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

arXiv: https://arxiv.org/abs/2409.09684 · HTML: https://mlsanity.com/paper/2409.09684/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 15 Sep 2024.

## Builds on (most cited first, 12 of 12)

- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimize](https://mlsanity.com/paper/2305.16830/) (2023)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [Locally Convex Global Loss Network for Decision-Focused Learning](https://mlsanity.com/paper/2403.01875/) (2024)

## Built on by (most cited first, 5 of 5)

- [Decision-Focused Learning via Tangent-Space Projection of Prediction Error](https://mlsanity.com/paper/2605.01361/) (2026)
- [The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tails](https://mlsanity.com/paper/2606.27462/) (2026)
- [Generating Input Distributions for Explaining Portfolio Optimization Pipelines](https://mlsanity.com/paper/2606.25808/) (2026)
- [End-to-End Neural Shrinkage of Indefinite Pairwise Correlation Matrices for Small-Cap-Inclusive Portfolios](https://mlsanity.com/paper/2608.30446/) (2026)
- [Decision-Focused Learning for Mean-Variance Portfolio Optimization via KKT-Based Reformulation](https://mlsanity.com/paper/2609.21427/) (2026)

## Abstract (arXiv)

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 investigates how DFL adjusts stock return prediction models to optimize decisions in MVO. Theoretically, we show that DFL's gradient can be interpreted as tilting the MSE-based prediction errors by the inverse covariance matrix, effectively incorporating inter-asset correlations into the learning process, while MSE treats each asset's error independently. This tilting mechanism leads to systematic prediction biases where DFL overestimates returns for assets included in portfolios while underestimating excluded assets. Our findings reveal why DFL achieves superior portfolio performance despite higher prediction errors. The strategic biases are features, not flaws.