raditional treatments of T et. al. (1988), Myers ( 3 the optimal hedging problem, e.g., Rolfo (1980), Cecchetti 991), ignore the possibility that the optimizing trader can use hedging instruments other than futures. This distinction is particularly important in cases where the precise amount to be hedged is uncertain when the hedge is initiated. For example, this can happen to farmers who must determine the quantity to be hedged at planting time based on the (uncertain) potential crop at harvest time.' Hence, the farmer must hedge against both price and quantity uncertainty. To do this, farmers have a number of practical alternatives. In addition to being able to hedge with derivative securities such as futures contracts, farmers have access to (possibly subsidized) crop insurance plans. The primary objective of this article is to provide solutions to various specifications of the farmer's optimal hedging problem when both futures and crop insurance are available to hedge sources of uncertainty. The following section provides an overview of previous approaches to the farmer's hedging problem. A brief discussion of crop insurance is provided also. The next section examines the conventional specification and solution of the farmer's optimal hedging problems without crop insurance; the third section extends this model to allow for asymmetries in the distribution for terminal wealth. Starting from these initial results, the fourth section introduces crop insurance into the problem specification. This involves reformulating the terminal wealth function associated with the underlying optimization. The last section evaluates the impact of crop insurance on farmer hedging behavior. Unlike previous treatments of the optimal hedging problem, the asymmetric nature of the terminal wealth distribution is introduced into the specification of the expected utility function. Among other things, it is demonstrated that with both price and quantity uncertainty, futures hedging activity depends fundamentally on the type of crop insurance provided.
BACKGROUND
Despite the obvious practical connection, analysis of the farmer's hedging problem has traditionally omitted the possibility of using crop insurance.2 This practical omission is
The author would like to thank George Blazenko for suggesting the problem, as well as John Heaney and, especially the anonymous referees for making useful suggestions. This article was completed while G. Poitras was a visiting Senior Fellow at the National University of Singapore.
'The potential crop is subject to the uncertainties of weather, pests, and plant disease. These problems are not applicable to situations where the production functions are more controllable, e.g., feeder cattle.
*Turvey (1989) and Turvey and Baker (1990) demonstrate that higher farm debtiequity ratios will increase the (optimal) use of derivatives. Hence, subsidized government farm loan programs and other initiatives which (indirectly) increase the farmers ability to borrow, e.g., marketing boards, may also impact the optimal risk management decision.