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Economies 2017, 5(4), 38; https://doi.org/10.3390/economies5040038

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

1
,
2
and
3,4,5,6,*
1
School of Statistics, Beijing Normal University, Beijing 100875, China
2
Department of Mathematics, South University of Science and Technology of China, Shenzhen 518055, China
3
Department of Finance and Big Data Research Center, Asia University, Taichung 41354, Taiwan
4
Department of Economics and Finance, Hang Seng Management College, Hong Kong, China
5
Department of Economics, Lingnan University, Hong Kong, China
6
Department of Finance, College of Management, Asia University, 500, Lioufeng Rd., Wufeng, Taichung 41354, Taiwan
*
Author to whom correspondence should be addressed.
Academic Editor: Ralf Fendel
Received: 23 August 2017 / Revised: 29 September 2017 / Accepted: 2 October 2017 / Published: 19 October 2017
(This article belongs to the Special Issue Efficiency and Anomalies in Stock Markets)
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Abstract

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 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 opportunities and anomalies in the Hong Kong real estate market. Our findings are useful for investors and policy makers in real estate. View Full-Text
Keywords: stochastic dominance; Omega ratio; risk averters; risk seekers; utility maximization; market efficiency; anomaly stochastic dominance; Omega ratio; risk averters; risk seekers; utility maximization; market efficiency; anomaly
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Guo, X.; Jiang, X.; Wong, W.-K. Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly. Economies 2017, 5, 38.

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