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Portfolio Selection with Monotone Mean-Variance Preferences

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Author Info
Fabio Maccheroni () (Istituto di Metodi Quantitativi and IGIER, Università Bocconi)
Massimo Marinacci () (Collegio Carlo Alberto and Università di Torino)
Aldo Rustichini () (Department of Economics, University of Minnesota)
Marco Taboga () (Bank of Italy, Economic Outlook and Monetary Policy Department)

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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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Paper provided by Bank of Italy, Economic Research Department in its series Temi di discussione (Economic working papers) with number 664.

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Date of creation: Apr 2008
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Handle: RePEc:bdi:wptemi:td_664_99

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Related research
Keywords: Portfolio Selection; Decision Theory; Mean-Variance;

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Find related papers by JEL classification:
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
D8 - Microeconomics - - Information, Knowledge, and Uncertainty
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Dynamic Variational Preferences," Carlo Alberto Notebooks 1, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  2. Marcello Pericoli & Marco Taboga, 2008. "Canonical Term-Structure Models with Observable Factors and the Dynamics of Bond Risk Premia," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(7), pages 1471-1488, October. [Downloadable!] (restricted)
  3. Domenico Menicucci, 2001. "Optimal two-object auctions with synergies," ICER Working Papers - Applied Mathematics Series 18-2001, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
  4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  6. Sharpe, William F, 1991. " Capital Asset Prices with and without Negative Holdings," Journal of Finance, American Finance Association, vol. 46(2), pages 489-509, June. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Bibliography 7616, UCLA Department of Economics. [Downloadable!]
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  9. Eugenio Gaiotti & Alessandro Secchi, 2004. "Is there a cost channel of monetary policy transmission? An investigation into the pricing behaviour of 2,000 firms," Temi di discussione (Economic working papers) 525, Bank of Italy, Economic Research Department. [Downloadable!]
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  10. Dedola, Luca & Lippi, Francesco, 2005. "The monetary transmission mechanism: Evidence from the industries of five OECD countries," European Economic Review, Elsevier, vol. 49(6), pages 1543-1569, August. [Downloadable!] (restricted)
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  11. 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. [Downloadable!] (restricted)
  12. Lars Peter Hansen & Thomas J. Sargent, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  14. Luigi Guiso & Luigi Pistaferri & Fabiano Schivardi, 2002. "Insurance within the firm," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 C3-1, International Conferences on Panel Data. [Downloadable!]
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  15. 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. [Downloadable!]
  16. William Fuchs & Francesco Lippi, 2004. "Monetary union with voluntary participation," Temi di discussione (Economic working papers) 512, Bank of Italy, Economic Research Department. [Downloadable!]
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  17. Dybvig, Philip H & Ingersoll, Jonathan E, Jr, 1982. "Mean-Variance Theory in Complete Markets," Journal of Business, University of Chicago Press, vol. 55(2), pages 233-51, April. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Esteban Jaimovich, 2008. "Adverse Selection and Entrepreneurship in a Model of Development," Carlo Alberto Notebooks 78, Collegio Carlo Alberto. [Downloadable!]
  2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Dynamic Variational Preferences," Carlo Alberto Notebooks 1, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
    Other versions:
  4. Daron Acemoglu & Davide Ticchi & Andrea Vindigni, 2008. "A Theory of Military Dictatorships," Carlo Alberto Notebooks 74, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  5. Esteban Jaimovich, 2007. "Sectoral Differentiation, Allocation of Talent, and Financial Development," Carlo Alberto Notebooks 59, Collegio Carlo Alberto, revised 2009. [Downloadable!]
  6. Elisa Luciano & Elena Vigna, 2006. "Non mean reverting affne processes for stochastic mortality," Carlo Alberto Notebooks 30, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  7. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  8. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2007. "Revealed Ambiguity and Its Consequences: Updating," Carlo Alberto Notebooks 44, Collegio Carlo Alberto. [Downloadable!]
  9. Ales Cerný & Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2008. "On the Computation of Optimal Monotone Mean-Variance Portfolios via Truncated Quadratic Utility," Carlo Alberto Notebooks 79, Collegio Carlo Alberto. [Downloadable!]
  10. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April. [Downloadable!] (restricted)
  11. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2008. "Objective and Subjective Rationality in a Multiple Prior Model," Carlo Alberto Notebooks 73, Collegio Carlo Alberto, revised 2008. [Downloadable!]
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