Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly

Xu Guo, Xuejun Jiang and Wing Keung Wong

MPRA Paper from University Library of Munich, Germany

Abstract: 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 that second-order stochastic dominance (SD) and/or second-order risk-seeking SD (RSD) alone for any two prospects is not sufficient to imply Omega-ratio dominance insofar that the Omega ratio of one asset is always greater than that of the other one. We extend the theory of risk measures by proving that the preference of second-order SD 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 the second-order RSD implies the preference of the corresponding Omega ratios only when the return threshold is larger than the mean of the smaller-return asset. Nonetheless, first-order SD does imply Omega-ratio dominance. Thereafter, we apply the theory developed in this paper to examine the relationship between property size and property investment in the Hong Kong real estate market. We conclude that the Hong Kong real estate market is not efficient and there are expected arbitrage opportunity and anomaly in the Hong Kong real estate market. Our findings are useful for investors and policy makers in real estate.

Keywords: Stochastic Dominance; Omega Ratio; Risk Averters; Risk Seekers; Utility Maximization; Market Efficiency; Anomaly (search for similar items in EconPapers)
JEL-codes: C0 D81 G10 (search for similar items in EconPapers)
Date: 2017-10-04
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