Bayesian Performance Evaluation

This paper proposes a Bayesian method of performance evaluation for investment managers. We begin with a flexible set of prior beliefs that can be elicited without any reference to probability distributions or their parameters. We then combine these prior beliefs with a general multi-factor model and derive an analytical solution for the posterior expectation of alpha', the intercept term from the model. This solution can be computed using only a few extra steps beyond maximum likelihood estimation and does not require a comprehensive or bias-free database. We then apply our methodology to a sample of domestic diversified equity mutual funds and ask what prior beliefs would imply zero investment in active managers?' To justify such a zero-investment strategy, we find that a mean-variance investor would need to believe that less than 1 out of every 100,000 managers has an expected alpha greater than 25 basis points per month. Overall, our analysis suggests that even when the average manager is expected to underperform passive benchmarks, it requires very strong prior beliefs to imply zero investment in managers with the best past performance.