Properties of optimal forward exchange positions are examined in an expected utility framework. Models considered include multiple forward exchange markets and other alternatives for investment. The responses of optimal forward positions to changes in distributions of returns to speculation are examined, including changes in dispersion about a constant mean, held to be a more general notion of riskiness than variance. Policies to alter speculative behavior are suggested by the analysis. The results are distribution-free, and generalize and extend those of Feldstein (1968).