Make Almost Stochastic Dominance really Almost

Guo, Xu and Wong, Wing-Keung and Zhu, Lixing (2013): Make Almost Stochastic Dominance really Almost.

Abstract

Leshno and Levy (2002) extend stochastic dominance (SD) theory to almost stochastic dominance (ASD) for {\it most} decision makers. When comparing any two prospects, Guo, et al.\ (2013) find that there will be ASD relationship even there is only very little difference in mean, variance, skewness, or kurtosis. Investors may prefer to conclude ASD only if the dominance is nearly almost. Levy, et al. (2010) have provided two approaches to solve the problem. In this paper, we extend their work by first recommending an existing stochastic dominance test to handle the issue and thereafter developing a new test for the ASD which could detect dominance for any pre-determined small value. We also provide two approaches to obtain the critical values for our proposed test.

• Item Type: MPRA Paper
• Language: English
• Keywords: stochastic dominance; almost stochastic dominance; risk aversion, stochastic dominance test, almost stochastic dominance test
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions

References

Anderson, G., 1996. Nonparametric tests of stochastic dominance in income distributions. Econometrica 64, 1183 - 1193.

Bai, Z.D., H. Li, H.X. Liu and W.K. Wong, 2011, Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications. Econometrics Journal, 2011, 122, 1--26.

Bali, T.G., Demirtas, K. O., Levy, H., Wolf, A. (2009), Bonds versus stocks: Investors' age and risk taking. Journal of Monetary Economics, 56(6), 817-830.

Barrett, G., Donald, S., 2003. Consistent tests for stochastic dominance. Econometrica 71, 71-104.

Chan, C.Y., C. de Peretti, Z. Qiao and W.K. Wong, Empirical Test of the Efficiency of UK Covered Warrants Market: Stochastic Dominance and Likelihood Ratio Test Approach. Journal of Empirical Finance, 2012, 19(1), 162--174.

Davidson, R. and J.Y. Duclos, Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality. Econometrica, 2000, 68, 1435--1464.

Fong, W.M., Lean, H.H., Wong, W.K., 2008. Stochastic Dominance and Behavior towards Risk: The Market for Internet Stocks. Journal of Economic Behavior and Organization 68(1), 194-208.

Fong, W.M., Wong, W.K., Lean, H.H., 2005. International Momentum Strategies: A Stochastic Dominance Approach. Journal of Financial Markets 8, 89-109.

Gasbarro, D., Wong, W.K., Zumwalt, J.K., 2007. Stochastic dominance analysis of iShares. European Journal of Finance 13, 89-101.

Gasbarro, D., Wong, W.K., Zumwalt, J.K. 2012. Stochastic Dominance and Behavior towards Risk: The Market for iShares, Annals of Financial Economics 7(1), 1250005.

Guo, X., Wong, W.K., Zhu, L.X., 2013. Almost Stochastic Dominance and Moments, working paper.

Guo, X., Zhu, X.H., Wong, W.K., Zhu, L.X. 2013a, A Note on Almost Stochastic Dominance. Economics Letters, forthcoming.

Hadar J., Russell W.R. (1969), Rules for Ordering Uncertain Prospects. American Economic Review, 59, 25-34.

Hanoch, G., Levy, H. (1969), The Efficiency Analysis of Choices Involving Risk. Review of Economic studies, 36, 335-346.

Lean, H.H., Smyth, R., Wong, W.K., 2007. Revisiting calendar anomalies in Asian stock markets using a stochastic dominance approach. Journal of Multinational Financial Management 17(2), 125-141.

Lean, H.H., Wong, W.K., Zhang, X., 2008. Size and Power of Some Stochastic Dominance Tests: A Monte Carlo Study, Mathematics and Computers in Simulation 79, 30-48.

Leshno, M., Levy, H. (2002), Preferred by ``all'' and preferred by ``most'' decision makers: Almost stochastic dominance. Management Science, 48(8), 1074-1085.

Levy, H. (2006), Stochastic Dominance: Investment Decision Making Under Uncertainty. Springer, New York.

Levy, M. (2009), Almost Stochastic Dominance and stocks for the long run. European Journal of Operational Research, 194, 250-257.

Levy, H., Leshno, M, Leibovitch, B. (2010), Economically relevant preferences for all observed epsilon. Annals of Operations Research, 176, 153-178.

Linton, O., Maasoumi, E., Whang, Y-J., 2005. Consistent testing for stochastic dominance under general sampling schemes. Review of Economic Studies 72, 735-765.

Qiao, Z., Clark, E., Wong, W.K. 2012, Investors' Preference towards Risk: Evidence from the Taiwan Stock and Stock Index Futures Markets, Accounting & Finance, DOI: 10.1111/j.1467-629X.2012.00508.x.

McFadden, D., 1989. Testing for stochastic dominance. In: T.B. Fomby and T.K. Seo, (Eds.), Studies in the Economics of Uncertainty. Springer Verlag, New York.

Rothschild M., Stiglitz J. E. (1970), Increasing risk: I. A definition. Journal of Economic Theory, 2, 225-243.

Tse, Y.K., Zhang, X., 2004. A Monte Carlo investigation of some tests for stochastic dominance. Journal of Statistical Computation and Simulation 74, 361-378.

Tzeng, L. Y., Huang, R. J., Shih, P-T. (2012), Revisiting Almost Second-Degree Stochastic Dominance. Management Science, DOI:10.1287/mnsc.1120.1616.

van der Vaart, A.W., Wellner, J. A. (1996), Weak Convergence and Empirical Processes. Springer Series in Statistics. Springer-Verlag, New York. With applications to statistics.

Wong, W.K. Ma, C., 2008. Preferences over location-scale family, Economic Theory 37(1), 119-146.

Wong, W.K., Phoon, K.F., Lean, H.H., 2008. Stochastic dominance analysis of Asian hedge funds, Pacific-Basin Finance Journal 16(3), 204-223.