Residual Learning Deepens Shallow Asset Pricing Models and Improves Out-of-Sample Performance

01 ABSTRACT

Deep models should theoretically outperform shallow ones, but existing empirical asset pricing literature shows stronger benchmarks for shallow models. The authors use residual learning to deepen neural networks while preserving shallow model information, improving out-of-sample performance. The deep residual model's value-weighted long-short portfolio out-of-sample Sharpe ratio is 2.07, higher than the shallow counterpart's 1.92 and more than twice the deep feedforward model's 0.89. The authors argue model depth is a source of additional economic value in asset pricing and that residual learning can deepen other neural-network-based asset pricing models with intermediate layers.

02 KEY FINDINGS

1. The deep residual asset pricing model's value-weighted long-short portfolio out-of-sample Sharpe ratio is 2.07, higher than the shallow model's 1.92 and the deep feedforward model's 0.89.
2. Residual learning allows neural networks to go deeper by preserving and refining shallow counterparts, mitigating the underperformance of deep models.
3. The authors argue model depth is a source of additional economic value in asset pricing and that this design offers a path to scale native 'large asset pricing models'.