Risk aversion vs. the Omega ratio: Consistency results

This paper clarifies when the Omega ratio and related performance measures are consistent with second order stochastic dominance and when they are not. To avoid consistency problems, the threshold parameter in the ratio should be chosen as the expected return of some benchmark - as is commonly done in the Sharpe ratio. When the ratio is below one, its value should be discarded - just like a negative Sharpe ratio. Finally, we show that a class of closely related performance measures has both better consistency properties and greater flexibility.