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Diversification quotients based on VaR and ES

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  • Han, Xia
  • Lin, Liyuan
  • Wang, Ruodu

Abstract

The diversification quotient (DQ) is recently introduced for quantifying the degree of diversification of a stochastic portfolio model. It has an axiomatic foundation and can be defined through a parametric class of risk measures. Since the Value-at-Risk (VaR) and the Expected Shortfall (ES) are the most prominent risk measures widely used in both banking and insurance, we investigate DQ constructed from VaR and ES in this paper. In particular, for the popular models of elliptical and multivariate regular varying (MRV) distributions, explicit formulas are available. The portfolio optimization problems for the elliptical and MRV models are also studied. Our results further reveal favorable features of DQ, both theoretically and practically, compared to traditional diversification indices based on a single risk measure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:113:y:2023:i:c:p:185-197
    DOI: 10.1016/j.insmatheco.2023.08.006
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    References listed on IDEAS

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    More about this item

    Keywords

    Value-at-Risk; Expected Shortfall; Diversification quotient; Elliptical models; Regular varying models;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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