Paper Test Assets and Weak Factors

Weak factors—those to which test assets have limited exposure—pose a significant challenge and have been extensively studied in empirical asset pricing. Meanwhile, despite its empirical relevance, the selection of test assets has received comparatively less systematic study. We introduce supervised-PCA (SPCA), a novel methodology addressing both of these problems and bridging these seemingly unrelated literature strands. SPCA iterates supervised selection, principal-component estimation, and factor projection. It enables risk premia estimation and factor model diagnosis even when weak factors are present and not all factors are observed. We establish SPCA's asymptotic properties and showcase its empirical applications.

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