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Portfolio selection and duality under mean variance preferences

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  • Eichner, Thomas

Abstract

This paper uses duality to analyze an investor's behavior in a n-asset portfolio selection problem when the investor has mean variance preferences. The indirect utility and wealth requirement functions are used to derive Roy's identity, Shephard's lemma and the Slutsky equation. In our simple Slutsky equation the income effect is characterized by decreasing absolute risk aversion (DARA) and the substitution effect is always positive [negative] with respect to an asset's holding if the asset's mean return [risk] increases. Substitution effect and income effect work in the same direction presupposed mean variance preferences display DARA.

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  • Eichner, Thomas, 2011. "Portfolio selection and duality under mean variance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 146-152, January.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:146-152
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    1. Meyer, Jack & Ormiston, Michael B, 1994. "The Effect on Optimal Portfolios of Changing the Return to a Risky Asset: The Case of Dependent Risky Returns," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 603-612, August.
    2. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-172, March.
    3. Binswanger, Hans P, 1981. "Attitudes toward Risk: Theoretical Implications of an Experiment in Rural India," Economic Journal, Royal Economic Society, vol. 91(364), pages 867-890, December.
    4. Lars Tyge Nielsen & Fatma Lajeri, 2000. "Parametric characterizations of risk aversion and prudence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 469-476.
    5. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    6. Aivazian, Varouj, 1977. "The Demand for Assets under Conditions of Risk: Comment," Journal of Finance, American Finance Association, vol. 32(3), pages 927-929, June.
    7. Lajeri-Chaherli, Fatma, 2003. "Partial derivatives, comparative risk behavior and concavity of utility functions," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 81-99, August.
    8. Ardeshir J. Dalal, 1983. "Comparative Statics and Asset Substitutability/Complementarity in a Portfolio Model: A Dual Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(2), pages 355-367.
    9. Agnar Sandmo, 1977. "Portfolio Theory, Asset Demand and Taxation: Comparative Statics with Many Assets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 369-379.
    10. Carmen F. Menezes & X. Henry Wang, 2005. "Duality and the Slutsky income and substitution effects of increases in wage rate uncertainty," Oxford Economic Papers, Oxford University Press, vol. 57(3), pages 545-557, July.
    11. Chavas, Jean-Paul & Holt, Matthew T, 1996. "Economic Behavior under Uncertainty: A Joint Analysis of Risk Preferences and Technology," The Review of Economics and Statistics, MIT Press, vol. 78(2), pages 329-335, May.
    12. Levy, Haim, 1994. "Absolute and Relative Risk Aversion: An Experimental Study," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 289-307, May.
    13. Chamberlain, Gary, 1983. "A characterization of the distributions that imply mean--Variance utility functions," Journal of Economic Theory, Elsevier, vol. 29(1), pages 185-201, February.
    14. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    15. Ormiston, Michael B & Schlee, Edward E, 2001. "Mean-Variance Preferences and Investor Behaviour," Economic Journal, Royal Economic Society, vol. 111(474), pages 849-861, October.
    16. Hadar, Josef & Seo, Tae Kun, 1990. "The Effects of Shifts in a Return Distribution on Optimal Portfolios," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 721-736, August.
    17. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    18. Menezes, Carmen F. & Henry Wang, X. & Bigelow, John P., 2005. "Duality and consumption decisions under income and price risk," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 387-405, April.
    19. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
    20. Levy, Haim, 1973. "The Demand for Assets Under Conditions of Risk," Journal of Finance, American Finance Association, vol. 28(1), pages 79-96, March.
    21. Carmen F. Menezes & X. Henry Wang, 2006. "Optimal Decisions With Linear Random Payoff," Manchester School, University of Manchester, vol. 74(3), pages 251-265, June.
    22. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    23. Carmen F. Menezes & X. Henry Wang, 2005. "Duality, income and substitution effects for the competitive firm under price uncertainty," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 249-257.
    24. Mitchell, Douglas W & Douglas, Stratford M, 1997. "Portfolio Response to a Shift in a Return Distribution: The Case of n-Dependent Assets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 945-950, November.
    25. Thomas Eichner & Andreas Wagener, 2009. "Multiple Risks and Mean-Variance Preferences," Operations Research, INFORMS, vol. 57(5), pages 1142-1154, October.
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