The Hedging of an Uncertain Future Foreign Currency Cash Flow

This paper derives the optimal hedge of an uncertain (unknown quantity) future foreign currency cash flow. This more general optimal hedge includes the traditional hedge for a certain (known quantity) future foreign currency cash flow as a special case. The optimal hedge is found to be unbounded and determined by firm-specific conditions, including the variance of the expected cash flow, and the correlation of that future cash flow with actual exchange rate movements. Simulated optimal hedge values are found for U.S.-based multinational firms possessing S/Dm cash flows, using exchange rate data for the 1981–1987 period. Special cases in which the optimal hedge ratio equals zero and one also are identified and we show that cash flow uncertainty can strongly affect the effectiveness of hedging.