Arbitrage Pricing with Estimation Risk

This paper considers the Arbitrage Pricing Theory when investors have incomplete information on the parameters generating asset returns. Each asset in the economy may have a different amount of information available on it. Bayesian investors use their prior beliefs in conjunction with the total available information to assign an expected return and a set of factor betas to each asset. The assigned expected returns are shown to be linear in their associated factor betas. However, the factor betas and prices of assets differ from those under complete information. Specifically, risky assets with high (low) information are priced relatively higher (lower). On the other hand, factor betas of high (low) information assets are relatively lower (higher). The analysis has econometric implications for testing the APT. In this paper's framework, maximum likelihood estimates of factor betas, which are based on normality assumptions, are too high (low) for high (low) information assets. In addition, sequentially increasing the sample size by adding new securities to a factor analysis procedure can result in the detection of apparent additional priced factors when they do not really exist.