Economy – Quantitative Finance – Statistical Finance
Scientific paper
2010-10-11
Eur. Phys. J. B 79, 55-60 (2011)
Economy
Quantitative Finance
Statistical Finance
Scientific paper
10.1140/epjb/e2010-90492-x
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.
Eom Cheoljun
Jung Woo-Sung
Kim Seunghwan
Oh Gabjin
Stanley Eugene H.
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