Almost Marginal Conditional Stochastic Dominance

Marginal Conditional Stochastic Dominance (MCSD) developed by Shalit and Yitzhaki (1994) gives the conditions under which all risk-averse individuals prefer to increase the share of one risky asset over another in a given portfolio. In this paper, we extend this concept to provide conditions under which most (and not all) risk-averse investors behave in this way. Instead of stochastic dominance rules, almost stochastic dominance is used to assess the superiority of one asset over another in a given portfolio. Almost stochastic dominance means that the expected utility of most risk-averse investors can be improved by increasing the share of the dominant asset at the expense of the dominated one, excluding investors with extreme forms of preferences. Switching from MCSD to Almost MCSD (AMCSD) helps to reduce the inconsistency between common practice in asset allocation and the elegant decision rules in modern portfolio theory inspired by stochastic dominance relations. A financial application is further provided to demonstrate that using AMCSD could improve investment efficiency.