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. 

Short Bio:  Dr. Ruodu Wang is Tier-1 Canada Research Chair in Quantitative Risk Management and Professor of Actuarial Science and Quantitative Finance at the University of Waterloo. He received his PhD in Mathematics (2012) from the Georgia Institute of Technology, after completing his Bachelor (2006) and Master’s (2009) degrees at Peking University. He is on the board of 7 leading journals in operations research, actuarial science, statistics, and economics as co-editors or associate editors. He is the first winner of the SOA Actuarial Science Early Career Award (2021) from the Society of Actuaries, and a Fellow of the Institute of Mathematical Statistics (elected 2022).