Diversification Quotients: Quantifying Diversification via Risk Measures

• 成果类型: Article
• 署名作者: Han, Xia; Lin, Liyuan; Wang, Ruodu
• 署名单位: Nankai University; Nankai University; Monash University; University of Waterloo
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2023.00513
• 发表日期: 2025
• 关键词: EXPECTED SHORTFALL; axiomatic framework; diversification benefit; portfolios; quasiconvexity

摘要

We establish the first axiomatic theory for diversification indices using six intuitive axioms: nonnegativity, 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 DQs based on coherent risk measures. The 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, the DQ is intuitive to interpret, and its performance is competitive against other diversification indices.