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Inverse statistics in stock markets: Universality and idiosyncracy

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  • Wei-Xing Zhou

    (ECUST)

  • Wei-Kang Yuan

    (ECUST)

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.

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  • Wei-Xing Zhou & Wei-Kang Yuan, 2004. "Inverse statistics in stock markets: Universality and idiosyncracy," Papers cond-mat/0410225, arXiv.org, revised Oct 2004.
  • Handle: RePEc:arx:papers:cond-mat/0410225
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    1. Ren, Fei & Guo, Liang & Zhou, Wei-Xing, 2009. "Statistical properties of volatility return intervals of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 881-890.
    2. Mu, Guo-Hua & Zhou, Wei-Xing, 2008. "Relaxation dynamics of aftershocks after large volatility shocks in the SSEC index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5211-5218.
    3. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractality in stock indexes: Fact or Fiction?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3605-3614.
    4. Łukasz Bil & Dariusz Grech & Magdalena Zienowicz, 2017. "Asymmetry of price returns—Analysis and perspectives from a non-extensive statistical physics point of view," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-24, November.

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