On the Third Order Stochastic Dominance for Risk-Averse and Risk-Seeking Investors with Analysis of their Traditional and Internet Stocks

Chan, Raymond H. and Clark, Ephraim and Wong, Wing-Keung (2016): On the Third Order Stochastic Dominance for Risk-Averse and Risk-Seeking Investors with Analysis of their Traditional and Internet Stocks.

Abstract

This paper presents some interesting new properties of third order stochastic dominance (TSD) for risk-averse and risk-seeking investors. We show that the means of the assets being compared should be included in the definition of TSD for both investor types. We also derive the conditions on the variance order of two assets with equal means for both investor types and extend the second order SD (SSD) reversal result of Levy and Levy (2002) to TSD. We apply our results to analyze the investment behaviors on traditional stocks and internet stocks for both risk averters and risk seekers.

• Item Type: MPRA Paper
• Language: English
• Keywords: Third order stochastic dominance, expected-utility maximization, risk aversion, risk seeking, investment behaviors.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C00 - General; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions

References

Aboudi, R., & Thon, D. (1994). Efficient algorithms for stochastic dominance tests based on financial market data. Management Science, 40(4), 508-515.

Arditti, F.D. (1967). Risk and the required return on equity. Journal of Finance, 22(1), 19-36.

Asness, C., Moskowitz, T., Pedersen, L. (2013). Value and Momentum Everywhere. Journal of Finance 68(3), 929-985.

Bai, Z., Li, H., Liu, H., & Wong, W. K. (2011). Test statistics for prospect and Markowitz stochastic dominances with applications. The Econometrics Journal, 14(2), 278-303.

Bai, Z., 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.

Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2(1), 95-121.

Bawa, V. S., Lindenberg, E. B., & Rafsky, L. C. (1979). An efficient algorithm to determine stochastic dominance admissible sets. Management Science, 25(7), 609-622.

Bonferroni, C. E. (1936). Il Calcolo delle assicurazioni su gruppi di teste. Studii in onore del prof. SO Carboni. 1st Sup. Sci. Econ. Comm. Firenze (Roma), 8, 1-62.

Chabot, B., Ghysels, E., Jagannathan, R. (2009). Price Momentum in Stocks: Insights from Victorian Age Data. National Bureau of Economic Research Working Papers 14500.

Chow, S. C., Lui, F. T., Valenzuela, M. R., & Wong, W. K.(2015). Tests for Richness and Poorness: A Stochastic Dominance Analysis of Income Distributions in Hong Kong, working paper, the Sixth Meeting of the Society for the Study of Economic Inequality, the Universit'e du Luxembourg.

Clark, E. A., Qiao, Z., & Wong, W. K. (2016). Theories of risk: testing investor behaviour on the Taiwan stock and stock index futures markets. Economic Inquiry, 54(2), 907-924.

Crainich, D., Eeckhoudt, L., & Trannoy, A. (2013). Even (mixed) risk lovers are prudent. The American Economic Review, 103(4), 1529-1535.

Davies, J., & Hoy, M. (1994). The normative significance of using third-degree stochastic dominance in comparing income distributions. Journal of economic theory, 64(2), 520-530.

Dillinger, A. M., Stein, W. E., & Mizzi, P. J. (1992). Risk averse decisions in business planning. Decision Sciences, 23(4), 1003-1008.

Eeckhoudt, L., & Kimball, M. (1992). Background risk, prudence, and the demand for insurance. Contributions to insurance economics (pp. 239-254). Springer Netherlands.

Fishburn, P. C. (1964). Decision and value theory (No. 10). Wiley, New York.

Fishburn, P. C. (1974). Convex stochastic dominance with continuous distribution functions. Journal of Economic Theory, 7(2), 143-158.

Fishburn, P. C., & Kochenberger, G. A. (1979). Two-piece Von Neumann-Morgenstern utility functions. Decision Sciences, 10(4), 503-518.

Fishburn, P. C., & Vickson, R. G. (1978). Theoretical foundations of stochastic dominance. Stochastic dominance, 39-113.

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 & 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(1), 89-109.

Frankfurter, G.M., Phillips, H.E.. & Seagle, J.P. (1971). Portfolio Selection: The Effects of Uncertain Means, Variances and Covariances, Journal of Financial and Quantitative Analysis, 6, 1251-1262.

Friedman, M., & Savage, L. J. (1948). The utility analysis of choices involving risk. Journal of political economy, 56(4), 279-304.

Gasbarro, D., Wong, W. K., & Zumwalt, K. J. (2007). Stochastic dominance analysis of iShares. European Journal of Finance, 13(1), 89-101.

Geczy, C., Samonov, M. (2016). Two Centuries of Price Momentum, Financial Analysts Journal, (forthcoming).

Gotoh, J. Y., & Konno, H. (2000). Third degree stochastic dominance and mean-risk analysis. Management Science, 46(2), 289-301.

Guo, X., Wong, W.K. (2016). Multivariate Stochastic Dominance for Risk Averters and Risk Seekers. RAIRO - Operations Research, 50(3), 575-586.

Hadar, J., & Russell, W. R. (1971). Stochastic dominance and diversification. Journal of Economic Theory, 3(3), 288-305.

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.The Review of Economic Studies, 36(3), 335-346.

Hartley, R., & Farrell, L. (2002). Can expected utility theory explain gambling?. American Economic Review, 92(3), 613-624.

Hong, H., Scheinkman, J., & Xiong, W. (2006). Asset float and speculative bubbles. Journal of Finance, 61(3), 1073-1117.

Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291.

Kim, S. J., Moshirian, F., & Wu, E. (2006). Evolution of international stock and bond market integration: Influence of the European Monetary Union. Journal of Banking & Finance, 30(5), 1507-1534.

Le Breton, M., & Peluso, E. (2009). Third-degree stochastic dominance and inequality measurement. Journal of Economic Inequality, 7(3), 249-268.

Lean, H.H., McAleer, M., & Wong, W.K. (2015). Preferences of risk-averse and risk-seeking investors for oil spot and futures before, during and after the Global Financial Crisis, International Review of Economics and Finance, 40, 204-216.

Levy, H. (2015), Stochastic Dominance: Investment Decision Making Under Uncertainty. Third Edition, Springer, New York.

Levy, M., & Levy, H. (2002). Prospect theory: much ado about nothing? Management Science, 48(10), 1334-1349.

Li, C. K., & Wong, W. K. (1999). Extension of Stochastic Dominance Theory to Random Variables. RAIRO – Operations Research, 33(4), 509-524.

Markowitz, H. (1952). The utility of wealth. Journal of Political Economy, 60, 151-158.

Menezes, C., Geiss, C., & Tressler, J. (1980). Increasing downside risk. American Economic Review, 70(5), 921-932.

Meyer, J. (1977). Second degree stochastic dominance with respect to a function. International Economic Review, 18(2), 477-487.

Ofek, E., & Richardson, M. (2003). DotCom mania: A survey of market efficiency in the Internet sector. Journal of Finance, 58, 1113-1138.

Ng, M. C. (2000). A remark on third degree stochastic dominance. Management Science, 46(6), 870-873.

Porter, R. B., Wart, J. R., & Ferguson, D. L. (1973). Efficient algorithms for conducting stochastic dominance tests on large numbers of portfolios. Journal of Financial and Quantitative Analysis, 8(1), 71-81.

Post, T., Fang, Y., & Kopa, M. (2015). Linear Tests for DARA Stochastic Dominance, Management Science, 61, 1615-1629.

Post, T., & Milos, K. (2016). Portfolio Choice Based on Third-Degree Stochastic Dominance, Management Science, forthcoming.

Post, T., & Levy, H. (2005). Does risk seeking drive stock prices? A stochastic dominance analysis of aggregate investor preferences and beliefs. Review of Financial Studies, 18(3), 925-953.

Post, T., Van Vliet, P., & Levy, H. (2008). Risk aversion and skewness preference. Journal of Banking & Finance, 32(7), 1178-1187.

Post, T., & Versijp, P. (2007). Multivariate tests for stochastic dominance efficiency of a given portfolio. Journal of Financial and Quantitative Analysis, 42(2), 489-515.

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. & Fung, J.K.W. (2013). Stochastic Dominance Relationships between Stock and Stock Index Futures Markets: International Evidence, Economic Modelling, 33, 552-559.

Quirk, J. P., & Saposnik, R. (1962). Admissibility and measurable utility functions. Review of Economic Studies, 29(2), 140-146.

Rothschild, M., & Stiglitz, J. E. (1970). Increasing risk: I. A definition. Journal of Economic theory, 2(3), 225-243.

Rothschild, M., & Stiglitz, J. E. (1971). Increasing risk II: Its economic consequences. Journal of Economic Theory, 3(1), 66-84.

Rupert Jr, G. (1981). Simultaneous statistical inference. Springer Science & Business Media.

Scheinkman, J.A., & Xiong, W. (2003). Overconfidence and speculative bubbles. Journal of political Economy, 111(6), 1183-1220.

Schmid, F. (2005). A note on third degree stochastic dominance. OR Spectrum, 27(4), 653-655.

Stoyan, D., & Daley, D. J. (1983). Comparison methods for queues and other stochastic models. John Wiley & Sons, New York, USA.

Thaler, R. H., & 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(6), 643-660.

Tobin, J. (1958). Liquidity preference as behavior towards risk. Review of Economic Studies, 25(2), 65-86.

Thorlund-Petersen, L. (2001). Third-degree stochastic dominance and axioms for a convex marginal utility function. Mathematical Social Sciences, 41(2), 167-199.

Von Neumann, J., & Morgenstern, O. (2007). Theory of games and economic behavior. Princeton university press.

Weeks, J. K. (1985). Stochastic dominance: a methodological approach to enhancing the conceptual foundations of operations management theory. Academy of Management Review, 10(1), 31-38.

Whitmore, G. A. (1970). Third-degree stochastic dominance. American Economic Review, 457-459.

Williams, C.A.Jr. (1966). Attitudes toward Speculative Risks as an Indicator of Attitudes toward Pure Risks, Journal of Risk and Insurance 33(4), 577-586.

Wong, W. K. (2007). Stochastic dominance and mean?畝riance 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., & Ma, C. (2008). Preferences over location-scale family. Economic Theory, 37(1), 119-146.

Zagst, R., & Kraus, J. (2011). Stochastic dominance of portfolio insurance strategies. Annals of Operations Research, 185(1), 75-103.