Researchers from the Federal Reserve of Bank of Atlanta estimated mutual fund skill by letting the population distribution be entirely unknown, estimating it, and using it to infer the skill level of the funds. They do this by modeling the unknown population distribution with a Bayesian, nonparametric, hierarchical prior.
This nonparametric prior is an infinite mixture of normals with unknown mixture weights, locations, scales, and mixture order. They infer these mixture unknowns with an unsupervised learning approach where they partition the panel of mutual funds into a finite number of groups (mixture clusters) where the members of a group all have the same average stock-picking ability and variability (mixture location and scale).
They leverage these random partitions to resolve the uncertainty in the skill level of a member fund by pooling the information of the group’s other funds. Sharing the group’s information is especially important in resolving the uncertainty around the skill level of newer funds with short performance histories. Partitioning the funds also eliminates the global shrinkage issues that plague parametric hierarchical priors.
Extraordinarily skilled funds are allowed to have their own group and not have their estimate of skill shrunk towards the idea of judging a fund by the company it keeps. However, our approach is unsupervised and, hence, does not use any information about a fund beyond its return history. Using return data from the entire actively managed, US domestic equity fund, industry, they find the population distribution of skill to be fat-tailed, slightly skewed towards better stock-picking ability, and having three modes.
These three modes are i) a minor mode where skill is extraordinarily high, ii) a secondary mode where funds lose money for its investors, and iii) a primary mode at a skill level where funds cover the average fees charged investors. As a result of our nonparametric population distribution, there is a greater chance a fund will be extraordinarily skilled relative to a normally distributed population. They also see that the exceptionally skilled and unskilled funds uncovered with the nonparametric population distribution look rather ordinary under a normal population distribution.
With the team’s Bayesian nonparametric learning approach, they find the posterior population distribution for the actively manage mutual fund industry to be fat-tailed, multi-modal, and skewed towards higher levels of skill. The population’s primary mode is 1.8% per year, followed by a secondary mode at −0.65%, and lastly, a minor mode of 6%.
As a result of the location for the minor mode and the skewness of the population distribution towards 37 higher skilled funds, a fund for which we have no information about has a greater chance of being skilled than previously thought. Under a parametric, normal, hierarchical, prior for alpha, the probability of finding an extraordinarily skilled fund is pushed back towards the primary mode; i.e., back toward a typical fund’s alpha.
In comparison to when they treated skill idiosyncratically, the nonparametric approach finds fewer skilled and unskilled funds. Out of 5,136 funds, they find 22 (50) funds have a 95% chance of its alpha (not) exceeding the average fee charged by a fund of 1.5%. Each of these exceptional funds has a unique posterior distribution relative to the population distribution where their likelihood function drives a wedge between its posterior for alpha and the posterior population distribution. Researchers found these highly skilled funds to be truly skilled and not just lucky.
The posterior mean alphas were similar under both our nonparametric prior and the idiosyncratic priors, whereas, many of the funds that had larger posterior means under the idiosyncratic prior lacked the empirical performance to drive a wedge between their posterior and the nonparametric population distribution.
Learning the cross-sectional distribution of mutual fund skill with the Bayesian nonparametric approach can be applied to other related questions. For instance, any finance or economic problem where one is inferring a parameter and estimating the cross-sectional distribution of the parametric can be analyzed nonparametrically. For example, one can estimate how the multiple risk-factors’ coefficients of an asset pricing model are distributed across different assets. The research team is currently investigating this and other similar types of research ideas with the Bayesian nonparametric learning approach.