Could Omega Ratio Perform Better Than Sharpe Ratio?

In this paper, we will investigate whether there is any Sharpe ratio rule or Omega ratio rule that can be used to show that one asset outperforms another asset if it has a higher Sharpe ratio and/or Omega ratio. We find that Sharpe ratio rule could not detect preference of both risk averters and risk seekers in some strong dominance cases. We set up the Omega ratio rule and find that the Omega ratio rule is better than the mean-variance rule because the former could the former can detect the first order stochastic dominated asset but the latter cannot. We also show the superiority of the Omega ratio rule over any Sharpe ratio rule by using hedging funds data