Scaling of the distribution of price fluctuations of individual companies

TL;DR

This study analyzes the distribution of stock price fluctuations across various time scales and markets, revealing power-law tails with an exponent around 3 for short to medium durations and a slow convergence to Gaussian behavior over longer periods.

Contribution

It provides a comprehensive empirical analysis of return distributions over a wide range of time scales and markets, highlighting the power-law behavior and correlation effects.

Findings

Power-law tails with exponent ~3 for time scales up to 16 days

Slow convergence to Gaussian distribution for longer time scales

Cross correlations influence market index return distributions

Abstract

We present 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: (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 US companies for the 2-year 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-year period 1962--96. We study the probability distribution of returns over varying time scales $\Delta t$, where $\Delta t$ varies by a factor of $\approx 10^5$---from 5 min up to $\approx$ 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 power-law decay, characterized by an exponent $\alpha \approx 3$ ---well outside the stable L\'evy regime $0 < \alpha < 2$. For time scales $\Delta t \gg (\Delta t)_{\times} \approx 16 $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.