Journal of the Korean Physical Society

pISSN 0374-4884 eISSN 1976-8524


Brief Reports

J. Korean Phy. Soc. 2005; 47(1): 171

Published online July 15, 2005

Copyright © The Korean Physical Society.

Zipf's Law Distributions in Korean Financial Markets

J. S. Choi, Kyungsik Kim, S. M. Yoon, K. H. Chang and C. Christopher Lee


We investigate the rank distribution and the cumulative probability for stock prices, and the probability density of price returns for stocks traded the Korean Stock Exchange (KSE) and the Korean Securities Dealers Automated Quotations (KOSDAQ) market. We show that the upper tails of the distributions can be fitted with a power-law and find that the rank distribution scales approximately as a power law with exponents $alpha = -0.99$ ($pightarrow$small) and $-1.33$ ($pightarrow$large) for the KSE and $alpha~=-1.31$ for the KOSDAQ. These values are similar to those of stock prices traded on the Tokyo Stock Exchange (TSE). In addition, the cumulative probability distribution follows a power law with the scaling exponent $eta = -1.23$ (KSE) or $-1.45$ (KOSDAQ). In particular, the evidence shows that the probability density of normalized price returns for two kinds of assets almost has the form of an exponential function, which is similar to the result for the TSE and the New York Stock Exchange (NYSE).