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Naive Diversification Preferences and their Representation

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  • Enrico G. De Giorgi
  • Ola Mahmoud

Abstract

A widely applied diversification paradigm is the naive diversification choice heuristic. It stipulates that an economic agent allocates equal decision weights to given choice alternatives independent of their individual characteristics. This article provides mathematically and economically sound choice theoretic foundations for the naive approach to diversification. We axiomatize naive diversification by defining it as a preference for equality over inequality and derive its relationship to the classical diversification paradigm. In particular, we show that (i) the notion of permutation invariance lies at the core of naive diversification and that an economic agent is a naive diversifier if and only if his preferences are convex and permutation invariant; (ii) Schur-concave utility functions capture the idea of being inequality averse on top of being risk averse; and (iii) the transformations, which rebalance unequal decision weights to equality, are characterized in terms of their implied turnover.

Suggested Citation

  • Enrico G. De Giorgi & Ola Mahmoud, 2016. "Naive Diversification Preferences and their Representation," Papers 1611.01285, arXiv.org, revised Nov 2016.
  • Handle: RePEc:arx:papers:1611.01285
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    References listed on IDEAS

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    3. Tu, Jun & Zhou, Guofu, 2011. "Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies," Journal of Financial Economics, Elsevier, vol. 99(1), pages 204-215, January.
    4. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-169, January.
    5. 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.
    6. Robert A. Korajczyk & Ronnie Sadka, 2004. "Are Momentum Profits Robust to Trading Costs?," Journal of Finance, American Finance Association, vol. 59(3), pages 1039-1082, June.
    7. 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.
    8. Roll, Richard, 1981. "A Possible Explanation of the Small Firm Effect," Journal of Finance, American Finance Association, vol. 36(4), pages 879-888, September.
    9. 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.
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