Zipf's Law Distributions for Korean Stock Prices

TL;DR

This paper analyzes stock price distributions in Korean markets, finding they follow Zipf's law and power laws, with probability densities resembling exponential functions, similar to other major stock exchanges.

Contribution

It demonstrates that Korean stock prices follow Zipf's law and power law distributions, extending the universality of these statistical patterns to the KSE and KOSDAQ markets.

Findings

Rank distribution aligns with Zipf's law with specific exponents.

Cumulative probability follows a power law with identified exponents.

Probability density of normalized returns resembles an exponential function.

Abstract

This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent approximately with the Zipf's law with exponent $\alpha = -1.00$ (KSE) and -1.31 (KOSDAQ), similar that of stock prices traded on the TSE. In addition, the cumulative probability distribution follows a power law with scaling exponent $\beta = -1.23$ (KSE) and -1.45 (KOSDAQ). In particular, the evidence displays that the probability density of normalized price returns for two kinds of assets almost has the form of an exponential function, similar to the result in the TSE and the NYSE.