On the Application of the Cross-Correlations in the Chinese Fund Market: Descriptive Properties and Scaling Behaviors

On the basis of the relative daily logarithmic returns of 88 different funds in the Chinese fund market (CFM) from June 2005 to October 2009, we construct the cross-correlation matrix of the CFM. It is shown that the logarithmic returns follow an exponential distribution, which is commonly shared by some emerging markets. We hereby analyze the statistical properties of the cross-correlation coefficients in different time periods, such as the distribution, the mean value, the standard deviation, the skewness and the kurtosis. By using the method of the scaled factorial moment, we observe the intermittence phenomenon in the distribution of the cross-correlation coefficients. Also by employing the random matrix theory (RMT), we find a few isolated large eigenvalues of the cross-correlation matrix, and the distribution of eigenvalues exhibits the power-law tails. Furthermore, we study the features of the correlation strength with a simple definition.

[1]  P. A. Mello,et al.  Random matrix physics: Spectrum and strength fluctuations , 1981 .

[2]  Taisei Kaizoji,et al.  Empirical Laws of a Stock Price Index and a Stochastic Model , 2003, Adv. Complex Syst..

[3]  Nicolas Vandewalle,et al.  Non-random topology of stock markets , 2001 .

[4]  Binghong Wang,et al.  Scaling invariance in spectra of complex networks: a diffusion factorial moment approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[6]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[7]  V. Plerou,et al.  Random matrix approach to cross correlations in financial data. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Nobuko Fuchikami,et al.  Dynamical model of financial markets: fluctuating 'temperature' causes intermittent behavior of price changes , 2003 .

[9]  R. Mahnke,et al.  Application of Heston model and its solution to German DAX data , 2004 .

[10]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.

[11]  V. Eguíluz,et al.  Transmission of information and herd Behavior: an application to financial markets. , 1999, Physical review letters.

[12]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[13]  October I.  Physical Review Letters , 2022 .

[14]  B. Hong,et al.  Journal of the Korean Physical Society: Preface , 2003 .

[15]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[16]  A K Mohanty,et al.  Factorial moments analyses show a characteristic length scale in DNA sequences. , 2000, Physical review letters.

[17]  Jerzy Jurkiewicz,et al.  Free random Lévy and Wigner-Lévy matrices. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Diane Wilcox,et al.  An analysis of cross-correlations in an emerging market , 2007 .

[19]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[20]  Richard K. Crump,et al.  Nonparametric Tests for Treatment Effect Heterogeneity , 2006, The Review of Economics and Statistics.

[21]  Z. Burda,et al.  Spectral moments of correlated Wishart matrices. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  B. Swart,et al.  Quantitative Finance , 2006, Metals and Energy Finance.

[23]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[24]  Journal of business , 2022 .

[25]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[26]  J. Nadal,et al.  International Journal of Modern Physics C C World Scientiic Publishing Company Neural Networks as Optimal Information Processors , 1994 .

[27]  V. Yakovenko,et al.  Probability distribution of returns in the Heston model with stochastic volatility , 2002, cond-mat/0203046.

[28]  Wei Li,et al.  NONLINEAR PROPERTIES, FRACTAL BEHAVIOR AND LONG-RANGE CORRELATION ANALYSIS OF THE CHINESE FUND MARKET , 2010 .

[29]  Victor M. Yakovenko,et al.  Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact , 2004 .

[30]  H. Eugene Stanley,et al.  Scale-Dependent Price Fluctuations for the Indian Stock Market , 2004 .

[31]  Eric Ghysels,et al.  Editors' Introduction to Twentieth Anniversary Commemorative Issue of the Journal of Business and Economic Statistics , 2002 .

[32]  D. Saad.  Europhysics Letters , 1997 .

[33]  Noh.  Model for correlations in stock markets , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[34]  R. Mantegna.  Hierarchical structure in financial markets , 1998, cond-mat/9802256.

[35]  Gabjin Oh,et al.  Deterministic factors of stock networks based on cross-correlation in financial market , 2007, 0705.0076.

[36]  Kathy P. Wheeler,et al.  Reviews of Modern Physics , 2013 .

[37]  F. Lillo,et al.  Specialization and herding behavior of trading firms in a financial market , 2008 .

[38]  I.-M. Kim,et al.  Scale-Free Network in Stock Markets , 2002 .

[39]  R. Riera,et al.  Truncated Lévy walks and an emerging market economic index , 2001 .

[40]  R. Huisman,et al.  Tail-Index Estimates in Small Samples , 2001 .

[41]  Michel L. Goldstein,et al.  Problems with fitting to the power-law distribution , 2004, cond-mat/0402322.

[42]  NUCLEAR PHYSICS B , 1994 .

[43]  Victor M. Yakovenko,et al.  Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes , 2003 .

[44]  Xu Cai,et al.  Scaling and correlations in foreign exchange market , 2007 .