Scaling of the distribution of price fluctuations of individual companies

We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major U.S. stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider (i) the trades and quotes database, for which we analyze 40 million records for 1000 U.S. companies for the 2-yr period 1994–95; and (ii) the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16 000 companies in the 35-yr period 1962–96. We study the probability distribution of returns over varying time scales [Formula Presented] where [Formula Presented] varies by a factor of [Formula Presented] from 5 min up to [Formula Presented] yr. For time scales from 5 min up to approximately 16 days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent [Formula Presented] well outside the stable Lévy regime [Formula Presented] For time scales [Formula Presented] days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices.