Equilibrium in a Futures Market

Abstract

Normal backwardation, the hypothesis that futures prices normally lie below expected future spot prices, was justified by Keynes [6] and Hicks [2] by the contention that speculators, while risk averse, are less so than hedgers. Consequently, hedgers pay speculators to bear that hedgers' risk. Houthakker [5] supported this view arguing that according to all available data short hedging (and conversely long speculation) is the more common type. Working [9] favored the view that futures prices are unbiased predictors of future spot prices. If this is true, hedgers are not, on average, paying to reduce their risk nor are speculators, on average, earning a premium for assuming risk. Risk averse speculators will participate in such a market only if there are nonhomogeneous beliefs regarding the expected spot price. The level of futures prices is important not only because it determines the cost of hedging, but also because it influences production decisions. In light of the competing views in the literature of both the level of futures prices and the factors which determine them, we will analyze these issues in this paper. To do so, we employ a model based on incomplete markets in certainty claims. In this, and other respects identified later, the model parallels existing futures markets in agricultural commodities. The analysis shows, in the absence of speculators, that the relative magnitudes of the futures price, pf, and the expected future spot price, E(P), are determined by the business transactions of, and markets available to, those economic units with a commercial or production interest in the commodity. This defines the conditions under which there is a role for speculators even if they have the same degree of risk aversion and share the expectations of other market participants. Thus, neither differences in degrees of risk