Paper: arXiv 2301.03517
Authors: Xia Han, Liyuan Lin, Ruodu Wang
Abstract
The diversification quotient (DQ) is recently introduced for quantifying the degree of diversification of a stochastic portfolio model. It has an axiomatic foundation and can be defined through a parametric class of risk measures. Since the Value-at-Risk (VaR) and the Expected Shortfall (ES) are the most prominent risk measures widely used in both banking and insurance, we investigate DQ constructed from VaR and ES in this paper. In particular, for the popular models of elliptical and multivariate regular varying (MRV) distributions, explicit formulas are available. The portfolio optimization problems for the elliptical and MRV models are also studied. Our results further reveal favourable features of DQ, both theoretically and practically, compared to traditional diversification indices based on a single risk measure.
Complexity vs Empirical Score
- Math Complexity: 8.0/10
- Empirical Rigor: 3.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper provides a strong theoretical and mathematical foundation for diversification quotients using VaR and ES, offering explicit formulas for elliptical and MRV distributions. However, it is primarily a theoretical risk management paper lacking empirical validation and real-world portfolio backtesting.
Research Flowchart
flowchart TD
A[Research Goal: Quantify portfolio diversification using VaR and ES-based Diversification Quotients] --> B[Data Inputs: Elliptical & Multivariate Regularly Varying Distribution Models]
B --> C[Methodology: Axiomatic DQ Framework & Risk Measure Formulation]
C --> D[Computational Process: Derive Explicit DQ Formulas & Conduct Portfolio Optimization]
D --> E[Outcomes: Analytical DQ Expressions for Elliptical/MRV Models]
D --> F[Outcomes: Superior Diversification Metrics vs Single Risk Measure Indices]