arXiv 2409.096842024-09q-fin.PMcs.AI

均值-方差投资组合选择中的收益预测：决策聚焦学习如何塑造预测模型

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

UNIST（全南国立大学）；KAIST（韩国科学技术院）

Junhyeong Lee, Haeun Jeon, Hyunglip Bae, Yongjae Lee

备注：: 9 pages, 5 figures, 2 tables
DOI：: 10.1145/3768292.3770423

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AI总结：

本文研究决策聚焦学习（DFL）如何调整收益预测模型以优化均值-方差投资组合，证明DFL通过逆协方差矩阵倾斜预测误差并产生系统性偏差，从而在预测误差更高的情况下仍实现更优组合表现。

摘要：

Markowitz通过均值-方差优化（MVO）框架奠定了投资组合理论的基础。然而，MVO的有效性取决于对资产收益的期望收益、方差和协方差的精确估计，而这些通常具有不确定性。机器学习模型在估计不确定参数方面正变得越来越有用，这类模型的训练目标是最小化预测误差，例如均方误差（MSE），而MSE对所有资产的预测误差一视同仁。近期研究指出，这种方法会导致次优决策，并提出决策聚焦学习（Decision-Focused Learning，DFL）作为解决方案，将预测与优化相结合以改善决策结果。尽管已有研究表明DFL具有提升投资组合表现的潜力，但DFL如何具体修改面向MVO的预测模型的详细机制仍未得到探索。本研究考察了DFL如何调整股票收益预测模型以优化MVO中的决策。在理论上，我们证明DFL的梯度可以解释为通过逆协方差矩阵对基于MSE的预测误差进行倾斜，从而有效地将资产间相关性纳入学习过程，而MSE则独立处理每项资产的误差。这种倾斜机制导致了系统性的预测偏差：DFL会高估被纳入投资组合的资产的收益，同时低估被排除在外的资产。我们的发现揭示了为什么DFL尽管预测误差更高，却能实现更优的投资组合表现。这些策略性偏差是特性，而非缺陷。

英文摘要：

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.

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