Apart from credit risk-evaluation indicator systems in the existing literature, especially firms’ attribute features, including the government structure, liquidity, profitability, solvency, operation capability, growth, capital market performance and cashflow conditions, this study innovated in incorporating RPT network features.
4.2.1. Construction of an RPT Network
It is given that, in contrast with unlisted firms, listed firms have more information disclosed, as well as greater impacts on the entire financial system. Therefore, this study built an RPT network based solely on listed firms. RPT data during the period from 2011 to 2019 were fetched from the Wind and CSMAR databases (the Wind Economic Database is the most widely used database in the financial industry in China, and its clients cover investment institutions, research institutions, academic institutions and regulatory agencies. The CSMAR, which is short for the China Stock Market and Accounting Research Database, is a comprehensive research-oriented database focusing on China’s Finance and Economy. CSMAR was developed by Shenzhen CSMAR Data Technology Co., Ltd. (Shenzhen, China), based on academic research needs, meeting international professional standards while adapting to China’s features) There were 231,964 records in total. This study used the deep network embedding algorithm. We processed the raw data into an adjacency matrix of RPTs between listed companies as the model input, the size of which was
. The detailed steps are explained later. Therefore, from the perspective of statistical learning, the sample size was adequate. To ensure the reliability and accuracy of the data, data from these two databases were cross-checked. We further referred to financial statements for random inspection of whether the RPTs of the companies were recorded correctly. The fields of RPTs included codes and abbreviations of securities, announcement dates, related parties and relations, amounts, trading methods and currencies. The attribute features of the disclosing party and related party included their full names in Chinese, their used names, IPO dates, listing segments, controlling shareholders and ownership, industrial sectors and business scope.
Table 1 shows an overview of the annual RPTs in the last decade.
According to data from CSMAR, the related relations, transaction methods, payment methods and industries involved were diverse. In terms of categories of related relations, the most common scenarios were the disclosure party and related party belonging to the same controller or parent firm and the related party being the controlling shareholder or sharing the same key personnel. In terms of transaction methods, sales or purchases and the provision or acceptance of labor accounted for the greatest proportions. These were common upstream and downstream relationships in the supply chain. In contrast, mergers and acquisitions, contractual joint ventures and technology services accounted for a small proportion. In terms of payment methods, cash, bank transfers and acceptance bills were more common than equity, bonds and physical assets. In terms of industry distribution, 24 secondary industries were involved. Listed firms in materials, capital goods, technical hardware and equipment, transportation and the energy industry disclosed the largest number of RPTs, while those involved in telecommunication services, family and personal products, insurance, banking, food and main product retailing had the least disclosure. The industry classification adopted in this study was the Wind industry classification, which is based on the GICS (Global Industries Classification Standard) adapted to China’s market.
This study used a weighted adjacency matrix to represent the RPT network. We define the network as , where is a node set and denotes the i-th listed firm. All of the listed firms were sorted in ascending securities code order. denotes an edge set, representing whether any two firms have related party connections.
In the weighted graph, if there is no related party connection between the i-th firm and the j-th firm, the weight of the edge between them equals zero. Otherwise, is the ratio of the RPT amount to the total assets of the j-th firm. In the same way, the denominator of represents the total assets of the i-th firm instead. Therefore, this adjacency matrix is unsymmetrical. If several transactions are disclosed between two firms, the numerator will be the sum of the transaction amount. Elements on the diagonal are all zero due to the fact that there are no RPTs with a firm itself.
Then, this study processed the raw data on RPTs to construct an adjacency matrix. Firstly, records of unlisted firms were eliminated, and missing values were filled with zeros. The currencies of all the transactions were converted into yuan. After that, transactions with the same disclosure party and related party were combined to derive the sum of amounts.
Table 2 shows the statistics on the two most important elements of the RPT network: nodes and edges. Taking the RPT network in 2019 as an instance, there were only 505 non-isolated nodes, which was far below the total number of listed firms disclosing RPTs. This was because only RPTs between two listed firms were included in this network. There were 376 edges; in other words, the adjacency matrix had 752 non-zero elements. However, the dimension of the matrix was
, so this network was highly sparse.
4.2.2. Structural Pattern Mining of the RPT Network
This study investigated the structural patterns of connected subgraphs in the RPT network using Networkx in Python, which is widely used in the study of the structure, dynamics and functions of complex networks. Firstly, we computed the degrees of all the nodes in the network. The degree refers to the number of edges connected with a certain node. A firm disclosing no RPTs is an isolated node whose degree is zero. The higher the degree of the node, the more RPT relations it has with other firms, thus exerting a larger impact on the network. A connected subgraph refers to an undirected graph whose nodes are all connected in pairs. Then, connected subgraphs with different numbers of nodes were counted. In
Table 3, we took the network in 2019 as an instance. It was divided into 187 connected subgraphs. There were 127 two-node connected subgraphs, which had the largest number. The “largest” connected sub-graph consisted of 31 nodes.
Considering the fact that connected subgraphs have different structures due to their different connection modes even if they share the same number of nodes, this study classified subgraphs based on node degrees. Taking a three-node subgraph as an instance, it had two different structures. One was circular, while the other was linear. The node degree lists were
and
, respectively, which allowed differentiation between these two structures.
Table 4 shows the statistics on the classification of the connected subgraph’s structural pattern.
Figure 2 is a schematic of each type of structural pattern.
From
Table 4 and
Figure 2, it is obvious that the RPT network represented by the adjacency matrix was high-dimensional and sparse. Therefore, it could not be directly used as an input for machine learning tasks such as classification and regression. This study employed network embedding algorithms [
5,
47] to represent structural features of nodes using vectors in the low-dimensional and dense space. In the meantime, local and global structures were well preserved. Then, the adjacency matrix was fed into SDNE to learn a two-dimensional vector representation. The values of the vector in two dimensions were
and
, respectively, both of which were input into credit risk-evaluation models.