Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models
Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models
This paper investigates how Decision-Focused Learning (DFL) modifies stock return prediction models for Mean-Variance Optimization (MVO). The authors demonstrate that DFL's gradient tilts MSE-based prediction errors by the inverse covariance matrix Σ⁻¹, incorporating inter-asset correlations into the learning process. This tilting creates systematic biases where DFL overestimates returns for assets that will be included in the portfolio and underestimates those that will be excluded, leading to extreme portfolio concentration—using the minimum number of assets allowed by constraints regardless of risk aversion. Empirically, using DOW 30 and S&P 100 data, the authors show that intermediate DFL weights (α between 0.25 and 0.75) achieve superior Sharpe ratios and lower regret compared to pure MSE or pure DFL, despite higher prediction errors. The strategic biases are identified as features that improve decision quality, not flaws. The study provides both theoretical analysis (via unconstrained MVO closed-form) and extensive experiments (with varying risk aversion λ and DFL weight α) to uncover the mechanism behind DFL's success in portfolio optimization.
Highlights
- 1DFL for MVO tilts MSE prediction errors by the inverse covariance matrix Σ⁻¹, incorporating inter-asset correlations into learning.
- 2DFL induces systematic prediction biases: overestimating returns for portfolio assets and underestimating excluded assets.
- 3DFL-trained models consistently concentrate portfolios to the minimum number of assets allowed by constraints, regardless of risk aversion.
- 4Intermediate DFL weights (α ∈ [0.25, 0.75]) achieve superior Sharpe ratios and lower regret compared to pure MSE or pure DFL.
- 5The strategic biases introduced by DFL are features, not flaws, leading to improved portfolio performance despite higher prediction errors.
Methods
- MDecision-Focused Learning (DFL) with a combined loss function ℒ_combined = αℒ_MVO + (1-α)ℒ_MSE to balance prediction accuracy and decision quality.
- MMean-Variance Optimization (MVO) with constraints (sum-to-one, non-negativity, maximum weight limits) for portfolio selection.
- M4-layer MLP prediction model trained with AdamW optimizer, using 60-day historical returns as features.
- MGradient analysis of the unconstrained MVO closed-form solution to derive the Σ⁻¹ tilting mechanism.
Results
- RDFL models achieve higher Sharpe ratios and lower maximum drawdowns compared to MSE models across DOW 30 and S&P 100 datasets.
- RAs DFL strength increases, prediction bias polarizes: assets with positive predicted returns become overestimated, negative ones underestimated.
- RDFL creates a clear separation in predicted return distributions between assets included in the portfolio (In group) and those excluded (Out group).
- RUnder pure DFL, top-weighted assets show persistent positive bias (0.5–1.5) while bottom-weighted assets show negative bias (-0.5 to -1.5), unlike MSE where biases are random.
- RHigher risk aversion λ reduces the magnitude of predicted return differentiation, as DFL adapts to the optimizer's focus on variance.
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