Sequential Tests of the Arbitrage Pricing Theory: A Comparison of Principal Components and Maximum Likelihood Factors.

The authors examine the cross-sectional pricing equation of the arbitrage pricing theory using the elements of eigenvectors and the maximum likelihood factor loadings of the covariance matrix of returns as measures of risk. The results indicate that, for data assumed stationary over twenty years, the first vector is a surprisingly good measure of risk when compared with either a one-factor or a five-factor model or a five-vector model. The authors conclude that principal components analysis may be preferred to factor analysis in some circumstances. Copyright 1990 by American Finance Association.