Tradable Factor Risk Premia and Oracle Tests of Asset Pricing Models

Tradable factor risk premia are defined by the negative factor covariance with the Stochastic Discount Factor projection on returns. They are robust to misspecification or weak identification in asset pricing models, and they are zero for any factor weakly correlated with returns. We propose a simple estimator of tradable factor risk premia that enjoys the Oracle Property, i.e., it performs as well as if the weak or useless factors were known. This estimator not only consistently removes such factors, but it also gives rise to reliable tests of asset pricing models. We study empirically a family of asset pricing models from the factor zoo and detect a robust subset of economically relevant and well-identified models, which are built out of factors with a nonzero tradable risk premium. Well-identified models feature a relatively low factor space dimension and some degree of misspecification, which harms the interpretation of other established notions of a factor risk premium in the literature.