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Unformatted text preview: Electronic copy of this paper is available at: http://ssrn.com/abstract=963510 1 Random Fractals and Turbulence in U.S. Bond Fund Flows Andrew Clark Lipper, a Reuters Company February 16, 2007 Evidence is found of fully developed turbulence in the increments of U.S. bond fund flows. These flow increments are found to be both anisotropic and locally isotropic. The response function of the market participants generating the flow turbulence is linked to both renormalization and scale invariance in physics and aggregation and representative agent theory in economics. In this paper we show that these two topics are closely related to each other and that the cluster of opinions represented by representative agents renormalization is fractal. The fractals from the renormalization are shown to be random. PACS: 47.27.eb, 47.27.E-, 47.27.ed, 89.65Gh 1. INTRODUCTION In 1996 Ghashghaie et al.  compared the probability density function (pdf) and scaling properties of the velocity increments in a turbulent fluid with the pdfs of returns in certain foreign exchange markets. The authors discovered a striking similarity between the two systems. From this evidence they proposed that financial markets present a cascade of volatilities from long to short time scales. This conjecture was criticized by Mantegna and Stanley [2 and 3] and others for two main reasons: 1. The financial returns Ghashghaie et al . studied had negligible autocorrelation, whereas changes in the velocity of turbulent particles have been shown to be highly correlated in an anti-persistent manner. 2. Turbulence is characterized by time-dependent pdf characteristics, and foreign exchange returns do not have these time-dependent pdf characteristics. In this paper we use the turbulence testing methods of Mantegna and Stanley to show that strong evidence exists for fully developed turbulence in a group of U.S. bond mutual fund flows. We also demonstrate that this turbulence is homogeneous and heterogeneous ( a la Lynch and Zumbach [4 and 5]). We also link representative agent theory from economics to the renormalization group and scaling and demonstrate the random fractal nature of the cluster of opinions that is generating the turbulence. 2. TURBULENCE A. DATA USED The net flows of a mutual fund are defined as the difference between share purchase and share redemption over a particular period. At Lipper 1 daily net flow data are available from April 2000 through September 2006. Using these daily data, we compute fund flows for a variety of periods (from one day to one year). 1 Lipper is a wholly owned subsidiary of Reuters that collects, analyzes, and publishes mutual fund, hedge fund, and separate account data on a global basis. Electronic copy of this paper is available at: http://ssrn.com/abstract=963510 2 Though there are more than 100 types of U.S. bond funds, here we examine the change in net flows of just six types: Corporate A-Rated Debt funds (funds that tend to invest in corporate paper with an investment grade of A or better), General U.S. Government funds, High Yield paper with an investment grade of A or better), General U....
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