The Distribution of Returns of Stock Prices

We perform a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets. We consider (i) the trades and quotes (TAQ) database, for which we analyze 40 million records for 1000 US companies for the 2-year period 1994–95, and (ii) the Center for Research and Security Prices (CRSP) database, for which we analyze 35 million daily records for approximately 16,000 companies in the 35-year period 1962–96. We study the probability distribution of returns over varying time scales — from 5 min up to 4 years. 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 powerlaw decay, characterized by an exponent α ≈ 3 — well outside the stable Lévy regime 0 < α < 2. For time scales greater than 16 days, we observe results consistent with a slow convergence to Gaussian behavior.