An empirical study of the tails of 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 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.Comment: 6 pages, 3 figure

The cause of universality in growth fluctuations

Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth fluctuations. The fluctuations display characteristic features, including double exponential scaling in the body of the distribution and power law scaling of the standard deviation as a function of size. To explain this we propose a remarkably simple additive replication model: At each step each individual is replaced by a new number of individuals drawn from the same replication distribution. If the replication distribution is sufficiently heavy tailed then the growth fluctuations are Levy distributed. We analyze the data from bird populations, firms, and mutual funds and show that our predictions match the data well, in several respects: Our theory results in a much better collapse of the individual distributions onto a single curve and also correctly predicts the scaling of the standard deviation with size. To illustrate how this can emerge from a collective microscopic dynamics we propose a model based on stochastic influence dynamics over a scale-free contact network and show that it produces results similar to those observed. We also extend the model to deal with correlations between individual elements. Our main conclusion is that the universality of growth fluctuations is driven by the additivity of growth processes and the action of the generalized central limit theorem.Comment: 18 pages, 4 figures, Supporting information provided with the source files

Epidemic spreading in evolving networks

A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to suppress epidemic spreading. In particular it is found that as in static networks, rewiring networks with degree distribution exponent $\gamma >3$ exhibit a threshold in the infection rate below which epidemics die out in the steady state. However the threshold is higher in the rewiring case. For $2<\gamma \leq 3$ no such threshold exists, but for small infection rate the steady state density of infected nodes (prevalence) is smaller for rewiring networks.Comment: 7 pages, 7 figure

Complex Phenomena in Social and Financial Systems: From Bird Population Growth to the Dynamics of the Mutual Fund Industry

This work explores different aspects of the statics and dynamics of the mutual fund industry. In addition, we answer a major question in the field of complex systems; the anomalous growth fluctuations observed for systems as diverse as breeding birds, city population and GDP. We study how much control is concentrated in the hands of the largest mutual funds by studying the size distribution empirically. We show that it indicates less concentration than, for example, personal income. We argue that the dominant economic factor that determines the size distribution is market efficiency and we show that the mutual fund industry can be described using a random entry, exit and growth process. Mutual funds face diminishing returns to scale as a result of convex trading costs yet there is no persistence nor a size dependence in their performance. To solve this puzzle we offer a new framework in which skillful profit maximizing fund managers compensate for decreasing performance by lowering their fees. We show that mutual fund behavior depends on size such that bigger funds charge lower fees and trade less frequently in more stocks. We present a reduced form model that is able to describe quantitatively this behavior. We conclude with an investigation of the growth of mutual funds due to investor funds flows. We show that funds exhibit the same unusual growth fluctuations that have been observed for phenomena as diverse as breeding bird populations, the size of U.S. firms, the GDP of individual countries and the scientific output of universities. To explain this we propose a remarkably simple additive replication model. To illustrate how this can emerge from a collective microscopic dynamics we propose a model based on stochastic influence dynamics over a scale-free contact network.</p

What drives mutual fund asset concentration?

Is the large influence that mutual funds assert on the U.S. financial system spread across many funds, or is it is concentrated in only a few? We argue that the dominant economic factor that determines this is market efficiency, which dictates that fund performance is size independent and fund growth is essentially random. The random process is characterized by entry, exit and growth. We present a new time-dependent solution for the standard equations used in the industrial organization literature and show that relaxation to the steady-state solution is extremely slow. Thus, even if these processes were stationary (which they are not), the steady-state solution, which is a very heavy-tailed power law, is not relevant. The distribution is instead well-approximated by a less heavy-tailed log-normal. We perform an empirical analysis of the growth of mutual funds, propose a new, more accurate size-dependent model, and show that it makes a good prediction of the empirically observed size distribution. While mutual funds are in many respects like other firms, market efficiency introduces effects that make their growth process distinctly different. Our work shows that a simple model based on market efficiency provides a good explanation of the concentration of assets, suggesting that other effects, such as transaction costs or the behavioral aspects of investor choice, play a smaller role.