Is the Average Mutual Fund Better than We Think? Analyzing Mutual Funds with a Bayesian Hierarchical Model

This paper utilizes a Bayesian hierarchical model to study the distribution of skill (alphas) among mutual funds. The hierarchical model specifies a probability distribution over all parameters and funds, making it possible to formally analyze the variability of alphas across funds. In addition, the hierarchical model allows one to explicitly model the variance-covariance structure of returns across funds and through time. Failure to correctly model this covariation leads to biased parameter estimates. In particular, standard 3- and 4-factor alphas are biased downward by 10 to 13 basis points per month. By expressing the model in a Bayesian framework and generating a posterior sample of model parameters, one can easily examine the statistical properties of many complex functions, yielding insights unavailable in a frequentist setting