Mimicking portfolios, economic risk premia, and tests of multi-beta models

We consider two formulations of the linear factor model (LFM) with nontraded factors. In the first formulation, LFM, risk premia and alphas are estimated by a cross-sectional regression of average returns on betas. In the second formulation, LFM*, the factors are replaced by their projections on the span of e,,cess returns, and risk premia and alphas are estimated by time series regressions. We compare the two formulations and study the small-sample properties of estimates and test statistics. We conclude that the LFM* formulation should be considered in addition to, or even instead of, the more traditional LFM formulation.