This paper addresses the question: do risk premia account for the observed time-varying discrepancies between forward and corresponding future spot exchange rates? A simple theoretical framework is used to derive testable restrictions on the parameters of a multivariate regression model. Using various econometric procedures and different estimation periods, the data reject the restrictions. In contrast to past investigations, the empirical results are inconsistent with a world in which time-varying risk premia are the sole determinants of observed deviations from the unbiased expectations hypothesis. Anticipated real exchange rate movements may explain the rejection.