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.