Eur. Phys. J. B 79, 55-60 (2011)
https://doi.org/10.1140/epjb/e2010-90492-x

Statistical properties of cross-correlation in the Korean stock market

¹ Division of Business Administration, Chosun University, 501-759 Gwangju, Korea
² Division of Business Administration, Pusan National University, 609-735 Busan, Korea
³ Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, 02215, USA
⁴ Graduate Program for Technology and Innovation Managemant, Pohang University of Science and Technology, 790-784 Pohang, Korea
⁵ Department of Physics, Pohang University of Science and Technology, 790-784 Pohang, Korea
⁶ Asia Pacific Center for Theoretical Physics, 790-784 Pohang, Korea

Corresponding author: ^a wsjung@postech.ac.kr

Received: 29 June 2009
Revised: 24 September 2010
Published online: 22 November 2010

Abstract

We investigate the statistical properties of the cross-correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the cross-correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original cross-correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function with the portfolio risk σ for the original and filtered cross-correlation matrices are consistent with a power-law function, E(σ) ~ , with the exponent γ ~ 2.92 and those for Asian currency crisis decreases significantly.