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
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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010