The Preferences of Omega Ratio for Risk Averters and Risk Seekers

Abstract

It is well-known that under some conditions, the mean-variance rule is equivalent to stochastic dominance rule. Some academics hypothesize that there could exist mean-Omega ratio rule that could be equivalent to stochastic dominance rule under certain conditions. To explore this possible, in this paper, we aim to establish the necessary conditions between Omega ratio and stochastic dominance that leads to the preferences of risk averters/seekers. We find that it is possible to establish the necessary conditions between and Omega ratio and the preferences of risk averters/seekers under the condition that the variables being compared belong to the location-scale family or the same linear combination of location-scale families.

Keywords: downside risk, value-at-risk, conditional-VaR, stochastic dominance, utility

JEL Classification: C0, D81, G10