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.