Note—A Note on First-Degree Stochastic Dominance and Portfolio Composition

Suppose an investor is faced with two assets with stochastic rates of return such that in an either-or choice situation the investor can express a preference over the marginal probability distributions of the rates of returns of the assets. If the investor is able to form a portfolio containing both assets, does the fact that he can express a preference over the marginal distributions of the rates of return of the assets allow us to state qualitative restrictions on the composition of his optimal portfolio?