A large body of literature documents that returns from currency speculation are highly volatile and possess a predictable component, which is itself highly volatile and serially correlated. Explaining the returns from currency speculation through the presence of a risk premium has proven difficult, however. In particular, models with complete markets and time-separable preferences generate risk premia that are nearly constant. This paper solves a model consisting of two monetary economies with incomplete markets, in which agents are subject to borrowing constraints. The paper investigates if such a framework is able to account for the volatility and the size of the foreign exchange risk premium. Under very restrictive borrowing constraints, the model succeeds in increasing substantially the volatility of the risk premium and generates predictable excess returns, although not sufficiently large to match the data. It thus appears unlikely that excess returns from currency speculation can be uniquely explanined by a time-varying risk premium in an incomplete-markets economy.