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

Guo, Xu and Jiang, Xuejun and Wong, Wing Keung (2017): Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly. Published in: Economies

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stochastic Dominance; Omega Ratio; Risk Averters; Risk Seekers; Utility Maximization; Market Efficiency; Anomaly
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; G - Financial Economics > G1 - General Financial Markets > G10 - General

References

Aumann, R., Serrano, R. (2008). An economic index of riskiness. Journal of Political Economy 116, 810-836. Bai, Z.D., Li, H., McAleer, M., Wong, W.K. (2015). Stochastic Dominance Statistics for Risk Averters and Risk Seekers: An Analysis of Stock Preferences for USA and China. Quantitative Finance 15(5), 889-900. Balder, S., Schweizer, N. (2017). Risk aversion vs. the Omega ratio: Consistency results. Finance Research Letters 21, 78-84. Bellini, F., Klar, B., M¨uller A. (2017). Expectiles, Omega ratios and Stochastic Orderings. Methodology and Computing in Applied Probability, to appear. Bernard, V.L., and Seyhun, H.N., 1997, Does post-earnings-announcement drift in stock prices reflect a market inefficiency? A stochastic dominance approach, Review of Quantitative Finance and Accounting 9, 17-34. 20 Broll, U., Egozcue, M., Wong, W.K., and Zitikis, R., 2010, Prospect theory, indifference curves, and hedging risks, Applied Mathematics Research Express 2, 142-153. Cannon, S., Miller, N.G., Pandher, G.S. (2006). Risk and return in the U.S. housing market: A cross-sectional asset-pricing approach. Real Estate Economics 34(4): 519-552. Caporin, M., Costola, M., Jannin, G.M., Maillet, B.B. (2016). On the (Ab)Use of Omega? Social Science Research Network Working Paper Series 2559216 Darsinos, T., Satchell, S. (2004). Generalizing universal performance measures. Risk (June), 80-84. Egozcue, M., Fuentes Garc´ıa, L., Wong, W.K., and Zitikis, R., 2011, Do investors like to diversify? A study of Markowitz preferences, European Journal of Operational Research 215(1), 188-193. Guastaroba, G., Mansini, R., Ogryczak, W., Speranza, W.G. (2016). Linear programming models based on Omega ratio for the enhanced index tracking problem. European Journal of Operational Research 251(3), 938-956. Ghent, A.C., Owyang, M.T. (2010). Is housing the business cycle? Evidence from US cities. Journal of Urban Economics 67(3): 336-351. Guo, X., Jiang, X.J., Wong, W.K., (2016), A note on Stochastic Dominance and the Omega Ratio. Social Science Research Network Working Paper Series 2827058 Guo, X., Jiang, X.J., Wong, W.K., (2017a), Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly, Economies, forthcoming Guo, X., Wagener, A., Wong, W.K., Zhu, L.X. (2017). The Two-Moment Decision Model with Additive Risks, Risk Management, forthcoming. Guo, X., Wong, W.K. (2016). Multivariate Stochastic Dominance for Risk Averters and Risk Seekers. RAIRO-Operations Research 50(3), 575-586. Guo, X., Wong, W.K., (2017), The Preferences of Omega Ratio for Risk Averters and Risk 21 Seekers. Social Science Research Network Working Paper Series 2938547. Haila, A. (2000), Real estate in global cities: Singapore and Hong Kong as property states, Urban studies 37(12), 2241-2256. Hammond, J.S. (1974). Simplifying the choice between uncertain prospects where preference is nonlinear. Management Science 20(7), 1047-1072. Hanoch G., Levy, H. (1969). The Efficiency Analysis of Choices Involving Risk. Review of Economic studies 36, 335-346. Henderson JV and Ioannides Y (1987). Owner occupancy: Consumption vs. investment demand. Journal of Urban Economics 21(2): 228-241. Hoang, T.H.V., Wong, W.K., Zhu, Z.Z. (2015). Is gold different for risk-averse and risk-seeking investors? An empirical analysis of the Shanghai Gold Exchange. Economic Modelling 50, 200-211. Homm, U., Pigorsch, C. (2012). Beyond the Sharpe ratio: An application of the AumannCSerrano index to performance measurement. Journal of Banking & Finance 36, 2274-2284. Falk, H., Levy, H., 1989, Market reaction to quarterly earnings’ announcements: a stochastic dominance based test of market efficiency, Management Science 35, 425-446. Flavin, M., Nakagawa, S. (2008). A model of housing in the presence of adjustment costs: A structural interpretation of habit persistence. American Economic Review 98(1): 474-495. Friedman, M., Savage, L.J. (1948). The Utility Analysis of Choices Involving Risk, Journal of Political Economy 56, 279-304. Jarrow, R. (1986). The relationship between arbitrage and first order stochastic dominance, Journal of Finance 41, 915-921. Kallberg, J.G., Liu, C.H., Greig, D.W. (1996). The role of real estate in the portfolio allocation process. Real Estate Economics 24(3): 359-359. Keating, C., Shadwick, W. (2002). A universal performance measure. Journal of Performance Measurement 6, 59-84. 22 Kapsos, M., Christofides, N., Rustem, B. (2014). Worst-case robust Omega ratio, European Journal of Operational Research 234, 499-507. Larsen G.A., Resnick, B.G. (1999). A performance comparison between cross-sectional stochastic dominance and traditional event study methodologies, Review of Quantitative Finance and Accounting 12, 103-112. Levy, H. (1992). Stochastic dominance and expected utility: Survey and analysis. Management Science 38(4), 555-593. Levy, H. (1998). Stochastic dominance: Investment decision making under uncertainty. Kluwer, Boston. Levy, H. (2015). Stochastic Dominance: Investment Decision Making Under Uncertainty. Third Edition, Springer, New York. Li, C.K., Wong, W.K. (1999). Extension of Stochastic Dominance Theory to Random Variables, RAIRO-Operations Research 33(4), 509-524. Markowitz, H.M. (1952). The Utility of Wealth, Journal of Political Economy 60, 151-156. Meyer, J. (1977). Second Degree Stochastic Dominance with Respect to a Function, International Economic Review 18, 476-487. Niu, C.Z., Wong, W.K., Zhu, L.X., (2016), First Stochastic Dominance and Risk Measurement, MPRA Paper 75027, University Library of Munich, Germany. Niu, C.Z., Wong, W.K., Xu, Q.F. (2017), Kappa Ratios and (Higher-Order) Stochastic Dominance, Risk Management, to appear. Qiao, Z., Clark, E., Wong, W.K., 2012, Investors’ Preference towards Risk: Evidence from the Taiwan Stock and Stock Index Futures Markets, Accounting & Finance 54(1), 251-274. Qiao, Z., Wong, W.K. 2015, Which is a better investment choice in the Hong Kong residential property market: a big or small property? Applied Economics 47(16), 1670-1685. Quirk, J.P., Saposnik, R. (1962). Admissibility and measurable utility functions. Review of Economic Studies 29(2), 140-146. 23 Sriboonchitta, S., Wong, W.K., Dhompongsa, D., Nguyen, H.T., 2009. Stochastic Dominance and Applications to Finance, Risk and Economics. Chapman and Hall/CRC, Boca Raton, Florida. Stoyan, D., Daley, D.J. (1983). Comparison methods for queues and other stochastic models, John Wiley & Sons, New York, USA. Thaler, R.H., and Johnson E.J., 1990, Gambling with the House Money and Trying to Break Even: the Effects of Prior Outcomes on Risky Choice, Management Science 36, 643-660. Tsang, C. K., Wong, W. K., Horowitz, I. (2016). Arbitrage opportunities, efficiency, and the role of risk preferences in the Hong Kong property market. Studies in Economics and Finance 33(4), 735-754. Wong, W.K. (2006). Stochastic Dominance Theory for Location-Scale Family, Advances in Decision Sciences 2006, 1-10. Wong, W.K. (2007). Stochastic dominance and mean-variance measures of profit and loss for business planning and investment. European Journal of Operational Research 182(2), 829-843. Wong, W.K., Li, C.K. (1999). A note on convex stochastic dominance. Economics Letters 62(3), 293-300. Wong, W.K., Phoon, K.F., and Lean, H.H., 2008, Stochastic dominance analysis of Asian hedge funds, Pacific-Basin Finance Journal 16(3), 204-223. Ziering B and McIntosh W (2000). Property size and risk: Why bigger is not always better. Journal of Property Management 5(2): 62-70.