We examine the pricing performance of out-of-sample pricing factors in the broad cross-section of currency returns. To this end, we develop a methodology for estimating empirical minimum-dispersion stochastic discount factors (SDFs) under constraints on maximum position leverage. Under leverage constraints compatible with those observed in the currency markets, our empirical SDFs deliver smaller out-of-sample pricing errors than existing factor models, and are priced in individual currency and hedge fund cross-sections. After transaction costs, an investable SDF portfolio delivers a Sharpe ratio of around 0.8 and positively skewed returns. These empirical SDFs offer tractable benchmarks for candidate currency pricing models.