Statistical Properties of Cross-Correlation in the Korean Stock Market

TL;DR

This paper analyzes the statistical properties of correlation matrices in the Korean stock market, revealing deviations from random matrix theory predictions and their impact on portfolio risk and entropy.

Contribution

It provides new insights into the eigenvalue distribution and entropy behavior of correlation matrices in the Korean stock market, highlighting deviations from RMT and their implications.

Findings

Correlation matrix distribution is positively skewed and varies over time.

Eigenvalue distribution deviates from RMT predictions, with a significantly larger largest eigenvalue.

Entropy function follows a power-law with respect to portfolio risk, affected by market crises.

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.