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Portfolio Selection with Monotone Mean-Variance Preferences

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Author Info
Fabio Maccheroni
Massimo Marinacci
Aldo Rustichini
Marco Taboga

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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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Publisher Info
Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 6.

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Length: 46 pages
Date of creation: 2004
Date of revision: 2007
Handle: RePEc:cca:wpaper:6

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Related research
Keywords: Mean-Variance Preferences; Optimal Portfolios;

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Find related papers by JEL classification:
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk 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)
Full references

Cited by:
(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. 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:
  2. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2007. "Revealed Ambiguity and Its Consequences: Updating," Carlo Alberto Notebooks 44, Collegio Carlo Alberto. [Downloadable!]
  3. Esteban Jaimovich, 2008. "Adverse Selection and Entrepreneurship in a Model of Development," Carlo Alberto Notebooks 78, Collegio Carlo Alberto. [Downloadable!]
  4. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Dynamic Variational Preferences," Carlo Alberto Notebooks 1, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  5. Daron Acemoglu & Davide Ticchi & Andrea Vindigni, 2008. "A Theory of Military Dictatorships," Carlo Alberto Notebooks 74, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  6. Esteban Jaimovich, 2007. "Sectoral Differentiation, Allocation of Talent, and Financial Development," Carlo Alberto Notebooks 59, Collegio Carlo Alberto, revised 2009. [Downloadable!]
  7. Elisa Luciano & Elena Vigna, 2006. "Non mean reverting affne processes for stochastic mortality," Carlo Alberto Notebooks 30, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  8. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  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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