This article provides an exact Bayesian frame­ work for analyzing the arbitrage pricing the­ ory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of interest in the factor modeL In particular, we propose a measure of the APT pricing deviations and obtain its exact posterior distribution. Using monthly portfolio returns grouped by industry and market capitalization, we find that there is little improvement in reduc­ ing the pricing errors by including more factors beyond the first one. As an important extension of the asset pricing model of Sharpe (1964) and Lintner (196 5), Ross (1976, 1977) derived the arbitrage pricing theory (APT) which addresses a fundamental problem in finance: to char­ acterize the expected return on a security. The APT implies that the expected return is approximately a