[A Bayesian approach is used to investigate a sample's information about a portfolio's degree of inefficiency. With standard diffuse priors, posterior distributions for measures of portfolio inefficiency can concentrate well away from values consistent with efficiency, even when the portfolio is exactly efficient in the sample. The data indicate that the NYSE-AMEX market portfolio is rather inefficient in the presence of a riskless asset, although this conclusion is justified only after an analysis using informative priors. Including a riskless asset significantly reduces any sample's ability to produce posterior distributions supporting small degrees of inefficiency.]

To provide a framework for judging the economic significance of departures from the arbitrage pricing theory, we adopt a utility-based metric based on optimal portfolio choices. This measure is examined using both predictive and posterior analysis. Our predictive analysis shows very large and economically significant departures from the model restrictions. However, the high level of parameter uncertainty suggests that we cannot conclusively either affirm or reject the APT. Our conclusions differ markedly from other studies which employ traditional significance-testing procedures and, in many instances, fail to reject the APT restrictions.

A Bayesian approach is used to investigate a sample’s information about a portfolio’s degree of inefficiency. With standard diffuse priors, posterior distributions for measures of portfolio inefficiency can concentrate well away from values consistent with efficiency, even when the portfolio is exactly efficient in the sample. The data indicate that the NYSE–AMEX market portfolio is rather inefficient in the presence of a riskless asset, although this conclusion is justified only after an analysis using informative priors. Including a riskless asset significantly reduces any sample’s ability to produce posterior distributions supporting small degrees of inefficiency.