Inverse statistics in stock markets: Universality and idiosyncracy

TL;DR

This study demonstrates that the distribution of exit times in stock markets universally follows a power law with an exponent around 1.5, but the scaling of optimal investment horizons varies across markets and data frequencies.

Contribution

It provides extensive empirical evidence that the power-law distribution of exit times is universal, while revealing market-specific differences in investment horizon scaling.

Findings

Power-law distribution of exit times with exponent ~1.5 is universal.

Scaling of optimal investment horizon varies between developed and emerging markets.

Discrepancies in scaling are not due to record size differences.

Abstract

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.