Integrating Factor Models

Abstract

This paper develops a comprehensive framework to address uncertainty about the correct factor model. Asset pricing inferences draw on a composite model that integrates over competing factor models weighted by posterior probabilities. Evidence shows that unconditional models record near-zero probabilities, while postearnings announcement drift, quality-minus-junk, and intermediary capital are potent factors in conditional asset pricing. Out-of-sample, the integrated model performs well, tilting away from subsequently underperforming factors. Model uncertainty makes equities appear considerably riskier, while model disagreement about expected returns spikes during crash episodes. Disagreement spans all return components involving mispricing, factor loadings, and risk premia.FINANCIAL ECONOMISTS HAVE IDENTIFIED A PLETHORA of firm characteristics that predict future stock returns (e.g., Cochrane (2011) andHarvey, Liu, andZhu (2016)). The literature has further proposed two major approaches to reduce the expanding number of predictors. The first invokes economic rationales, for example, plausible restrictions on the admissible Sharpe ratio, the present-value model, and the q-theory, to identify a small set of common factors, while the second approach formulates the dependence of average returns on common factors or firm characteristics through regression regularization techniques including deep learning extensions. However, the collection of factors that matter most remains subject to research controversy. 1 Signifi-

Diagnostics for asset pricing models

“…Beyond these well-known factor models, there are new asset pricing models from increasing applications of machine learning (ML) to finance, such as the instrumented principal component analysis (IPCA) model of Kelly et al (2019) and the autoencoder model of Gu et al (2021), as well as ML models of Gu et al (2020) and others. 1 While there is a huge literature on these models that improves our understanding on modeling expected returns (the essence of asset 1 See Hutchinson et al (1994), Rapach et al (2013), Chinco et al (2019), Feng et al (2020), Freyberger et al (2020), Kozak et al (2020), Avramov et al (2023), pricing), to the best of our knowledge, there is a lack of studies on the properties of the pricing errors (PEs) from these models.…”