A Note on Stochastic Dominance and the Omega Ratio

10 Pages Posted: 23 Aug 2016 Last revised: 12 Oct 2016

See all articles by Xu Guo

Xu Guo

Beijing Normal University (BNU)

Xuejun Jiang

South University of Science and Technology of China

Wing-Keung Wong

Asia University, Department of Finance

Date Written: August 20, 2016

Abstract

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 proving that the preference of second-order stochastic dominance implies the preference of the corresponding Omega ratios only when the return threshold is less than the mean of the higher-return asset. On the other hand, the preference of second-order risk-seeking stochastic dominance implies the preference of the corresponding Omega ratios only when the return threshold is bigger than the mean of the smaller-return asset. Nonetheless, the preference of first-order stochastic dominance does imply the preference of the corresponding Omega ratios for any return threshold.

Keywords: Stochastic Dominance, Omega Ratio, Risk Averters, Risk Seekers, Utility Maximization

JEL Classification: C0, D81, G10

Suggested Citation

Guo, Xu and Jiang, Xuejun and Wong, Wing-Keung, A Note on Stochastic Dominance and the Omega Ratio (August 20, 2016). Available at SSRN: https://ssrn.com/abstract=2827058 or http://dx.doi.org/10.2139/ssrn.2827058

Xu Guo

Beijing Normal University (BNU)

19 Xinjiekou Outer St
Haidian District
Beijing, Guangdong 100875
China

Xuejun Jiang

South University of Science and Technology of China

No 1088, Xueyuan Rd.
District of Nanshan
Shenzhen, Guangdong 518055
China

Wing-Keung Wong (Contact Author)

Asia University, Department of Finance ( email )

Taiwan
Taiwan

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