Finding Near-Optimal Portfolios With Quality-Diversity

ArXiv ID: 2402.16118 “View on arXiv”

Authors: Unknown

Abstract

The majority of standard approaches to financial portfolio optimization (PO) are based on the mean-variance (MV) framework. Given a risk aversion coefficient, the MV procedure yields a single portfolio that represents the optimal trade-off between risk and return. However, the resulting optimal portfolio is known to be highly sensitive to the input parameters, i.e., the estimates of the return covariance matrix and the mean return vector. It has been shown that a more robust and flexible alternative lies in determining the entire region of near-optimal portfolios. In this paper, we present a novel approach for finding a diverse set of such portfolios based on quality-diversity (QD) optimization. More specifically, we employ the CVT-MAP-Elites algorithm, which is scalable to high-dimensional settings with potentially hundreds of behavioral descriptors and/or assets. The results highlight the promising features of QD as a novel tool in PO.

Keywords: Portfolio Optimization, Mean-Variance Framework, Quality-Diversity Optimization, CVT-MAP-Elites, Risk Aversion, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts from optimization theory and evolutionary computation (quality-diversity, CVT-MAP-Elites), resulting in high math complexity. It also demonstrates empirical rigor through computational experiments, algorithmic implementation details, and discussion of real-world factors like transaction costs, placing it above the threshold for practical application.

  flowchart TD
    A["Research Goal<br>Find diverse near-optimal portfolios<br>beyond single-solution MV framework"] --> B{"Key Methodology"}
    
    B --> C["Data Inputs<br>Asset returns & covariance matrix"]
    C --> D["Algorithm: CVT-MAP-Elites<br>Quality-Diversity Optimization"]
    
    D --> E["Computational Process<br>Divide behavioral space into cells<br>Iterate through solutions<br>Archive best per cell"]
    
    E --> F["Key Findings<br>1. Scalable to high dimensions<br>2. Diverse set of near-optimal portfolios<br>3. Robust alternative to MV sensitivity"]
    
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    style B fill:#fff3e0
    style C fill:#f3e5f5
    style D fill:#e8f5e8
    style E fill:#fce4ec
    style F fill:#e8f5e8