Empirical Analysis of AH-Shares

1 Introduction

Recently, the complex network theory is widely used to investigate the stock market. A number of works^[1–3] have been done to analyze the topological properties of stock networks and the correlations among stocks based on those methods including Random Matrix Theory (RMT)^[4–7], Principal Component Analysis (PCA)^[8], Planar Maximally Filtered Graph (PMFG)^[9], correlation based on clustering^[10], and hierarchical structure^[11]. For example, Mantegna^{[12, 13]} studied the hierarchical structure in financial markets based on minimum spanning tree and hierarchical tree with the time series of stock returns. Utsugi^[14] investigated correlated groups of issues in these markets and proposed a refined method to identify correlated groups based on RMT. Tolga^[15] reported on complexity of major UK companies between 2006 and 2010 by using Hierarchical structure method approach. Numerous researches at home and abroad have focused on global stock markets. Du, et al.^[16] found the comovement effect of stock market by the community structure and obtained the accurate block in the Chinese stock market. Zhang, et al.^[17] applied Partial Correlation Coefficients and Simple Correlation Coefficients to construct network of stocks. Hu, et al.^[18] discussed the dynamic characteristics of the stock networks evolution based on calculating the correlation coefficient, setting threshold and combining the financial index system. Gui, et al.^[19] detected some characters of dynamic communities in each time window based on Blondel's algorithm. Yang, et al.^[20] analyzed the linkage effects among industry sectors in Chinese stock market before and after the financial crisis. Onnela, et al.^[21] investigated the dynamics of market correlations and taxonomy analysis in detail. Michael^[11] has shown that hierarchical structure methods can be used to analyze the topology of foreign exchange markets and found that the price determination structure of international currency markets is tree like and sparsely clustered. This implies dynamic behavior related to complex networks can be applied to currency markets. In other words, the stock market is a complex network because of their price fluctuations. Therefore, in this research, we analyze the dynamic evolution of AH-shares companies in Chinese stock market by virtue of graphs. A-shares purchased and traded on the Shanghai and Shenzhen stock exchanges are shares of Renminbi currency, while H-shares listed in Hong Kong are foreign capital stocks. We choose those shares published both in Chinese Mainland and Hong Kong to represent Chinese stock market. In this paper we also need to take account of Chinese industry characteristic and circumstances to explore the topological characteristics of Chinese stock market. We can find financial business companies, industry companies, service industry companies and energy industry companies have cluster behavior. In the case of the emerging market, there are only a few large companies separated from other companies of the market. In this work, we also find individual stocks are clustered based on their individual sectors to which they belong.

In Section 2, we describe the sample datasets. In Section 3, we show the methodology used in this paper. In Sections 4 and 5, we present the dynamic behaviors and our empirical results and analysis of this study. Finally, conclusions are given in Section 6.

2 Sample Dataset

In this paper, to better understand the correlation structures under different market environments, we select 41 AH-shares stocks traded on Shanghai and Hong Kong Stock Exchange from March 10, 2008 to November 24, 2014 (excluding weekends and market closed dates). The dataset is filtered as follows: 1) Make sure that the stocks have enough number of trading days; 2) Delete those stocks from the dataset when the stock has missing closing prices for more than 10 continuous trading days; 3) Use the closing prices of the previous trading day to fill those missing closing prices. According to the above principles, 41 stocks remain in the sample dataset and each stock has 1632 observations. Stocks and codes are listed in Table 1. In accordance with the China Securities Index Co. Ltd, the listed companies are classified into 7 industries by the China Industry Classification Standard (CICS). These companies are divided into 12 Financial and Real Estate Industry, 14 Industry and Service Industry, 3 Public Service Industry, 6 Energy Industry, 2 Consumer Staple Industry and 4 Material Industry.

The database analyzed in this paper contains the daily stock data of 41 AH-shares companies in China traded on both Shanghai Stock Exchange (SHSE) and Hong Kong Exchanges and Clearing Limited (HKEx). The data source is from NetEase Finance.

3 Methods

4 Dynamical Behavior

From above, we first analyze the distribution of the elements C_ij of the correlation matrix to obtain the statistical properties. In Figure1, the probability density function P(c_ij) of the correlation coefficients calculated from the return series of 41 AH-shares stocks evolved with the time t is shown. It will be found in the figure that the center of the distribution clearly deviates from zero. We observe the values of the coefficient C_ij located at the peaks of P(c_ij) are significantly positive. As t tends to 2009 and 2011, the peaks of P(c_ij) show two local maximum of C_ij. The valleys of P(c_ij) are probably at 2010 and 2012. On September 15, 2008, the fifth-largest US investment bank Lehman Brothers declared bankruptcy and Merrill Lynch was also acquired by Bank of America, which caused the global financial crisis. Moreover, the stock markets around the world, certainly including the Chinese stock market, have been hit hard in the downturn. This indicates that stock price variations are more likely to be correlated around the market crashes.

Figure 1

Dynamics of correlation coefficient distribution

To further verify the dependence of the stock correlations on the time and the dynamic stability of the network, we also compute the mean correlation coefficient 〈C_ij〉 and the mean distance 〈D_ij〉 in the moving window. In Figures 2, 3 we present a plot of the mean correlation coefficients and the mean distances among all stocks.

Figure 2

Dynamic of mean correlation coefficient of AH-shares companies

Figure 3

Dynamic of mean distances of AH-shares companies

As shown in Figures 2 and 3, we can find that the mean correlation coefficients and the mean distances have a relatively strong negative correlation. With the reduction of distances, correlations among the stocks increased dramatically and the relevance became more closely. By observing the dynamic of mean correlation coefficient figure we can see that for the years 2008, 2010 and 2012 the mean value of the correlation coefficient matrix increased dramatically. In fact, during these years there was a sudden decline in the Chinese stock market (as in the rest of the world). This large increase of the mean correlation value suggests that during this crisis period all stocks were so highly correlated. Figure 2 shows that the mean correlation coefficients are stable in most of the time,but we can also see great volatility during three periods, which are late 2008, mid-2010 and early 2012. So in this paper we use March 10, 2010 and March 13, 2012 as dividing points. We can see clearly that the mean correlation coefficient is in decline as a whole, while the mean distance is gradually increasing over time. It is enough to suggest that the correlation of stock market is increasingly weaking.

5 Empirical Results and Analysis

In this section, using 41 AH-shares companies price indicators, we show the MSTs and their HTs, and investigate the topology and structure of the correlation networks in Chinese stock market. A number of researches about the engaged connections among the listed companies can be implemented by analyzing the MSTs and HTs. Analyzing these trees it can be checked that companies working in the same branch of production tend to cluster. The MSTs showed in Figures 4, 5 and 6 are obtained by using Kruskal's algorithm as we have discussed above. The HTs of the subdominant ultrametric space associated with the MST are shown in Figures 7, 8 and 9. Through a comprehensive comparative analysis of the 41 AH-shares company indices minimum spanning tree structures, we note that obvious clusters exist in all periods, especially among the similar industries. It will be found in the research that both MSTs and HTs show significantly different structures in three periods: From March 10, 2008 to March 10, 2010, from March 11, 2010 to March 12, 2012, and from March 13, 2012 to November 24, 2014. Notice that almost three groups are easily identified, financial and estate industry market (black dash line circle), industry and service industry market (green dash line circle), and energy industry market (blue dash circle). See Figure 4, inside each group, we find that financial and estate industry (black colour nodes) are linked to energy industry (blue colour nodes). Energy industry (blue colour nodes) are also linked to industry and service industry (green colour nodes). Thus the energy industry market acts as a bridge between the financial and estate industry market and the industry and service industry market. In Figure 4, the different colours represent the different sectors of economic activity. The black nodes mean the stocks included in Financial and Real Estate Industry. The blue nodes denote stocks from Energy Industry. The green nodes stand for Industry and Service Industry. Red nodes mean the stocks which are not included.

Figure 4

Minimum spanning tree of AH-Shares Companies from 2008/3/10 to 2010/3/10

Figure 5

Minimum spanning tree of AH-Shares Companies from 2010/3/11 to 2012/3/12

Figure 6

Minimum spanning tree of AH-Shares Companies from 2012/3/13 to 2014/11/24

Figure 7

Hierarchical tree of AH-Shares Companies from 2008/3/10 to 2010/3/10

Figure 8

Hierarchical tree of AH-Shares Companies from 2010/3/11 to 2012/3/12

Figure 9

Hierarchical tree of AH-shares Companies from 2012/3/13 to 2014/11/24

In order to find the main important companies appeared in different periods, we investigate the degrees of the core nodes in the networks. The degrees of the core nodes in different periods are shown in Table 2, 3 and 4. As Tables show, we can find that ChinaCoal (CC) is still a central node in different networks. Meanwhile, the degree of ChinaCoal rises from 4 to 9, indicating that its linkage effect with other companies has improved. While it must be pointed out that Beijing North Star (BEIJF), China Shipping Development (CSDC) and ChinaCoal (CC) belong to financial and estate industry, industry and service industry and energy industry respectively. Thus it can be seen that the center of the market is quite different in different periods due to the various market environment. By comparing those MSTs, we find that Figure 4 shows a structure that differs greatly from that in Figure 5 especially the industry and service industry market (green dash line circle). Figure 6 also shows that the boundaries separating companies.

In hierarchical tree, each horizontal line denotes a listed company, while the height of the vertical line represents the ultrametric distance at which the two companies are merged. The HTs can show the classification information of all these companies and present the linkage effects among company clusters. The hierarchical trees can reveal the correlation degrees of companies where the ones strongly linked in the network are at the same level. For instance, Air China (CA) and China Southern Airlines (CZ) are always at the same level in Figures 7–9, indicating that they are closely related. However, the distance between CA and CZ and other companies has gradually become larger, indicating that their linkage with other companies has weakened. Moreover, Tsingtao Beer (TB) is almost always at the highest level in all the three periods. It is enough to show that TB's linkage with other companies is rather weak. From Figure 7, we can see that the distance between ChinaCoal (CC) and China Shenhua Energy (CSE) is the smallest of the sample, indicating a strong relationship between these two companies. Financial and estate companies and industry companies are very close so that they make up the cluster.

6 Conclusion

In this paper, we investigated the clustering properties of individual industrial sectors in MST and HT structures estimated from a correlation matrix describing 41 individual AH-shares stocks listed on Shanghai and Hong Kong. The dynamic evolution study of stock network stability indicates that the network is stable in most of the time and the network has significantly fluctuation during the years 2008, 2010 and 2012, which this paper takes as dividing points. We find that the stock returns behave more collectively in volatile periods, showing the distribution of correlation coefficients centered around larger positive coefficients and larger values of mean correlation coefficient as the time approaches the three big crashes.