Several papers argue that financial economics faces a replication crisis because the majority of studies cannot be replicated or are the result of multiple testing of too many factors. We develop and estimate a Bayesian model of factor replication that leads to different conclusions. The majority of asset pricing factors (i) can be replicated; (ii) can be clustered into 13 themes, the majority of which are significant parts of the tangency portfolio; (iii) work out‐of‐sample in a new large data set covering 93 countries; and (iv) have evidence that is strengthened (not weakened) by the large number of observed factors.

We propose a new asset pricing framework in which all securities' signals predict each individual return. While the literature focuses on securities' own‐signal predictability, assuming equal strength across securities, our framework includes cross‐predictability—leading to three main results. First, we derive the optimal strategy in closed form. It consists of eigenvectors of a “prediction matrix,” which we call “principal portfolios.” Second, we decompose the problem into alpha and beta, yielding optimal strategies with, respectively, zero and positive factor exposure. Third, we provide a new test of asset pricing models. Empirically, principal portfolios deliver significant out‐of‐sample alphas to standard factors in several data sets.