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Inverse statistics in stock markets: Universality and idiosyncracy

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  • Zhou, Wei-Xing
  • Yuan, Wei-Kang

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 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.

Suggested Citation

  • Zhou, Wei-Xing & Yuan, Wei-Kang, 2005. "Inverse statistics in stock markets: Universality and idiosyncracy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 433-444.
    • Handle: RePEc:eee:phsmap:v:353:y:2005:i:c:p:433-444
    DOI: 10.1016/j.physa.2005.02.011
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    References listed on IDEAS

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    1. D. Sornette, 2003. "Critical Market Crashes," Papers cond-mat/0301543, arXiv.org.
    2. Ingve Simonsen & Mogens H. Jensen & Anders Johansen, 2002. "Optimal Investment Horizons," Papers cond-mat/0202352, arXiv.org.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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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