Paper: arXiv 2610.09613

Authors: Dexin Peng, Xiaoyu Wang

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.

Complexity vs Empirical Score

  • Math Complexity: 6.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel application of residual learning to asset pricing, demonstrating significant empirical improvements. The methodology is clearly articulated, and the provision of code enhances reproducibility, making it a strong contribution to the field.

Research Flowchart

  flowchart TD
    A[Research Goal: Deepen Asset Pricing Models for Better Performance] --> B{Key Methodology: Residual Learning & Deep/Shallow Models};
    B --> C[Data Input: Asset Pricing Factors & Returns];
    C --> D{Computational Process: Neural Network Training & Portfolio Construction};
    D --> E[Key Outcome 1: Deep Residual Model (Sharpe Ratio 2.07)];
    D --> F[Key Outcome 2: Shallow Model (Sharpe Ratio 1.92)];
    D --> G[Key Outcome 3: Deep Feedforward Model (Sharpe Ratio 0.89)];
    E & F & G --> H[Conclusion: Model Depth via Residual Learning Adds Economic Value];