Tracking scaling effects in mutual funds return time series

Data coming from many fields of science and technology, ranging from hydrology through network traffic to economics, show long range dependence and self-similarity. These properties result in significant consequences and usually require a redefinition of well grounded assumptions and theories. In the case of financial markets, the classical models which often assume that the dynamics of economic time series is described by the random walk, may incorrectly evaluate the investment risk. Therefore, it is important to understand the dynamics of returns generated by different financial instruments. In this work, we tested fifteen different mutual funds investing in stocks through a stock exchange. We found that the distribution of funds daily returns cannot be described by the random walk. Furthermore, using several different method, we provide empirical evidence, that the daily returns of the analysed funds may exhibit long-range correlations and fractal behaviour.