This paper examines the determination of risk premiums in foreign exchange markets. The statistical model is based on a theoretical model of asset pricing, which leads to severe cross-equation constraints. Statistical tests lead to a rejection of these constraints. We examine the robustness of these tests to time variation in parameters and to the presence of heteroskedasticity. We find that there is evidence for heteroskedasticity and that the conditional expectation of the risk premium is a nonlinear function of the forward premium. Accounting for this nonlinearity, the specification appears to be time invariant. Out of sample portfolio speculaton is profItable but risky.