Stochastic dominance, efficiency and separation in financial markets

A portfolio problem exhibits separation when all of its solutions can be expressed as affine combinations of a small number of mutual funds. The concept of separation is one of the cornerstones of modern portfolio theory, underlying everything from the mean-variance portfolio selection rule of [7. and 8.] and [11.] to the equilibrium pricing model of [10.], [6.] and [2.]. A great deal of effort has been put into investigating conditions which validate separation assumptions: [3.] as well as [4.] study this problem in terms of utility functions while [9.] takes a distributional approach. The purpose of this note is to show that for the distributional approach, the so-called weak and strong forms of separation are actually equivalent.