Working Paper, Federal Reserve Bank of Atlanta 2005-4
This paper considers two alternative formulations of the linear factor model (LFM) with nontraded factors. The first formulation is the traditional LFM, where the estimation of risk premia and alphas is performed by means of a cross-sectional regression of average returns on betas. The second formulation (LFM*) replaces the factors with their projections on the span of excess returns. This formulation requires only time-series regressions for the estimation of risk premia and alphas. We compare the theoretical properties of the two approaches and study the small-sample properties of estimates and test statistics. Our results show that when estimating risk premia and testing multi-beta models, the LFM* formulation should be considered in addition to, or even instead of, the more traditional LFM formulation.