The probability distribution of stock price changes is studied by anal
ysing a database (the Trades and Quotes Database) documenting every tr
ade for all stocks in three major US stock markets, for the two year p
eriod January 1994 - December 1995. A sample of 40 million data points
is extracted, which is substantially larger than studied hitherto. We
find an asymptotic power-law behavior for the cumulative distribution
with an exponent alpha approximate to 3, well outside the Levy regime
(0 < alpha < 2).