Growth fluctuations and market efficiency
speaker: Doyne Farmer (Santa Fe Institute and LUISS, Rome)abstract: Firms, bird populations, output of scientific papers by universities, GDP of countries, and flow of money in and out of mutual funds, and several other systems have now been shown to show interesting anaomalous behavior in their growth fluctuations. This includes an hypothesized Laplacian (double exponential) distribution of fluctuations and a power law relationship for the standard deviation of growth fluctuations as a function of size. We present a very simple additive replication model for growth, and show that under the central limit theorem it leads to a Levy stable distribution. This fits the data very well in fact, under closer examination for the data for birds, firms, and mutual funds, we show that the purported Laplacian is well fit by a Levy distribution, and that the properties of the Levy give a good prediction for the standard deviation vs. size. In the second part of my talk I will discuss the distribution of firm sizes in general and mutual funds in particular. Based on the stochastic equations for entry and exit, the long term evolution of size depends on the asymptotic behavior of growth fluctuations as a function of size. Mutual funds are different than other firms in that market efficiency makes the asymptotic growth independent of size. This implies a long-term evolution to a power law. This takes a long time, however, and in fact because of the size-dependent diffusion discussed in the previous paragraph, it takes more than a century. In the meantime the distribution is well-approximated by a log normal. For other types of firms, where market efficiency is not a reasonable approximation, the asymptotic growth rate fluctuations go to zero and the limiting behavior is a stretched exponential (and the behavior for shorter time scales is still a log-normal). Finally, for mutual funds I will discuss the question of the role of transaction costs in determining the size distribution, and attempt to resolve the debate between Fama and Berk and Green by presenting an alternative hypothesis about how money flows in and out of funds.
timetable:
Sat 3 Oct, 10:00 - 11:00, Aula 3
documents:
farmer
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