Scaling of the distribution of price fluctuations of individual companies

We present a phenomenological study of stock price fluctuations of individu al companies. We systematically analyze two different databases covering se curities from the three major U.S. stock markets: (a) the New York Stock Ex change, (b) the American Stock Exchange, and (c) the National Association o f Securities Dealers Automated Quotation stock market. Specifically, we con sider (i) the trades and quotes database, for which we analyze 40 million r ecords for 1000 U.S. companies for the 2-yr period 1994-95; and (ii) the Ce nter for Research and Security Prices database, for which we analyze 35 mil lion daily records for approximately 16000 companies in the 35-yr period 19 62-96. We study the probability distribution of returns over varying time s cales Delta t, where Delta t varies by a factor of approximate to 10(5), fr om 5 min up to approximate to 4 yr. For time scales from 5 min up to approx imately 16 days, we find that the tails of the distributions can be well de scribed by a power-law decay, characterized by an exponent 2.5<proportional to<4, well outside the stable Levy regime 0<alpha<2. For time scales Delta t much greater than(Delta t)(x)approximate to 16 days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze th e role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indice s. [S1063-651X(99)11412-0].