Power Laws and Market Crashes : Empirical Laws on Bursting Bubbles

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Author(s)

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)~x^<-α>, with an exponent that moves in the range of 1.09 <α<1.27. Furthermore, we found that as the power-law exponents α approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst.

Journal

  • Progress of Theoretical Physics

    Progress of Theoretical Physics (162), 165-172, 2006-07-20

    Progress of Theoretical Physics

References:  17

  • <no title>

    BARRO R. J.

    Black Monday and the Future of Financial Markets, 1989

    Cited by (1)

  • <no title>

    USHITA U.

    Illusions of A big Power, Japan, 2002

    Cited by (1)

  • <no title>

    KINDLBERGER C. P.

    Manias, Panics and Crashes : A History of Financial Crises, 1989

    Cited by (1)

  • <no title>

    SHILLER R. J.

    Irrational Exuberance, 2000

    Cited by (1)

  • <no title>

    NOGUCHI Y.

    Economics of Bubbles, 1992

    Cited by (1)

  • <no title>

    PERKINS A. B.

    The Internet Bubble, 1999

    Cited by (1)

  • <no title>

    LOWENSTEIN Roger

    Origins of The Crash : The Great Bobble and Its Undoing, 2004

    Cited by (1)

  • <no title>

    SORNETTE D.

    Why Stock Markets Crash, 2003

    Cited by (1)

  • <no title>

    LILLO F.

    Phys. Rev. E 68, 016119, 2003

    Cited by (1)

  • <no title>

    LILLO F.

    Physica A 338, 125, 2004

    Cited by (1)

  • <no title>

    KAIZOJI T.

    Physica A 287, 493, 2000

    Cited by (1)

  • <no title>

    KAIZOJI T.

    Physica A 344, 138, 2004

    Cited by (1)

  • <no title>

    YAMANO T.

    Euro. Phys. J. B 38, 665, 2004

    Cited by (1)

  • <no title>

    ANDERSSON C.

    Phys. Rev. E 68, 036124, 2003

    Cited by (1)

  • <no title>

    COWELL F. A.

    Measuring Inequality, 1995

    Cited by (1)

  • <no title>

    SORNETTE D.

    J. de Phys. I 6, 167, 1996

    Cited by (1)

  • <no title>

    FEIGENBAUM J.

    Int. J. Mod. Phys. B 10, 3737, 1996

    Cited by (1)

Codes

  • NII Article ID (NAID)
    110004729517
  • NII NACSIS-CAT ID (NCID)
    AA00791466
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    03759687
  • NDL Article ID
    7929478
  • NDL Source Classification
    ZM35(科学技術--物理学)
  • NDL Call No.
    Z53-A468
  • Data Source
    CJP  NDL  NII-ELS  NDL-Digital 
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