Scaling Law for the Distribution of Fluctuations of Share Volume

TL;DR

This study uncovers power-law scaling behaviors in share volume fluctuations across a large dataset of Tokyo Stock Exchange companies, revealing stable Levy domain characteristics and Zipf's law adherence in distribution exponents.

Contribution

It is the first comprehensive analysis demonstrating power-law decay in share volume fluctuations across multiple companies over several decades.

Findings

Cumulative distributions follow power-law decay.

Most distributions have exponents within the stable Levy domain.

Over 35% of distributions approximate Zipf's law.

Abstract

We show power-scaling behaviors for fluctuations in share volume, which no other studies have so far done. After analyzing a database of the daily transactions for all securities listed on the Tokyo Stock Exchange, we selected 1050 large companies that each had an unbroken series of daily trading activity from January 1975 to January 2002. We found that the cumulative distributions of daily fluctuations in share volumes can be well described by a power-law decay, and that the cumulative distributions for almost all of the companies can be characterized by an exponent within the stable Levy domain. Furthermore, more than 35 percent of the cumulative distributions can be well approximated by Zipf's law, that is, the cumulative distributions have an exponent close to unity.