Time Evolution of The Mutual Fund Size Distribution

We investigate the size distribution of equity mutual funds. We show that the heavy tail of the upper size distribution of equity funds is best described by a log-normal as opposed to a power law. The size of an equity fund was taken to be the real dollar value of the Total Assets Managed by the equity fund as given in the CRSP database. Previous analysis of the mutual fund industry treated the process as stationary without identifying the time scales in which the process converges. Such a treatment predicts a stationary size distribution with a power law tail that was argued to follow Zipf’s law. Using a stochastic growth model, we argue that the mutual fund ecology is young and as such it is in a transient state and given enough time it will converge to a steady state in which the large tail of the distribution follows a power law. We construct a stochastic growth model for the ecology of mutual funds in which the evolution is governed by three processes; growth, modeled as a Gibrat process, creation and annihilation of funds. We provide an analytical solution to the model which allows us to identify the time scales of the evolution process and treat the process as time dependent. Our model can be made more realistic by modifying the growth process with the empirical observations that the variance and drift of the growth process are size dependent. Using simulations, we show that the modified model does an excellent job of describing the upper tail of the size distribution. As was argued by Herbert Simon, we show by describing the distribution using a random process that investor choice is not of fundamental importance for the description of all of the observable attributes of the economy.