Bayesian Nonparametric Learning of How Skill Is Distributed across the Mutual Fund Industry
Mark Fisher, Mark J. Jensen, and Paula Tkac
Working Paper 2019-03
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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.
JEL classification: G11 ,C11, C14
Key words: Bayesian nonparametrics, mutual funds, unsupervised learning
The authors thank Vikas Agarwal, Wayne Ferson, Kris Gerardi, Siva Nathan, Jay Shanken. and the conference participants at the 10th Annual All Georgia Finance Conference, the 2014 Southern Finance Meetings, the Economics, Finance, and Business Section of ISBA Bayes 250, the 2014 Bayesian Workshop of the Remini Centre of Economic Analysis, the 2015 NBER-NSF Seminar on Bayesian Inference in Econometrics and Statistics, the 2015 European Seminar on Bayesian Econometrics, the 2017 ISBA Conference on Bayesian Nonparametric, the 2018 Workshop on Bayesian Methods in Finance held at the ESSEC Business School, and the department members at the Institution of Statistics and Mathematics at Vienna University of Business and Economics, the DeGroote School of Business at McMaster University, Clemson University, the University of North Carolina--Charlotte, Queen Mary--University of London, and the University of Montreal for their helpful comments and suggestions. The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’ responsibility.
Please address questions regarding content to Mark Fisher, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street NE, Atlanta, GA 30309-4470, 404-498-8757, firstname.lastname@example.org; Mark J. Jensen, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street NE, Atlanta, GA 30309-4470, 404-498-8019, email@example.com; or Paula Tkac, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street NE, Atlanta, GA 30309-4470, 404-498-8813, firstname.lastname@example.org.
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