What determines mutual fund size?

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 can be 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 better described by a log-normal than a power law, indicating less concentration than, for example, personal wealth. We postulate that the reasons for this stem from market efficiency and the stochastic nature of fund returns; they otherwise have very little to do with investor choice. To demonstrate this we study mutual fund entry, exit and growth empirically and develop a stochastic model. Under simplifying assumptions we obtain a time-dependent analytic solution. The distribution evolves from a log-normal into a power law only over long time scales, suggesting that log-normality comes about because the industry is still young. Numerical solutions under more realistic conditions support this conclusion and give good agreement with the data. Our study shows that, while mutual funds behave in many respects like other firms, there some respects in which they are quite unusual. Surprisingly, it appears that transaction costs and investor choice play only a minor role in determining fund size.