Both stochastic dominance and Omegaratio can be used to examine whether the market is efficient, whether there is any arbitrage opportunity in the market and whether there is any anomaly in the market. In this paper, we first study the relationship between stochastic dominance and the Omega...

Both stochastic dominance and Omegaratio can be used to examine whether the market is efficient, whether there is any arbitrage opportunity in the market and whether there is any anomaly in the market. In this paper, we first study the relationship between stochastic dominance and the Omega...

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...

This paper is on decision theoretical foundations for various types of VaR models, including VaR and conditional-VaR, as objective measures of downside risk for financial prospects. We establish the connections of the VaRs with the first- and the second-order stochastic dominance investment...

Extending the work of Jobson and Korkie (1981), Lo (2002) and Memmel (2003), this paper applies the technique of the repeated measures design to develop the Multiple Sharpe ratio test statistic to test the hypothesis of the equality of the multiple Sharpe ratios. We also work out the asymptotic...

We first show that second-order stochastic dominance (SSD) and/or second-order risk-seeking stochastic dominance (SRSD) alone for any two prospects is not sufficient to imply the Omega ratio of one asset is always greater than that of the other one. We then extend the theory of risk measures by...

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...

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...

Both stochastic dominance and Omega ratio can be used to examine whether market is efficient, whether there is any arbitrage opportunity in the market, and whether there is any anomaly in the market. In this paper, we first study relationship between stochastic dominance and Omega ratio. We find...

Farinelli and Tibiletti (F-T) ratio, a general risk-reward performance measurement ratio, is popular due to its simplicity and yet generality that both Omega ratio and upside potential ratio are its special cases. The F-T ratios are ratios of average gains to average losses with respect to a...