Measuring the pricing error of the arbitrage pricing theory

This article provides an exact Bayesian framework for analyzingthe arbitrage pricing theory (APT). Based on the Gibbs sampler,we show how to obtain the exact posterior distributions forfunctions of interest in the factor model. In particular, wepropose a measure of the APT pricing deviations and obtain itsexact posterior distribution. Using monthly portfolio returnsgrouped by industry and market capitalization, we find thatthere is little improvement in reducing the pricing errors byincluding more factors beyond the first one.