# Statistical Properties of Cross-Correlation in the Korean Stock Market

## Author Info

• Gabjin Oh
• Cheoljun Eom
• Fengzhong Wang
• Woo-Sung Jung
• H. Eugene Stanley
• Seunghwan Kim
Registered author(s):

## Abstract

We investigate the statistical properties of the 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 correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original 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 $\beta_{473}$ 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 $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly.

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File URL: http://arxiv.org/pdf/1010.2048

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1010.2048.

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 Length: Date of creation: Oct 2010 Date of revision: Publication status: Published in Eur. Phys. J. B 79, 55-60 (2011) Handle: RePEc:arx:papers:1010.2048 Contact details of provider: Web page: http://arxiv.org/

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