An empirical study of the tails of mutual fund size

TL;DR

This study empirically analyzes the distribution of mutual fund sizes, finding that their tail behavior is better described by a log-normal distribution than a power law, indicating less concentration and perpetual out-of-equilibrium dynamics.

Contribution

It provides the first comprehensive empirical evidence that mutual fund sizes follow a log-normal distribution, challenging previous theories of power law tails.

Findings

Tail is better described by a log-normal distribution

Contradicts theories of power law tails in trading volume

Distribution remains perpetually out of equilibrium

Abstract

The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively discussed in terms of the tail behavior of the mutual fund size distribution. We study the distribution empirically and show that the tail is much better described by a log-normal than a power law, indicating less concentration than, for example, personal income. The results are highly statistically significant and are consistent across fifteen years. This contradicts a recent theory concerning the origin of the power law tails of the trading volume distribution. Based on the analysis in a companion paper, the log-normality is to be expected, and indicates that the distribution of mutual funds remains perpetually out of equilibrium.