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Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

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  • Kevin Moran
  • Benoît Carmichael
  • Gilles Boevi Koumou

Abstract

This paper extends the use of Rao (1982b)'s Quadratic Entropy (RQE) to modern portfolio theory. It argues that the RQE of a portfolio is a valid, exible and unifying approach to measuring portfolio diversification. The paper demonstrates that portfolio's RQE can encompass most existing measures, such as the portfolio variance, the diversification ratio, the normalized portfolio variance, the diversification return or excess growth rates, the Gini-Simpson indices, the return gaps, Markowitz's utility function and Bouchaud's general free utility. The paper also shows that assets selected under RQE can protect portfolios from mass destruction (systemic risk) and an empirical illustration suggests that this protection is substantial.

Suggested Citation

  • Kevin Moran & Benoît Carmichael & Gilles Boevi Koumou, 2015. "Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy," CIRANO Working Papers 2015s-16, CIRANO.
    • Handle: RePEc:cir:cirwor:2015s-16
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    Cited by:

    1. Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The RQE-CAPM : New insights about the pricing of idiosyncratic risk," CIRANO Working Papers 2021s-28, CIRANO.
    2. Contreras, Javier & Rodríguez, Yeny E. & Sosa, Aníbal, 2017. "Construction of an efficient portfolio of power purchase decisions based on risk-diversification tradeoff," Energy Economics, Elsevier, vol. 64(C), pages 286-297.
    3. Koumou, Gilles Boevi, 2020. "Mean-variance model and investors’ diversification attitude: A theoretical revisit," Finance Research Letters, Elsevier, vol. 37(C).
    4. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    5. Benoit Carmichael & Gilles Boevi Koumou & Kevin Moran, 2015. "A New Formulation of Maximum Diversification Indexation Using Rao's Quadratic Entropy," Cahiers de recherche 1519, CIRPEE.
    6. Benoit Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The political reception of innovations," Cahiers de recherche 2107, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    7. 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.
    8. Marielle Jong, 2018. "Portfolio optimisation in an uncertain world," Journal of Asset Management, Palgrave Macmillan, vol. 19(4), pages 216-221, July.

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    More about this item

    Keywords

    Portfolio diversification; Rao's quadratic entropy; diversification return; diversification ratio; portfolio variance normalized; Gini-Simpson index; Markowitz's utility; function; Bouchaud's General free utility;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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