Bayesian Inference and Portfolio Efficiency (Revised: 4-93)

Bayesian posterior distributions allow one to investigate the approximate efficiency of a portfolio without specifying the maximum degree of inefficiency a priori. The difference in expected returns between the value-weighted equity portfolio and an efficient portfolio of equal variance has a disperse posterior distribution, and our experiments confirm that such uncertainty is inherent in the sample sizes typically encountered in empirical studies. The maximum correlation between the value-weighted portfolio and an efficient portfolio has a posterior that is concentrated, often around low values, but this result appears to reflect nonlinearity in the function rather than information in the sample.