Forward and spot exchange rates are modelled as an unrestricted bivariate autoregression from weekly data on the New York foreign exchange market for June, 1973 to April, 1980. The null hypothesis that the forward exchange rate is an unbiased estimate of the corresponding future spot exchange rate is tested by means of a nonlinear Wald test and is rejected for all six currencies considered. The results cast doubt on a central assumption in many current models of exchange rate behavior.