  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
time follows a power law $p(\tau_\rho) \sim \tau\rho^{-\alpha}$ with $\alpha
\approx 1.5$ at large $\tau_\rho$ and the optimal investment horizon
$\tau_\rho^*$ scales as $\rho^\gamma$ [1-3]. We have performed an extensive
analysis based on unfiltered daily indices and stock prices and high-frequency
(5-min) records as well in the markets all over the world. Our analysis
confirms that the power-law distribution of the exit time 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 exponent. Specifically, $\gamma \approx 1.5$ for
the daily data in most of the developed stock markets and the five-minute
high-frequency data, while the $\gamma$ values of the daily indexes and stock
prices in emerging markets are significantly less than 1.5. We show that there
is of little chance that this discrepancy in $\gamma$ stems from the difference
of record sizes in the two kinds of stock markets.
