  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 < \alpha < 1.27 $. Furthermore, we found that as the power-law
exponents $ \alpha $ approached unity, the bubbles collapsed. This suggests
that Zipf's law for stock prices is a sign that bubbles are going to burst.
  PACS: 89.65.Gh
