Diversification Quotients: Quantifying Diversification via Risk Measures

To overcome several limitations of existing diversification indices, we introduce the quotient (DQ). Defined through a parametric family risk measures, DQ satisfies three natural properties, namely, non-negativity, location invariance and scale invariance, which are shown to be conflicting for any traditional index based on single measure. We pay special attention two most important classes measures in banking insurance, Value-at-Risk (VaR) Expected Shortfall (ES, also called CVaR). DQs VaR ES enjoy many convenient technical they efficient optimize portfolio selection. By analyzing popular multivariate models elliptical regular varying distributions, find that can properly capture tail heaviness common shocks neglected by indices. When illustrated with financial data, is intuitive interpret, its performance competitive when contrasted other methods optimization.