Abstract The optimal factor timing portfolio is equivalent to the stochastic discount factor. We propose and implement a method to characterize both empirically. Our approach imposes restrictions on the dynamics of expected returns, leading to an economically plausible SDF. Market-neutral equity factors are strongly and robustly predictable. Exploiting this predictability leads to substantial improvement in portfolio performance relative to static factor investing. The variance of the corresponding SDF is larger, is more variable over time, and exhibits different cyclical behavior than estimates ignoring this fact. These results pose new challenges for theories that aim to match the cross-section of stock returns. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.