Deep Partial Least Squares for Nonlinear Equity Risk Factors
Summary
The document describes deep partial least squares (DPLS), a model for explaining individual stock returns using a small set of latent risk factors and firm characteristics. Projected least squares jointly maps returns and characteristics into a latent factor space, while a deep learning network models nonlinear relationships between factor loadings and returns. This structure is intended to capture both linear factor exposure and interactions that may help explain return anomalies.
The study applies the model to 3,290 Russell 1000 assets from December 1989 to January 2018. It reports better performance than LASSO and standard deep learning, including information ratios about 1.2 times those of deep learning, and says the more compact architecture reduces training time. The authors also report that DPLS explains variation and pricing errors and identifies prominent latent factors and characteristics. These are results from the described historical sample; the document gives no details here on transaction costs, out-of-sample design, or how robust the findings are under other universes and periods.
Key ideas
- DPLS combines projected least squares with a deep network to model nonlinear asset pricing relationships.
- The model uses firm characteristics and returns to identify a compact latent factor space.
- Nonlinear interactions may help describe anomalies alongside linear factor exposures.
- In the Russell 1000 sample, DPLS reportedly outperforms LASSO and plain deep learning.
- The document does not specify transaction cost treatment or robustness beyond the stated sample.
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Full text
# Deep Partial Least Squares for Empirical Asset Pricing # Deep Partial Least Squares for Empirical Asset Pricing We use deep partial least squares (DPLS) to estimate an asset pricing model for individual stock returns that exploits conditioning information in a flexible and dynamic way while attributing excess returns to a small set of statistical risk factors. The novel contribution is to resolve the non-linear factor structure, thus advancing the current paradigm of deep learning in empirical asset pricing which uses linear stochastic discount factors under an assumption of Gaussian asset returns and factors. This non-linear factor structure is extracted by using projected least squares to jointly project firm characteristics and asset returns on to a subspace of latent factors and using deep learning to learn the non-linear map from the factor loadings to the asset returns. The result of capturing this non-linear risk factor structure is to characterize anomalies in asset returns by both linear risk factor exposure and interaction effects. Thus the well known ability of deep learning to capture outliers, shed lights on the role of convexity and higher order terms in the latent factor structure on the factor risk premia. On the empirical side, we implement our DPLS factor models and exhibit superior performance to LASSO and plain vanilla deep learning models. Furthermore, our network training times are significantly reduced due to the more parsimonious architecture of DPLS. Specifically, using 3290 assets in the Russell 1000 index over a period of December 1989 to January 2018, we assess our DPLS factor model and generate information ratios that are approximately 1.2x greater than deep learning. DPLS explains variation and pricing errors and identifies the most prominent latent factors and firm characteristics.
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