions, and return to the input section of the software, before exiting ELICIT. This
was a useful feature of ELICIT that should have helped managers reconsider yield

variability.

Table 5.2 Workshop Summary for GENRINC and ELICIT Results

 

Soy Cost/ Cost/ Mean StDev Stdev
Code Ac. acre bush G.M. G.M. E(Yld) Yld *

 

FRAl 810 93.14 0.18 99589 37178 41.0 7.92
FRAZ 420 79.21 0.19 65342 24514 44.6 10.10
FRA3 85 74.30 0.11 10632 4723 37.3 9.95
FRA4 77 86.00 0.12 10035 4096 40.7 9.69
FRA5 300 75.00 0.10 41729 17012 40.0 10.07
FRA6 350 57.00 0.10 57698 24999 41.8 12.93
FRA7 420 79.00 0.19 62226 21402 42.5 8.86
FRAB 700 90.00 0.18 88000 38240 41.0 9.76
CAL2 320 75.00 0.23 46180 15451 37.2 6.29
CAL3 250 57.00 0.30 38122 11280 36.8 6.85
CAL4 160 84.00 0.20 27337 8550 43.3 6.90
MONl 400 136.00 0.32 32086 28949 37.7 10.61
MON2 480 66.00 0.48 75532 25943 40.6 7.85
MON3 605 89.00 0.43 81269 31319 39.9 9.11
MON4 350 100.00 0.40 52708 18256 45.0 7.59
MONS 98 53.00 0.45 20146 4280 45.9 5.80
MON6 500 168.00 0.36 44997 27767 44.8 7.80
MON7 630 96.00 0.44 72383 26095 37.5 6.01
MON8 300 114.00 0.48 44054 1345 47.7 6.21
MON9 34 77.00 0.37 107202 36709 44.7 7.71
MONll 120 73.00 0.40 19394 5563 38.9 7.48
MON12 225 91.30 0.40 38934 9737 46.6 4.71
MON13 500 66.00 0.47 81756 25653 40.1 7.43
MON14 347 84.38 0.50 47551 18888 40.0 8.59
SHIl 629 75.00 0.10 76354 30307 35.3 7.14
SHI2 187 68.06 0.18 23666 7486 35.6 6.24
SHI3 162 73.50 0.10 18638 6966 33.5 5.50
SHI6 190 71.85 0.06 22113 8063 33.6 5.41
SHI7 200 95.00 0.10 22140 8004 36.6 4.59

* Expected yield and standard deviation are from ELICIT output.

 

160
Workshop coordinators felt that 40 to 60 percent of the producers did back up

and make changes in yield intervals. Roughly half of those who re-entered values,
made substantive changes affecting the mean and/or standard deviation. These
estimates are from workshop coordinators, but they point out the care that producers
took in constructing their yield pdf‘s.

Conditional Normativists would say that regardless of the “truth,“ these are the
beliefs (subjective probabilities) from which decision-makers are acting. That
statement is only true if the elicitation method is transparent; that is, having no affect
on producer's beliefs. Additionally, producers need some experience to form
probabilities and retain confidence in them.

Once each producer had run ELICIT, a “*.PRB“ file was created and stored to
the hard disk in the microcomputer. The “*“ is the portion of the filename entered by
the workshop attendee. A listing of yield pdf‘s can be found in Appendix D. All
workshop participants also printed out their pdf's for soybean yields, revealed through
ELICIT. This was the first computer exercise at each workshop and many of the

workshop attendees had never used a microcomputer.

5.6 Crop Costs and Effective Acreage

The program contained sample crop budgets for 30 bushel per acre yield goal
and 40 bushel per acre yield goal for 1990-91 soybean production (see Appendix B).
Per acre items in the budget included seed, fertilizer and lime, chemicals, fuel and
repairs, labor and miscellaneous, and interest on the above until harvest. Per bushel

variable costs include harvest, transport, drying, and other. Each producer was asked

161
to create their own budget, based upon the format in the program. A few producers
included land rent, but most did not.

Producers were reminded that the costs and gross revenues would create a
gross margin value. Such a value will likely be positive, but does not cover all
enterprise costs, such as land, operator and family labor, capital investment in
machinery, and more. Producers were asked to keep this in mind and to think about
goals for the gross margin levels they would reasonably hope to receive.

A short worksheet was built for considering different land rental arrangements.
To simplify matters, producers were asked to multiply the number of share-rent acres
times the percent of their share, to get effective shared acres. These were added to

cash rent and owned land, to get total effective soybean acres (see Appendix B).

5.7 Running GENRINC

The input for GENRINC is rather simple and is listed below:

What filename contains the ELICIT data

(Enter only characters left of the decimal)? SOYS
How many Monte Carlo observations should be run? 200
How many acres are planted to soybeans? 250
Costs PER ACRE that you wish to consider’.7 $57
Costs PER BUSHEL you wish to consider? $.30

The producer is prompted by the computer to answer five questions shown
above. GENRINC outputs a vector of Monte Carlo Observations to a file that is
automatically named “BUANDINC.DAT.“ At the bottom of the file are summary
statistics for production and gross margin. The summary statistics for production and
gross margins are also printed to the screen after GENRINC is done running. The

Monte Carlo values of production and costs, that were stored to file, are used later by

162

MKTOPT, while the summary statistics seed the starting values for eliciting risk

attitudes in ELRISK.

5.8 Soybean Outlook and Volatility Forcasting

This section of the program included a fundamental analysis of USDA supply
and demand for new crop soybeans. Following the fundamental analysis was a
presentation and discussion of the efficient market hypothesis. Farmers at the
workshops conducted were not entirely comfortable with the efficient market
hypothesis, but admitted that they had little chance of “beating the market“ over an
extended period of time. One farmer pointed out that if he could arbitrage the market,
he could quit farming and speculate in commodities for a living.

This section ended with a description of how price distributions were formed
using an OPM. Producers were told the market location and basis distribution. Since
all of these prices were entered onto the workshop computers, there were no
calculations for producers, or data to enter in this section. A sample price distribution

was sorted (for a CDF) and is listed in Appendix E.

5.9 Estimating Utility Functions with ELRISK

At each workshop, ELRISK was demonstrated with sample farm data, before
producers ran their own situations. Extra effort was made to focus on the process,
rather than the sample data. The emphasis was on making sure producers first
decided which marketing plan (A or B) they preferred. Once they decided which plan
they preferred and entered an answer, the software recommended whether they

should revise elicitation up or down.

 

163
All 29 producers in the workshop were able to operate the ELRISK software

(after seeing it demonstrated), but some needed more assistance than others. Initially
managers wanted to edit more than one cell, in order to make Plan A and Plan B
equally preferred. Perhaps 3 or 4 people had enough difficulty that they started over.
None of the producers seemed to have ever used an ELRO method of risk elicitation
before. Each producer played 9 to 13 games. Some persons worked faster and
more decisively, while other producers carefully pondered each situation. ELRISK
stored each keystroke entered, including those when backing up. Some of this
information could be analyzed in further behavioral research, but its main purpose was
for trouble-shooting problems that users could have had in elicitation.

Data from the 29 discrete utility functions elicited are summarized in Table 5.3
in order of risk attitude, from risk neutral at the top, to most risk averse at the bottom.
Following the workshops, data from each individual was fitted to the negative
exponential utility function.

The far right column of Table 5.3 (CARA, R(X)) was solved using non-linear
regression, when solving the negative exponential utility function. The negative
exponential function is U(x) = k - a*EXP(-b*x) where x = income and a, b, c, k are
constants of regression. The quadratic function is U(x) = k + a*x + c*x*x and the
semi-log Is U(x) = k + a*LN(x) (and x must be greater than 0).

The negative exponential function was fitted using a modified Box’s Complex,
(non-linear search routine) with an objective function to minimize the sum of squared
error between the fitted and the research data. The negative exponential function is
commonly used in empirical work as well as theory. One measure'of risk is the

absolute risk aversion R(x) = -U”(x)/U’(x). For the negative exponential function, this

164

R(x) value is constant and equal to b in the equation shown in the previous

paragraph.

Table 5.3 Function Evaluation in CARA Order

 

 

r3 values

 

 

NEGATIVE

USER EXPONENT LINEAR QUAD SEMILOG CARA, R(x)
MON13 NA 1.000 1.000 .931758 0

FRAB .972151 .980680 .991503 .456601 0.000002
FRA6 .981886 .980501 .98220§ .756708 0.000003
MON12 .987494 .987507 .987890 .977658 0.000009
MON3 .989913 .915625 .979585 .995698 0.000017
FRAl .996183 .865203 .980685 .985124 0.000018
MONl .961897 .930499 .956556 .974156 0.000024
FRAZ .996954 .908581 .991213 .989488 0.000024
MON4 .993433 .935317 .985698 .997972 0.000024
SHIl .988731 .868287 .966161 .970580 0.000028
MON2 .981150 .863456 .962666 .950985 0.000031
MON14 .989108 .936740 .982139 .992106 0.000031
MON9 .983787 .871433 .959733 .935131 0.000035
CAL3 .994405 .932073 .988513 .990281 0.000042
MON6 .967589 .840537 .930279 .946161 0.000042
FRA5 .974626 .840972 .942543 .965365 0.000048
MONB .994565 .900257 .981346 .970757 0.000053
MON7 .976526 .777136 .931139 .885739 0.000057
FRA7 .962971 .810394 .922116 .896759 0.000064
CAL2 .952248 .873173 .932353 .920276 0.000071
CAL4 .989818 .904731 .977411 .977964 0.000071
NONI .965596 .940867 .958683 .965567 0.000087
SHI6 .973757 .920799 .962540 .970512 0.000095
8813 .974707 .922686 .965213 .971865 0.000115
SHI2 .869241 .802432 .854719 .844191 0.000119
MONS .956746 .922310 .949118 .947446 0.000128
SHI7 .912430 .786505 .910180 .886192 0.000146
FRA4 .983675 .857501 .954866 .953484 0.000267
FRA3 .985868 .703571 .882362 .883265 0.000352

One producer exhibited perfect risk neutral behavior, while three other
producers were very nearly risk neutral. This conclusion is based on the observation
that linear r2 values were quite high for the top four producers in Table 5.3. The fifth
individual (MON3), showed higher r2 values in the other functions than in the linear

one. The remaining soybean producers show various degrees of risk aversion. They

165

are listed in order of least risk averse (smallest R(X)) to most risk averse (largest R(X)).
Underlining is used in Table 5.3 to indicate the highest 1* functional form for each
producer.

It is difficult to compare the CARA coefficients across different research. While
the CARA is independent of the value of the x variable, the x’s must be similar in
nature and measured in the same units. This study examined risk attitudes on annual
gross margins related to soybeans. Using whole-farm income, per acre measures, or
any other x to measure performance, changes the problem since x is not held
constant from one project to another. However, since all other empirical work
reviewed attempted to summarize and compare producer risk behaviors, it seems

only fitting to try.

 

CARA Coefficient

800
+ .00001

600

400 —"— .00005
200 —*—' .0001
o —-i-— .0001 5

- 200

vN—u Utlllty

-400

-800

- 000

 

- 1903

0 “10000 20000 30000 40000 50000 60000
sum ‘15!!!) 25000 3300!) 45:11: 53000

bilaro of Goes Wain

 

 

Figure 5.1 Negative Exponential Functions

 

166

Studies using the interval approach to elicitation usually categorize risk neutral
as having a CARA of -.0001 to .0001. These include King and Robison (1981),
Thomas (1987), Wilson and Eidman (1983), Tauer (1986) and others. Using this
range, all but six producers in this study would be risk neutral. In Figure 4.5 there are
four negative exponential functions for a situation where the second standard
deviations below and above the mean are $0 and $60,000. The curve marketed by
the small triangles is R(x) = .0001. it hardly seems risk neutral.

Rister et al. (1984) categorized -.00001 to .00001 as risk neutral when analyzing
annual grain storage. These figures more closely match those in this study.
Ramaratnam et al. (1986) also found the negative exponential function to be superior
in their sample of 23 farmers. In their study, the CARA values ranged from
.0000026 to .0000135. Because Rister et al.(1984) and Ramaratnam et al. (1986) were
dealing with different crops and income measures this limits the degree to which they
should be compared. Their measures were less risk averse than most producers in
this research.

Based on Figure 5.1, and the values of R(x) in Table 5.3, we can conclude that
risk neutral producers (4 of them) were 0 s R(x) .00001, while moderate aversion (23)
occurred where .00001 5 R(x) 5 .00015 and two producers were found to be very risk
averse.

An added conclusion from Table 5.3 is that the negative exponential function is
best, of the functional forms tested, for the 29 producers. Even risk neutral functions
that approached linearity had good r2 values when fitted to the negative exponential
function. The only exception is when the utility function is strictly linear. The negative

exponential utility function approaches linearity asymptotically, but cannot become

167

strictly linear and upward sloping at the same time. For this reason, the strictly linear
case was not fitted to the negative exponential function.

In examining the data on risk aversion and gross margin, it appeared that a
strong negative correlation existed, suggesting that larger farmers were less risk
averse than smaller farmers (ceteris paribus). One explanation for this is that the
standard deviations for large farms are larger, and that only less risk averse producers
could accept such large risks. Using Borland’s Ouattro Pro”, an ordinary least
squares regression was performed. The dependent variable was the CARA coefficient
of the 29 producers and the independent or explanatory variable was the expected
gross margin (EGM). The estimated equation was CARA = K + (-1.8E-9)EGM, where
K is the y-axis intercept, the standard error was 4.53E-10, and the t-statistic was -3.93
(very significant). Thus larger producers are predicted to have smaller CARA (less risk
averse). The r! for the equation was .414, which is relatively high for a cross-sectional
analysis.

Correlations between gross margin and the CARA coefficient do not indicate
that producers are Decreasing Absolute Risk Averse (DARA) in their behavior. Time
series data for a particular producer would need to be collected, especially since the
performance variable is indirect income from a crop. In the simple linear regression
performed, there should be no causation implied. Perhaps less risk averse producers
become larger farmers, due to their risk neutrality. Intuition says that an 800 acre
soybean farmer would need a nearly risk neutral behavior. Such a large problem
would be too risky for a more risk averse producer.

The workshop experience also allowed for evaluation of the model

performance. ELRISK was intended to elicit risk attitudes from the second standard

168

deviation below the mean gross margin up to the second standard deviation above
the mean (or beyond). The reason for this, is that points on the utility curve are used
in a table-lockup function to convert from gross margin to utility. Monte Carlo gross
margin values beyond those in the utility curve were extrapolated (linearly) from the
last two endpoints. For MKTOPT to function, it is best to get a utility function that
covers as much of the gross margin distribution as is practical.

ELRISK was largely successful at surpassing the second standard deviation
above the mean. Only six times were the highest user values below the mean plus
two standard deviations. ELRISK did not perform as well on the lower end of the
gross margin distribution. Was the expectation unreasonable on the lower end? Are
improvements needed in ELRISK or ELRO methods, or is it unreasonable to think that
producers should feel the same way (marginally) about incomes that are two standard
deviations below the expected?

The methods used gave mixed risk attitudes when examining values in the
neighborhood of $0.00 gross margin. Cochran et al. (1990) noted that when
elicitation reaches certain biases areas, such as zero, this can effect the elicitation.
One other weakness of the elicitation method used, (common to many elicitations) is
serial dependence. This occurs in the ELRO method, when previous answers are
used to build new situations. For example: a person may transpose two digits in their
response, and not realize their mistake. Such a mistake affects subsequent
elicitations. Fortunately, ELRISK allows the decision-maker to back up and revise

previous input values.

5.10 Marketing Solutions

There are five groups or types of data, that directly resulted from field testing.
The first type of data is the subjective pdf for yields. These were summarized in Table
5.2 and available in Appendix D. The second group of data is results of risk
measurements taken with ELRISK These were discussed in Section 5.9 and are
presented in Appendix C. Third are the marketing alternatives that each producer
received from running the programs (the farmer results). These are discussed in this
section. The fourth and fifth types of data are producer and presenter workshop
evaluations (discussed in the next section).

Since the workshops were conducted using microcomputers, each producer’s
input was stored to disk, reducing the data collection problems. These same data
saves were also needed for the model to function correctly. The output for each
farmer included the best 15 marketing plans from the MKTOPT program. This output
was both printed and stored to file. In fact, several producers ran MKTOPT more than
once to change data inputs.

Summarizing the best 15 plans for each of the 29 producers was not simple.
When solutions were reduced to a single marketing plan, the sensitivity of the solution
was lost. This is particularly true with risk neutral persons and slightly risk averse
producers. Due to unintentional biases in measuring market volatility, options seldom
came into solution for any producers at significant levels (more than 1% of expected
production). Producer solutions were converted from bushels to be marketed, into
percentages of expected production. This helped reduce the farm size effect of each

marketing plan.

 

170

Table 5.4 Summary of Producer MKTOPT Results

Portions of Expected Production

 

 

FORWARD FUTURES BASIS CARA RISK* RP*/

USER CONTRACT HEDGE CONTRACT R(x) E[Bu.] PREM ACRES Acre

MON13 .000 0 .053 0 20503 S 0 500 $0

FRAB .732 0 .209 .0000016 28670 104 700 .15
FRA6 .867 .019 0 .0000032 14653 238 350 .68
MON12 .542 0 0 .0000087 10462 448 225 1.99
MONB .119 0 0 .0000170 24023 127 605 .21
FRAl .078 0 0 .0000183 33213 2233 810 2.76
MONl .756 .323 0 .0000236 14945 758 400 1.90
FRA2 .489 .130 0 .0000238 18737 455 420 1.08
MON4 .852 0 0 .0000239 15427 1709 350 4.88
SHIl .618 0 .014 .0000284 22039 2873 629 4.57
MON2 .759 0 .013 .0000306 19133 2542 480 5.30
MON14 .554 0 .015 .0000311 13772 382 347 1.10
MON9 .845 .292 0 .0000350 26438 10212 575 17.76
CAL3 .500 0 0 .0000415 9082 373 250 1.49
MON6 .796 0 .034 .0000420 22582 781 500 1.56
FRA5 .331 .463 .134 .0000479 12008 667 300 2.22
MONB .771 0 0 .0000526 13988 1401 300 4.67
MON? .570 .016 .026 .0000571 23593 5521 630 8.76
FRA7 .308 .284 0 .0000640 18121 2484 420 5.91
CAL2 .715 0 0 .0000709 11992 1909 320 5.97
CAL4 .807 0 .019 .0000709 6928 668 160 4.18
MONll .466 0 0 .0000868 4975 443 120 3.68
8816 .790 0 .062 .0000947 6321 1858 190 9.78
SHI3 .734 0 0 .000115 5450 923 162 5.70
8812 .586 0 0 .000119 6603 140 187 .75
MONS .371 .058 0 .000128 4506 611 98 6.24
SHI7 .693 0 0 .000146 7336 2198 200 10.99
FRA4 .207 .030 .435 .000267 3133 130 77 1.69
FRA3 .601 .245 .018 .000352 3172 261 85 3.07

* RP is Risk Premium Above doing No Marketing (RPANM).

Table 5.4 shows that forward contracting was the major pricing instrument
selected. Fonivard contracting was very similar to futures hedging in the model,
except for two differences. First, the basis was uncertain with futures hedging.
Second, when producers over-contracted they had to pay a $.05/bushel penalty to
buy back additional grain to meet contract obligations. This user adjustable value

called ASK-BID, was set at $.05/bushel. The ASK-BID spread could represent any per

 

171

bushel penalty for not meeting cash contract obligations. It further separates the
characteristics of the two pricing methods. Most farmers at the workshops did not
adjust the ASK-BID spread.

There were few pricing patterns among the producers listed in Table 5.4. The
producers are listed in reverse order of their risk aversion. Those with the smallest
CARA coefficients (least risk averse) are at the top, and the most risk averse are listed
at the bottom. Even though price variability was the same for all producers, there was
considerable difference in their means and standard deviations of gross margins.
There were also differences in yield distributions, acreage, variable costs, and costs
per bushel. The smaller the per bushel costs and/or the smaller the yield variance,
the less variability in gross margin.

Several producers had sizeabie “Risk Premiums Above doing No Marketing“
(RPANM), indicated in the seventh column (Table 5.4). Placing these values on a per
acre basis, put them in clearer perspective by reducing farm size effects. The
monetary value of the workshop to five producers was less than one dollar per acre.
For these decision-makers, the workshop had little risk-management benefit, ex_cep_t
for educational value. Thirteen producers indicated RPANM of more than $5 per acre.
The workshop was worthwhile to these persons if they followed some of the
suggestions presented by the FIRM model, and if they revealed their risk attitudes

accurately.

5.11 Producer and Presenter Evaluation

Producers were given an evaluation form at the start of each workshop. Every

producer but one completed the form. The results are summarized in Table 5.5.

172

There was also additional space on the worksheet for open comments. A copy of the
evaluation forms are in Appendix B and the unstructured comments offered by twenty

of the producers are in Appendix A.

Table 5.5 Producer evaluations

WORKSHOP EVALUATION: Needs

goLd £ai_i; Improvement
1. Program overview 26 2 0 *
2. ELICIT yield distributions —-20-- ---5-- ---1—-
3. Market outlook & volatility --20-- ---6-- ---I--
4. Risk preference elicitation --15-- --IO-- ---2-“

5. Finding optimal
marketing strategies 14 12 1

* Totals across are not 29, because of missing data. Numbers
indicate occurrences of each response.

Most producers indicated the workshop was worthwhile, interesting or gave a
positive description (11/20). A number of producers made suggestions for
improvements (9/20). One or two suggested making things simpler, while others had
more specific suggestions. One workshop attendee expressed doubt about the
potential success, but enjoyed the day. One producer felt the day might have been a
waste and he would never use this kind of software. Finally, there was a person who
simply asked a question about how FIRM related to market fundamentals.

Several managers made the observation that the solution from MKTOPT was

similar to rules of thumb they had heard in the past. This was a comforting

173
observation to workshop presenters. There was a slightly bigger group who felt that
the recommendations were a little aggressive (more forward pricing than they
preferred).

After each workshop, time was spent evaluating the workshop
accomplishments among the workshop presenters, as well as among the extension
hosts. Most of the tone was guarded optimism, and like the producers, there were
several ideas about how the workshop model of FIRM could be improved.

Ideas were also exchanged with producers who lingered, following the
workshop. At least three or four producers suggested that a price “trend“ could be
entered along with the efficient market assumptions about mean and market variance.
This contradiction of ideas turned out to be a tremendous teaching moment for
forming market expectations.

In Harsh and Alderfer (1990), they wrote that:

Based upon the experience gained in these workshops, the package needs

minor refinement and features added. It appears that FIRM is a valuable

workshop tool to teach risk principles and management. The marketing
alternatives suggested to the producers were found to be very acceptable.

The producers were able to use the various software models and thus they felt
the workshop was a valuable learning exercise.

5.12 Testing Other Utility Curves on a Case Farm

Earlier in this chapter marketing plans were specific for individual producers
and their risk attitudes. The solutions depended on changes of the input data. In this
section, changes to the model and the data set will be more systematic for more
controlled testing of the model. This section is much like some of the tests in Chapter
4, except rather than constructing five synthetic utility functions, we will focus on 5

empirical functions gathered at the workshops.

174

Table 5.6 Static Data for Producer CAL3

PARAMETER VALUES FOR THIS RUN

The upper constraints for
Forward Contracting = 18163.13
Futures Hedging = 18163.13
Put Hedging = 18163.13

Basis Contract = 18163.13
Speculative Call = 18163.13

Today’s month is 1

The contract month is 11

The unbiased Futures price is ($/bu) 6.1825

The forward contract price is ($/bu) 6.08

The Price of a basis contract is ($/bu) -.1

The Call premium is ($/bu) .44

The Strike for the Call is ($/bu) 6

The Put premium is ($/bu) .28

The Strike for the Put is ($/bu) 6

Round trip trans. costs for futures (cents/bu) = 1.5
ONE-WAY trans. costs for options (cents/bu) = 1.5
Margin costs per bushel on futures ($/bu) = .30
Margin costs per bushel on options ($/ bu) = 0

The ANNUAL interest rate is 10.000

The cash elevator spread for ASK - BID is ($/bu) .05

The base farm for testing in this chapter is CAL3. This 250 acre soybean farm
expects to produce 36.8 bu. /acre for an expected gross margin of $3812. Static
pricing data is listed in Table 5.6 for CAL3.

The tests in this section are the type that could have been performed without
conducting workshops, except that they use workshop data. These tests involve
slight changes In the model or data, from a particular reference point. The next

section involves such a test on producer utility functions and their effect on marketing

175

recommendations. The primary purpose of the test is to examine whether discrete or
fitted utility functions should be used to represent the decision-maker’s risk attitude.

The CAL3 farm was re-run with the same costs, prices, probabilities and
stochastic production with only two slight changes in the model. The change involved
setting all of the control variables except forward contracting to zero. This constriction
of a single marketing alternative allows easier comparisons across producers. The
second important change was the use of three classes of utility functions.

The first type of utility function was the discrete data from four of the workshop
attendees, as well as the case farm. These five producers all had utility curve
endpoints extending beyond (or very close to), the second deviation above and below
the expected gross margin of CAL3. The range to cover for CAL3 was
$15,500 to 60,600. Figure 5.2 shows the discrete points elicited from the farmer
(FRA5) as well as the fitted negative exponential function. Graphs of the other four
discrete curves are listed in Appendix C.

Each of the 5 producers in Table 5.7 were similarly fitted to negative
exponential functions in the manner done in Figure 5.2. The result is three utility
curves for each of five producers. The first curve (Curve 1) for each producer is the
original discrete curve used in optimization, in the table-lockup function. These curves
have between 9 and 13 observations (pairs of values) for income and utility. In Figure
5.2 these discrete values are represented by small boxes that are connected by lines.
The lines between boxes are the linear interpolations used in conversion of $ to utility

(and back).

 

176

Table 5.7 Utility Value Coordinates for Five Farms

 

UTIL FRA6 MON14 CAL3 FRA5 MON8
-500 14000 18000 13000 22000
-400 17000 19000 14000 24000
-300 2000 18000 20000 16000 26000

-200 12000 19000 22000 18000 28000
-100 20000 25000 25000 22000 30000
0 40000 28000 28000 30000 32000
100 44000 31000 31000 40000 36000
200 49000 38000 35000 56500 40000
300 55000 43000 40000 75000 48000
400 65000 55000 45500 100000 56000
500 75000 63000 52000 66000
600 90000 70000 59000\ 74000
700 105000 79000 68000

CARA .000003 .000031 .000042 .000048 .000053
r2* .9819 .9891 .9944 .9746 .9946

* Correlation of fitted to actual data values for
negative-exponential utility functions.

 

The second curve (Curve 2) for each producer is also discrete, with the same
number of observations as the elicited discrete curves. The difference is that these
points are from the best fitted negative exponential function. Like the first curves,
these curves were linearly extrapolated between points for conversion of $ to utility.
Figure 5.2 shows this fitted discrete “curve.“

The final curve (Curve 3) is smooth and continuous, using the fitted negative
exponential function directly, with no linear interpolation. The inverse of the function
was used to solve for certainty equivalents ($), from expected utility. Curve 3 is not
graphed in Figure 5.2 since It would be almost exactly on top of the fitted discrete

curve.

177

 

500 original
—-—

Fitted

 

 

400 /

Utility 2cm

 

 

-200

 

-4OD

 

 

 

-800

 

I | I I
D 20 40 60 BO 100

SOYBEAN INCOME (Thousands)

 

 

 

Figure 5.2 Discrete and Fitted Utility Curves for FRA5

It was expected that there would be very little difference between fitted discrete
functions and using the smooth continuous function. In fact, the differences between
these two represent the difference in error between a smooth function and the discrete
one. Also, with risk averse behavior, the expected utility should be higher as the
straight lines between utility become arcs. Thus, the local risk aversion was changed
from risk neutral along the line segments, to be locally more risk averse. It was
expected that discrete utility curves with poor r1 values for the nonlinear function,
would have more changes in amounts marketed when moving from one type of utility

curve to another.

178

Table 5.8 Comparisons of Utility Functions

BU T0 FORWARD CONTRACT

Curvel CurVeZ Curve3
USER R42 r(x) Direct Discrete Fitted

FRA6 .98188 .000003 0 5196 5088
MONl4 .98011 .000031 6054 5828 5577
CAL3 .99441 .000042 4343 6278 5515
FRA5 .97463 .000048 4070 5422 5364
MON8 .99456 .000053 6822 6523 5302

UTILITY RISK PREM ABOVE DOING
N0 MARKETING
Curvel Curve2 Curve3 Curve] Curve2 Curve3
USER Direct Discrete Fitted Direct Discret Fitted

FRA6 45 82.1 82.4 0 21.2 23.1
MONl4 174.4 178.1 180.0 272.4 287.5 312.8
CAL3 205.1 213.7 225.3 373.2 398.8 411.6
FRA5 55.4 81.4 85.6 674.4 391.1 469.8
MON8 68.9 59.2 63.9 586.0 441.1 511.4

In Table 5.8, several patterns did emerge. The differences between Curve 2
and Curve 3 in both the utility section and the risk premium sections were uniform in
their direction of change. As expected, smoother functions increased expected utility
and the RPANM. The changes in Curve 2 and Curve 3 in the marketing section were
uniform. The average absolute change in the number of bushels marketed was 480
bushels per farm, when moving from Curve 2 to Curve 3. The change in risk premium
for such small changes in marketing can be very small (depending on the R(X) of the
function. This can be seen in the nearly risk neutral producer (FRA6). The FRA6
marketing plans increased from zero forward contracting to 5196, while the RPANM

changed very little. The change in forward contracting levels between Curve 1 and

179

Curve 2 were sizable, but the nearly risk neutral producer (FRA6) was responsible for
much of the difference, even though the change in risk premiums were small.

Figure 5.2 shows why the FRA5 producer had big risk premium changes
between curve 1 and curve 2. The FRA5 bushels marketing (curve 1) and the curve 1
RPANM also seem a little high. The fitted curve across the first six observations of
FRA5 at first “under“ estimates the utility curve, only to later over estimate it. The net
result is that below the U($) = 0 point, incomes on the fitted line give less utility and
above that point they give more utility (than Curve 1). FRA5 had the poorest fit to the
negative exponential utility function of any of the five producers in Table 5.8.
Fortunately, less than one third of the producers had r8 values lower than the FRA5
producer, and most of these poorer fitting functions involved much higher risk averse
behavior.

One possibility that was not examined is the use of a smoothing function to
convert the 10 to 13 discrete producer values into a larger number of smoother
coordinate values. Smoothing functions should be a final recourse for the program
design since the system designer looses some control or understanding of the

system.
5.13 Changing Price Data for the Case Farm

The next three tests are changes in ending period distribution of futures and
basis. The case farm (CAL3) is again used as a starting point along with utility
functions from a nearly risk neutral producer (FRA6) and a producer (MON8) who is

slightly more risk averse than CAL3.

 

180

Table 5.9 Testing Futures Price Biases
—

BEST MARKETING PLANS

Risk Prem
Frwd Futures Put Basis Spec. Expectd Above doing Descri
USER Cont. Hedge Hedge Cont. Call Utility Ho Mrktng ~ption

FRA6 0 0 0 0 0 38.9 0. Low Bias
CAL3 6425 0 0 0 0 201.8 658.8 E[futures]
MOMB 8257 0 0 0 0 68.0 996.9 minus $.05
FRA6 0 0 0 0 0 45.0 0.

CAL3 4541 0 O O 0 205.1 372.6 Base
MON8 6554 0 0 0 0 68.8 584.5 (no bias)
FRA6 0 0 0 O 0 51.0 0. Hi bias
CAL3 2478 0 0 2421 0 211.7 180.9 E[futures]
MON8 4541 0 0 0 0 71.6 262.6 plus $.05

Table 5.9 above shows systematic changes in the ending distribution for
futures contracts. Each of the 200 Monte Carlo observations were lowered by $.05 in
the top three rows, held constant in the middle, and in the last three rows raised by
$.05. This bias between today’s futures price of $6.18 and $.05 higher or lower is a
violation of the efficient market hypothesis, but shows how persons with a biased view
of the market would behave.

Table 5.9 shows FIRM is well behaved to changing price expectations.
Producers who envision higher futures prices in the final period will contract less, get
higher utility, and reduce their risk premium. All of these are as expected.

Table 5.10 involves the same type of biased expectations ($.05), but on the

basis level, rather than futures.

181
Table 5.10 Changing Biases in Basis

BEST MARKETING PLANS
Risk Prem
Frwd Futures Put Basis Spec. Expectd Above doing Descri
USER Cont. Hedge Hedge Cont. Call Utility No Mrktng -ption

FRA6 0 0 0 13000 0 44.9 237.7 Base

CAL3 4133 0 0 7346 0 205.5 846.1 E[Basis]
MON8 7874 0 0 3694 0 68.7 1027.3 minus $.05
FRA6 O 0 0 0 0 45.0 0. Base

CAL3 4541 0 0 0 0 205.1 372.6 E[Basis]
MON8 6554 0 0 0 0 68.8 584.5 (no bias)
FRA6 0 O O 0 0 51.0 0. Base

CAL3 2200 0 0 0 0 211.2 157.2 E[Basis]
MON8 0 6500 O 0 0 73.7 345.8 plus 8.05

Similar results were found in Table 5.10, where basis was expected to widened
(first three rows), hold constant (middle three rows) and increase (last three rows. In
the first three rows, each producer attempts to capture what he sees as mis-priced
basis contracts. In the last triple rows, the basis is expected to improve, so producers

reduce forward contracting levels to capture improving basis.

5.14 Summary

In this chapter summaries of results were presented for all the farmers who
attended one of four marketing workshops. In addition, all utility curve data appears
in Appendix C, and all producer yield distributions appear in Appendix D. It is
producer behavioral aspects that are the emphasis of this chapter. Farmer yield
distributions and utility curve summaries are the main contributions reviewed in this
chapter. Unfortunately, there are few ways to judge the quality of these attitudes or

beliefs can be double-checked. One interesting way would be to conduct the

182

workshops a second time, to see how producer answers and yield expectations
changed. Time did not allow for this.

One important finding presented in the chapter was the superiority of the
negative exponential function compared to the other three utility functions tested.
While marketing plans exhibited a large variety of solutions, risk premiums proved
valuable in analysis. There was a noted significant negative correlation between gross
margin and the CARA coefficient for the producers. This should be expected, not
because producers should or should not be DARA, but because large farms constitute
more risk (larger standard deviations) than a highly risk averse person could accept.

Producers, as well as presenters, felt the workshop was educational and
worthwhile, with only one dissatisfied workshop participant (out of 29). All workshop
attendees stayed for the entire workshop, with none leaving early.

This chapter also examined FIRM and tests of discrete utility functions versus
fitted ones. Discrete utility was not as “well-behaved“ as fitted data. Changes from
actual data to fitted behavior changed marketing recommendations. This gives some
evidence that perhaps utility functions should be exponentially smoothed (or some
other smoothing function). How this should best be done is not clear at this time and
will require additional research.

There was also a test of sensitivity of data biases. Such biases alter
recommendations, and risk premiums. If persons expect futures or basis to increase

[decrease], then marketing will decrease [increase] as expected.

 

CHAPTER SIX

SUMMARY AND CONCLUSIONS

6.1 The Problem .......................................... 184
6.2 The Research Objectives ................................. 184
6.3 Research Findings and their Implications ..................... 185
6.4 Limitations of the Research ............................... 188

6.5 Future Research

183

184
6.1 The Problem

Commercial grain farmers can use several cash and futures market
instruments prior to harvest, to manage their crop income risk. The producer problem
addressed in this research is: “Which pricing alternatives should i use and how many
bushels to price for a particular grain commodity, when production and ending period
prices are uncertain?“ The research problem is to improve marketing information by
developing and testing microcomputer tools that help farmers consider their risks and

decide how many bushels to price with each pricing alternative.

6.2 The Research Objectives

The objectives of this research were to (1) review relevant literature, (2) build or
identify software components to solve the research (and farm) problem, (3) test the
model for usefulness, workability and whether the model solutions are close to what
should be expected, and (4) identify research contributions and challenges for further
research. All of these objectives were reached, in the course of the research. Other '
research models and microcomputer simulation models were reviewed, along with
decision theory and other methods related to the research. ELRISK and MKTOPT
were constructed to measure utility and to optimize expected utility for a single period,
single crop, marketing problem. Tests of FIRM (the collective components) were
promising. None of the solutions from FIRM seemed to contradict what was known
about risk reduction and marketing, except with regard to the use of options. Futures
price volatility was underestimated, enough that options only entered into solution

when no other risk reducing strategies were available.

185

6.3 Research Findings and their Implications

1 Forward contracting can substantially reduce risk for producers. The reasons for
this is that with forward contracting, transaction costs are non-explicit and both futures
and basis volatilities are managed. The explicit costs of trading futures (and
maintaining margins) reduces the desirability of futures hedging in this stochastic but
non-dynamic model. This corresponds to what is known about farmer behavior and

their favoring the use of fonivard contracting.

a Changing the futures price distribution from normal, to log-normal, to randomly )
drawn from a normal, had little change on solutions. The normal and log-normal
solutions were more alike in their marketing solutions than the 200 Monte Carlo draws

from a normal. All three distributions had nearly identical means and variances.

9_. Using Utility Theory allows calculation of risk premiums, that are not easily attained
through other decision methods. Risk premiums supplement solutions by giving easy
to understand measurements that serve as a confidence factor in comparing risk
related solutions. They are also useful to measure the direct producer benefits of the
risk reduction. The implications of this for the 29 workshop participants was varied.
Some had small risk premiums, and others were larger, but as a group nearly $40,000
of risk reduction was computed.

g; The model testing in Chapter four ,using synthetic CARA utility functions, gave
results very similar to tests using utility curves of actual producers elicited in marketing

workshops. This consistency helped validate the FIRM model.

 

186

e_. Workshop data indicate the negative exponential utility ( U(x) = K -a-e"’“) s the
best candidate for functional form, of those forms that were tested. Even when it was
not the best fitting form (compared to semi-log and quadratic) its r2 values were still
excellent. This finding is important for decision theory, giving strength to E-V analysis.
Quadratic and semi-log were inferior functional forms except in some of the more
linear (risk neutral) producers. Even in those cases, the negative exponential function
fit very well. These results are based on utility functions with 9 to 13 utility

coordinates.

f_. ELRISK is a powerful context sensitive expert system, that was developed and
tested in this research for risk elicitation. It is seeded by the mean and standard
deviation of the expected income distribution, making the elicitation very context
sensitive. It differs from the original Halter and Mason (1978) method, to give 9 to 13
discrete “income, utility“ coordinates (rather than just 4 or 5). ELRISK is a personal-
computer software program, based upon a risk elicitation method that is usually called

the Equally Likely Risky Outcome method.

9, The workshops conducted had very positive ratings and comments. Not a single
workshop participant (of the 29), left early from the all-day program. Most producers
ran extra analysis. Several persons indicated an interest in participating again, and a

few persons wondered if and when FIRM would be available for their use.

L The use of graphics to represent preferences, along with changes in certainty
equivalents (risk premiums) were very important to this research, and are strongly

recommended for persons working with risk and decision-making.

-‘A- 4.—

 

187

i_. One workshop participant (of 29) was risk neutral, three were nearly risk neutral

(0 < R(x) < .00001), two were very risk averse (R(x) > .0002) when examining the
specific problem of soybean marketing risks. The remainder (23) exhibited various
degrees of moderate risk aversion (.00001 < R(x) < .0002). Risk aversion was shown
to be significantly related to the size of the producer problem. Large risky problems

require decision-makers who are less risk averse than small problems.

1, Pre-harvest basis contracting did very little to reduce producer risk exposure,
compared to methods of pricing the futures portion of price. This was expected to
occur, since basis Is such a small part of the total soybean price. This might not be

the case with some commodities with larger basis risk.

5, Options seldom came into solution, until premiums were lowered. This
miscalibration of the ending futures price distribution was unfortunate. An
unintentional bias in the futures price volatility was created, possibly due to using a 10
percent interest rates for the producers and a seven percent risk-free short-term
interest rate in the OPM. Closer calibration of futures price distributions must be
made. Fackler and King (1990) have completed substantial new work in this area,
and provide updated non-parametric methods that will be beneficial to future work in
the area of price probability distributions.

This research will be useful for other problems where stochastic factors and
decision-maker risk attitudes are important. With some effort this approach might be
useful for examining investments in irrigation, evaluation of land rental arrangements,

factors related to government commodity program participation, and more.

188

6.4 Limitations of the Research

While the tools developed in this research (GENRINC, ELRISK, and MKT OPT)
were successful in meeting the research objectives, there are limitations to FIRM and
this research that need to be mentioned. FIRM is a non-dynamic model trying to
address a dynamic problem. Ignoring the dynamic aspects of the problem helped
keep solutions simple so that farmers could easily provide the data, and understand
the solutions. Karp (1987) and Berg (1987) have both examined dynamic marketing,
but neither have indicated that their developments provide results that farmers can
directly use and understand. While Karp (1987) does capture the dynamic aspects of
marketing, other pricing alternatives and strategies available to real decision-makers
are not considered.

Users of FIRM must understand the static nature of the model and the market
dynamics. Not all of the pricing recommendations from running FIRM need to be
taken on the day FIRM is run. Workshop participants were informed that the risk
costs computed, were over the entire time until harvest. It may be that a rule of thumb
to price 1/3 at planting, 1 /3 at harvest and 1 /3 post harvest, would be superior over
the solutions from FIRM. Working with dynamic strategies, requires conditional
probability data that are not available, and the problem may become more difficult
than many producers are capable of comprehending

There was no follow-up with producers regarding whether they had followed
recommendations from FIRM computed at the workshops. This follow-up idea was
presented after the'season and the harvest, so workshop participants might not
remember workshop answers, and due to the passing of time would probably

discount the influence of the workshop.

189

6.5 Future Research

An end-user design of FIRM must allow use of multivariate distributions, but
the research model developed, used independent (uncorrelated) distributions.
Research with FIRM incorporating multivariate distributions should be done as quality
correlation data becomes available. Further efforts are also needed regarding the
best smoothing function for utility, as well as price distributions. This research points
out a need for further research in calibrating price distributions based upon options
premiums.

In this research, every entry in ELRISK was recorded to disk as entered. If the
entry was later revised that second entry was also recorded. Future research with
ELRISK could (and should) involve further examination of this data. Behaviorists with
interests in decision-making could incorporate the time or time change in seconds for
every entry, to gather human behavioral data. From only a brief analysis of this entry
by entry data, it appears that most decision-makers started out slowly with the
process, making numerous revisions, but few to evaluate the decisions in ELRISK
more promptly and perhaps more reliably. There are numerous research
opportunities related to the human or behavioral elements of ELRISK One example
of this kind of research is exploring the difficulty that decision-makers have when
elicitation reaches critical lower levels.

In future research with FIRM, follow-up discussions with workshop participants
should be done to measure the user acceptance and potential benefits. This same
process should also be used if a research project were to involve decision-maker use
of FIRM throughout the growing season. Periodic evaluation could assess the use of

FIRM up until harvest. With a user database and an end-user version of FIRM, the

190

database would record the marketing decisions, and if made available to the
researcher after harvest, could provide additional feedback.

Much of the elicitation literature reviewed in Chapter 2, indicates that decision-
makers have diffictu with changing probabilities. in order to shed more light on this,
ELRISK could be modified to include other probabilities. The probability of a good
year could be changed from 50 percent to 40 percent (and 60% bad year) or vice
versa.

FIRM performed very well in an extension workshop setting to teach
elementary applied probability, risk principles, and marketing. If the producers adopt
the marketing plans suggested substantial risk reduction would occur. This research
was not only an educational program for nearly all who participated, but allows for
computation of its own potential benefits. The software development, to date, is very
suitable for a workshop setting, but is m ready for individual producer use. Much
database development is needed, as well as empirical work on ending period price
distributions.

FIRM adds more support for the negative exponential function in empirical and
theoretical use. Further tests of the model are needed. Some of these should involve
additional workshops and data collection. At this stage FIRM is best used as a
supervised educational tool. It could be used by trained Extension personnel, or
marketing consultants. Like the B.E.A.R. package discussed in Chapter 2, FIRM

could be offered to individuals, but only if they attend a training session.

191

Based upon the evaluation forms and comments, FIRM has tremendous
potential. Very little research has been done to date on context sensitive risk
elicitation to solve farm problems. While FIRM is not perfect, it has helped identify

needed research, and provided a framework to build upon.

APPENDICES

192

APPENDIX A - Comments from Workshop Participante

(1) Could it be simplified? (2) Most problems with this one = ELRISK.

(3) It was unclear where the game was headed. Additional background is needed.
(4) Improved ideas on marketing opportunities, interesting. (5) One-on-one was great!

(6) How does this relate to market fundamentals? (7) Nice meeting, but it probably
won’t

change the way I market soybeans. It does open the mind up! (8) First time to use a
Computer. Market Risk game- a little hard to understand. I enjoyed the day.

(9) I wish we had been given better cost - acreage information to reduce guessing. It
was a very good meeting with lots of excellent information given. It was a very
worthwhile day. It would be nice to be able to work through this again with the
understanding gained after a “once through.“

(10) if we had more time, would liked to have heard something about hedging.

(11) This program was real interesting. Never seen anything like this before, we have in
our farmer discussion group talked about something similar.

(12) The risk preference elicitation requires more time, thought, practice -- to accurately
reflect preferences or to give us confidence in the outcome.

(13) Need a workshop to understand how the software works. There were some parts
that were

hard to understand and I wish (software) were more friendly to use. (14) The risk
preferences and
yield distribution tools put hard to measure subjects into useful facts.

(15) l strongly doubt that what I learned was worth the time spent. It seems like too
much theory and too little practical use.

(16) One of the best workshops! Please continue and include us!
(17) This type of program stirs the brain and encourages you to investigate more.

(18) I had trouble figuring out how to compare Plan A and B. I feel there is good
possibilities for a program like this.

(19) An imperfect science, but keep up the good work.

(20) Needs simplifying before it will be much use to average farmer. Enjoyed workshop.

 

193
APPENDIX B - Worlgsflbp Program

HOW TO PRICE PRE-HARVEST SOYBEANS AND HOW MANY BUSHELS
TO PRICE IN ORDER TO MANAGE RISK

WORKSHOP SPEAKERS: Jim Hilker - Professor, Ag. Econ.
Steve Harsh - Professor, Ag. Econ.
Rich Alderfer - Research Assistant, Ag. Econ.

SCHEDULE

8:00 Setup Computers and A.V. Equipment
9:00 Coffee & Donuts (get acquainted)

- 9:15 A Brief Overview of the Program - Steve and Rich
9:30 Presentation on Yields and Probabilities - Rich
Run Elicit Software for Soybean Yields - Jim
F ill out Crop Costs Worksheets - Steve
Generate Income Distributions - Rich
10:30 Ten Minute Break
10:40 Soybean Outlook and Volatility Forecast (including basis forecast) - Jim
11:00 Risk Preferences (based on income distributions) - Rich
Run the ELRISK Software

12:30 LUNCH

1:30 Solve Individual Marketing Plans Under Base Assumptions
3:00 Discussion and Evaluation
3:15 Adjourn

l. A YIELD DISTRIBUTION

Prior to harvest, the final soybean yield per acre is uncertain. In fact, as the crop develops during
the growing season, the yield becomes more certain. To examine income risks in soybean
production it is necessary to measure this yield uncertainty. To describe the degree of uncertainty
in yields at this date we can use a program called ELICIT.

You are welcome to keep the printout of your yield distribution from ELICIT. Please be sure to
remember the file name in which you stored your output from ELICIT.

File Name 9-

 

2. BUDGETING SOYBEAN EXPENSES

In order to determine the risks related to different marketing options it is necessary to know your
cost of growing and harvesting the crop. On the following page we have given you some guideline
cost figures for your consideration. These are only costs directly associated with soybean
production. They do not include any overhead costs. A11 marketing costs such as brokerage fees
are not included in the cost figures since they will be automatically added by the OPT program.
You should only use these cost figures to assist you in developing your own cost figures.

 

 

Appendix 8 continued. 194

40 bu. 30 bu. Your Cost
-------------- Dollars per acre-----------

Seed 14 14

Fert & Lime 19 12

Chemicals 21 21

Fuel & Repair 18 18

Labor, Irig. Misc 0 0

Interest till Hrvst 5 4

Var. Cost / ac. 77 69
------ Dollars per Bushel-------«

Harvest 0.23 0.23

Transport 0.20 0.20

Drying 0.05 0.05

Other 0.00 0.00

Var. Cost / bu. 0.48 0.48

Now lets examine share rental arrangements if any. Owned and cash rented soybean acres can
usually just be added together. In a 50/50 share lease the tenant farms half of the land for himself
and supplies labor and equipment for the landowner on the other acres. Of course the tenant and
landowner split all production evenly, but it is easy to visualize the costs as previously described.
Thus when budgeting for total production expenses, it is helpful to add all owned and cash rented
acres to only half of the share rented land.

acres
share rent
X

share

+ + =

owned acres cash rented effective Total Soy§an Acres
shared

3. GENERATE INCOME DISTRIBUTION
This short simple program (GENRYLDS) generates random observations based on your acreage,
costs, yields and distribution of futures and basis. The important output from this program is the
average (or mean) income, and the standard deviation. Record them below to the nearest dollar.

Average Income 3 Standard Deviation of Income 3

4. IDENTIFYING YOUR PREFERENCE FOR RISK

This program (ELRISK) divides a large problem into a series of small ones. It examines your
preferences for risky situations, based on the income distribution you described. By breaking the
larger marketing problem into a series of smaller ones it is possible to solve the larger one.

Be sure to view (on the screen) or print your risk attitude curve when you complete the situations
presented.

 

Appendix 8 continued. 195

5. DEVELOP MARKETING PLAN

This is a program (OPT) that examines approximately 100 marketing plans for 200 'years' of
different combinations of yields and prices to find a set of marketing plan that consider your risk
preferences, production costs, and acreage. When finished computing it finds a "best" plan and 14
other similar plans in the area of the best one. The user can also enter custom marketing plans
to see how they compare with the first solution.

 

6. WORKSHOP EVALUATION

Name (optional):

 

Age: Number of years fanning.

Approximate percentage of total gross farm income from soybean production: %

Needs
Good Ea_ir Improvement

 

1. Program overview _ _ _
2. Elicitation of yield distributions _ _ _
3. Market outlook and volatility _ _ __
4. Risk preference elicitation _ _ _
5. Finding optimal marketing strategies _ _ _

Other comments:

 

 

 

 

 

 

Thank you for your cooperation and assistance.

n D ta196

UN

- Prod cer

APPENDIX

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197

- Producer Curves

APPENDIX

 

 

 

 

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198

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201

APPENDIX D - Discrete Yield Data

Data here is user code followed by expected yield and standard deviation.

The first 2 columns under the user code are the yield interval, the

middle column is raw or unadjusted confidence scores. The fourth and fifth

columns are the pdf and CDF respectively.

88.

 

 

 

 

 

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Nn.F~ 0F. 00.00 00.0w 00.0w 00.00 0F. 00.05 00.00 00.n0

5F.FF 00. 00.0w 00.0w 00.m~ 00.00 0N. 00.00F 00.00 00.00

00.0 no. 00.0F 00.0~ 00.0~ 00.00 0N. 00.00F 00.0n 00.nn

mm.n F0. 00.m 00.0F 00.mF 00.0w 0F. 00.05 00.0n 00.0n

0~.~ F0. 00.m 00.0F 00.0F 00.~F 00. 00.0n 00.0~ 00.m~

~0.F F0. 00.~ 00.0 00.0 00.0 00. 00.0~ 00.0~ 00.0w

Fm.0 F0. 00.~ 00.0 00.0 00.~ N0. 00.0F 00. 0F 00.mF
m0.0 ~5.00 0<zu 00.0 0F. F0 m<¢m

00.00F F0. 00. 0F 00. 00 00. m0

00.00F N0. 00.0F 00.0w 00.nm 0m.00 00. 00. 0M 00. 00 00. 00

0m.50 0F. 00.00 00.0w 00.0w 0F.00 00. 00.00 00.00 00.mm

00.50 NF. 00.00 00.00 00.m0 00.n0 ~F. 00.n0 00.0w 00.0w

F0.m5 -. 00.00 00.00 00.00 00.~5 MF. 00.00 00.00 00.n0

00.nm 0N. 00.00F 00.0n 00.mn no.0m 0F. 00.n0 00.00 00.00

5~.0~ 0~. 00.00 00.0n 00.0n 00.n0 nF. 00.00F 00.0» 00.nn

05.0 50. 00.0n 00.0w 00.m~ 0m.Fn nF. 00.00 00.0m 00.0w

00.~ N0. 00.0F 00. 0~ 00.0w m~.oF 00. 00.00 00.0N 00.m~

00.5 00. 0n F<¢u 00.0 00. 00.00 00.0~ 00.0~

50.~F 50.F0 0<xu
00. 00F F0.0 00.m 00.00 00.m0
FF. 00 No.0 00.0F 00.00 00.00

 

~m.50 nF.0 00.05 00.0m 00.mm 00.00F N0. 00.0F 00.00 00.00
~0.00 0F.0 00.00 00.0w 00.0m 00.50 00. 00.0n 00.0w 00.nm
0m.05 0F.0 00.00 00. 00 00.n0 00.F0 0F. 00.05 00.0w 00.0w
00.0w 0F.0 00. 00F 00. 00 00.00 mm.55 0F. 00.00 00.00 00.n0
F0.0n 0F.0 00. 00 00. 0n 00.nn -.F0 0~. 00.00F 00.00 00.00
0n.0~ 0F.0 00.00 00.0n 00.0n No.00 0F. 00.00 00.0w 00.nn
m~.0 00.0 00.0~ 00.0w 00.m~ m0.- 0F. 00.00 00.0w 00.0n
00.~ ~0.0 00.0F 00.0~ 00.0w ~F.0 00. 00.0w 00.0~ 00.m~
00.0 F0.0 00.m 00.0F 00.mF 00.~ N0. 00.0F 00.0~ 00.0~

~0.0 n0.n0 ~<¢m 00.0 00.~0 5<um

 

203

ix D continued.

Append

00.

5F.
0m.
FF.
00.

mF.
0N.
mF.
50.
~0.

 

00. .00 00. m0

N0. 0n. 5:5

00. 00 00. m0

F0.nn 0:5

00. 00 00.0.0

 

O-
O
I-

33888

-
ONN
.—

33:23:33:

No.
50.
0F.
0n.

0F.
50.
N0.

00.
N0.
00.
50.
-.
5n.
0F.
50.
N0.
00.

~0.

00.

5F.
5F.
00.
N0.
00.
00.

 

 

00.0 00. 0m 00. on
00.0w 00.00 00. m0
00.00 00.00 00.00
00.00F 00.0n 00.nn
00.00 00.00. 00.0n
00.00 00.0~ 00.m~
00.0w 00.0~ 00.0w
00.m 00. 0F 00.mF
0F.5 0n. mm :5
00. F 00. 00 00. m0
00. m 00. 00 00. 00
00.0F 00.0w 00.nm
00.0w 00.0w 00.0w
00.00 00.00 00.00
00.00F 00.00 00.00
00.0w 00.0n 00.nn
00.0~ 00.0n 00.0n
00.0 00.0w 00.m~
00.F 00. 0m 00. 0N
00.0 0n. n0 0.20
00.m 00.0w 00.0w
00. ON 00. 00 00. m0
00. 00 00. 00 00. 00
00.00F 00.0n 00.3
00.00 00.0m 00.0m
00.0~ 00.0w 00.m~
00.0F 00.0~ 00.0~
00.m 00.0F 00.mF
00.0 00.0F 00.0F
00.0 00.0 00.m
no.0 55.0n 33
00.~ 00. 0m 00. mm
00.m 00.0w 00. cm
00.nF 00.00 00.n0
00.n5 00.00 00.00
00.00F 00.0n 00.nm
00.m0 00.0w 00.0n
00.0n 00.0~ 00.m~
00.m 00.0w 00.0N
00.~ 00. 0F 00. mF

0m. 0 0... 5m ~43

00. 0F 00. 0m 00. mm
00. m~ 00. 0m 00. 0m
00.00 00.00 00.n0
00.00F 00.00 00.00
00.3 00.0n 09mm
00.0w 00.0w 00.0n
00.m~ 00.0N 00.m~
00.0~ 00.0~ 00.0~
00.m 00.0F 00.mF
00.F 00.0F 00.0F
00.F 00.0 00.m
0nd 50.0m 0F.5:

204
APPENDIX E - Discrete Price Distributions

Values of the Standard Normal distribution with
the same mean and standard deviation.

Ang&Tang eqn 3.32 zeta= 0.112582
lambda: 1.815385
mu= 6.1825
sd= 0.69825
normal In norml
Stand. mu=6.1825

Normal Prob. sd=.69825 DIFF
—3. 0 3.738625 4.140102 —0.40148
-2.57583 0.005 4.383927 4.59435 —0.21042
—2.32635 0.01 4.558126 4.725295 -0.16717
-2.17009 0.015 4.667235 4.809204 —0.14197
-2.05375 0.02 4.748469 4.872643 -0.12417
-1.95996 0.025 4.813958 4.924394 -0.11044
-1.88079 0.03 4.869238 4.968505 -0.09927
-l.81191 0.035 4.917334 5.007204 —0.08987
—1.75069 0.04 4.960081 5.041852 —0.08177
—1.6954 0.045 4.998687 5.07335 -0.07466
-1.64485 0.05 5.033983 5.10232 -0.06834
-1.59819 0.055 5.066564 5.129207 -0.06264
-1.55477 0.06 5.096882 5.154354 -0.05747
-1.5141 0.065 5.12528 5.178021 -0.05274
-1.47579 0.07 5.15203 5.200413 -0.04838
-1.43953 0.075 5.177348 5.221696 -0.04435
—1.40507 0.08 5.20141 5.242004 —0.04059
-1.3722 0.085 5.224361 5.261448 -0.03709
-1.34076 0.09 5.246314 5.280113 -0.0338
—1.31058 0.095 5.267388 5.298093 —0.03071
-1.28155 0.1 5.287658 5.315445 —0.02779
—1.25357 0.105 5.307195 5.332224 —0.02503
—l.22653 0.11 5.326075 5.348489 -0.02241
-1.20036 0.115 5.344349 5.364278 —0.01993
-1.17499 0.12 5.362063 5.379629 —0.01757
-l.15035 0.125 5.379268 5.39458 -0.01531
-1.l2639 0.13 5.395998 5.409158 -0.01316
-1.10306 0.135 5.412288 5.423391 —0.0111
—1.08032 0.14 5.428167 5.4373 —0.00913
-1.05812 0.145 5.443668 5.450913 —0.00725
-1.03643 0.15 5.458813 5.464246 -0.00543
-1.01522 0.155 5.473623 5.477316 -0.00369
-O.99446 0.16 5.488118 5.490139 -0.00202
-O.97411 0.165 5.502328 5.502737 -0.00041
-0.95416 0.17 5.516258 5.515116 0.001142
-0.93458 0.175 5.52993 5.527293 0.002637
-0.91537 0.18 5.543343 5.539265 0.004078
—0.89647 0.185 5.55654 5.55107 0.00547
-0.8779 0.19 5.569506 5.562693 0.006814
—0.85962 0.195 5.58227 5.574158 0.008113
—0.84162 0.2 5.594839 5.58547 0.009368
—0.8239 0.205 5.607212 5.596629 0.010582
-0.80642 0.21 5.619417 5.607659 0.011758
-0.78919 0.215 5.631448 5.618553 0.012896
-0.77219 0.22 5.643318 5.629321 0.013997
-0.75542 0.225 5.655028 5.639964 0.015064
-0.73885 0.23 5.666598 5.6505 0.016098
-0.72248 0.235 5.678028 5.660928 0.0171
-O.7063 0.24 5.689326 5.671254 0.018072

-0.69031
-0.67449
-0.65884
-O.64335
-0.62801
—0.61281
-0.59776
-0.58284
-0.56805
-0.55338
-0.53884

-0.5244
-0.51007
-0.49585
-0.48173

—0.4677
-0.45376
-0.43991
-0.42615
-0.41246
-0.39886
-0.38532
—0.37186
-0.35846
-0.34513
-0.33185
~0.31864
-0.30548
-0.29237

-0.18912
-0.l7637
-0.16366
-0.15097
-0.l383
-0.12566
-0.11304
-0.10043
-0.08784
-0.07527
—0.06271
—0.05015
—0.03761
-0.02507
-0.01253
0
0.01253
0.02507
0.03761
0.05015
0.06271
0.07527
0.08784
0.10043
0.11304
0.12566

Appendix E continued.

5.700491
5.711537
5.722465
5.733281
5.743992
5.754605
5.765114
5.775532
5.785859
5.796102
5.806255
5.816338
5.826344
5.836273
5.846132
5.855928
5.865662
5.875333
5.884941
5.8945
5.903996
5.91345
5.922849
5.932205
5.941513
5.950786
5.96001
5.969199
5.978353
5.987465
5.996549
6.005598

6.156239
6.164995
6.173751
6.1825
6.191249
6.200005
6.208761
6.217517
6.226287
6.235057
6.243834
6.252625
6.26143
6.270242

205

5.681477

5.69161
5.701652
5.711608
5.721485
5.731289
5.741012
5.750668
5.760256
5.769781
5.779238
5.788645
5.797996
5.807289
5.816533
5.825731
5.834885
5.843995
5.853059
5.862091
5.871077
5.880038
5.888959
5.897853
5.906715
5.915557
5.924365
5.933152

5.94192

5.95066
5.959386
5.968091
5.976782
5.985466
5.994128
6.002783
6.011423
6.020061
6.028686
6.037308

6.04593
6.054543
6.063155
6.071773
6.080389
6.089003
6.097623
6.106255
6.114886
6.123528
6.132183
6.140843
6.149516
6.158207
6.166911
6.175627
6.184369
6.193124
6.201898
6.210699
6.219526
6.228373

0.019014
0.019927
0.020813
0.021673
0.022507
0.023317
0.024102
0.024864
0.025603
0.026321
0.027017
0.027693
0.028348
0.028983
0.0296
0.030197
0.030777
0.031338
0.031882
0.032409
0.032919
0.033413
0.03389
0.034352
0.034798
0.035229
0.035645
0.036046
0.036433
0.036805
0.037163
0.037507
0.037838
0.038155
0.038458
0.038748
0.039024
0.039288
0.039539
0.039777
0.040002
0.040215
0.040414
0.040602
0.040777
0.040939
0.04109
0.041228
0.041353
0.041467
0.041568
0.041657
0.041734
0.041798
0.04185
0.04189
0.041918
0.041933
0.041936
0.041926
0.041904
0.04187

0.1383
0.15097
0.16366
0.17637
0.18912
0.20189

0.2147
0.22754
0.24043
0.25335
0.26631
0.27932
0.29237
0.30548
0.31864
0.33185
0.34513
0.35846
0.37186
0.38532
0.39886
0.41246
0.42615
0.43991
0.45376

0.4677
0.48173
0.49585
0.51007

0.5244
0.53884
0.55338
0.56805
0.58284
0.59776
0.61281
0.62801
0.64335
0.65884
0.67449
0.69031

0.7063
0.72248
0.73885
0.75542
0.77219
0.78919
0.80642

0.8239
0.84162
0.85962

0.8779
0.89647
0.91537
0.93458
0.95416
0.97411
0.99446
1.01522
1.03643
1.05812
1.08032

Appendix E continued.

0.555
0.56
0.565
0.57
0.575
0.58
0.585
0.59
0.595
0.6
0.605
0.61
0.615
0.62
0.625
0.63
0.635
0.64
0.645
0.65
0.655
0.66
0.665
0.67
0.675
0.68
0.685
0.69
0.695
0.7
0.705
0.71
0.715
0.72
0.725
0.73
0.735
0.74
0.745
0.75
0.755
0.76
0.765
0.77
0.775
0.78
0.785
0.79
0.795
0.8
0.805
0.81
0.815
0.82
0.825
0.83
0.835
0.84
0.845
0.85
0.855
0.86

6.279068
6.287915
6.296776
6.30565
6.314553
6.32347
6.332414
6.34138
6.35038
6.359402
6.368451
6.377535
6.386647
6.395801
6.40499
6.414214
6.423487
6.432795
6.442151
6.45155
6.461004
6.4705
6.480059
6.489667
6.499338
6.509072
6.518868
6.528727
6.538656
6.548662
6.558745
6.568898
6.579141
6.589468
6.599886
6.610395
6.621008
6.631719
6.642535
6.653463
6.664509
6.675674
6.686972
6.698402
6.709972
6.721682
6.733552
6.745583
6.757788
6.770161
6.78273
6.795494
6.80846
6.821657
6.83507
6.848742
6.862672
6.876882
6.891377
6.906187
6.921332
6.936833

206

6.237246
6.246153
6.255086
6.264047
6.273049
6.282078
6.291148
6.300252
6.309406
6.318593
6.327823
6.337102
6.346423
6.355801
6.365228
6.374706
6.384248

6.39384
6.403497
6.413211
6.422999
6.432845
6.442771
6.452764
6.462837
6.472992
6.483228
6.493547
6.503955

6.51446
6.525064
6.535758
6.546565
6.557479
6.568508
6.579651
6.590924
6.602321

6.61385
6.625518
6.637333
6.649297
6.661425
6.673718
6.686184
6.698824
6.711663
6.724699
6.737951
6.751412
6.765113
6.779055
6.793248
6.807723
6.822468

6.83753

6.85291
6.868634
6.884712
6.901178
6.918057
6.935376

0.041822
0.041762
0.041689
0.041603
0.041504
0.041392
0.041266
0.041127
0.040975
0.040808
0.040628
0.040433
0.040224
0.04
0.039762
0.039508
0.039239
0.038955
0.038655
0.038338
0.038005
0.037655
0.037288
0.036904
0.036501
0.03608
0.03564
0.035181
0.034702
0.034202
0.033681
0.03314
0.032576
0.031989
0.031378
0.030744
0.030084
0.029398
0.028685
0.027945
0.027176
0.026377
0.025547
0.024684
0.023788
0.022857
0.021889
0.020883
0.019837
0.018749
0.017617
0.016439
0.015212
0.013934
0.012602
0.011213
0.009763
0.008248
0.006665
0.005009
0.003275
0.001458

Appendix E continued .

1.10306
1.12639
1.15035
1.17499
1.20036
1.22653
1.25357
1.28155
1.31058
1.34076
1.3722
1.40507
1.43953
1.47579
1.5141
1.55477
1.59819
1.64485
1.6954
1.75069
1.81191
1.88079
1.95996
2.05375
2.17009
2.32635
2.57583
3.5

6.952712
6.969002
6.985732
7.002937
7.020651
7.038925
7.057805
7.077342
7.097612
7.118686
7.140639
7.16359
7.187652
7.21297
7.23972
7.268118
7.298436
7.331017
7.366313
7.404919
7.447666
7.495762
7.551042
7.616531
7.697765
7.806874
7.981073
8.626375
6.1825

207

6.95316
6.971454
6.990292
7.009717
7.029774
7.050524
7.072028
7.094349
7.117581
7.141815
7.167148
7.193729
7.221702
7.251254
7.282607

7.31604
7.351904
7.390639
7.432834
7.479262
7.531007
7.589655
7.657628
7.738941
7.841005
7.980211
8.207603
9.107855

6.18256

-0.00045
-0.00245
-0.00456
-0.00678
-0.00912
-0.0116
-0.01422
-0.01701
-0.01997
-0.02313
-0.02651
-0.03014
-0.03405
-0.03828
-0.04289
-0.04792
—0.05347
-0.05962
-0.06652
-0.07434
-0.08334
-0.09389
-0.10659
-0.12241
-0.14324
-0.17334
-0.22653
-0.48148
-6E—05

 

m

frF BDI T .EXE

APPENDIX F -

z: 0. 0:0 .0: .2: 0. . 6.0.. 0:.00 m. A 0.0:.

:— £03082; u A. wow
2: o— F u _ 303

603; >6u\.6> .6 :3 m. 3.66. 262. F 6 AN .338 622 F 3 AF .5306 2.
.5222... .000 ....00 6:...02 .0 6:0.
_ :wa
_. F262.
2. .338 n A. .338
22 0F _ u A. 302
. u A. .3306
2.2.0... .0 :02 60:0. .- 603: 40.600 .6626 .06. 22 o. F u _ 302
260A. :2. 6. 005.3 .:2. .0 ..06. n.. n Am .328.
6.600 .:0.. 0. 6.63 .62 .0 ..06. o. n An .3309
00.5.6. £2. 0. 2600 .62 .0 ..60. ~.. n 3 .328.
6.03 .5... 6. 00.5.6. .62 .0 ..00. n.. n An .3306.
00.5.3 .:2. 0. 60.5.6. .62 .0 ..00. o. u A0 .338.
20...... .>62 0. 00.5.6. .62 .0 ..00. F. n An .3309
u.n.6 .66. o. 6.2 .6 .66. 3.- . Am ...266.
26.6.6. .66. o. v.2 .6 .ou. ..- n A. ...266.
...-6 .>o2 6. 6.2 .6 660. ..- n Am ...266.
00.6.3 .6: o. 6; F0 :00. F.. n 3 .5300.

3 .3306 9.60.5.6. 6:0 2.6!. 501.02. 3:20.200 02. 60.5.. 56.:

a .262
A2 ...6.2> n An..6.<>626.
.m 6. . n a 262

$000 .0650 0..- 0202 203;. 2.2.0... .....00 .0 3:06.30 .026 :0 .02.
3.6.9.. >00}: 0.... 6.306 ..e. 0.5.0.6006 ....06 ..0. 8:00. .69...

A .262
6:0 .0 60¢: 05 0.02 60.0060 60303 _. CA6:
.60 ...... 9.3.3.6226 62:6... A366 .. A326 . A..>6 u AA. .3622
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209

Appendix F continued.

 

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210

Appendix F continued.

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Appendix F continued.

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212

Appendix F continued.

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214

Appendix F continued.

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216

Appendix G continued.

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226

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230

Appendix I continued.

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232

Appendix I continued.

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LIST OF REFERENCES

 

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Alderfer, Richard and Stephen Harsh. “Decision Support Software to Elicit Risk
Aversion Preferences.” Michigan State University Department of Agricultural
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Alderfer, Richard, Stephen Harsh, Jim Hilker and J. Roy Black. "Farm Income Risk
Management (FIRM): A Decision Support System Approach.” Paper presented
to NOR-134 conference on Applied Commodity Price Analysis, Forecasting,
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. “Selecting Commodity Marketing Alternatives to Manage Farm Income
Risk.“ Michigan State University Agricultural Economics Department Staff Paper
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. “Farm Income Risk Management (FIRM): A Decision Support System
Approach." Michigan State University Department of Agricultural Economics
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Applied Commodity Price Analysis, Forecasting, and Market Risk Management,
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Alexander, Vickie J., Wesley N. Musser and George Mason. "Futures Markets
and Firm Decisions Under Price, Production, and Financial

Uncertainty.“ Southern Journal gf Agrigultgral Economics 18(Dec. 1986):
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