Residual Learning in Empirical Asset Pricing

2026-10-07

AI Summary

This study addresses the challenge that deep learning models in asset pricing often fail to outperform shallow benchmarks, as deeper networks are prone to degradation. To overcome this limitation, the authors introduce residual learning to construct deep neural networks, which mitigates degradation by preserving and refining shallow features, thereby enabling large-scale, scalable asset pricing modeling. Theoretically, the work demonstrates that increased network depth encodes additional economic value. Empirically, the proposed deep residual model achieves an out-of-sample Sharpe ratio of 2.07, significantly outperforming both shallow architectures and standard feedforward networks. These findings establish a novel paradigm for deep learning applications in asset pricing, bridging the gap between network depth and economic interpretability while delivering superior predictive performance.

Abstract

Shallow models are special cases of deep models, and deep models theoretically have the potential to outperform the shallow ones. However, the existing empirical asset pricing literature provides strong benchmarks for shallow models. Residual learning allows neural network models in asset pricing to go deeper by preserving and refining their shallow counterparts. The out-of-sample Sharpe ratio for value-weighted long-short portfolios of deep residual models (2.07) is higher than that for the corresponding shallow ones (1.92) and more than twice that of the deep feedforward models (0.89). We show that model depth is a source of additional economic value in asset pricing. Residual learning can be used to deepen other neural-network-based asset pricing models if they contain intermediate layers. Our design also provides one way to scale asset pricing models, making native "large asset pricing models" more feasible.

Problem

• Empirical Asset Pricing
• Residual Learning
• Deep Neural Networks
• Model Depth
• Sharpe Ratio

Innovation

• Residual Learning
• Empirical Asset Pricing
• Deep Neural Networks
• Sharpe Ratio
• Model Scaling