his article develops a theory of spot and forwardl commodity pricing T under the assumption that both future prices and future harvests of agriculturd commodities are uncertain. With the exception of McKinnon (1967), output risks have been largely ignored in the literature of commodity hedging.? It is clear, however, that farmer's hedging decisions are influenced by expected output uncertainty. Therefore, the spot and forward prices of agricultural commodities should also be influenced by this uncertainty. In this article, we extend McKinnon's hedging model to develop a theory of pricing in an attempt to quantify the relationship between output risks and commodity prices. Thi article was written while both authors were affiliated with the Fuqua School of Business at Duke University. The Gnaneid support of Duke U n i d t y and the Chicago Mercantile Exchange is gratefully acknowledged. The authors wish to h k Kd Cohen, Dwight Grant, John Hughes. Steve Maier, George Morgan, and especially Pamela Brannen for providing halphrl comments.
'Recently, acveral rereuchm have pointed out that forward and futures prices will diITer in an economy with uncertain interest ratea (Jarrow and Oldfield (19811, Cox, Ingersoll. and Ross (1981). and Morgan (1981). Thia difference ocnvs because futurea contracts are resettled daily, and the parties involved in fulures contracting will be unabk to determine future fiiancing costs or reinvestment rat-in advance. To compensate for this risk, futures prices should be lower than the prices of similar forward contracts. To avoid complications, we will simply refer to forward contracts throughout the reminder of the article.
'After the o r i g i ~l draft of this article WM written, we became aware of recent papers by Baesel and Grant (I*), Rolfo (1960), and MacMinn. Morgan, and Smith (1982) which also ded with output risks. Baesel and Grant (1982) develop a model of futures prices baaed upon the interactions of farmers, processors. and spcculaton. While their approach is similar to ours, they do not consider the diversification effects provided by nonagrieulturd firuncial assets. Rolfo develops a model describing the demand for htdging by farmers faced with price and q~pntit]r uncertainty. He empirically tests this relationship using the futures market for cocoa. Unlike our paper he does not develop a pricing theory. MacMinn, Morgan, and Smith (1982) derive a model of futures pricea for a world with farmers and producers. They also do not consider the effect of diversification across assets. The thrust of their paper is to deal with commodity price regulation.