The Prior Adaptive Group Lasso and the Factor Zoo

This paper develops and presents the prior adaptive group lasso (pag-lasso) for generalized linear models. The pag-lasso is an extension of the prior lasso, which allows for the use of existing information in the lasso estimation. We show that the estimator exhibits properties similar to the adaptive group lasso. The performance of the pag-lasso estimator is illustrated in a Monte Carlo study. The estimator is used to select the set of relevant risk factors in asset pricing models while requiring that the chosen factors must be able to price the test assets as well as the unselected factors. The study shows that the pag-lasso yields a set of factors that explain the time variation in the returns while delivering estimated pricing errors close to zero. We find that canonical low-dimensional factor models from the asset pricing literature are insufficient to price the cross section of the test assets together with the remaining traded factors. The required number of pricing factors to include at any given time is closer to 20.