Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models

Junhyeong Lee, Haeun Jeon, Hyunglip Bae, Yongjae Lee

Abstract: Markowitz laid the foundation of portfolio theory through mean-variance optimization (MVO). However, MVO's effectiveness depends on precise estimation of expected returns, variances, and covariances, which are typically uncertain. Machine learning models are increasingly used to estimate these parameters, trained to minimize prediction errors like MSE, which treats errors uniformly across assets. Recent studies show this leads to suboptimal decisions and propose Decision-Focused Learning (DFL), integrating prediction and optimization to improve outcomes. While studies demonstrate DFL's potential to enhance portfolio performance, the mechanisms of how DFL modifies prediction models for MVO remain unexplored. This study investigates how DFL adjusts stock return prediction models to optimize MVO decisions. We show that DFL's gradient tilts MSE-based prediction errors by the inverse covariance matrix $\Sigma^{-1}$, incorporating inter-asset correlations into learning, while MSE treats each asset independently. This tilting creates systematic biases where DFL overestimates returns for portfolio assets while underestimating excluded assets. Our findings reveal why DFL achieves superior performance despite higher prediction errors. The strategic biases are features, not flaws.