The existing literature documents a number of cross-sectional stock return anomalies. This article examines how pervasive these anomalies are and whether factor models provide valid inferences on anomalous returns. First, by shrinking the stock space along the dimension of a predictive variable, we show that the book-to-market ratio (BM) and net stock issues effects are pervasive, whereas the size, momentum, and illiquidity effects are driven mainly by stocks on the long side, and the idiosyncratic volatility, accrual, capital expenditure, and sales growth effects mainly by stocks on the short side. Second, we provide evidence that commonly used factor models have limited explanatory power of stock returns. Restricting to stock samples where the four-factor model adequately explains the size, BM, and momentum effects, we show that only the idiosyncratic volatility, accrual, and net stock issues effects remain significant.