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Portfolio Selection with Monotone Mean-Variance Preferences

Author

Listed:
  • Fabio Maccheroni

    () (Istituto di Metodi Quantitativi and IGIER, Universit� Bocconi)

  • Massimo Marinacci

    () (Collegio Carlo Alberto and Universit� di Torino)

  • Aldo Rustichini

    () (Department of Economics, University of Minnesota)

  • Marco Taboga

    () (Bank of Italy, Economic Outlook and Monetary Policy Department)

Abstract

We propose a portfolio selection model based on a class of monotone preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to be monotone and are therefore not economically meaningful. The functional associated to this new class of preferences is the best approximation of the mean-variance functional among those which are monotonic. We solve the portfolio selection problem and we derive a monotone version of the CAPM, which has two main features: (i) it is, unlike the standard CAPM model, arbitrage free, (ii) it has empirically testable CAPM-like relations. The monotone CAPM has thus a sounder theoretical foundation than the standard CAPM and a comparable empirical tractability.

Suggested Citation

  • Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2008. "Portfolio Selection with Monotone Mean-Variance Preferences," Temi di discussione (Economic working papers) 664, Bank of Italy, Economic Research and International Relations Area.
  • Handle: RePEc:bdi:wptemi:td_664_99
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    References listed on IDEAS

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    Cited by:

    1. Fabio Maccheroni & Massimo Marinacci & Doriana Ruffino, 2013. "Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis," Econometrica, Econometric Society, vol. 81(3), pages 1075-1113, May.
    2. Eichner, Thomas & Wagener, Andreas, 2012. "Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 422-430.
    3. repec:wsi:ijtafx:v:11:y:2008:i:03:n:s0219024908004828 is not listed on IDEAS
    4. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    5. Sergio Ortobelli & Svetlozar Rachev & Haim Shalit & Frank Fabozzi, 2009. "Orderings and Probability Functionals Consistent with Preferences," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 81-102.
    6. Faro, José Heleno, 2015. "Variational Bewley preferences," Journal of Economic Theory, Elsevier, vol. 157(C), pages 699-729.
    7. Kozhan, Roman & Salmon, Mark, 2009. "Uncertainty aversion in a heterogeneous agent model of foreign exchange rate formation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1106-1122, May.
    8. Jakub Trybu{l}a & Dariusz Zawisza, 2014. "Continuous time portfolio choice under monotone preferences with quadratic penalty - stochastic interest rate case," Papers 1404.5408, arXiv.org.
    9. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    10. Takanori Adachi & Takao Asano, 2011. "Entrepreneurial Choice and Knightian Uncertainty with Borrowing Constraints," KIER Working Papers 803, Kyoto University, Institute of Economic Research.
    11. Černý, Aleš & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2012. "On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 386-395.
    12. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April.
    13. André, Eric, 2014. "Optimal portfolio with vector expected utility," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 50-62.
    14. Karl-Theodor Eisele & Sonia Taieb, 2013. "Lattice Modules Over Rings Of Bounded Random Variables," Working Papers of LaRGE Research Center 2013-06, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    15. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    16. Jakub Trybu{l}a & Dariusz Zawisza, 2014. "Continuous time portfolio choice under monotone preferences with quadratic penalty - stochastic factor case," Papers 1403.3212, arXiv.org.
    17. Filipovic, Damir & Kupper, Michael, 2007. "Monotone and cash-invariant convex functions and hulls," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 1-16, July.
    18. Zhijun Zhao, 2011. "Preference Relativity, Ambiguity and Social Welfare Evaluation," Working Papers 352011, Hong Kong Institute for Monetary Research.
    19. Yehuda Izhakian & David Yermack, 2014. "Risk, Ambiguity, and the Exercise of Employee Stock Options," NBER Working Papers 19975, National Bureau of Economic Research, Inc.
    20. Oyarzun, Carlos & Sarin, Rajiv, 2012. "Mean and variance responsive learning," Games and Economic Behavior, Elsevier, vol. 75(2), pages 855-866.
    21. Thomas Eichner & Daniel Weinreich, 2015. "Welfare stigma and risk taking in the welfare state," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 319-348, February.
    22. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.
    23. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214.
    24. Stadje, Mitja, 2010. "Extending dynamic convex risk measures from discrete time to continuous time: A convergence approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 391-404, December.

    More about this item

    Keywords

    Portfolio Selection; Decision Theory; Mean-Variance;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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