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From the perspective of equity holdings, this article selects the stock and equity data related to the financial sector in the Shanghai and Shenzhen securities markets in China, uses the bipartite network model to construct stock-shareholders associated network and performs a single-mode projection on the network to obtain the stock correlation network, further study the structure and financial nature of the network. The study found that in the stock-shareholders associated networks, minority shareholders hold a large number of stocks, which on the one hand illustrates the investment direction of major shareholders, and has become a vein for retail shareholders to invest in stocks; on the other hand, it is confirmed that the long-term and large-scale holding of major shareholders can stabilize the financial market to a certain extent. The weight and degree distribution of the stock correlation network are non-uniform, and many of the state-owned banks have higher weight values, which reflects the close relationship between state-owned banks. Finally, the shareholder’s holding behavior reflects that their identification with financial stocks in the A-share market tends to be consistent.

Since the 2008 financial crisis, people have begun to pay attention to the study of financial markets, and there are more and more research methods on financial markets. In recent years, a large number of scholars have used complex network methods to construct financial or stock networks, studying the relationship between various entities in the financial market and the spread of market risks. Yan Lin and Zhixin (2018) put forward a set of grade evaluation indicators of financial institutions in the financial network communication by studying the risk communication mechanism between financial institutions and combining with the financial network, so that the relevant regulatory agencies can supervise the financial institutions [

A bipartite network is a common network in life. It is a graph composed of two groups of nodes. The nodes in the group are not connected, and the nodes between the two groups can be connected. For example, the relationship between products and customers, the relationship between music works and audiences, the relationship between scientists and papers, etc., these relationships can be modeled and researched using a binary network. Shan Lu and Huiwen Wang (2019) studied the bank-asset dichotomy network and concluded that the collection of the same assets between different banks will lead to risk contagion, which in turn leads to large-scale bank bankruptcy [

Generally speaking, the typical stock correlation network modeling is based on the logarithmic return rate of stock daily trading, calculating the correlation coefficient between stocks, and then establishing the connection relationship between stocks according to the threshold method to build the correlation network model. This modeling method uses high-frequency data among stocks, which reflects the correlation of short-term stock return fluctuations. This article uses listed company equity and shareholder data, from the perspective of equity holdings, and uses a bipartite network model to establish a stock-shareholders associated network, reflecting the stable relationship between listed companies and shareholders over a long period of time. And further carry out single-mode projection on this bipartite network to obtain the stock correlation network, and analyze the network topology and financial statistics properties from the matrix weight, degree distribution, degree center and K-core.

The paper is structured as follows. Some preliminaries are introduced in Section 2. Section 3 studies the stock-shareholder associated Network. In Section 4, the stock correlation network is studied. Finally, Section 5 gives the conclusion of this paper.

A graph G is an order triple ( V ( G ) , E ( G ) , Ψ G ) consisting of a nonempty vertex set V ( G ) , a set E ( G ) of edges, and an incidence function Ψ G that associates with each edge an unordered pair of vertices of G. Let G be a graph with the vertex set V ( G ) = { v 1 , v 2 , ⋯ , v n } and the edge set E ( G ) = { e 1 , e 2 , ⋯ , e m } [

A = ( a 11 ⋯ a 1 n ⋮ ⋱ ⋮ a n 1 ⋯ a n n )

where

a i j = { 1 , if v i and v j are adjacent 0 , otherwise

A bipartite network is a special type of network. Its nodes are divided into two groups. There is no edge between the nodes in the group, and the nodes between the two groups can be connected, as shown in

Generally, a bipartite network can be expressed as, G = ( X , Y , E ) where X = { x 1 , x 2 , ⋯ , x n } and Y = { y 1 , y 2 , ⋯ , y m } are the sets of two groups of nodes with different properties, and E is the set of edges between nodes,

E = { e i j | x i and y j are connected , i = 1 , ⋯ , n ; j = 1 , ⋯ , m } . The adjacency matrix of network G is recorded as A = ( a i j ) n × m , where a i j = { 1 , e i j ∈ E 0 , e i j ∉ E .

Since X and Y in the bipartite network are two sets of nodes with different properties, in general, matrix A is asymmetric, which can reflect the topological structure of networkG, and matrix A represents networkG, which is convenient for calculation and analysis of the topological properties of network G.

Single-mode projection is to project the bipartite network relationship onto one of the node sets, and project a two-dimensional bipartite network into a one-dimensional network to study. For example, the X-projection network refers to the projection of the bipartite networkG onto the node set. The specific projection method is: if in the bipartite network, nodes x i and x j are connected to the node y k at the same time, then in theX-projection network, the nodes x i and x j have connected edges, as shown in

Take the bipartite network shown in

A = [ 1 1 0 1 0 1 1 0 1 0 1 1 ]

Thus, the X-projection network and Y-projection network are obtained, and the adjacency matrices W X and W Y are respectively:

W X = [ 0 1 2 1 0 1 2 1 0 ] , W Y = [ 0 1 1 2 1 0 1 1 1 1 0 1 2 1 1 0 ]

To generalize the above process, write the adjacency matrix of the X-projection network as W X = ( w i j ) n × n , then where w i j = ∑ k = 1 m a i k ⋅ a j k , i , j = 1 , ⋯ , n , and similarly write the adjacency matrix of the Y-projection network as W Y = ( w i j ) m × m , then there is w i j = ∑ k = 1 n a k i ⋅ a k j , i , j = 1 , ⋯ , m .

In fact, the adjacency matrices W X and W Y of theX-projection network and Y-projection network are both symmetric weight matrices. In theX-projection network in

This article mainly studies the stocks of related industries in the financial field, that is the stocks issued by listed companies such as banks, insurance, and securities. Obtain the public data information of listed companies in the financial sector from China’s Shanghai Stock Exchange and Shenzhen Stock Exchange, and obtain the top ten shareholders of stocks. This article selected 78 financial stocks (including 29 bank stocks, 6 insurance stocks and 43 securities stocks) and 68 of the top ten shareholders of these stocks (hereinafter referred to as shareholders). Due to the limitation of the number of shares, we excluded individual shareholders and shareholders who only hold one stock in the study.

Divide the data into two categories. The first category is a collection of 78 financial stocks, denoted as node set X = { x 1 , x 2 , ⋯ , x i , ⋯ , x 78 } , and the second category is a collection of the top ten shareholders/institutions (excluding individual shareholders) whose shareholders are the above financial stocks. It is node set Y = { y 1 , y 2 , ⋯ , y j , ⋯ , y 68 } . Rows represent nodes of the first type, and columns represent nodes of the second type. If the institution y j in the second type set is a shareholder of the first type of stock x i , the corresponding element is a i j = 1 , otherwise a i j = 0 . This results in the adjacency matrix A 78 × 69 of the stock-shareholder associated network, which reflects the topological structure of the bipartite network.

It can be seen from

Assuming that shareholder y j ’s shareholding (the number of shares y j held by x i ) is h j , the expression of h j is as follows:

h j = ∑ i = 1 n a i j . (1)

According to this definition, the shareholding h j of each shareholder in the stock-shareholder associated network can be calculated and presented in a table. As shown in

It can be seen from

Rank | Shareholders h_{j} | Shareholder company y_{j} |
---|---|---|

1 | 45 | Hong Kong Securities Clearing Company Limited |

2 | 39 | China Securities Finance Corporation Limited |

3 | 27 | Central Huijin Asset Management Co., Ltd. |

4 | 25 | Hong Kong Securities Clearing (Nominees) Limited |

5 | 18 | China Construction Bank Co., Ltd.-Cathay Pacific China Securities All Index Securities Company Trading Open Index Securities Investment Fund |

6 | 7 | Central Huijin Investment Co., Ltd. |

7 | 6 | China Construction Bank Co., Ltd.-Huabao China Securities All Index Securities Company Trading Open Index Securities Investment Fund |

8 | 4 | Shanghai Haiyan Investment Management Co., Ltd. |

9 | 4 | China Life Insurance Co., Ltd.-Universal Insurance Products |

10 | 4 | Yunnan Hehe (Group) Co., Ltd. |

11 | 4 | Wutongshu Investment Platform Co., Ltd. |

12 | 3 | Shenergy (Group) Co., Ltd. |

13 | 3 | Linghang Investment Australia Limited-Linghang Emerging Markets Stock Index Fund (Exchange) |

14 | 3 | Industrial and Commercial Bank of China-SSE 50 Trading Open Index Securities Investment Fund |

15 | 3 | Dacheng Fund-Agricultural Bank-Dacheng China Securities Financial Asset Management Plan |

16 | 3 | China Asset Management-Agricultural Bank of China-China Securities Financial Asset Management Plan |

17 | 3 | China Europe Fund-Agricultural Bank-China Europe and China Securities Financial Asset Management Plan |

18 | 3 | Shanghai Jiushi (Group) Co., Ltd. |

19 | 3 | China Everbright Group Corporation |

20 | 3 | China Construction Bank Investment Co., Ltd. |

21 | 3 | Yinhua Fund-Agricultural Bank-Yinhua China Securities Financial Asset Management Plan |

22 | 3 | China Life Insurance Company Limited-Traditional- General Insurance Products-005L-CT001Shanghai |

23 | 3 | Ministry of Finance of the People’s Republic of China |

Ltd. and Hong Kong Securities Clearing (Nominees) Limited. Among them, Hong Kong Securities Clearing Co., Ltd. and Hong Kong Securities Clearing (Nominees) Co., Ltd., ranked first and fourth, are both wholly-owned subsidiaries of the Hong Kong Stock Exchange. The former represents a collection of A shares held by the Hong Kong Stock Exchange, and the latter Represents a collection of shares held by H-share shareholders. Hong Kong Securities Clearing Company Limited is a clearing institution that operates the Hong Kong Securities Clearing and Settlement System, and investors will centrally deposit the A shares they purchase in Hong Kong Securities Clearing Company Limited. The business model of Hong Kong Securities Clearing Company Limited is similar to that of Hong Kong Securities Clearing Company Limited, except that it trades H shares. In other words, Hong Kong and overseas investors hold and trade A shares and H shares through these two companies. The holdings of these two companies are very high. Among them, Hong Kong Securities Clearing Company holds more than half of the online stocks, and their status in the Internet is very important. Because these two companies are the channels for some major shareholder companies to purchase A shares and H shares, their buying and selling may become the vane for ordinary shareholders to buy stocks.

China Securities Finance Co., Ltd. and Central Huijin Asset Management Co., Ltd., ranked second and third, are wholly state-owned companies funded by the state. According to the authorization of the State Council, it represents the state in accordance with the law to exercise the rights and obligations of investors in key financial enterprises such as state-owned commercial banks. They have the role of regulating and stabilizing the market.

In order to better display the relationship between stocks, the stock-shareholder associated network is single-mode projection of the stock direction, and the stock correlation network and its adjacency matrix W X are obtained. The topological structure of the stock correlation network is shown in

According to the definition, the adjacency matrix W X is a weight matrix. The weight w i j is expressed as the number of common neighbor nodes owned by stock x i and stock x j in shareholder Y. The greater the weight, the more common neighbor nodes between the two stocks. More, it means that the more organizations that are optimistic about the two listed companies at the same time, the higher the degree of recognition of the stock by the organization.

It can be seen from

Weights g_{ij} | stock x_{i} | Stock x_{j} |
---|---|---|

6 | Agricultural Bank of China (x_{i} = 10) | Bank of China (x_{j} = 5) |

6 | Everbright Securities (x_{i} = 40) | Everbright Ban (x_{j} = 19) |

5 | Construction Bank (x_{i} = 13) | Agricultural Bank of China (x_{j} = 10) |

5 | Industrial and Commercial Bank (x_{i} = 15) | Agricultural Bank of China (x_{j} = 10) |

5 | Everbright Bank (x_{i} = 19) | Agricultural Bank of China (x_{j} = 10) |

5 | Everbright Bank (x_{i} = 19) | Construction Bank (x_{j} = 13) |

… | … | … |

4 | China CITIC Bank (x_{i} = 12) | Agricultural Bank of China (x_{j} = 10) |

4 | Bank of Communications (x_{i} = 25) | Agricultural Bank of China (x_{j} = 10) |

4 | China Merchants Securities (x_{i} = 34) | Agricultural Bank of China (x_{j} = 10) |

… | … | … |

3 | Construction Bank (x_{i} = 13) | Bank of China (x_{j} = 5) |

3 | Everbright Bank (x_{i} = 19) | Bank of China (x_{j} = 5) |

3 | Agricultural Bank of China (x_{i} = 10) | Industrial Bank (x_{j} = 6) |

… | … | … |

2 | Industrial Bank (x_{i} = 6) | Bank of China (x_{j} = 5) |

2 | China CITIC Bank (x_{i} = 12) | Bank of China (x_{j} = 5) |

… | … | … |

1 | Bank of Chengdu (x_{i} = 2) | Changshu Bank (x_{j} = 1) |

1 | Hangzhou Bank (x_{i} = 4) | Changshu Bank (x_{j} = 1) |

… | … | … |

reflects that China Everbright Group is favored by many shareholders. At the same time, we can also see that traditional state-owned banks such as China Construction Bank and Industrial and Commercial Bank are also heavily weighted.

From

Stock | Top ten shareholders |
---|---|

Bank of China | Central Huijin Investment Co., Ltd., Hong Kong Securities Clearing (Nominees) Limited, Wutongshu Investment Platform Co., Ltd., China Life Insurance Company Limited-Dividend-Individual Dividend-005L-FH002 Shanghai, Hong Kong Securities Clearing Company Limited, China Life Insurance Company Limited-Traditional-General Insurance Product-005L-CT001 Shanghai. |

Agricultural Bank of China | Central Huijin Investment Co., Ltd., Ministry of Finance of the People’s Republic of China, Hong Kong Securities Clearing (Nominees) Limited, China Securities Finance Corporation Limited, Hong Kong Securities Clearing Company Limited, Central Huijin Asset Management Co., Ltd., Wutongshu Investment Platform Co., Ltd., China Life Insurance Company Limited-Traditional-General Insurance Products-005L-CT001 Shanghai, China Life Insurance Company Limited-Dividend-Individual Dividend-005L-FH002 Shanghai |

Construction Bank | Central Huijin Investment Co., Ltd., Hong Kong Securities Clearing (Nominees) Limited, China Securities Finance Corporation Limited, Hong Kong Securities Clearing Company Limited, Central Huijin Asset Management Co., Ltd. |

Industrial and Commercial Bank | Central Huijin Investment Co., Ltd., Ministry of Finance of the People’s Republic of China, China Ping An Life Insurance Co., Ltd.-Traditional-General Insurance Products, China Securities Finance Corporation Limited, Central Huijin Asset Management Co., Ltd., China Life Insurance Company Limited-Traditional-General Insurance Products-005L-CT001Shanghai. |

The degree distribution k of an undirected network is defined as the probability that the degree P ( k ) of a randomly selected node in the network is expressed as follows:

P ( k ) = N k N (2)

where N k represents the number of nodes with degree k in the network, and N is the number of nodes in the network.

It can be seen from

Since the stock association network is a weighted network, the point weight distribution analysis of the nodes in the network is carried out. The point weight distribution is similar to the degree distribution of nodes, which is defined as:

P ( w ) = N w N (3)

where P ( w ) refers to the probability that a randomly selected node in the

network has a weight of w, N w represents the number of nodes in the network with a weight of w, and N is the number of nodes in the network.

It can be seen from

In the network, degree centrality is an indicator reflecting the importance of nodes. The greater the degree of a node, the greater its degree centrality, which means that the node is more important. In a network containing N nodes, the maximum possible value of the node degree is N − 1, and the centrality index is usually normalized for the convenience of comparison. The normalized degree centrality value of the node with degree is defined for:

D C i = k i N − 1 (4)

In order to more clearly extract the important information of various stocks, the original stocks are divided into three categories, namely, banking, brokerage and insurance. Tables 4-6 show the degree centrality of the three types of stocks.

It can be seen from

Stock x_{i} | Stock name | Degree k_{i} | DC_{i} (Hundred differentiation) |
---|---|---|---|

12 | China CITIC Bank | 65 | 84.416 |

13 | Construction Bank | 65 | 84.416 |

10 | Agricultural Bank of China | 65 | 84.416 |

19 | Everbright Bank | 65 | 84.416 |

27 | China Merchants Bank | 63 | 81.818 |

7 | Bank of Nanjing | 59 | 76.623 |

16 | Ping An Bank | 59 | 76.623 |

8 | Bank of Beijing | 59 | 76.623 |

6 | Industrial Bank | 58 | 75.325 |

29 | Shanghai Pudong Development Bank | 57 | 74.026 |

5 | Bank of China | 57 | 74.026 |

9 | Bank of Guiyang | 57 | 74.026 |

18 | Chongqing Rural Commercial | 56 | 72.727 |

… | … | … | … |

Stock x_{i} | Stock name | Degree k_{i} | DC_{i} (Hundred differentiation) |
---|---|---|---|

40 | Everbright Securities | 69 | 89.610 |

34 | China Merchants Securities | 65 | 84.416 |

37 | GF Securities | 65 | 84.416 |

49 | Northeast Securities | 64 | 83.117 |

61 | Pacific Securities | 63 | 81.818 |

42 | Huatai Securities | 63 | 81.818 |

35 | CITIC Securities | 63 | 81.818 |

39 | Dongxing Securities | 63 | 81.818 |

47 | Guoyuan Securities | 60 | 77.922 |

53 | Founder Securities | 59 | 76.626 |

50 | Industrial Securities | 59 | 76.623 |

55 | China Galaxy | 58 | 75.325 |

43 | Guotai Junan | 58 | 75.325 |

… | … | … | … |

Stock x_{i} | Stock name | Degree k_{i} | DC_{i} (Hundred differentiation) |
---|---|---|---|

74 | China Pacific Insurance | 65 | 84.416 |

73 | China Life Insurance | 57 | 74.026 |

77 | Ping An of China | 53 | 68.831 |

75 | Xinhua Insurance | 51 | 66.234 |

78 | Tianmao Group | 45 | 58.442 |

76 | China People’s Insurance | 26 | 33.776 |

first in degree centrality, and the degree of the four stocks is as high as 65, reflecting the fact that these four stocks and most stocks in the network all of them are connected, occupy an important position in the network, and can reflect the overall market situation of such stocks.

It can be seen from

Through the above analysis, we have obtained some important nodes in the stock correlation network. These nodes are in an important position in the network and will have a greater impact on the stock-related network than ordinary stocks. The relevant departments need to supervise and manage them. At the same time, when ordinary shareholders buy stocks, the market conditions of these stocks have great reference value.

The k-core of a graph refers to repeatedly removing nodes with a degree value less than k and the remaining subgraphs after connecting them [

k-core | Stock x_{i} |
---|---|

44 | Bank of Changshu, Bank of Chengdu, Bank of Hangzhou, Bank of China, Industrial Bank, Bank of Nanjing, Bank of Beijing, Bank of Guiyang, Agricultural Bank, China CITIC Bank, Construction Bank, Ping An Bank, Chongqing Rural Commercial, China Everbright Bank, Bank of Shanghai, Bank of Ningbo, China Merchants Bank, Bank of Jiangsu, Shanghai Pudong Development Bank, China Merchants Securities, CITIC Securities, GF Securities, Western Securities, Dongxing Securities, Everbright Securities, Huatai Securities, Guotai Junan, Oriental Fortune, Guoyuan Securities, Northeast Securities, Industrial Securities, Guosen Securities, Founder Securities, Zheshang Securities, Hongta Securities, Caitong Securities, Pacific Securities, West China Securities, First Ventures, Shanxi Securities, Jinlong Stocks, China Life, China Pacific Insurance, Xinhua Insurance |

38 | Hua Xia Bank, Bank of Communications, Orient Securities, Haitong Securities, China Investment Capital, Shenwan Hongyuan, China Sea Securities, Soochow Securities, Yangtze River Securities, China Galaxy, Southwest Securities, Ping An |

26 | Bank of Qingdao |

24 | Postal Savings Bank, Zhengzhou bank, Minsheng Bank, China Zheshang Bank, China People’s Insurance |

17 | China Securities, Nanjing Securities, Huaxin shares, Hualin Securities |

1 | Bank of Wuxi, Zhangjiagang Bank, South China Futures, Ruida Futures, Bank of China Securities, Huaan Securities, Huachuang Yangan, Great Wall Securities |

This paper studies the equity and shareholder data of financial listed companies in China’s A-share market. From the perspective of equity holdings, the dichotomous network model is used to establish a stock-shareholder associated network, and the stock correlation network is further established through single-mode projection, reflecting the longer stable relationship between listed companies in the time period. The analysis of shareholders in the stock-shareholder associated network found that the number of shares held by some holding companies is huge, among which the number of shares held by Hong Kong Securities Clearing Company Limited, China Securities Finance Co., Ltd. and Central Huijin Asset Management Co., Ltd. ranks in the first three, Hong Kong Securities Clearing Co., Ltd. is a channel for overseas investors to purchase domestic stocks, and has a certain role as a weather vane for retail investors, while China Securities Finance and Central Huijin are state-owned enterprises with national backgrounds. The main responsibility of China Securities Finance Corporation and Central Huijin is to stabilize the market. Research on the stock-related network found that for traditional state-owned banks, the equity components between them are similar and they are closely related. This situation exists because of my country’s special system and basic national conditions. State-owned equity can provide protection for the development of banks. State-owned equity can enhance the ability of banks to resist risks and make banks less likely to fall when encountering risks. Therefore, the state-owned equity holding structure is the foundation for my country’s commercial banks to govern industrial institutions. The next study on the degree distribution of the stock related network found that the stock related network is not a general rule network, which is inconsistent with the traditionally believed stock network to be scale-free, and its degree distribution is non-uniform. Through the research on the centrality of the network degree, the important nodes in the stock association network are discovered. In addition, k-core analysis is performed on the network, which characterizes the risk spread ability of each node in the stock-related network. The number of nodes in the core area of the network is 45, and the k-core value is as high as 44. This result shows that this is a network with strong risk spreading ability. Therefore, relevant departments should supervise the listed companies in the core area of the network to prevent financial risks occur.

This paper introduces the bipartite network model into the construction of the financial stock network. Compared with the traditional threshold method, network modeling of stocks from the perspective of equity holding can study the stable relationship between stocks and shareholders over a longer period of time, and can analyze the structure and financial nature of the network through a variety of indicators. It provides new ideas for the application of complex networks in finance. It also has a certain guiding significance for investors to choose stocks, and it also provides a certain reference for financial supervision departments. At the same time, there are still some problems that have not been solved in this paper, such as single-mode projection will lose part of the information in the bipartite network, only the static network structure has been studied, and the dynamic network has not been further studied. I hope to continue to deepen the research in these aspects in the future.

This project was supported by the Natural Science Foundation of Guangxi (No. 2018GXNSFAA138095) and the National Natural Science Foundation of China (No. 61563013).

The authors declare no conflicts of interest regarding the publication of this paper.

Tong, H.P., Jia, Z., Zhang, M. and Qi, J.Z. (2021) Analysis of Stock-Shareholder Associated Network Based on Complex Network. Journal of Mathematical Finance, 11, 107-122. https://doi.org/10.4236/jmf.2021.111005