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Using recently developed model selection procedures, we determine that exchange rate returns are driven by a two‐factor model. We identify them as a dollar factor and a euro factor. Exchange rates are thus driven by global, U.S., and euro‐zone stochastic discount factors. The identified factors can also be given a risk‐based interpretation. Identification motivates multilateral models for bilateral exchange rates. Out‐of‐sample forecast accuracy of empirically identified multilateral models dominates the random walk and a bilateral purchasing power parity fundamentals prediction model. Twenty‐four‐month‐ahead forecast accuracy of the multilateral model dominates those of a principal components forecasting model.