A return-diversification approach to portfolio selection

ArXiv ID: 2312.09707 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we propose a general bi-objective model for portfolio selection, aiming to maximize both a diversification measure and the portfolio expected return. Within this general framework, we focus on maximizing a diversification measure recently proposed by Choueifaty and Coignard for the case of volatility as a risk measure. We first show that the maximum diversification approach is actually equivalent to the Risk Parity approach using volatility under the assumption of equicorrelated assets. Then, we extend the maximum diversification approach formulated for general risk measures. Finally, we provide explicit formulations of our bi-objective model for different risk measures, such as volatility, Mean Absolute Deviation, Conditional Value-at-Risk, and Expectiles, and we present extensive out-of-sample performance results for the portfolios obtained with our model. The empirical analysis, based on five real-world data sets, shows that the return-diversification approach provides portfolios that tend to outperform the strategies based only on a diversification method or on the classical risk-return approach.

Keywords: risk parity, diversification measure, bi-objective model, Conditional Value-at-Risk (CVaR), Expectiles, Portfolio Management

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper introduces advanced mathematical concepts like coherent risk measures, diversification ratios, and bi-objective optimization with rigorous theorems, indicating high math complexity. It also includes extensive out-of-sample performance results based on five real-world datasets, demonstrating strong empirical rigor.

  flowchart TD
    A["Research Goal<br>Propose a general bi-objective model<br>for portfolio selection"] --> B["Methodology<br>Maximize both diversification and return"]
    B --> C["Data Input<br>5 real-world datasets<br>for out-of-sample testing"]
    C --> D["Computational Process<br>Formulate bi-objective model for:<br>Volatility, MAD, CVaR, Expectiles"]
    D --> E["Key Findings<br>Portfolios outperform<br>single-objective strategies<br>Risk Parity = Max Diversification<br>under equicorrelation"]