Power law for ensembles of stock prices

TL;DR

This study analyzes the statistical distribution of stock prices in the Tokyo Stock Exchange, revealing that their ensemble follows a power-law distribution with a specific exponent range.

Contribution

It provides a quantitative analysis of the power-law behavior in stock price ensembles, which was not previously characterized in this detail.

Findings

The tail of the distribution follows a power-law with exponent between 1.7 and 2.2.

The power-law distribution accurately describes the ensemble's tail behavior.

The exponent varies over the observed period.

Abstract

In this paper we quantitatively investigate the statistical properties of an ensemble of {\it stock prices}. We selected 1200 stocks traded in the Tokyo Stock Exchange and formed a statistical ensemble of daily stock prices for each trading day in the 5 year period from January 4, 1988 to December 30, 1992. We found that the tail of the complementary cumulative distribution function of the ensembles is accurately described by a power-law distribution with an exponent that moves in the range of $ 1.7 < \alpha < 2.2 $.