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.
JEL classification: G12
Key words: mimicking portfolios, economic risk premia, multi-beta models
The authors thank Raymond Kan, Wayne Ferson, Jay Shanken, and Dan Waggoner for several useful conversations and comments. The authors also thank seminar participants at Boston College, the 1999 Meetings of the Society for Computational Economics, the 2000 Meetings of the European Finance Association, and the 2004 All Georgia Finance Conference for useful comments. An earlier, related working paper circulated in 1999 under the title “Minimum-variance Kernels, Economic Risk Premia, and Tests of Multi-beta Models.”
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