Abstract

This paper examines the second-degree stochastic dominance (SSD) efficiency of the portfolios on the mean-variance (EV) frontier. By applying Post's linear programming tests to our weekly and monthly data of a sample of U.S. equity funds, we find that the higher portion of the EV frontier is SSD-efficient, while the lower portion is SSD-inefficient. The quadratic utility test confirms that the top of the EV frontier is SSD-efficient where the SSD-efficient portfolios have higher-means and higher-variances. Based on Perrakis' theoretical inequalities on the central moments derived from polynomial utility functions, we test SSD efficiency on the third central moment and find more SSD-undominated portfolios following the quadratic utility-efficient portfolios; thus extending the SSD-efficient portion on the EV frontier. Then, we maximize the polynomial utility functions on the third and the fourth central moments for SSD and on the fourth central moment for TSD without constraining them to lie on the EV efficient set. Hence, those new generated portfolios should be SSD- or TSD-efficient, but may or may not be on the EV frontier. Our empirical work shows that such optimal portfolios further extend the SSD-efficient portion of the EV frontier, but still lie on the EV frontier, whose upper part lies entirely within the SSD-efficient set.