Anomaly or Risk Factor? A Stepwise Evaluation

In empirical asset pricing, traded candidate factors can be either on the left- or right-hand side of the factor model as an anomaly or true risk factor, because anomalies should be explained by the set of risk factors with zero intercepts --- pricing errors. This unsupervised factor selection is a new statistical problem that cannot be answered by existing model selection studies that rely on test assets. This paper proposes a stepwise evaluation framework that sequentially separates a small set of risk factors from a large number of anomalies, resulting in a robust selection of true factors without (or with) test assets. With the statistical guarantee of selection consistency, our method utilizes the asset pricing duality between the minimal GRS statistic and the maximal Sharpe ratio when approximating the stochastic discount factor. Empirically, we find that seven selected factors can explain the remaining cross section of anomalies, along with exceptional factor investment performance.