Arbitrage pricing restrictions and the predictability of stock returns by statistical factor analysis

Abstract

In standard principal components estimation of the APT, the factors are obtained without employing the restrictions on mean returns implied by the APT. We modify the principal components methodology to allow mean returns to reflect the theoretical restrictions up to any level of accuracy and generate optimal constrained APT factors from the eigenvectors of a suitably modified covariance matrix. With the 30 industry portfolios as test assets, the resulting risk factors predict returns hedged for systematic risk better out of sample than the standard CAPM, Fama-French, and Carhart asset pricing models and better than conventional principal component factors. Valuation Insight: The technical approach developed in this paper allows for a better estimate of the proper cost of capital to be used in valuation. By incorporating restrictions implied by arbitrage, the revised estimates of the cost of capital are empirically better in the sense of forecasting out of sample the returns of the firm to be valued.