The Role of Expectations in Commodity Futures Markets

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There exist a variety of commodity futures markets depending on the natures, characteristics, and the transaction customs of individual commodity. Thus, I would like to construct a a realistic, as well as a general model. In order to elucidate the role of expectations explicitly, I classified the participating entities in the commodity futures markets by their functions into (1)hedgers, (2)speculators, (3)holders of unhedged inventories, and (4)consumners. Next, I formulated the demand and the supply schedules of commodity futures by the former two entities. Furthermore, I tried to formulate unhedged inventories and consumption schedules in rather simple functional forms. I tried to formulate these schedules, except the consumption one, to emphasize the role of expectations, because they in general depend on the expected values of cash and futures prices in future, or the difference between the expected future cash price and the current futures price. I formulated them by linear approximation, because my primary purpose is to solve the model. Furthermore, by imposing two equilibriun conditions for the market for futures and inventories, I derived the the semi-reduced forms of equilibrium futures and cash prices under given price expectations. It was made clear that, within such a simplified model, the signs of coefficient of exogenous variables in the semi-reduced forms cannot be determined under some stringent assumptions. The route and the direction of the effects of expectations on the demand and the supply were, to some extent, made clear under still more stringent assumptions.It was made clear that, because both the cash and the futures prices are determined basically in a dynamic model, it may be necessary in the future to reformulate the model in a dynamic setting, and in that case, an optimization of an assumed utility function will be an appropriate analytical framework.