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Portfolio Selection With Monotone Mean-Variance Preferences

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  • Fabio Maccheroni
  • Massimo Marinacci
  • Aldo Rustichini
  • Marco Taboga

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.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 19 (2009)
Issue (Month): 3 ()
Pages: 487-521

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Handle: RePEc:bla:mathfi:v:19:y:2009:i:3:p:487-521

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  1. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September.
  2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  3. Shumel Kandel & Robert F. Stambaugh, . "A Mean-Variance Framework for Tests for Asset Pricing Models," Rodney L. White Center for Financial Research Working Papers 25-88, Wharton School Rodney L. White Center for Financial Research.
  4. Fabio Maccheroni & Massimo Marinacci, 2004. "A strong law of large numbers for capacities," ICER Working Papers - Applied Mathematics Series 28-2004, ICER - International Centre for Economic Research.
  5. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
  6. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
  7. Sharpe, William F., 1990. "Capital Asset Prices With and Without Negative Holding," Nobel Prize in Economics documents 1990-3, Nobel Prize Committee.
  8. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
  9. Dybvig, Philip H & Ingersoll, Jonathan E, Jr, 1982. "Mean-Variance Theory in Complete Markets," The Journal of Business, University of Chicago Press, vol. 55(2), pages 233-51, April.
  10. Mark Britten-Jones, 1999. "The Sampling Error in Estimates of Mean-Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, 04.
  11. Domenico Menicucci, 2003. "Optimal two-object auctions with synergies," Review of Economic Design, Springer, vol. 8(2), pages 143-164, October.
  12. Bigelow, John Payne, 1993. "Consistency of mean-variance analysis and expected utility analysis : A complete characterization," Economics Letters, Elsevier, vol. 43(2), pages 187-192.
  13. MacKinlay, A Craig & Richardson, Matthew P, 1991. " Using Generalized Method of Moments to Test Mean-Variance Efficiency," Journal of Finance, American Finance Association, vol. 46(2), pages 511-27, June.
  14. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks 12, Collegio Carlo Alberto, revised 2006.
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