A State-of-the-Art Fund Performance Index: Higher-Order Omega and Its Consistency with Almost Stochastic Dominance

This paper provides a mathematical proof and theoretical analysis of the one-to-one consistency between higher-order Omega and Almost Stochastic Dominance rules when evaluating fund performance. The consistency between higher-order Omega and Almost Nth-degree Stochastic Dominance reinforces the effectiveness of applying the higher-order Omega function in fund performance measurement, as the Almost Stochastic Dominance rules are more likely to be observed in real life. This study also clarifies that the higher-order Omega decreases when threshold L increases. The ranking of funds based on higher-order Omega changes at different thresholds. Hence, it is critical to specify the L so that the consistency holds. Through evaluating the performance of eleven U.S. funds between 2010 and 2020, we demonstrate the applications of the Nth-order Omega in the concept of Almost Stochastic Dominance rules. Furthermore, the empirical results also show the superiority of the Nth-order Omega over the traditional fund performance measure, i.e., Sharpe ratio and the lower-order Omega. The ranking of fund performance based on higher-order Omega is consistent with Almost Stochastic Dominance rules.