Risk premia from the cross-section of individual assets

We propose the continuous updating estimator (CUE) for estimating ex-post risk premia from large cross-sections of individual asset returns over limited time periods. We analyze its properties while also allowing for an unknown number of unobserved factors. The CUE then provides an estimator of its, so-called, pseudo-true value, the risk premia on the observed factors without assuming that they comprise all priced factors. We develop size-correct procedures for testing hypotheses on the estimand of the CUE, which are more precise than existing ones. The proposed methodology is used to examine risk factors widely analyzed using a small number of portfolios. Our findings are that market, size, and momentum factors carry largely positive risk premia, while many other factors much less so. Different factors therefore stand out in the cross-section of individual assets.