TY - JOUR
T1 - Stochastic dominance and omega ratio
T2 - Measures to examine market efficiency, arbitrage opportunity, and anomaly
AU - Guo, Xu
AU - Jiang, Xuejun
AU - Wong, Wing Keung
N1 - Funding Information:
Acknowledgments: The authors are grateful to the Editor and two anonymous referees for constructive comments and suggestions that led to a significant improvement of an early manuscript. The third author would like to thank Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. Xu Guo’s work is partially supported by the China Postdoctoral Science Foundation (2017M610058), the National Natural Science Foundation of China (No. 11601227 and No. 11626130) and the Natural Science Foundation of Jiangsu Province, China (No. BK20150732). Xuejun Jiang’s work is partially supported by the National Natural Science Foundation of China (No. 11101432) and the Natural Science Foundation of Guangdong Province, China (No. 2016A030313856). Wing-Keung Wong’s work is partially supported by grants from Asia University, Hang Seng Management College, Lingnan University, Ministry of Science and Technology (MOST), Taiwan, and the Research Grants Council (RGC) of Hong Kong.
Publisher Copyright:
© 2017 by the authors.
PY - 2017/10/19
Y1 - 2017/10/19
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85071386845&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85071386845&partnerID=8YFLogxK
U2 - 10.3390/economies5040038
DO - 10.3390/economies5040038
M3 - Article
AN - SCOPUS:85071386845
SN - 2227-7099
VL - 5
JO - Economies
JF - Economies
IS - 4
M1 - 38
ER -