论文标题
多元化商：通过风险措施量化多元化
Diversification quotients: Quantifying diversification via risk measures
论文作者
论文摘要
我们使用六个直观的公理建立了第一个用于多元化指数的公理理论：非负性，位置不变性，规模不变性，理性，归一化和连续性。满足这些公理的独特类别（称为多元化商（DQ））的独特类别是根据风险度量的参数家族来定义的。基于连贯的风险度量，投资组合凸的进一步的公理销钉将DQ降低。 DQ具有许多吸引人的属性，它可以解决现有指数的几个理论和实际限制。特别是，对于流行的风险措施和预期的缺口，相应的DQ允许简单公式，并且在投资组合选择中进行优化是有效的。此外，它可以正确捕获尾巴的沉重和常见冲击，这些冲击被传统多元化指数所忽略。当用财务数据说明时，DQ是直观的解释，其性能与其他多元化指数具有竞争力。
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.
