Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models

Abstract

We propose a novel framework for analyzing linear asset pricing models: simple, robust, and applicable to high-dimensional problems. For a (potentially misspecified) stand-alone model, it provides reliable price of risk estimates for both tradable and nontradable factors, and detects those weakly identified. For competing factors and (possibly nonnested) models, the method automatically selects the best specification—ifa dominant one exists—or provides a Bayesian model averaging–stochastic discount factor (BMA-SDF), if there is no clear winner. We analyze 2.25 quadrillion models generated by a large set of factors and find that the BMA-SDF outperforms existing models in- and out-of-sample.