Forward and Futures Markets and the Competitive Firm under Price Uncertainty

Abstract

Recent remedies for managing the output price risk faced by a competitive firm sometimes include the prescription of hedging. This practice usually entails combining spot market sales with trading opportunities in forward or futures markets. The forward hedge represents a risk free price. The futures hedge offers a risky alternative which arises because of basis, the variable relationship between the spot and futures quotations. Rather than treating forward and futures as mutually exclusive or as perfect substitutes, a competitive firm can carefully construct a portfolio which combines spot, forward, and futures positions. Holthausen [9] and Feder, Just, and Sclmitz [5] (hereafter FJS), initiate an extensive discussion of a risk-averse firm which uses futures contracts when faced with an uncertain output price but no basis risk. Both articles employ general utility and density functions to derive their results. Their conclusions include independence of the production decision from the probability density of the spot price and the firm's degree of risk aversion. Extensions of these two articles usually focus on the robustness of the separation conclusion to either the addition of basis or the addition of production uncertainty to the models. The risk free characteristic that Holthausen and FJS attribute to futures contracts really better describes a forward contract. Jarrow and Oldfield [11], Paul, Heifner, and Helmuth [17], and many others document the importance of recognizing the unique charapteristics of these two different types of contracts. Batlin [2] builds on the Holthausen and FJS foundation by adding basis risk to his model. FJS explicitly qualify their model as applicable to only those commodities with little or no production uncertainty. Subsequent articles augment their analysis with the condition of stochastic production. Chavas and Pope [3], Anderson and Danthine [1], Marcus and Modest [15], Ho [8], and Grant [6] all include production uncertainty in different permutations of the fundamental model. Those which simultaneously include both basis and production risk achieve analytical solutions by assuming specific utility or density functions.