Autoencoder Asset Pricing Models

Source: Gu, S., Kelly, B. T. & Xiu, D. (2021). Journal of Econometrics 222(1), 429–450.

TL;DR

A nonlinear conditional latent-factor model built as a neural-network autoencoder. It

generalizes IPCA: both the latent factors and the characteristic-conditioned loadings are

learned by neural networks, while the architecture enforces the no-arbitrage (beta-pricing)

structure. Allowing loadings to be nonlinear functions of characteristics improves out-of-sample

pricing over linear factor models, PCA, and IPCA.

That the mapping from firm characteristics to risk exposures is nonlinear, and that embedding

asset-pricing restrictions inside a deep model yields better, economically-disciplined factors.

A "conditional autoencoder": one network maps characteristics → factor loadings (betas); the

factors themselves are latent and estimated from returns.

Returns are reconstructed as loadings × factors (the no-arbitrage restriction), trained end-to-end;

reduces to IPCA when the networks are linear.

Nonlinear loadings deliver higher out-of-sample Sharpe ratios and lower pricing errors than linear

conditional models.

A few latent factors suffice; the gains come from the functional form of the loadings.

A bridge between the factor-model tradition and deep learning, showing how to impose economic

structure on neural networks — influential for the deep-SDF literature.

Neural estimation needs care (regularization, ensembling) and is less interpretable than IPCA.

Latent factors remain statistical constructs.

Gu, S., Kelly, B. & Xiu, D. (2021) — Autoencoder Asset Pricing Models — Journal of Econometrics

Gu, S., Kelly, B. & Xiu, D. (2020) — Empirical Asset Pricing via Machine Learning — Review of Financial Studies

Kelly, B., Pruitt, S. & Su, Y. (2019) — Characteristics Are Covariances — Journal of Financial Economics