Test Assets and Weak Factors

Stefano Giglio, Dacheng Xiu, Dake Zhang

Abstract: Weak factors – factors to which test assets are only weakly exposed – represent an important concern in empirical asset pricing. We propose a novel methodology to address this issue, supervised-PCA (SPCA). SPCA iterates a supervised asset selection step, in which only informative test assets are selected, and a principal-component estimation step to extract factors. It can be used to estimate risk premia and diagnose factor models even when weak factors are present and not all true factors are observed. We derive SPCA’s asymptotic properties and illustrate several empirical applications of our methodology.