The assessment of credit risk of real-estate of Chinese banks has become a hot point nowadays. Traditional gross risk-evaluation methods are mainly Discriminant Analysis (DA) and logistic regression, and the most common approach is a credit rating system based on logistic regression. Yet the daily ripening neural network technique has opened up a new idea for experts in fields of bank credit and credit evaluation. In this paper, two methods-the logistic model and the BP-neural network technique, are compared in their application in the evaluation of credit risk of real-estate in Chinese banks and then tested with samples of listed real estate agencies. Results show that the BP-neural network technique has superiority over the logistic model in quantizing and classifying gross risk of real estate agencies.
[Keywords] Credit risk in real estate agencies; logistic model; BP-neural network
Along with the capitalization process of housing and urbanization, real estate is improving. That real estate fever keeps warming has gradually engendered bad assets for several commercial banks. As a result, they are likely to adopt a discreet and conservative strategy when getting involved in housing credit. In view of this, it is necessary to select an appropriate evaluation method for credit rating to effectively warn of housing credit risks.
Traditional risk assessment methods include Discriminant Analysis (DA) and Logistic Regression. Altaian (1968) built a famous warning model of multi- variables, the Z-model, by using multi- variate discriminate analysis and then revised it as the ZETA model. Ohlson (1980) is the first one who used the logistic regression model to warn of financial risks. Wiginton (1980) applied a logistic regression model and discriminant analysis to credit rating and then compared the two methods, which showed that the former was better than the latter. Tang Youyu (2002) tested the accuracy of the Logistic Model by sampling 5 listed companies with good financial conditions and 5 companies with bad conditions from the Shanghai and Shenzhen Securities markets. Qi Zhiping, Yu Miaozhi (2002) got satisfactory results by building a Logitstic Model with quadratic terms and intercross terms. However, the common limitations of these methods are that they focus on financial analysis of companies, but ignore the facts of projects involved. Good projects will help enterprises with poor performance get out of bad conditions, but those methods tend to reject loans. On the other hand, the generality of these models is bad. They need to re-estimate the parameters of samples when the environment and time change.
Through continuous learning, neural networks can now find the law from a large number of complex data in an unknown pattern. Continuous learning overcomes the complexity of traditional analysis and the difficulties of selecting an appropriate function, since it puts forward a higher request in Basel Treaty on total risk evaluation models about the classification of credit rating and the grades have to fall into the five categories as banks have noted. A neural network approach meets these needs well, and credit risk can be better involved in this model. In 1992, Jensen (1992) used a BP neural network to categorize loan corporations, and the accuracy of rating was up to 76%-80%. Trippi and Turba (1996) introduced the application of neural networks in finance and investment. In 2000, David West modeled five different neural networks to investigate the accuracy of credit rating marked by commercial banks. Malhotra (2002) used neuron-fuzzy system to differentiate "credit-good" and "credit-bad" borrowers.
Wang Chunfeng (1999) adopted the neural network technique to evaluate the credit risks of commercial banks. Yu Ruifeng (2007) introduced an index system to firm credit risk assessment using the BP neural network based on supply chains to evaluate loan applicants' total solvency. This research shows that this system is capable of rating loan applicants effectively and precisely. These findings indicate that the neural network technique presents a good prospective application for risk evaluation for commercial banks. Therefore, focusing on the evaluation of the housing credit risk of banks, this paper tests two different methods: the logistic model and the BP neural network. Then, the results are compared in detail to verify the applicability and relative superiority of each method in quantizing and categorizing housing credit risk for Chinese commercial banks.
Test Process of Logistic Model
Introduction to Logistic Model
Regression is one of the most widely used methods for credit rating, and logistic regression is the most representative one. From mathematical programming, we obtain some indexes from samples of variables in certain ways and take them as eigenvectors. The basic idea of regression is to model these indexes to be a dependent variable, which can predict the default rate p of loan applicants:
On the left side of (1), the ratio in the parenthesis is called "risk rate" or "occurrence rate," and its value span is in accord with the spans of the variables on the right side of the equation.
When we estimate the values of parameters (β^sub 0^, β^sub 1^,...β^sub k^) by regression, according to (2), we can forecast the probability of default of new credit appliers and assign the probability to appropriate categories classified by credit evaluation. Then, we use logistic regression to rate credit. Further- more, to make the total rating results clearer, we can assign the credit rate to independent variables among Eigen-variables.
First, a logistic model is built up with 2006 financial data of 53 listed real estate companies. Among these companies, 40 are selected as a sample to build up the model, and the other 13 are sampled to test the results. Twenty variables (from Xl to X20) are chosen by factor analysis when building this model: current ratio, asset-liability ratio, inventory turnover ratio, main operating margins, ROE, earnings per share, ROA, growth ratio of net profit, operating cash flow per share, main operating cash ratio, bad assets ratio, total profit, order of clients, sales status of real estate, quality rate of product development, supply of real estate in the district, market share, level of financial management, willingness to pay debt, and land reserve. The 40 companies are divided into two sets: one is companies with the total scores below 60, another is those above 60. The main parameters used in the logistic model include all 20 variables; circulation stops when the reduction of the log value of likelihood function L is less than 1%. Results are shown in Table 1.
Table 1 illustrates that the accuracy of the logistic model with 20 variables is 70. 83%, but the accuracy rate for low-risk real estate companies is 75%; for high-risk companies, it is only 66. 67%. According to the implication of logistic models, we have the following logistic regression equation of probability classification:
We can use the above equation to forecast the risk of a firm, and the judging standard is: when p>0. 5, the corresponding company is classified into the set of high risk; when p <0. 5, it is classified into the set of low risk.
Predictability of Logistic Model
According to the logistic model built on 40 listed real estate companies and the derived probability classification equation, we input the other 13 companies into the equation as a test sample. Among the 13 companies, there are 7 low-risk firms with scores above 60 set and 6 high risk firms with scores below 60. XK X2 ...X20 represent 20 financial and non-financial indexes as mentioned. In the end, the results show there are 5 companies of low risk classified as low risk, so the correctness is 57. 14%; the number of high-risk companies classified as high risk is 4, and the correctness is 66. 67%. To summarize the sample that comprises the 20 listed real estate companies, the forecasting accuracy of logistic model is 61. 90%, as illustrated in Table 2.
Test Process of BP Neural Network Technique
Basic Principles of BP Neural Network Technique
The BP neural network is a prorsad network with multi-layers that propagate in one dimension, which can be seen as a highly nonlinear mapping from input to output. Its basic structure is shown in Figure 1.
Input signals originate from input layer nodes and pass through each hidden layer node toward output layer nodes. The nodes on each layer only affect the nodes on the next layer, and every node is a neuron. Define input nodes in the BP network as xj, hidden nodes as yi, output nodes as oe, net weights from input nodes to hidden nodes as Wij, net weights from hidden nodes to output nodes as Tei, and expected results of output nodes as te. By adjusting weights and threshold values of each node, we can make the deviation between output of neural network and target values meet the requirement training accuracy and accomplish the training of network.
1) Model confirmation. According to results found by Hecht-Nielsen, when the nodes of the neuro-cloud network have different threshold values, continuous functions of any closed interval can be approximated through a net of a hidden layer, so any mappings from n-dimension to m-dimension can be attained by a three-layer neuronal network based on the BP algorithm. In 1988, Cybenko pointed out that when every node is structured to an s-type function, one hidden layer is enough to realize any classifications, while two hidden layers are enough to denote any functions of input graphs. In sum, any required adjudicated boundaries can be obtained by a network with two hidden layers to realize classification, but for small networks, two-layer networks have no advantage over one-layer networks.
As a consequence, in this paper, we are going to use a three-layer network, that is, one input layer, one hidden layer, and one output layer.
2) Confirmation of neuron number. There are some empirical formulas to refer to about the number of BP network layers and nodes on the hidden layer, but there is no completed theory. So, to a larger extent, it is empirical and experimental to determine the node number of the net. In 1987, Hecht-Nielsen 's findings suggest setting the node number of the hidden layer of one-hidden-layer neural network at 2N+1 , and N represents node number of the input layer.
3) Selection of accuracy. As is generally acquired, a limitation of error between output and real value should be set (which is usually variance of output value and actual value). According to Matlab and the model, we can set different accuracies at 10-3 or 10-5.
4) Selection of transfer function. Transfer functions of BP network are mainly purelin function (linear function), tansig function, logsig function and so on. For input financial indexes varying from positive to negative and the variance is so big that we choose to use a tansig function as transfer function of input layer nodes. It fits BP network for its mapping is from ( - oo,+oo ) to (-1, 1).
5) Selection of training function. There are many training functions of the BP network in which the grathent descent function, Levenberg-Marquardt momentum method and pycno-BP algorithm, are normally used. The main difference between these algorithms is learning efficiency. LevenbergMarquardt momentum method is the optimization of grathent descent function. The merit of this method is its speed, but it needs larger memory.
Credit Rating Model of BP Neural Network
Input and Output. Take all secondary grading indexes as an input vector X=(ul, u2, u3, ..., u25) and the total values of credit rating as an output value Y. Input vector contains 12 financial indexes and 13 non-financial indexes. Financial indexes include current ratio, inventory turnover ratio, earnings per share, growth ratio of net profit, business gains, total profit, asset liability ratio, main operating margins, ROE, operating cash flow per share, main operating cash ratio, and ROA, while non-financial indexes include order of clients, exploitation capability, sales status of real estate, quality rate of product development, backup by government, government grounds, brand reputation, customer location, quality of leader, basic management level, financial management level, willingness to pay debt, firm profit prospect, market tendency, market ability of real estate, and land reserve. We choose interval methods to quantize credit rating. That is to say, credit grades of real estate companies correspond to interval spaces of output values, according to the categories indicated in Table 3.
Structure of Network. There is no complete method to determine the number of neurons of the hidden layer. In this paper, the empirical method is adopted. That is, when the size (or number of learning specimen) is N, then the number of neurons of the hidden layer is approximately 2[the square root of]2. In this way, a 25-10-1 three-layer BP neural network is chosen as the basic structure of the net.
Software MATLAB. Matlab6. 0 for Windows is adopted in the course of network training, and for the training on BP neuron network, Neural Networks Toolbox for Matlab is used.
Application of BP Neural Network
Let us target the 53 real estate companies. At first, we quantize the 53 companies according to the credit rating index system and get input vector group Xi, i=l, 2, ..., 53. Experts have estimated the credit grades of these firms, which are represented by vector group Yi, i =1, 2, ..., 53. Take (Xi, Yi) as learning samples, where i =1, 2, ..., 48; and take (Xj, Yj) as rating objects, where j =49, 50, 51, 52, 53. The purpose of the experiment is to compare the result evaluated by BP neural network with that by experts to demonstrate the effectiveness of the application of BP network on the credit ratings of listed real estate companies.
The BP neural network's structure confirms to the input layer-hidden layer-output layer order and is set as 25-10-1. Initial weights among neurons are random values in (0, 1), with learning accuracy e=0. 005, and gaining item of pycno-descending algorithm ?=0. 5. To illuminate the effectiveness of BP neural network, the experiment was performed 10 times to compare the expected output values Y49=68. 410, Y50=66. 530, Y51=58. 328, Y52=57. 930, Y53=47. 100 (the corresponding credit grades are normal, concerned, inferior, suspicious and loss) with network output values Yi*(i=49, 50, 51, 52, 53), and further to compare their credit grades.
Each of the 5 real estate firms chosen from the sample represents one type of the 5 bank credit grades: normal, concerned, inferior, and suspicious and loss. Findings are shown in Table 4, Table 5, Table 6, Table 7, and Table 8.
From Table 5, for the ones of the second type classified as concerned, there are two false judgments, so the misjudgment rate is 10%.
From Table 6, for the ones of the third type classified as inferior, there are three false judgments in ten times, so misjudgment rate is 30%.
From Table 7, the rate of false judgments made by the BP neural network is 40%, where two suspicious one are graded as concerned, and two suspicious one are graded as losses. However, from the perspective of bad bank loans, the misjudgment rate can be reduced to 20%.
Last, from Table 8, the misjudgment rate made by the BP neural network about this type is high, where there are four misjudgments, in which three losses are marked as suspicious and one loss is marked as concerned, so the misjudgment rate is 40%.
Comparison of BP Neural Network with Logistic Model
As above, the logistic model is used to categorize the 53 listed real estate firms into two types: bad and good. Simulated results are displayed in Table 3. From Table 3, the accurate rate of total classification is 61. 90%. However, by using a BP neural network, we further categorize these firms into five sorts: normal, concerned, inferior, and suspicious and loss, which made the accurate rate of total classification 72%. The accuracy of forecasting by the BP neural network is higher according to this. Based on results above, we can conclude that the credit rating model based on the BP neural network has an advantage over other models in the respect of judgment accuracy. Although the results are not as significant as those found by foreign experiments on the same level, for the learning samples, which are not selected by experts and are doubtful in their reliability and veracity, these results are sufficient to verify that the BP neural network is a better model in the field of credit rating judgment of bank's clients.
Based on the analysis of the fundamental characteristics of neural networks and artificial neural networks, this paper explores credit risk classification based on a three-layer output BP neural network with a single node on each layer and tries to match our evaluation results with the classification standard of loans in the Basel Treaty. This classification is credit-in-five-sorts method, which has now been widely accepted and used in Chinese commercial banks to divide real estate companies into normal, concerned, inferior, suspicious, and loss in respect of credit risk. According to above classification, we tested the BP-neural network and the logistic model. The results suggest that that BP-neural network has superiority over other models in total risk evaluation of real estate for Chinese commercial banks.
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Wei Guo, Meiyan Cao, Ke Gong
School of Management, Huazhong University of Science & Technology, Wuhan, China
Dr. Wei Guo is Associate Professor of School of Management, Huazhong University of Science & Technology (HUST). He holds Ph.D of management. He finished his postdoctoral research during 2003-2005 in postdoctoral research center of Control Science & Engineering in Wuhan, China. He has published 53 papers in core journals in the areas of capital markets, real estate credit risk management, finance and accounting both in Chinese and in English. He is the vice secretary general of Wuhan System Engineering Society, a member of IEEE. Dr. Guo can be reached at firstname.lastname@example.org…