A demonstration of the non-necessity of marginal conditional stochastic dominance for portfolio inefficiency

This paper demonstrates that a finding of marginal conditional stochastic dominance between two sub-portfolios of a portfolio, while sufficient for showing inefficiency of the portfolio and hence sub-optimality of the portfolio for all risk-averse investors, is not necessary. It is shown by an example that a portfolio can be inefficient even if, for all pairs of sub-portfolios, there is no marginal conditional stochastic dominance. In such a situation, a universally preferred portfolio can be constructed on the margin only by adjusting the shares of more than two sub-portfolios.