In this paper, we use a cross-sectional approach to get a deeper comprehension of the common risk profile of stock returns. Instead of employing static and ad hoc factor selection procedures as in Fama and French (1993), we use asymptotic developments of Bai and Ng (2002, 2006) to select the relevant factors. We thus reconcile two methodologies: a statistical one and the other, founded on observed factors. We apply our approach to French and US stock markets over the period 1999 to 2008 and test the performance of several traditionally observed factors, such as credit spread and firm-characteristic variables of Fama and French (1993) and Carhart (1997). Our results uncover strong time and country dependencies of stock risk profile.