Autoencoder Asset Pricing Models

35 Pages Posted: 7 Mar 2019 Last revised: 1 Oct 2019

See all articles by Shihao Gu

Shihao Gu

University of Chicago - Booth School of Business

Bryan T. Kelly

Yale SOM; AQR Capital Management, LLC; National Bureau of Economic Research (NBER)

Dacheng Xiu

University of Chicago - Booth School of Business

Date Written: September 30, 2019


We propose a new latent factor conditional asset pricing model. Like Kelly, Pruitt, and Su (KPS, 2019), our model allows for latent factors and factor exposures that depend on covariates such as asset characteristics. But, unlike the linearity assumption of KPS, we model factor exposures as a flexible nonlinear function of covariates. Our model retrofits the workhorse unsupervised dimension reduction device from the machine learning literature—autoencoder neural networks—to incorporate information from covariates along with returns themselves. This delivers estimates of nonlinear conditional exposures and the associated latent factors. Furthermore, our machine learning framework imposes the economic restriction of no-arbitrage. Our autoencoder asset pricing model delivers out-of-sample pricing errors that are far smaller (and generally insignificant) compared to other leading factor models.

Keywords: stock returns, conditional asset pricing model, nonlinear factor model, machine learning, autoencoder, neural networks, big data

JEL Classification: G10, C10, C45

Suggested Citation

Gu, Shihao and Kelly, Bryan T. and Xiu, Dacheng, Autoencoder Asset Pricing Models (September 30, 2019). Yale ICF Working Paper No. 2019-04, Chicago Booth Research Paper No. 19-24, Available at SSRN: or

Shihao Gu

University of Chicago - Booth School of Business ( email )

Chicago, IL
United States

Bryan T. Kelly (Contact Author)

Yale SOM ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States

AQR Capital Management, LLC ( email )

Greenwich, CT
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Dacheng Xiu

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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