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 τρ, defined as the waiting time needed to obtain a certain increase ρ in the price, follows a power law p(τρ)∼τρ-α with α≈1.5 for large τρ and the optimal investment horizon τρ* scales as ργ when ρ 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 α=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, γ≈1.5 for the daily data in most of the developed stock markets and the 5-min high-frequency data, while the γ 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 γ is due to the difference in sample sizes of the two kinds of stock markets.