Which factor model? A systematic return covariation perspective

•We explore which factor model best captures systematic return covariation out-of-sample.•We focus on the economic implications for portfolio risk control.•The Fama and French (2015) model, the Barillas and Shanken (2018) model, and the Fama and French (2018) model are the winners for the model-implied minimum risk portfolios.•For the minimum tracking error portfolios, the Barillas and Shanken (2018) model and the Fama and French (2018) model are the top performers.•Our findings survive transaction costs and a battery of robustness checks. We examine which factor model best captures systematic return covariation by focusing on the economic implications for portfolio risk control. The pairwise variance equality test and the model confidence set procedure suggest that the Fama and French (2015) five-factor model, the Barillas and Shanken (2018) six-factor model, and the Fama and French (2018) six-factor model are the top performers for the factor model-implied minimum risk portfolios in the out-of-sample. When it comes to the minimum tracking error portfolios, the Barillas and Shanken (2018) six-factor model and the Fama and French (2018) six-factor model are the overall winners in the horse race.