Risk Factors’ Cpdag Roots and the Cross-Section of Expected Returns

The Asset pricing literature has produced hundreds of risk factor candidates aimed at explaining the cross-section of expected excess returns, although risk factors which are in fact capable of providing independent information remains an open question. Appling a sparse model, Kozak, Nagel, and Santosh (2020) achieve satisfactory results on explaining cross-sectional returns only with PCs (principal components). In this paper, we propose a new methodology that seeks to reduce risk factor predictor dimensions by estimating the joint risk factor distribution with CPDAG (complete partial directed acyclic graph), in addition to selecting the CPDAG root as the only new risk factor candidate set. Our approach yields a significant shrinkage in the original set of risk factors, whereas our findings lead to sparse models that pose better results than those attained with the standard models and with alternative methods proposed by PCs factor zoo-related research papers