Optimal Hedging in Futures Markets with Multiple Delivery Specifications




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    • Graduate School of Business Administration, University of Washington. We acknowledge the financial assistance of the Center for the Study of Banking and Financial Markets at the University of Washington, Graduate School of Business Administration. We thank Swee Sum Lam for her research assistance.


Nearly all futures contracts allow delivery of any of several qualities of the underlying asset. Consequently, the price of the futures contract is associated more with the price of the expected cheapest deliverable variety than with the price of the par-delivery variety. The delivery specifications introduce a delivery risk for every hedger in the market. We derive the optimal hedging strategies in these markets. Their hedging effectiveness is evaluated for wheat futures contracts in Chicago. Hedging optimally would have significantly reduced the variance of the rates of return on hedges while yielding similar mean returns.