Inverse statistics in stock markets: Universality and idiosyncracy

Investigations of inverse statistics (a concept borrowed from turbulence) in stock markets, exemplified with filtered Dow Jones Industrial Average, S&P 500, and NASDAQ, have uncovered a novel stylized fact that the distribution of exit times T, defined as the waiting time needed to obtain a certain increase rho in the price, follows a power law rho(tau(rho))similar to tau(-alpha)(rho) with alpha approximate to 1.5 for large tau(rho) and the optimal investment horizon tau(rho) scales as rho(gamma) when rho is not too small (Eur. Phys. J. B 27 (2002) 583-586; Physica A 324 (2003) 338-343; Int. J. Mod. Phys. B 17 (2003) 4003-4012). We have performed extensive analyses based on unfiltered daily indices and stock prices as well as high-frequency (5-min) records in numerous stock markets all over the world. Our analysis confirms that the power-law distribution of exit times with an exponent of about alpha = 1.5 is universal for all the data sets analyzed. In addition, all data sets show that the power-law scaling in the optimal investment horizon holds, but with idiosyncratic exponents. Specifically, gamma approximate to 1.5 for the daily data in most of the developed stock markets and the 5-min high-frequency data, while the 7 values for the daily indexes and stock prices in emerging markets are significantly less than 1.5. We show that there is little chance that the discrepancy in gamma is due to the difference in sample sizes of the two kinds of stock markets. (c) 2005 Elsevier B.V. All rights reserved.