arXiv:2409.09684q-fin.PMcs.AI2024-09被引 8

决策导向学习让预测模型主动偏袒投资组合中的资产,提升实际收益。

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

  • 用决策反馈调整预测误差,引入资产间相关性影响
  • 虽预测误差更高,但组合收益显著优于传统方法
  • 适合关注实际投资效果而非单纯预测精度的研究者

Markowitz的均值-方差优化(MVO)框架依赖对资产预期收益、方差和协方差的精确估计,而这些参数通常不确定。机器学习模型常用于估计这些参数,但传统训练目标如均方误差(MSE)对所有资产一视同仁。最近研究提出决策导向学习(DFL),将预测与优化过程结合以改善决策结果。本文揭示了DFL如何改变股票收益预测模型:其梯度可解释为用逆协方差矩阵对MSE误差进行加权倾斜,从而将资产间相关性纳入学习过程;这导致系统性偏差——被纳入组合的资产被高估,未被选中的被低估。尽管预测误差更大,但这种策略性偏差正是实现更优组合绩效的原因。

原文摘要 · Abstract (English)

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.

投资组合决策学习预测偏差

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