Statistical Regularities of Equity Market Activity

Equity activity is an essential topic for financial market studies. To explore its statistical regularities, we comprehensively examine the trading value, a measure of the equity activity, of the 3314 most-traded stocks in the U.S. equity market and find that (i) the trading values follow a log-normal distribution; (ii) the standard deviation of the growth rate of the trading value obeys a power-law with the initial trading value, and the power-law exponent beta=0.14. Remarkably, both features hold for a wide range of sampling intervals, from 5 minutes to 20 trading days. Further, we show that all the 3314 stocks have long-term correlations, and their Hurst exponents H follow a normal distribution. Furthermore, we find that the Hurst exponent depends on the size of the company. We also show that the relation between the scaling in the growth rate and the long-term correlation is consistent with beta=1-H, similar to that found recently on human interaction activity by Rybski and collaborators.