Anti-correlation network among China A-shares

TL;DR

The paper introduces anti-correlation networks as a parallel framework to traditional correlation-based stock networks, applying it to China A-shares with a 24-year, 387-window, sliding-window analysis. It defines two weight matrices from the correlation coefficient $\rho_{ij}$—anti-correlation weights $W^a_{ij}$ and positive-correlation weights $W_{ij}$—and computes topology metrics such as node strength, assortativity by strength, clustering, and path length. The results reveal that anti-correlation networks are largely scale-free and disassortative with lower clustering and longer path lengths than positive-correlation networks, and that market crashes produce asymmetric effects across the two network types. These findings imply distinct roles for anti-correlation structures in risk contagion and portfolio stabilization, offering a new lens for complex financial-system analysis and suggesting that prior studies should be reexamined under this methodology.

Abstract

The correlation-based financial networks are studied intensively. However, previous studies ignored the importance of the anti-correlation. This paper is the first to consider the anti-correlation and positive correlation separately, and accordingly construct the weighted temporal anti-correlation and positive correlation networks among stocks listed in the Shanghai and Shenzhen stock exchanges. For both types of networks during the first 24 years of this century, fundamental topological measurements are analyzed systematically. This paper unveils some essential differences in these topological measurements between the anti-correlation and positive correlation networks. It also observes an asymmetry effect between the stock market decline and rise. The methodology proposed in this paper has the potential to reveal significant differences in the topological structure and dynamics of a complex financial system, stock behavior, investment portfolios, and risk management, offering insights that are not visible when all correlations are considered together. More importantly, this paper proposes a new direction for studying complex systems: the anti-correlation network. It is well worth reexamining previous relevant studies using this new methodology.

Figures (5)

• Figure 1: The distribution properties of the correlation coefficients $\rho_{ij}$ in each time window. The top panel presents the probability of anti-correlation $p\left( \rho_{ij} < 0 \right)$. The middle panel presents the maximum (upper blue curve) and minimum (lower red curve) of $\rho_{ij}$. The bottom panel presents the kurtosis (upper red curve) and skewness (lower blue curve) of $\rho_{ij}$. Both horizontal dashed straight lines indicate the locations of 3 and 0, which are the kurtosis and skewness of the Gaussian distribution, respectively. In these three panels, the data points are plotted at the locations of the start dates of each time window.
• Figure 2: The visualization of an anti-correlation network and a fully connected network. The left panel shows a typical anti-correlation network with 994 nodes and 2,300 edges. This anti-correlation network is in the time window through Aug. 5, 2008 to Sept. 9, 2008, during which period the 2007-2008 global financial crisis was happening. In this panel, the nodes labeled by stock symbols are the top 3 stocks ranked by node's strength. The right panel shows the corresponding fully connected network with 1,124 nodes and 631,126 edges (see main text for details). In this network, the three tiny black nodes labeled by stock symbols are the top 3 stocks of the anti-correlation network shown in the left panel. In these two panels, a colored circle (node) represents a stock, whose color and size depend on its strength; a colored curve (edge) represents the correlation relationship between a pair of stocks linked by that curve, whose color and thickness depend on the corresponding correlation coefficient.
• Figure 3: The probability density functions of strength for the anti-correlation and positive correlation networks. The upper and lower panels are for the positive correlation and anti-correlation networks in the last time window, respectively. The solid purple circles are the estimated probability density functions of strength $s$. The solid red straight line denotes the result of the power-law fit to data points using non-linear least squares.
• Figure 4: The estimations of the tail shape parameters of strength distributions for the anti-correlation and positive correlation networks. The shape parameters are estimated from the GPD fit to the tail data. The purple and blue circles are the point estimations, and the corresponding vertical lines with caps denote the 95% confidence intervals. For the shape parameters below -0.5, only point estimations are shown because the confidence interval estimation is problematic. The markers are plotted at the locations of the start dates of each time window. For ease of comparison, the location of 0 is also denoted by the horizontal dashed line.
• Figure 5: The assortativity coefficient (top panel), the average local clustering coefficient (middle panel), and the average shortest path length (bottom panel) as functions of the return of the Shanghai Securities Composite Index. The left and right panels are for the positive correlation and anti-correlation networks, respectively. The circles represent mean values in the specific ranges of return as shown by the horizontal lines with caps. The vertical lines with caps are the standard deviations.