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Forward Market Equilibrium

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Abstract

Economists have long been interested in the functioning of forward (futures) markets. Keynes and Hicks were the first to write persuasively in support of the theory of backwardation. This theory says the futures price is biased downward relative to the expected future spot price as a means of compensating for taking long futures positions [12; 8]. In this theory, speculators are viewed as providing insurance to hedgers who desire to take short futures positions to reduce the riskiness of their commodity holdings. In addition to there are theories of unbiasedness and contango.' The unbiasedness theory says that the futures price equals the expected spot price while the contango theory says that the futures price exceeds the expected spot price [4; 19; 21]; however, the controversy over the three theories has not been entirely resolved. It has been suggested [4; 19] that each of the three theories could be applicable at various points during the planting-harvesting-processing cycle of a crop as the net hedging demand shifts from a large number of hedgers who desire to be short in the futures market to a large number of individuals who are long hedgers. Nonetheless, the traditional theories of futures markets have been criticized because they are not grounded in a general equilibrium model where participants' tastes, endowments, and beliefs interact so as to generate a market equilibrium incorporating both speculative and non-speculative transactions [9]. It is the purpose of this paper to provide a framework within which normal contango, normal backwardation, and unbiasedness can each occur for commodities which have certain well-specified characteristics, independent of the relative numbers of participants on each side of the futures market. In the spirit of [9], we consider the major source of uncertainty to be technological in nature (quantity risk) and argue that the commonly used definitions of hedger (one who sells forward some fraction of his crop yield) and speculator are not very useful for economic analysis. Instead, the more generally applicable concept of hedger as one who trades mean income for reductions in risk (in the Rothschild-Stiglitz sense [17]) is supported because it

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