Security factors as linear combinations of economic variables

A new framework is proposed to find the best linear combinations of economic variables that optimally forecast security factors. In particular, we obtain such combinations from Chen et al. (Journal of Business 59, 383-403, 1986) five economic variables, and obtain a new GMM test for the APT which is more robust than existing tests. In addition, by using Fama and French's (1993) five factors, we test whether fewer factors are sufficient to explain the average returns on 25 stock portfolios formed on size and book-to-market. While inconclusive in-sample, a three-factor model appears to perform better out-of-sample than both four- and five-factor models.