2022/06/28 by Xia Han, Liyuan Lin, Han, Xia +3 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Risk Management (q-fin.RM) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2206.13679
openalex publication_date 2022/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We establish the first axiomatic theory for diversification indices using six intuitive axioms: non-negativity, 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 DQ based on coherent risk measures. 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, DQ is intuitive to interpret, and its performance is competitive against other diversification indices.