Identification of the Credit Guarantee Network of Steel Trade Enterprises in Chi

MENG Xiao-lian(蒙肖莲) ，GU Wen-xiang(顾文祥)

School of Econonics and Management，Nanjing University of Science and Technology，Nanjing 210094，China

Introduction

Guarantee loan pattern is increasingly chosen by commercial banks for granting loans to enterprises.A guarantee network with complex relationship will usually form in the steel trade market as a result of the existence of mutual guarantee and serial guarantee.The profits of steel trade enterprises weaken gradually due to the changes of relevant national policies at present.More and more steel trade enterprises financed purely through the steel trade market gradually break away from the real economy.In addition，they even make various frauds to obtain loans from commercial banks.These loans are invested into other sectors such as real estate and the capital market instead of investing them into the steel business.The risks of steel trade market thus prominently increase.Exploring an effective method to identify the risk points in the credit guarantee network of steel trade enterprises has important practical and theoretical significance.

“Guarantee circle”is a unique economic phenomenon in China and the risk of the“guarantee circle”is a special credit risk.The risk spread of guarantee network has not been paid attention to so far.Most scholars focus on the spread and dynamic behavior of credit risk (or default)in the complex economic network.It has become popular that the financial connections among commercial banks and enterprises are precisely modeled as networks and the spread possibility of failures in them are estimated.A strand of literature in this field is to build the theoretical models for investigating the influence factors of the spread of failures.For example，Koopman and Lucas［1］thought that the credit link was a source of bankruptcy diffusion in economic network with three departments which were downstream enterprises，upstream enterprises，and banks.Lenzu and Tedeschi［2］found that the network architecture had a significant impact on the spread of systemic risk.Egloff et al.［3］put forward to embed the interdependence of microstructure in the macroeconomic factors model so as to analyze the mechanism of credit default contagion.The queuing theory was also used to analyze how the default of a company affected other companies in the network［4］.Some research explored how the failure of a bank spread through the banking system［5-6］.

Another strand of literature was to build a simulation model for describing the behaviour of the risks in the network.Barro and Basso［7］simulated the position of the company in the corporate network with the probability.Chen［8］built a simulation model based on the cellular automata.Some research contributions，such as in Refs.［9］and［10］，built simulation models to assess the danger of contagion in interbank markets.Krause and Giansantea［11］triggered a potential banking crisis by exogenously failing a bank and investigated the spread of this failure within the banking system.

There is not yet a unified definition of“guarantee circle”，because relatively perfect social credit systems have been established in most western developed countries，the related laws are perfect and various financing channels are unobstructed.“Guarantee circle”is a special interest group composed of many companies which are connected by mutual guarantee or serial guarantee［12］.Domestic scholars mainly focus on the cause，risk characteristics，operation mechanism of the“guarantee circle”among the listed companies because of the data availability［13-15］.Some research contributions also focus on the risk sharing mechanism of the guarantee chain［16］.

In this paper，we put forward an innovative method to identify the key risk points in the guarantee network.Firstly，the credit guarantee relationship among the steel trade enterprises in a market will be abstracted to form a guarantee network.Secondly，the key risk point will be found out based on the analysis of the related network structure indexes.Finally，the corresponding risk prevention strategies for guarantee network will be put forward.

1 Formation and Operation Mechanism of Steel Trade Credit Guarantee Network

1.1 Formation mechanism of steel trade credit guarantee network

A tangible steel market is usually comprised of the investors，steel trade enterprises，and guarantee companies.Most of the small steel trade enterprises in a market lack development funds in reality.They often set up a professional financing guarantee company through joint contribution in order to obtain loans from banks and the guarantee company will provide guarantee to these small enterprises to help them get credit loans from banks.In addition，enterprises in the steel market often combine to form a consortium and provide guarantee for each other.More and more enterprises in the steel market will gradually carry out mutual guarantee or joint guarantee，even the different consortiums guarantee for each other.A guarantee network with complex relationships thus will form in the steel market.Various complex guarantee networks are evolved from three types of guarantee network which are linear guarantee network，ring-form guarantee network，and star guarantee network (see Fig.1).Assume that there are four enterprises in the guarantee network，only when the neighbor enterprises guarantee for each other and all enterprises form a long chain，the linear guarantee network will form according to Fig.1(a).Figure 1(b)shows that the ring-form guarantee network will form based on the linear guarantee network，but the first and the last enterprises also guarantee for each other，then all enterprises form a closed ring.While star guarantee network has a core enterprise and all the other three enterprises only have guarantee relationships with the core enterprise as shown in Fig.1(c).

Fig.1 The structure chart of three types of basic guarantee network

1.2 The operation mechanism of steel trade credit guarantee network

Steel trade credit guarantee network is mainly composed of steel trade enterprises，guarantee companies，and commercial banks.The games among commercial banks，steel trade enterprises， and guarantee companies jointly promote the operation of the steel trade credit guarantee network.The games among these agencies for a simple guarantee business are shown in Fig.2.Small steel trade enterprises need a lot of capital for development，but the direct financing channel is blocked because of many limitations from commercial banks such as the enterprise-scale.Therefore，they must apply for loans from indirect financing channel.Banks tend to require enterprises to provide mortgage or pledge for a loan in order to reduce the risk.However，most small and medium sized steel trade enterprises are unable to meet the collateral requirements of the banks.They can acquire loans only from the third-party enterprises or guarantee companies.The guarantee company will provide guarantee for qualified enterprises and charge some guarantee fee after assessing the credit risk of these small and medium sized steel trade enterprises.

Fig.2 The relationship among banks，guarantee companies and steel trade enterprises

2 The Risk Analysis Method of Steel Trade Credit Guarantee Network

The risk of steel trade credit guarantee network makes up of the individual credit risk of the steel trade enterprises and the system risk of whole guarantee network.Risk management measures of the individual credit risk have become more and more mature，but the management of the system risk has been ignored so far.In this paper，an innovative network analysis method is put forward to identify the key risk points in the steel trade guarantee network.This method includes three steps as follows.

2.1 Establishing the database and matrix of steel trade credit guarantee network

The guarantee database of steel trade is built with the SQL Server 2008 database software whose attribute includes the serial number，bank name，bank code，company name，company number，guarantee amount，guarantor name，and guarantor number based on the guarantee data in a steel market provided by a commercial bank.The guarantee amount that every enterprise guarantees for all the other enterprises then can be added up into the database，and the matrix of guarantee network can be built by the Index function in EXCEL.

2.2 Building the steel trade credit guarantee network

The guarantee business involves only three partners which are the creditor (bank)，the debtor (steel trade enterprise)，and the guarantor (other steel trade enterprise or guarantee company)respectively.Each steel trade enterprise mostly has complex guarantee relationships with other enterprises or guarantee companies in the market，and thereby complex guarantee networks will form in the steel trade market.A guarantee network model is established in which the nodes represent the steel trade enterprises，the edges represent the guarantee relationships among the enterprises and the weights of the edge amount to the guarantee amounts respectively.

2.3 Analyzing the network structure indexes

The commercial banks cannot pay more attention to the risks of all enterprises and the system risk in the guarantee network，because there are so many enterprises and the steel trade guarantee network is so complex.They must find out and strengthen the management of the key risk points which are composed of the enterprises whose bankruptcy may lead to the rupture of many guarantee chains.The key risk points connect with many enterprises and act as a broker in the network.Three indexes are chosen to find out the key risk points in the network，which are centrality，honest broker，and structural hole.

3 The Empirical Analysis

The key risk points in a guarantee network will be identified based on the guarantee data of the 83 steel trade enterprises in a steel market.The network analysis method is described in section 3.3.

3.1 The descriptive statistics analysis

The descriptive statistics of the 83 steel trade enterprises in a market are calculated by sorting the data so as to make their basic information and guarantee amounts clear.The descriptive statistical analysis results of these enterprises are showed in Table 1 and the descriptive statistical analysis of guarantee data is shown in Table 2(the unit is ten thousand yuan).

Table 1 The descriptive statistics of the enterprises in a steel trade market

From Table 1，we can glean that these enterprises are mainly small and medium-sized enterprises，and most of them are in the growth and mature period.In addition，the enterprises'ownership patterns are mainly private enterprises，accounting for 84% of all.

Table 2 The descriptive statistics of the guarantee data in a steel trade market

Table 2 shows that the lowest guarantee amount is 100 000 yuan，meanwhile the highest amount reaches 23.7 million yuan.In addition，the differences of the variances between different intervals of the guarantee amount are very large，which means not only the guarantee relationships are very complex，but also the differences of guarantee amount are very large.Therefore，it is difficult to build a weighted guarantee network.

3.2 The build of steel trade credit guarantee network

The matrix of guarantee network can be generated by using the Index function.Only a part of the sample data is presented in Table 3 because of the big matrix.The first line and the first column of the table are the serial number of the enterprises，and the remaining parts represent the guarantee amount that enterprise i guarantees for enterprise j.The unit is ten thousand yuan.

Table 3 The matrix of the guarantee network in a steel trade market

The guarantee network model can be built and mapped by using the Ucinet software based on the matrix of the guarantee network of a steel trade market.And the biggest guarantee network formed by 44 enterprises in the steel trade market is shown in Fig.3.Meanwhile，the other networks which contain 35 isolated nodes and two networks formed by two nodes respectively are not shown in the figure.

Fig.3 The biggest guarantee network diagram of a steel trade market

3.3 The analysis of network structure indexes

Some measuring results of the three network structure indexes are showed in this section，which are centrality，honest broker，and structural hole.

3.3.1 The analysis of centrality

Centrality mainly includes two kinds of indexes which are absolute centrality and relative centrality.The absolute centrality refers to the amount of the nodes that connect to this node directly，while the relative centrality is the ratio of the absolute centrality of a node to the maximum possible absolute centrality in the network.The centrality can be used to measure the amount of the enterprises which guarantees for an enterprise，as far as the guarantee network is concerned.Only the measuring results of the nodes whose absolute centralities are at the top are given precisely from big to small in Table 4 because of the big size of the guarantee network，

Table 4 Centralitys of the enterprises in a guarantee network model

Table 4 shows that the largest absolute centrality is 23，and the corresponding relative centrality is 0.28.We can glean that both the absolute centrality and the relative centrality of the enterprise numbered as 1 are the biggest in those of all enterprises respectively.It means that the number of the enterprises guaranteeing for this enterprise is the largest.Meanwhile，the centralities of other enterprises are relatively small.The enterprise numbered as 1 thus has the largest number of guarantors and is located in the core of the networks.Once this enterprise runs into credit risks，the risk may spread to the guarantors and even trigger a chain reaction.This enterprise thus should be taken as a key risk point.

3.3.2 The analysis of honest broker

Honest broker index contains three kinds of indexes which are pure broker index HBI0，weak broker index HBI1，and nonbroker index HBI2.HBI0 is mainly used to measure the frequency of a node acting as a broker.HBI0 depicts that there is no relationship between any two nodes which are connected by the broker and it can be used to measure the controlling degree of the broker to the enterprises connected with it.As shown in Table 5，only the measuring results of those nodes whose HBI0 is at the top are given precisely from big to small due to the big size of the guarantee network.The first conclusion from Table 5 is that the size of individual network(the amount of nodes connected to one node)of the enterprise numbered as 1 is the largest，and its HBI0 is also the largest.Apparently，the frequency of this enterprise acting as a broker is the largest.Once the risk such as credit risk occurs in this enterprise， the risk may propagate through many other enterprises and make a lot of guarantee chains rupture.This enterprise thus should be taken as the key risk point.In addition，the sizes of the individual networks of enterprises numbered as 49 and 75 are listed as the second and the third large ones respectively.Their HBI0 are 18 and 12，accounting for 85.7% and 57.1% of the total amount of all relationships that it can connect respectively.These two enterprises also have an important role in the network and should be taken as the key risk points.For all other individual networks，the sizes and the pairs of relationships are much smaller than those of three individual networks numbered as 1，49，and 75.The enterprises numbered as 1，49，and 75 should be taken as the key risk points to manage based on the analysis of honest broker.

Table 5 Honest broker index of the enterprises in a steel trade guarantee network

3.3.3 The analysis of structural hole

Structural hole is usually measured by two indexes which are effective scale and degree of limitation.Effective scale is equal to the size of the individual network minus the redundancy of the individual network.Degree of limitation refers to the ability of the nodes using the structural holes in their own network.Only the measuring results of the nodes whose effective scales are at the top are given in Table 6 for the big size of the guarantee network.

Table 6 Structural holes of the enterprises in a steel trade guarantee network

The first conclusion from Table 6 is that the effective scale of the enterprise numbered as 1 is 51.72，which is the largest in the whole network;meanwhile its degree of limitation is 0.05，which is the smallest in the network.It means that this enterprise has more structural holes than other enterprises.Once the credit risk leads to the bankruptcy of this enterprise，the structural holes will be broken and lose the function as a buffer.Then the credit risk may spread rapidly over many enterprises in the guarantee chains.The effective scales of the rest enterprises are much smaller than those of the enterprise numbered as 1.We notice that the degrees of limitation of the enterprises numbered as 49，23，and 67 are all less than 0.4，which means that they also have many structural holes and the banks need to strengthen risk management on them.

Based on the analysis of the three network structure indexes above，we find that the enterprises numbered as 1，49，75，23，and 67 are located in a relatively important position and should be identified as the key risk points in the steel trade guarantee network.

4 Conclusions

Commercial banks have adopted sophisticated risk management technologies for individual steel trade enterprises at present.However，an effective management mechanism has not been established for identifying the system risks of steel trade credit guarantee networks.In this paper，we provide a new method for commercial banks to identify the system risks of the guarantee networks.On one hand，the commercial banks can build a guarantee network based on the guarantee relationships among the steel trade enterprises applying for loans so as to examine whether these enterprises will form a “guarantee circle”.If the“guarantee circle”has formed，the commercial banks need to analyze whether these enterprises are the key risk points and examine the repaying ability of the guarantors before lending to them so as to reduce the risk possibility.On the other hand，for the existing steel trade guarantees networks，the banks can sort through the guarantee data to build guarantee credit networks and use the network analysis method to identify the key risk points so that they can prevent the further risks propagation in it.

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