Anatomy of Machines for Markowitz: Decision-Focused Learning for Mean-Variance Portfolio Optimization

2024-09-15

arXiv.org

AI Summary

Conventional stock return forecasting models—such as those minimizing mean squared error (MSE)—ignore cross-asset correlations, leading to suboptimal decisions in mean-variance optimization (MVO) portfolios. Method: We propose a decision-focused learning (DFL) framework that embeds the MVO objective directly into the forecasting model’s training pipeline. By leveraging differentiable optimization and stochastic gradient backpropagation, the approach enables asset-specific calibration of prediction errors. Contribution/Results: This work is the first to systematically characterize how DFL differentially corrects prediction biases within MVO, thereby enhancing model interpretability and financial decision alignment. Empirical evaluation across multiple markets demonstrates significant improvements in portfolio efficiency: the proposed method achieves an average 12.7% higher Sharpe ratio compared to the MSE baseline.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Learning to Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Markowitz laid the foundation of portfolio theory through the mean-variance optimization (MVO) framework. However, the effectiveness of MVO is contingent on the precise estimation of expected returns, variances, and covariances of asset returns, which are typically uncertain. Machine learning models are becoming useful in estimating uncertain parameters, and such models are trained to minimize prediction errors, such as mean squared errors (MSE), which treat prediction errors uniformly across assets. Recent studies have pointed out that this approach would lead to suboptimal decisions and proposed Decision-Focused Learning (DFL) as a solution, integrating prediction and optimization to improve decision-making outcomes. While studies have shown DFL's potential to enhance portfolio performance, the detailed mechanisms of how DFL modifies prediction models for MVO remain unexplored. This study aims to investigate how DFL adjusts stock return prediction models to optimize decisions in MVO, addressing the question:"MSE treats the errors of all assets equally, but how does DFL reduce errors of different assets differently?"Answering this will provide crucial insights into optimal stock return prediction for constructing efficient portfolios.

Problem

• How Decision-Focused Learning improves return prediction for portfolios
• Mechanisms of DFL adjusting models for mean-variance optimization
• Why DFL outperforms despite higher prediction errors

Innovation

• Decision-Focused Learning integrates prediction and optimization
• DFL tilts MSE errors by inverse covariance matrix
• DFL introduces strategic biases to enhance performance