Diversification quotients based on VaR and ES

TL;DR

This paper explores diversification quotients based on VaR and ES, providing explicit formulas for elliptical and MRV models, and demonstrating their advantages over traditional indices.

Contribution

It introduces diversification quotients using VaR and ES, with explicit formulas for specific models, and compares their effectiveness to traditional measures.

Findings

Explicit formulas for DQ in elliptical and MRV models

Favorable theoretical and practical features of DQ

Enhanced portfolio diversification assessment

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 favourable features of DQ, both theoretically and practically, compared to traditional diversification indices based on a single risk measure.