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Diversification Quotients: Quantifying Diversification via Risk Measures

Author

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  • Xia Han

    (School of Mathematical Sciences, and The Key Laboratory of Pure Mathematics and Combinatorics, Ministry of Education, Nankai University, Tianjin 300071, China)

  • Liyuan Lin

    (Department of Econometrics and Business Statistics, Monash University, Clayton, Victoria 3168, Australia)

  • Ruodu Wang

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L3G1, Canada)

Abstract

We establish the first axiomatic theory for diversification indices using six intuitive axioms: nonnegativity, location invariance, scale invariance, rationality, normalization, and continuity. The unique class of indices satisfying these axioms, called the diversification quotients (DQs), are defined based on a parametric family of risk measures. A further axiom of portfolio convexity pins down DQs based on coherent risk measures. The DQ has many attractive properties, and it can address several theoretical and practical limitations of existing indices. In particular, for the popular risk measures value at risk and expected shortfall, the corresponding DQ admits simple formulas, and it is efficient to optimize in portfolio selection. Moreover, it can properly capture tail heaviness and common shocks, which are neglected by traditional diversification indices. When illustrated with financial data, the DQ is intuitive to interpret, and its performance is competitive against other diversification indices.

Suggested Citation

  • Xia Han & Liyuan Lin & Ruodu Wang, 2025. "Diversification Quotients: Quantifying Diversification via Risk Measures," Management Science, INFORMS, vol. 71(9), pages 7990-8006, September.
    • Handle: RePEc:inm:ormnsc:v:71:y:2025:i:9:p:7990-8006
    DOI: 10.1287/mnsc.2023.00513
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