Semivariance below the maximum: Assessing the performance of economic and financial prospects

Abstract

This paper examines the ordering of economic and financial prospects using a rescaled semivariance below the maximum (SVBMax). This indicator is consistent with stochastic dominance (SD) until order three, but is distinct from any expected utility framework, both in terms of construction and in terms of economic implications, despite an apparent formal similarity with the quadratic expected utility framework. SVBMax is able to deal with economic puzzles such as the restaurant puzzle or Rabin’s paradox. SVBMax also provides a consistent alternative performance measure to popular measures such as the Sharpe ratio, the Omega ratio, or lower partial moments with exogenous thresholds. Compared to almost stochastic dominance, SVBMax is devoid of the drawbacks associated with the determination of violation areas. SVBMax can also replace the Aumann-Serrano and Foster-Hart riskiness indicators, which do not conform to third order SD. Further, SVBMax can provide a way of reaching an optimal diversification of stock portfolios. Besides, we also show that SVBMax is consistent with mean-variance-skewness preferences.