SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS DECEMBER 1990
Quantifying Gains To Risk Diversification Using Certainty
Equivalence In A Mean-Variance Model: An Application To
Florida Citrus
Alien M. Featherstone and Charles B. Moss
Abstract
The marginal benefit and cost of diversification for
Horida orange producers is analyzed using certainty
equivalents. Results indicate that for moderate and
high levels of risk aversion, diversification into
strawberry, grapefruit, or additional orange produc-
tion is not optimal. However, moderately risk averse
Horida orange producers can gain by diversifying
into grapefruit production if the annual amortized
fixed costs can be reduced by as little as 10 percent.
Key words: certainty equivalence, mean-variance,
diversification, Horida orange
production
Increased variability of farm income and asset
values during the 1970s and 1980s has increased
interest in risk management. Risk can be managed
using several instruments ranging from forward con-
tracting and other marketing strategies to adaptive
control models for irrigation systems. One popular
risk management technique is enterprise diversifica-
tion. At the firm level, the manager tries to control
production and price risk by producing a combina-
tion or portfolio of enterprises.
A common approach used to evaluate diversifica-
tion opportunities involves the mean-variance ef-
ficiency criterion. This criterion states that an asset
is inefficient or dominated if another asset can
produce the same or higher rate of return for a lower
variance of return (Markowitz; Anderson et al.). In
diversification, a single asset is constructed by com-
bining two or more individual assets. Several studies
have shown diversification to be a useful tool in
managing risk (Heady; Jones; Freund).
However, past applications of the mean-variance
criterion have often failed to consider the marginal
costs and marginal benefits of additional diversifica-
tion (Adams et al.’, Schurle and Erven). In the
agricultural finance literature, the typical crop diver-
sification model emphasizes a set of crops that can
be grown from the same initial set of fixed resources.
Gross margins are often used to calculate the optimal
set of crops. However, diversification often will not
occur unless there is an increase in at least some
fixed resources. For example, a com farmer would
find it necessary to obtain a different header for the
combine before diversification into soybeans could
occur. The traditional method used for diversifica-
tion studies does not account for these additional
costs, including investment in specialized equip-
ment or the extra managerial ability required to
operate a diversified enterprise.
The first objective of this paper is to examine
diversification opportunities for a Horida orange
producer. The second objective is to illustrate how a
broader interpretation of results from a mean-
variance optimization model can be useful in
making decisions.
CERTAINTY EQUIVALENCE AND THE
MEAN-VARIANCE CRITERION
Under certain assumptions, the mean-variance
criterion is related to the expected utility hypothesis.
This linkage can be exploited to derive the certainty
equivalent of an investment opportunity. The fol-
lowing derivation is based on the results of Robison
and Barry, where the objective of a mean-variance
model can be interpreted as the certainty equivalent.
This derivation formalizes the assumptions neces-
sary for this linkage to hold in empirical work.
At the basic level, the mean-variance criterion has
a limited theoretical basis. The mean-variance
criterion reduces a set of all possible investments to
a smaller set of risk-efficient investments. Without
additional assumptions, there is little or no guarantee
that this efficient set of investments contains the
utility-maximizing choice. The usual assumption
required for equivalence between the mean-variance
set and the utility-maximizing set of investments is
Alien Featherstone is an Assistant Professor of Agricultural Economics, Kansas State University, and Charles Moss is an Assistant
Professor of Food and Resource Economics, University of Florida. The authors would like to acknowledge the helpful suggestions of
Bany Goodwin, Ted Schroeder, and three anonymous reviewers.
Florida Agricultural Experiment Station Journal Series No. R-00704.
Copyright 1990, Southern Agricultural Economics Association.
191