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Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation

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  • Gilles Boevi KOUMOU
  • Georges DIONNE

Abstract

We provide an axiomatic foundation for the measurement of correlation diversification measures in a one-period portfolio model. We propose a set of nine desirable axioms for this class of diversification measures. We name the measures satisfying these axioms coherent correlation diversification measures which we distinguish from coherent risk measures. We provide the decision theoretic foundations of our axioms by studying their compatibility with investors¡¯ preference for diversification in rank-dependent expected utility theory. We examine some of the most frequently used methods for measuring correlation diversification in terms of our axioms. Lastly, we explore whether our axioms have a representation function.

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  • Gilles Boevi KOUMOU & Georges DIONNE, 2021. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Working Papers 7, Africa Institute for Research in Economics and Social Sciences.
    • Handle: RePEc:aof:wpaper:wp-0007
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    3. Han, Xia & Lin, Liyuan & Wang, Ruodu, 2023. "Diversification quotients based on VaR and ES," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 185-197.

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    More about this item

    Keywords

    Portfolio Theory; Portfolio Diversification; Preference for Diversification; Correlation Diversification; Rank-Dependent Expected Utility Theory;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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