On a general class of portfolio diversification measures induced by risk measures
本文提出一种从任意风险度量构建投资组合分散化度量的新方法，通过优化框架建立风险与分散化的联系，并证明该度量满足关键公理性质，适用于多空投资组合，实证分析验证了其有效性。
Abstract This paper introduces a novel and effective methodology for constructing portfolio diversification measures derived from any reference risk measure. The central contribution lies in leveraging the extensive theoretical developments in risk measurement to systematically inform and enhance the design of diversification metrics. The link between risk and diversification is exploited through an optimization framework in which the objective function is defined as a weighted Euclidean distance dependent on risk. We prove that the resulting objective function satisfies key axiomatic properties typically required to diversification measures, and that the corresponding optimization problem admits a unique solution that is inherently related to the intuitive concept of geometric diversification, thereby providing theoretical support for it. The key economic interpretation relies on determining the point in the allocation space that is equally distant – under a risk-sensitive metric – from the vertices of the simplex, i.e. the fully concentrated portfolios. An important economic insight of our approach is its applicability within a general long-short investment framework–a significant advancement, given that most classical diversification measures are restricted to long-only portfolios. Finally, to support the robustness of our findings, we present a comprehensive empirical analysis across multiple real-world financial datasets, highlighting meaningful comparisons between our proposed measure and several widely used diversification metrics.