The Prior Adaptive Group Lasso with an Application to Risk Factor Selection

This paper develops and presents the prior adaptive group lasso for generalized linear models. The prior adaptive group lasso is an extension of the prior lasso developed by Jiang, He, and Zhang (2016), which allows for the use of existing information from previous or similar studies in the estimation of the lasso. We demonstrate that the estimator exhibits consistent variable selection and estimation similarly to those derived in Wang and Tian (2019) under at set of similar conditions. The performance of the prior adaptive group lasso estimator is illustrated in a Monte Carlo study. Finally, the estimator is applied in selecting the set of relevant risk factors in asset pricing models conditioning on the fact that the chosen factors must be able to price the test assets as well as the remaining factors. The empirical study shows that the prior adaptive group lasso yields a set of factors that explain the time variation in the returns while delivering 𝛼 estimates close to zero. We also show how this set of factors has evolved over time. We find that the canonical factor models of Fama and French (1993), (Carhart, 1997), (Fama and French, 2015), and (Hou, Xue, and Zhang, 2015) are insufficient to price the cross section of the test assets together with the remaining traded factors, and we find that the required number of pricing factors to include at any given time is closer to 20.