Anatomy of the Market: A Body-Tail Test of Factor Models

Abstract: I ask whether a factor model that prices the aggregate market also prices the market's internal components. I construct a CRSP investible market portfolio and split it into size-ranked body and tail legs that exactly recombine to the market. All models pass the aggregate market test. Yet q5 leaves systematic, offsetting alphas: negative in the body and positive in the tail. Random splits remove the rejection. The evidence suggests that the market can appear priced because internal pricing errors cancel.