Bayesian Nonparametric Learning of How Skill Is Distributed across the Mutual Fund Industry

In this paper, we use Bayesian nonparametric learning to estimate the skill of actively managed mutual funds and also to estimate the population distribution for this skill. A nonparametric hierarchical prior, where the hyperprior distribution is unknown and modeled with a Dirichlet process prior, is used for the skill parameter, with its posterior predictive distribution being an estimate of the population distribution. Our nonparametric approach is equivalent to an infinitely ordered mixture of normals where we resolve the uncertainty in the mixture order by partitioning the funds into groups according to the group's average ability and variability. Applying our Bayesian nonparametric learning approach to a panel of actively managed, domestic equity funds, we find the population distribution of skill to be fat-tailed, skewed towards higher levels of performance. We also find that it has three distinct modes: a primary mode where the average ability covers the average fees charged by funds, a secondary mode at a performance level where a fund loses money for its investors, and lastly, a minor mode at an exceptionally high skill level.