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Power laws and market crashes

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  • Taisei Kaizoji

Abstract

In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and its bursting in the Japanese stock market. We found that the tail of the complementary cumulative distribution function of the ensemble of stock prices in the high value of the price is well described by a power-law distribution, $ P(S>x) \sim x^{-\alpha} $, with an exponent that moves in the range of $ 1.09

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  • Taisei Kaizoji, 2006. "Power laws and market crashes," Papers physics/0603138, arXiv.org.
    • Handle: RePEc:arx:papers:physics/0603138
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    Cited by:

    1. Blackwell, Calvin, 2018. "Power Laws in Real Estate Prices? Some Evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 69(C), pages 90-98.
    2. Mizuno, Takayuki & Ohnishi, Takaaki & Watanabe, Tsutomu, 2017. "Stock market bubble detection based on the price dispersion among similar listed Firms," HIT-REFINED Working Paper Series 67, Institute of Economic Research, Hitotsubashi University.
    3. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2019. "Detecting stock market bubbles based on the cross-sectional dispersion of stock prices," Working Papers on Central Bank Communication 010, University of Tokyo, Graduate School of Economics.
    4. Borland, Lisa, 2016. "Exploring the dynamics of financial markets: from stock prices to strategy returns," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 59-74.
    5. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2016. "Power laws in market capitalization during the Dot-com and Shanghai bubble periods," CARF F-Series CARF-F-392, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Tabak, B.M. & Takami, M.Y. & Cajueiro, D.O. & Petitinga, A., 2009. "Quantifying price fluctuations in the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(1), pages 59-62.
    7. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2019. "Detecting stock market bubbles based on the cross-sectional dispersion of stock prices," CARF F-Series CARF-F-463, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2016. "Power laws in market capitalization during the Dot-com and Shanghai bubble periods," UTokyo Price Project Working Paper Series 070, University of Tokyo, Graduate School of Economics.
    9. T. Kaizoji, 2006. "A precursor of market crashes: Empirical laws of Japan's internet bubble," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 123-127, March.
    10. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2016. "Power laws in market capitalization during the dot-com and Shanghai bubble periods," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 445-454, December.
    11. Lisa Borland & Yoan Hassid, 2010. "Market panic on different time-scales," Papers 1010.4917, arXiv.org.
    12. Mizuno, Takayuki & Ohnishi, Takaaki & Watanabe, Tsutomu, 2016. "Power law in market capitalization during Dot-com and Shanghai bubble periods," HIT-REFINED Working Paper Series 60, Institute of Economic Research, Hitotsubashi University.

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