We show that two important issues in empirical asset pricing—the presence of weak factors and the selection of test assets—are deeply connected. Since weak factors are those to which test assets have limited exposure, an appropriate selection of test assets can improve the strength of factors. Building on this insight, we introduce supervised principal component analysis (SPCA), a methodology that 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.
We reconsider trend-based predictability by employing flexible learning methods to identify price patterns that are highly predictive of returns, as opposed to testing predefined patterns like momentum or reversal. Our predictor data are stock-level price charts, allowing us to extract the most predictive price patterns using machine learning image analysis techniques. These patterns differ significantly from commonly analyzed trend signals, yield more accurate return predictions, enable more profitable investment strategies, and demonstrate robustness across specifications. Remarkably, they exhibit context independence, as short-term patterns perform well on longer time scales, and patterns learned from U.S. stocks prove effective in international markets.