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Statistical properties of cross-correlation in the Korean stock market

Author

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  • G. Oh
  • C. Eom
  • F. Wang
  • W.-S. Jung
  • H. E. Stanley
  • S. Kim

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 $\beta_{473}$ 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 σ for the original and filtered cross-correlation matrices are consistent with a power-law function, E(σ) ~ $\sigma^{-\gamma}$ , with the exponent γ ~ 2.92 and those for Asian currency crisis decreases significantly. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Suggested Citation

  • G. Oh & C. Eom & F. Wang & W.-S. Jung & H. E. Stanley & S. Kim, 2011. "Statistical properties of cross-correlation in the Korean stock market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 79(1), pages 55-60, January.
    • Handle: RePEc:spr:eurphb:v:79:y:2011:i:1:p:55-60
    DOI: 10.1140/epjb/e2010-90492-x
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    Cited by:

    1. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Collective behavior of cryptocurrency price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 499-509.
    2. Kanjamapornkul, K. & Pinčák, Richard & Bartoš, Erik, 2016. "The study of Thai stock market across the 2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 117-133.
    3. F. Y. Ouyang & B. Zheng & X. F. Jiang, 2014. "Spatial and temporal structures of four financial markets in Greater China," Papers 1402.1046, arXiv.org.
    4. Ouyang, F.Y. & Zheng, B. & Jiang, X.F., 2014. "Spatial and temporal structures of four financial markets in Greater China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 236-244.
    5. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    6. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    7. Stefano Ferretti, 2023. "On the Modeling and Simulation of Portfolio Allocation Schemes: an Approach Based on Network Community Detection," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 969-1005, October.
    8. Wang, Gang-Jin & Xie, Chi & Chen, Shou & Yang, Jiao-Jiao & Yang, Ming-Yan, 2013. "Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3715-3730.
    9. Tang, Yong & Luo, Yong & Xiong, Jie & Zhao, Fei & Zhang, Yi-Cheng, 2013. "Impact of monetary policy changes on the Chinese monetary and stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4435-4449.
    10. Nobi, Ashadun & Maeng, Seong Eun & Ha, Gyeong Gyun & Lee, Jae Woo, 2014. "Effects of global financial crisis on network structure in a local stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 135-143.
    11. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa & Stosic, Tatijana, 2016. "Correlations of multiscale entropy in the FX market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 52-61.
    12. Mansooreh Kazemilari & Maman Abdurachman Djauhari & Zuhaimy Ismail, 2016. "Foreign Exchange Market Performance: Evidence from Bivariate Time Series Approach," Papers 1608.07694, arXiv.org.

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