Interpreting Factor Models

We argue that tests of reduced-form factor models and horse races between characteristics and covariances cannot discriminate between alternative models of investor beliefs. Since asset returns have substantial commonality, absence of near-arbitrage opportunities implies that the stochastic discount factor can be represented as a function of a few dominant sources of return variation. As long as some arbitrageurs are present, this conclusion applies even in an economy in which all cross-sectional variation in expected returns is caused by sentiment. Sentiment-investor demand results in substantial mispricing only if arbitrageurs are exposed to factor risk when taking the other side of these trades.