If a portfolio A is marginally conditionally stochastically dominated by some incrementally different portfolio B, then it is said to be inefficient in the sense that it is not the optimal portfolio for anyone. Note that this context of portfolio optimization is not limited to situations in which mean-variance analysis applies.
The presence of marginal conditional stochastic dominance is sufficient, but not necessary, for a portfolio to be inefficient. This is because marginal conditional stochastic dominance only considers incremental portfolio changes involving two sub-groups of assets — one whose holdings are decreased and one whose holdings are increased. It is possible for an inefficient portfolio to not be second-order stochastically dominated by any such one-for-one shift of funds, and yet to by dominated by a shift of funds involving three or more sub-groups of assets.
Yitzhaki and Mayshar presented a linear programming-based approach to testing for portfolio inefficiency which works even when the necessary conditional of marginal conditional stochastic dominance is not met. Other similar tests have also been developed.