Mathematics Colloquium
Liyuan Lin
University of Waterloo
Title: Risk Measure, Dependence and Diversification
Date: Friday, January 19, 2024
Place and Time: Love 101, 3:05-3:55 pm
Abstract. We establish the first axiomatic theory for diversification indices using six intuitive axioms -- non-negativity, location invariance, scale invariance, rationality, normalization, and continuity -- together with risk measures. The unique class of indices satisfying these axioms, called the diversification quotients (DQs), are defined based on a parametric family of 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, DQ admits simple formulas, it is efficient to optimize in portfolio selection, and 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.