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Asset Demands without the Independence Axiom

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  • Dekel, Eddie

Abstract

An important application of the theory of choice under uncertainty is to asset markets, and an important property in these markets is a preference for portfolio diversification. If an investor is an expected utility maximizer, then he is risk averse if, and only if, he exhibits a preference for diversification. This paper examines the relationship between risk aversion and portfolio diversification when preferences over probability distributions of wealth do not have an expected utility representation. Although risk aversion is not sufficient to guarantee a preference for portfolio diversification, it is necessary. Quasiconcavity of the preference functional (over probability distributions of wealth), together with risk aversion, does imply a preference for portfolio diversification. Copyright 1989 by The Econometric Society.

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  • Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-169, January.
    • Handle: RePEc:ecm:emetrp:v:57:y:1989:i:1:p:163-69
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    Cited by:

    1. Dillenberger, David & Segal, Uzi, 2017. "Skewed noise," Journal of Economic Theory, Elsevier, vol. 169(C), pages 344-364.
    2. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
    3. Assa, Hirbod & Zimper, Alexander, 2018. "Preferences over all random variables: Incompatibility of convexity and continuity," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 71-83.
    4. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    5. Egozcue, Martin & Wong, Wing-Keung, 2010. "Gains from diversification on convex combinations: A majorization and stochastic dominance approach," European Journal of Operational Research, Elsevier, vol. 200(3), pages 893-900, February.
    6. Loïc Berger & Louis Eeckhoudt, 2020. "Risk, Ambiguity, And The Value Of Diversification," Working Papers hal-02910906, HAL.
    7. Aldo Montesano, 2008. "Effects of Uncertainty Aversion on the Call Option Market," Theory and Decision, Springer, vol. 65(2), pages 97-123, September.
    8. Alain Chateauneuf & Ghizlane Lakhnati, 2007. "From sure to strong diversification," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 511-522, September.
    9. Chiu, W. Henry, 2019. "Comparative statics in an ordinal theory of choice under risk," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 113-123.
    10. Ghirardato, Paolo & Siniscalchi, Marciano, 2018. "Risk sharing in the small and in the large," Journal of Economic Theory, Elsevier, vol. 175(C), pages 730-765.
    11. Loïc Berger & Louis Eeckhoudt, 2021. "Risk, ambiguity, and the value of diversification," Post-Print hal-02910906, HAL.
    12. Jean-Marc Tallon & Alain Chateauneuf, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 509-523.
    13. Loïc Berger & Louis Eeckhoudt, 2021. "Risk, Ambiguity, and the Value of Diversification," Management Science, INFORMS, vol. 67(3), pages 1639-1647, March.
    14. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    15. Enrico G. De Giorgi & Ola Mahmoud, 2016. "Diversification preferences in the theory of choice," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 143-174, November.
    16. Ola Mahmoud, 2022. "The Willingness to Pay for Diversification," Management Science, INFORMS, vol. 68(8), pages 6235-6249, August.
    17. Alon Harel & Zvi Safra & Uzi Segal, 2003. "Ex-Post Egalitarianism," Boston College Working Papers in Economics 563, Boston College Department of Economics.
    18. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
    19. Enrico G. De Giorgi & Ola Mahmoud, 2016. "Naive Diversification Preferences and their Representation," Papers 1611.01285, arXiv.org, revised Nov 2016.
    20. Wakker, Peter P. & Yang, Jingni, 2021. "Concave/convex weighting and utility functions for risk: A new light on classical theorems," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 429-435.
    21. Alexander Zimper & Hirbod Assa, 2019. "Preferences Over Rich Sets of Random Variables: Semicontinuity in Measure versus Convexity," Working Papers 201940, University of Pretoria, Department of Economics.
    22. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.

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