Central China Normal University , Wuhan , China Scaling and Correlations of the Chinese Fund Market (CFM) Deng Weibing, Li Wei and Cai Xu Complexity Science Center Central China Normal University , Wuhan , China

Outline: [1] Fractal structure. [2] Long range correlation. [3] Whether there exists any correlation ? [4] Hurst exponents are different, What ? [5] Correlations of the relative return series.

The data: http://data.cnfund.cn/ June 2005 ~ October 2009 ⊿t = 1 day Stock Fund : 52 Active Configuration Fund : 36

p(t) is the price of a fund at time t r(t) is the return of a fund after a time interval ⊿t |r(t)| is the absolute return (volatility)

[1] The Fractal or Multi-Fractal structure The future return is correlated to the past one, the return series has similar statistical characteristics in different time scales.

Another kind of method* Considering the standard deviation of the return series as a new time series we may calculate the standard deviation of the new time series Std(t) is the standard deviation of the standard deviation time series *X.T. Zhuang, X.Y. Huang, Y.L. Sha, Physica A 333 (2004) 293-305. 7

The value of H close to 0.5 indicates a random walk, no correlation in the time series (2) The value of H between 0 and 0.5 exists in the time series with the anti-persistent behavior. an increase will tend to be followed by a decrease the strength of the mean reversion increases as H approaches 0. (3) The value of H between 0.5 and 1 implies the persistent behavior an increase will be inclined to follow an increase the larger the value of H, the stronger the trend.

The detrended fluctuation analysis of the standard deviation Δt=5 days, T=10 and t0=1, 2 ... 35

The Hurst exponent H in different time scales, Δt={1 day, 2 days, ... , 30 days}, T=10 and t0=1, 2 ... 35

[2] Long range correlation (DFA) The method of detrended fluctuation analysis has proven useful in revealing the extent of long-range correlations in time series.

|R(t)| Exist the Long range correlation

[3] The correlation

[4] What ?

Divide the return series sample N into n bins, The length of every bin is T = N/n, The standard deviation s(j) is calculated in all non- overlapping bins of length T

H D RISK

[5] Correlations of the relative return series

Distribution of the eigenvalues of the matrix C

Scaled factorial moment

Conclusions: [1] Whether there exists any correlation ? [2] Hurst exponents are different, What ? [3] Correlations of the relative return series.

Acknowledgement [1] Prof. Li Wei and Prof. Cai Xu [2] Prof. Didier Sornette [3] China Center of Advanced Science and Technology

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