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Diversification quotients based on VaR and ES

Author
Xia Han, Liyuan Lin, Ruodu Wang
Date Updated
2023/01/09
Category
q-fin.RM
Date Published
2023/01/09
Date Retrieved
2023/01/10
Description
The diversification quotient (DQ) is a recently introduced tool 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 multivariate 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 favourable features of DQ, both theoretically and practically, compared to traditional diversification indices based on a single risk measure.
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