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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.
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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.
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Network theory proved recently to be useful in the quantification of many properties of financial systems. The analysis of the structure of investment portfolios is a major application since their eventual correlation and overlap impact the actual risk diversification by individual investors. We investigate the bipartite network of US mutual fund portfolios and their assets. We follow its evolution during the Global Financial Crisis and analyse the interplay between diversification, as understood in classical portfolio theory, and similarity of the investments of different funds. We show that, on average, portfolios have become more diversified and less similar during the crisis. However, we also find that large overlap is far more likely than expected from models of random allocation of investments. This indicates the existence of strong correlations between fund portfolio strategies. We introduce a simplified model of propagation of financial shocks, that we exploit to show that a systemic risk component origins from the similarity of portfolios. The network is still vulnerable after crisis because of this effect, despite the increase in the diversification of portfolios. Our results indicate that diversification may even increase systemic risk when funds diversify in the same way. Diversification and similarity can play antagonistic roles and the trade-off between the two should be taken into account to properly assess systemic risk.
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We apply the knockoff procedure to factor selection in finance. By building fake but realistic factors, this procedure makes it possible to control the fraction of false discovery in a given set of factors. To show its versatility, we apply it to fund replication and to the inference of explanatory and prediction networks.
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