We propose a new model of exchange rates, which yields a theory of the forward premium puzzle. Our model is frictionless, has complete markets, and works for an arbitrary number of countries. Each country's exposure to disaster risk varies over time according to a mean-reverting process. Risky countries command high risk premia: they feature a depreciated exchange rate and a high interest rate. As their risk premium mean reverts, their exchange rate appreciates. Therefore, currencies of high interest rate countries appreciate on average. We calibrate the model and obtain quantitatively realistic values for the volatility of the exchange rate, the forward premium puzzle regression coefficients, and near-random walk exchange rate dynamics. A signature prediction of the model is that when a country's riskiness increases, its currency depreciates and put premia on this currency increase. The implied negative correlation between exchange rate movements and put premia is borne out by the data.
