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How Does Beta Explain Stochastic Dominance Efficiency?

Author

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  • Haim Shalit

    (Dept. of Economics, Ben-Gurion University of the Negev)

  • Shlomo Yitzhaki

    (Israeli Central Bureau of Statistics)

Abstract

Stochastic dominance rules provide necessary and sufficient conditions for characterizing efficient portfolios that suit all expected utility maximizers. For the finance practitioner, though, these conditions are not easy to apply or interpret. Portfolio selection models like the mean-variance model offer intuitive investment rules that are easy to understand, as they are based on parameters of risk and return. We present stochastic dominance rules for portfolio choices that can be interpreted in terms of simple financial concepts of systematic risk and mean return. Stochastic dominance is expressed in terms of Lorenz curves, and systematic risk is expressed in terms of Gini. To accommodate risk aversion differentials across investors, we expand the conditions using the extended Gini.

Suggested Citation

  • Haim Shalit & Shlomo Yitzhaki, 2008. "How Does Beta Explain Stochastic Dominance Efficiency?," Working Papers 0813, Ben-Gurion University of the Negev, Department of Economics.
  • Handle: RePEc:bgu:wpaper:0813
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    References listed on IDEAS

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    1. Gregory-Allen, Russell B & Shalit, Haim, 1999. "The Estimation of Systematic Risk under Differentiated Risk Aversion: A Mean-Extended Gini Approach," Review of Quantitative Finance and Accounting, Springer, vol. 12(2), pages 135-157, March.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Ronald Best & Charles Hodges & James Yoder, 2006. "Expected earnings growth and portfolio performance," Review of Quantitative Finance and Accounting, Springer, vol. 26(4), pages 431-437, June.
    4. Haim Shalit & Shlomo Yitzhaki, 2009. "Capital market equilibrium with heterogeneous investors," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 757-766.
    5. Carroll, Carolyn & Thistle, Paul D. & Wei, K. C. John, 1992. "The Robustness of Risk-Return Nonlinearities to the Normality Assumption," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(3), pages 419-435, September.
    6. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    7. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    8. Andrzej Ruszczynski & Robert J. Vanderbei, 2003. "Frontiers of Stochastically Nondominated Portfolios," Econometrica, Econometric Society, vol. 71(4), pages 1287-1297, July.
    9. Shalit, Haim & Yitzhaki, Shlomo, 2002. "Estimating Beta," Review of Quantitative Finance and Accounting, Springer, vol. 18(2), pages 95-118, March.
    10. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    11. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
    12. Samuelson, Paul A., 1967. "General Proof that Diversification Pays*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(1), pages 1-13, March.
    13. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
    14. Samuel Kotz & Christian Kleiber, 2002. "A characterization of income distributions in terms of generalized Gini coefficients," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 789-794.
    15. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
    16. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    17. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    18. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
    19. Haim Shalit & Shlomo Yitzhaki, 2003. "An Asset Allocation Puzzle: Comment," American Economic Review, American Economic Association, vol. 93(3), pages 1002-1008, June.
    20. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    21. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    22. Thistle, Paul D., 1993. "Negative Moments, Risk Aversion, and Stochastic Dominance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 301-311, June.
    23. Haim Shalit & Shlomo Yitzhaki, 1994. "Marginal Conditional Stochastic Dominance," Management Science, INFORMS, vol. 40(5), pages 670-684, May.
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    Cited by:

    1. Schröder, Carsten & Yitzhaki, Shlomo, 2017. "Revisiting the evidence for cardinal treatment of ordinal variables," European Economic Review, Elsevier, vol. 92(C), pages 337-358.
    2. Belghitar, Yacine & Clark, Ephraim & Deshmukh, Nitin, 2014. "Does it pay to be ethical? Evidence from the FTSE4Good," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 54-62.
    3. Haim Shalit & Frank Hespeler, 2016. "Mean-Extended Gini Portfolios: The Ultimate Frontier," Working Papers 1603, Ben-Gurion University of the Negev, Department of Economics.
    4. Denuit, Michel M. & Huang, Rachel J. & Tzeng, Larry Y. & Wang, Christine W., 2014. "Almost marginal conditional stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 41(C), pages 57-66.
    5. Chen, Tzu-Ying & Tsai, An-Mei & Tzeng, Larry Y., 2022. "Revisiting almost marginal conditional stochastic dominance," The Quarterly Review of Economics and Finance, Elsevier, vol. 85(C), pages 260-269.
    6. Shlomo Yitzhaki, 2016. "A Potential Contradiction Between Economic Theory and Applied Finance," Review of Economics & Finance, Better Advances Press, Canada, vol. 6, pages 13-27, May.
    7. Ephraim Clark & Konstantinos Kassimatis, 2013. "International equity flows, marginal conditional stochastic dominance and diversification," Review of Quantitative Finance and Accounting, Springer, vol. 40(2), pages 251-271, February.
    8. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2017. "Analysing assets’ performance inside a portfolio: From crossed beta to the net risk premium ratio," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1270251-127, January.
    9. Marta Cardin & Bennett Eisenberg & Luisa Tibiletti, 2012. "Bid and Ask Prices Tailored to Traders' Risk Aversion and Gain Propension: a Normative Approach," International Journal of Business Research and Management (IJBRM), Computer Science Journals (CSC Journals), vol. 3(6), pages 294-306, December.
    10. Hooi Lean & Kok Phoon & Wing-Keung Wong, 2013. "Stochastic dominance analysis of CTA funds," Review of Quantitative Finance and Accounting, Springer, vol. 40(1), pages 155-170, January.
    11. Yacine Belghitar & Ephraim Clark & Nitin Deshmukh, 2017. "Importance Of The Fund Management Company In The Performance Of Socially Responsible Mutual Funds," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 40(3), pages 349-367, September.
    12. Shlomo Yitzhaki & Peter Lambert, 2014. "Is higher variance necessarily bad for investment?," Review of Quantitative Finance and Accounting, Springer, vol. 43(4), pages 855-860, November.
    13. Belghitar, Yacine & Clark, Ephraim & Kassimatis, Konstantino, 2011. "The prudential effect of strategic institutional ownership on stock performance," International Review of Financial Analysis, Elsevier, vol. 20(4), pages 191-199, August.
    14. Clark, Ephraim & Kassimatis, Konstantinos, 2012. "An empirical analysis of marginal conditional stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1144-1151.

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    More about this item

    Keywords

    Systematic Risk; Gini; Extended Gini; Marginal Conditional Stochastic Dominance; Lorenz Curves;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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