We develop new likelihood-based methods to estimate factor-based Stochastic Discount Factors (SDF) that may accommodate Hidden Markov dynamics in the factor loadings. We use these methods to investigate whether it is possible to find a SDF that jointly prices the cross-section of eight U.S. portfolios of stocks, Treasuries, corporate bonds, and commodities. In particular, we test a range of possible different specification of the SDF, including single-state and Hidden Markov models and compare their statistical and pricing performances. In addition, we assess whether and to which extent a selection of these models replicates the observed moments of the return series, and especially correlations. We report that regime-switching models clearly outperform single-state ones both in term of statistical and pricing accuracy. However, while a four-state model is selected by the information criteria, a two-state three-factor full Vector Autoregression model outperforms the others as far as the pricing accuracy is concerned.