Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models
summary
The paper presents a novel framework for analyzing linear asset pricing models. The method is designed to be simple, robust, and applicable to high-dimensional problems. It can provide reliable price of risk estimates for both tradable and nontradable factors and detect those that are weakly identified. The method can also automatically select the best specification among competing factors and models, or provide a Bayesian model averaging-stochastic discount factor if there is no clear winner. The method is shown to outperform existing models in both in-sample and out-of-sample tests using a large set of factors. The authors argue that this method offers a solution to the "factor zoo" problem, where there are many empirically priced sources of risk, and the problem of weak factors, where factors with asymptotically zero covariance with asset returns appear to be relevant.
what to read
Shanken (1987) and Harvey and Zhou (1990) are among the first to use the Bayesian framework in portfolio choice and to develop GRS-type tests for mean-variance efficiency.
Pástor and Stambaugh (2000) and Pástor (2000) assign a prior distribution to the vector of pricing errors and apply it to portfolio choice.
Barillas and Shanken (2018) extend the aforementioned prior and derive a closed-form solution for the Bayes factor when all of the risk factors are tradable and use it to compare different linear factor models exploiting the time-series dimension of the data.
Chib, Zeng, and Zhao (2020) show that the improper prior specification of Barillas and Shanken (2018) is problematic and propose a new class of priors that leads to valid comparison for traded factor models.
Garlappi, Uppal, and Wang (2007) impose priors on expected returns and their variance-covariance matrix and find that the shrinkage-based analog leads to superior empirical performance.
The ridge-based approach to recovering the SDF of Kozak, Nagel, and Santosh (2020) can also be interpreted from a Bayesian perspective with priors on the expected returns distribution.
This paper naturally contributes to the literature on weak identification in asset pricing, starting from the seminal papers of Kan and Zhang (1999a, 1999b).
This paper provides the first attempt to develop a general Bayesian approach for both tradable and nontradable factors, capable of imposing tradable restrictions on the price of risk when needed.