Identifying Risk-Based Factors

Existing studies find that size, book-to-market, momentum and liquidity explain the crosssection of average returns, but debate continues over whether these variables are risk factors. We propose a new test of whether a candidate variable is a priced risk factor. Specifically, we test whether there is a relationship between the conditional mean and conditional variance of the return on the candidate variable’s factor-mimicking portfolio, and test whether risk, in the mean-variance frame-work, explains all of the return of a factor-mimicking portfolio. The test results on sizeand liquidity-based portfolios are consistent with these variables being risk-based factors. The results on the book-to-market based portfolio are consistent with book-to-market being a risk-based factor only in the 1963-2003 subsample. The results on the momentum factor are not consistent with a risk-based explanation in the mean-variance setting. JEL classification code: G12, G14