Deep Learning in Asset Pricing

Abstract

We use deep neural networks to estimate an asset pricing model for individual stock returns that takes advantage of the vast amount of conditioning information, keeps a fully flexible form, and accounts for time variation. The key innovations are to use the fundamental no-arbitrage condition as criterion function to construct the most informative test assets with an adversarial approach and to extract the states of the economy from many macroeconomic time series. Our asset pricing model outperforms out-of-sample all benchmark approaches in terms of Sharpe ratio, explained variation, and pricing errors and identifies the key factors that drive asset prices. This paper was accepted by Agostino Capponi, finance. Supplemental Material: The online appendix and data are available at https://doi.org/10.1287/mnsc.2023.4695 .

Integrating Factor Models

“…The conditional models display an aggregate posterior probability of 100%, implying that our Bayesian approach uniformly favors models with time‐varying parameters, even when prior beliefs are weighted against the inclusion of macro predictors. Our findings further highlight the importance of incorporating nonlinearities in asset pricing models, especially by conditioning on the macroeconomic states—a point also emphasized by Chen, Pelger, and Zhu (2023) in a nonparametric setup. Furthermore, our results complement prior work that focuses on the nonlinear relationship between firm characteristics and returns (e.g., Freyberger, Neuhierl, and Weber (2020)) and that employs a conditional factor model in which the factor loadings are nonlinear in firm characteristics (e.g., Gu, Kelly, and Xiu (2021)).…”

“…The first of these two components reflects estimation risk, that is, the risk that the underlying model parameters are estimated with error. The second Manresa, Peñaranda, and Sentana (2017), Feng, Giglio, and Xiu (2020), Freyberger, Neuhierl, and Weber (2020), Gu, Kelly, and Xiu (2020), Kozak, Nagel, and Santosh (2020), Chen, Pelger, and Zhu (2023), and Cong et al (2021) for the second. Notably, the various specifications could disagree on the set of factors that matter most.…”

Stock picking with machine learning

“…The control switches use sigmoid activation functions to efficiently learn how to weigh current observations against long‐term versus short‐term memory, and hyperbolic tangent activation functions are used for processing the data. This architecture makes the LSTM NN cell robust when dealing with long‐term dependencies and also for capturing non‐stationarity (Chen et al, 2019). One may argue that the architecture of an LSTM NN cell is rather heuristic and many alternative architectures with alternative activation functions and gates are possible.…”

“…Coqueret and Guida (2018) use regression trees to identify the most important firm characteristics for explaining stock returns. Chen et al (2019) build a nonlinear asset‐pricing model for individual stock returns based on DNNs with macroeconomic and firm‐specific information. The deep learning asset‐pricing model outperforms out‐of‐sample generating lower pricing errors.…”

Option Return Predictability with Machine Learning and Big Data

“…Neuhierl, Tang, Varneskov, and Zhou (2021) examine the predictive power of option characteristics for the cross-section of stock returns. Kozak, Nagel, and Santosh (2020) impose an economically motivated prior on stochastic discount factor coefficients that shrinks contributions of low-variance principal components for the cross-section of stock returns and Chen, Pelger, and Zhu (2020) add to these insights, using deep neural networks to estimate an asset pricing model for individual stock returns. Martin and Nagel (2022) show that asset returns may appear predictable in-sample when analyzing the economy ex-post and stress the importance of out-of-sample tests.…”