The paper develops a theoretical model of the risk premium in a bilateral exchange rate. Representative agents in both countries are assumed to hold open positions in foreign exchange together with risky assets denominated in their own currencies. Also, past surpluses in the current account of the balance of payments lead to net foreign asset positions which may (partially) be covered in the forward markets. Our two-period mean-variance model for optimizing investors is combined with standard assumption about the behavior of real exchange rates to give a reduced- form equation for the discrepancies between spot rates and lagged forward rates. The model is tested for the dollar-DM, dollar-sterling and dollar-yen exchange rates using monthly data for the period 1976-86. The null hypothesis of no risk premium is rejected for each of the currencies reported. © 1988.