Machine Learning in Asset Pricing: Expanding Multi-factor Models

Johann David Grøndahl & Nikolaj Bo Andersen

Student thesis: Master thesis


Machine learning in asset pricing is an extremely popular subject in the current finance literature, with several novel publications applying a variety of machine learning methods in order to challenge conventional asset pricing methods. A pioneering article in the field of machine learning, Shrinking the cross-section, challenging the conventional, sparse multi-factor models, were published by Kozak, Santosh & Nagel in 2020. We replicate this newly proposed dual-penalty estimator method for pricing the cross-section of stock returns, and subsequently test it in two high-dimensional data settings consisting of previously proven anomalies and a vast number of firm-specific financial ratios. The resulting factor models are based on the stochastic discount factor approach for asset pricing, which is the preferred approach in modern financial literature. Consistent with the findings of Kozak et al. (2020) it is evidently futile to create a sparse characteristics-based factor model sufficiently spanning the stochastic discount factor in order to achieve high out of sample performance in explaining cross-sections of stock returns. The best outof-sample performing model originates from the 𝐿2-only shrinkage estimator, summarizing the pricing information contained in a large number of characteristics-based factors. Testing the candidate factor models by construction of mean-variance efficient portfolios shows that the 𝐿2-only estimator significantly outperforms the Fama and French (2016) six-factor model. As such, this paper verifies the conclusion of Kozak et al. (2020) that the six-factor model of Fama and French (2016) leaves much of the cross-section of stock returns unexplained. Finally, rotating the factor returns into the space of principal components (PC) enables the possibility of creating PC-sparse factor models sufficiently spanning the stochastic discount factor, yielding good out-of-sample performance, as they perform uniformly better than characteristicssparse models.

Educations, (Graduate Programme) Final Thesis
Publication date2021
Number of pages130