AN IMPROVED CREDIT SCORING METHOD FOR CHINESE COMMERCIAL BANKS

AN IMPROVED CREDIT SCORING METHOD FOR CHINESE COMMERCIAL BANKS Jianping Li Jinli Liu Weixuan Xu 1.University of Science & Technology of China, Hefei, 230026, P.R. China 2.Institute of Policy and Management Chinese Academy of Sciences, Beijing 100080, P.R. China ljp@mail.casipm.cn 1.University of Science & Technology of China, Hefei, 230026, P.R. China 2.Institute of Policy and Management Chinese Academy of Sciences, Beijing 100080, P.R. China ljp@mail.casipm.cn Institute of Policy and Management Chinese Academy of Sciences, Beijing 100080, P.R. China wxu@mail.cassipm.cn Yong Shi College of information Science and Technology University of Nebraska at Omaha, Omaha, NE 68182, USA yshi@unomaha.edu Abstract This paper presents an improved credit scoring to the Chinese commercial bank for credit card risk management. To get a comprehensive scoring for classifying the grade, the principal component analysis is used, which enables us to calculate the weights of the original indexes, and to get a comprehensive function for computing the score of new applicants. Comparing with other methods, this method has an outstanding merit that it gives objective weights of original indexes and can easily adapt to the different economic & cultural environments in different regions and the population drift in same region which cause the disparity of credit scoring. A demonstration test shows that the model complies with the practice in credit card risk management, hence has an application foreground. A comparison study indicates that this method has better results than those scoring methods currently used in banks. Keywords: credit card; risk management; credit scoring; principal component analysis 1. Introduction With the conception of 2003, the prime year of credit card in China put forward by the China Merchants Bank, the competition in credit card market is increasingly heated, and the scale of issuing credit card is expanding rapidly in China. As to the credit card risk management, how to analyze the customers credit risk effectively and establish the reasonable credit issue criteria has become a key task of the credit card issuers. In credit card risk management, credit scoring is widely used. For example, more than 97% of banks use the scoring system to decide the credit card loan s application in USA. Credit scoring is a quantitative method to deal with large quantities of small loans in commercial banks. Based on the scoring models established by the mass historical data in bank, credit scoring predicts the default rate of the loan applicants or the exited loan. After collecting the applicant s

information, the bank gives a score via the credit scoring system, and decides whether grant the loan or not in a very short time according to the score. At present, the Chinese banks also use the scoring method in card issuing as the assistant technique. The general process includes the following steps: Choose some characters and attach different weights to according classes, score the applicant according to his/her characters and decide whether or not grant credit and how much will be granted considering the applicant s total score to the credit grade. At present, the social credit system has not been fully established and takes little effect in Chinese commercial banks. Many reasons pose great barrier to applying the scoring method to practice, such as: (1) Lack of characters The popular credit scores such as FICO score and Credit Bureau score choose at least 50 to 60 variables, while the Chinese banks use only 15 characters or so. This leads to inadequate assessment of the applicant s risk. (2) The methods in credit scoring have adaptability problem in practice Amongst different regions of China, there are remarkable differences in the economic development level, ideas and other aspects. Therefore, using the same score criteria will inevitably cause the evaluating error. Even in the same region, as China is experiencing a high speed development in economy, society and culture, the economy environment, population structure and the life style are changing very fast, which is called the fast population drift. This also causes unconformity between the scoring result under original criteria and the real situation. It is required that the scoring model adjust the weights of the characters, the score of the detailed class and the credit grade scores according to different samples. The prevailing score model in Chinese commercial banks is far from this requirement. The first problem lies mainly in the influence of the external credit environment, and the improvement is also based upon the total credit environment reform, which is a stepwise process. This paper aims to solve the second problem the adaptability of score model. An improved method credit scoring is presented which has a preferable adaptability in theory. The demonstration shows it meets the need of credit risk management, and is superior to the current method in use. And the test results show it has a promising applicative foreground. 2. The basic thoughts and construction process of the improved method We construct a new credit score method trying to overcome the current method s problem of adaptability. Its basic thought is as follows: Credit scoring can be expressed by a kind of comprehensive function of each primitive index, y = f ( x1, x2,..., x n ). n is the number of primitive index. In our method, suppose y is a linear function. This linear comprehensive function could be obtained by analyzing the historical samples. And the applicants score can be easily calculated using this function. According to the distribution of the bad person during the score, the bank will set up different grades and establish the scoring criteria based on the concrete strategy and the need of business. Then, the bank use the comprehensive function to predict the new applicants score, and determine whether to grant them credit or not and how much credit to be granted according to their scores and the existed scoring criteria. In the comprehensive function, how to get the index coefficients is a key problem. These coefficients satisfy at least the following conditions: (1) Can be changed easily if the sample is changed; (2) Are objective; (3) And can guarantee the rationality of the assessment result We use the principal component analysis method to get the coefficients according to the above terms. Principal Components Analysis (PCA) is a multivariate statistical method to reduce the dimensions through transforming multiple indexes into fewer comprehensive indexes, which was put forward by Hotelling in 1933. Dimension-decline and giving the relative importance by the difference of data are the main characteristics of this method. In current Chinese personal credit assessment, there are few indexes for using, therefore, choosing how much principal factors is not the main problem under the current circumstances. Our target of using the PCA is not to emphasize its dimension-decline function to reduce the complicated

degree of the problem, but to concentrate on the following purposes: (1) To obtain the objective coefficients The PCA method emphasizes the difference principle, and creates the coefficients fully based on data themselves. So, the coefficients have the objectivity and avoid too many human s interferences. (2) To remove the assessment deviations caused by macroscopic factors and the population drift. According to the principle of PCA, we can get different principal factors and indexes from different samples. So, we can divide China into different regions according to economic environment and apply different samples to compute and induce different scoring functions. Using the different score and the bad persons distributions, we can set up the different credit criteria in different regions. In the same way, this method can also easily realize the dynamic change of the comprehensive function in the same region. Once the bank considers there is a big population drift in one region, it can adjust the comprehensive scoring function of the new sample. The detailed constructing process can be divided into the following steps: (1) Sample selection Select a sample that is composed of a mount of good and bad records in history. The good and the bad will be defined by each bank themselves. Divide the total sample into two sets stochastically: one is a training set to compute the comprehensive function; and the other is a test sample to verify the validity of the comprehensive function. (2) Data pretreatment In order to guarantee the accuracy of using the PCA method, we carry out the data pretreatment primarily to make the data have the same direction and to guarantee the indexes have economic meanings. In the light of this thought, we classify the sample data by the current division standard of one Chinese commercial bank. And then, take the odds of good/bad as the input data to PCA computation in every certain class. The bigger the data are, the better they will be. For example, the age index is divided into 5 concrete categories: 18-22,23-34,35-40,41-60 and > 60. If there are 60 good and 34 bad in the 18-22 category, then the input data is 1.765(60/34). The other index may be handled similarly. (3) PCA calculation After the data pretreatment, the PCA could be calculated. Firstly, examination of PCA method s fitness is necessary. The tool for the examination is a KMO and Bartlett s spheroid test. If the KMO value is larger than 0.5, the Bartlett test is significant. This means the data are suitable for the PCA method. (4) To build the predicting function Suppose we have selected s principal factors, the scoring function of the principal factors in the training sample could be expressed as: rate : F = a1z1 + a2z2 +... + as zs (1) zi is the i th principal factor, a i is its contribution a i λ λ i m = k m= 1 a tl = k λ λ m m= 1 l m m= 1 ( i, l = 1, 2,..., k ) th ( λ i is the i eigenvalue sorted by descending, a tl is the cumulative variance contributions of principal factor z to z ). Then, 1 l Z = bx+ bx+ + bx (2) i i1 1 i2 2... in n Take the equation (2) into equation (1), we get: F = c x + c x + + c X (3) c j 1 1 2 2... n n s = a ib i j i = 1 ( i = 1, 2,..., s; j = 1, 2,..., n) (5) Setting up the credit grade According to the comprehensive score and the bad person s distribution in the training sample, we can set up the different grade by a certain method and standard. That is, one can classify the different class based on the comprehensive score. (6) Assessing new applicants After the same data pretreatment and data standardization like the train sample, the new applicants credit score could be predicted using equation (3). And it may be determined whether to grant him/her credit or not according to his/her score and the credit grade given by step 5. Figure 1 shows basic thought of the method and constructing process explicitly.

Original data Data pretreatment Principal Component Analysis Compute the comprehensive i Classify different credit grade according to the score and the odds of good/bad Compute the character weight Build the comprehensive function The score of new applicants Reject No Reach the cutoff? Yes Granting the corresponding credit Figure 1 the basic thought and construct process of our method varimax method rotation to conduct factor analysis, we 3. Demonstration results select ex-10 principal components, and the cumulative variance is 86.74%. Based on the method presented in part 2, here is a Table 1 KMO and Bartlett s test of spheroid demonstration of the model. We use a sample including Testing Value 1350 credit card records, and define two classes of credit card users: the bad and the good. 1000 records were selected at random as the calculating sample to get the comprehensive function. These 1000 records include 755 KMO Measure of Sampling Adequacy 0.787 good and 245 bad. The other records serve as the testing sample to test the validity of the comprehensive function. 262 good and 88 bad were within this sample. We choose 14 characters including age, income etc, and take the SPSS11.0 as the computing software. Bartlett's Test of phericity Approx.Chi-Square 1337.31 Df. 91 Sig. 0.000 3.1. The training results After the data pretreatment, SPSS gives KMO value and Bartlett examination, as is shown in the tale 1: The KMO value is 0.787>0.5 and the Bartlett examination is significant, so the principal component analysis is suitable. Take 0.8 as the cutoff to get the eigenvalue, using We use the equation 1 to compute the comprehensive score, and the result shows that the score of 1000-sample is very like a normal distribution, as the figure 2 shows: means is 0, and the standard deviation is 34.18 (considering the actual condition, we magnify the score 100 times).

-90.0-70.0-50.0-30.0-10.0 10.0 30.0 50.0 70.0 90.0 200 100 0 Std. Dev = 34.18 Mean = 0.0 N = 1000.00-130.0-110.0 110.0 ZHUFEN Figure 2 the distributions of the sample scores According to this characteristic, we classify the score into 6 class based on the standard deviation, the means, one standard deviation and two standard deviation as the cutoffs. Table 2 shows the detail. Table 2 Training results in multiple-class Score 68 34~68 0~34-34~0-68~-34 <-68 Class 1 2 3 4 5 6 Total Good credit 27 91 357 210 58 12 755 Bad credit 1 5 63 107 49 20 245 Total 28 96 420 317 107 32 1000 The bad rate 0.0357 0.0521 0.15 0.3375 0.4579 0.625 Odds of good/bad 27 18.2 5.67 1.96 1.18 0.6 *The score in every class includes the lower value and no t includes the upper value If the applicant s comprehensive score is larger than 68, this means larger than two standard deviation, accordingly be classified as the first grade and stands the highest credit. In this training sample, there are 28 records, 1 is bad and others are good, so the bad person s rate is 3.57% (1/28) in this grade. This bad rate can look like a type of default rate. Similarly, the comprehensive score between 34 to 68 belongs to the second grade, meaning a good credit in this class, and the bad person s ratio is 6.25%, and accordingly we get 6 grades. The bad person s ratio of every grade can be a measurement of credit risk in corresponding grade, the bigger the ratio is, the larger credit risk will be. According to the result, from the grade 1 to grade 6, with the reducibility of the comprehensive score, the default rate increases monotonously, that is, the lower comprehensive score, the bigger credit risk. This result accords with the theory of credit risk management. According to the general theories of the scoring, if the scoring of the applicant belongs to the grade that the odds of good/bad higher than 4, the bank will grant the credit to him/her. So, we classify the sample to two classes according to whether the odds of good/bad larger than 4, one class means good that will be granted the credit, and the other means bad that will be refused. In this training sample, if the applicant s score is higher than 0, he belongs to the good class, and if lower than 0, belongs to the bad class, see as the table 3:

Score Table 3 Training results in two-class 0 <0 Total Class 1( g ood credit) 2( bad credit) Good credit 475 280 755 Bad credit 69 176 245 Total 544 456 1000 The bad rate 6.88 1.59 Classification error 0.2816(type I) 0.3709(type II) Average error 0.349 The average error is 34.9%, the type I error, which grant credit to a bad risk applicant, is 28.16%, and type II applicants comprehensive score. By the result of SPSS, we can compute the coefficient of every index, table 4 shows error, which deny credit to a good risk applicant, is 37.09%. the result (for the convenience and corresponding with the comprehensive score, each coefficient all extended 100 (2) The testing results times). As to the prediction to new samples, we should get a predicting function, through which we can compute the new Table 4 the coefficient of each index Index X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 Coeffi cient 9.49 7.07 6.79 8.60 4.39 6.16 0.48 4.73 5.50 6.97 8.00 7.48 8.16 7.93 T hen, we get the comprehensive function as flows: y = 9.49X 1+7.07X 2 +6.79X 3 +8.60X 4 +4.39X 5 +6.16X 6 +0.48X 7 + 4.73X + 5.50X + 6.97X + 8.00X + 7.48X + 8.16X +7.93X 8 9 10 11 12 13 14 (4) After the data pretreatment and data standardization classify the scores with the same classifying method that has the same treatment as the training sample, we use introduced in train results part. Multiple-class results see the the equation 4 to compute each applicant s score, and table 5 and two-class results see table 6: Table 5 testing results in multiple-class Score 68 34~68 0~34-34~0-68~-34 <-68 Total Class 1 2 3 4 5 6 Good credit 16 58 126 45 13 4 262 Bad credit 0 3 27 30 19 9 88 Total The bad rate 16 61 0 0.0492 0.17647 0.4 0.594 0.692 Odds of good/bad - 19.33 4.667 1.5 0.684 0.444 * The score in every class includes the lower value and not includes the upper value 153 75 32 13 350

Table 6 testing results in two-class Score >0 <0 Total Class 1(good credit) 2(bad credit) Good credit 200 62 262 Bad credit 30 58 88 Total 230 120 350 The bad rate 0.1304348 0.48333333 The o dds of good/bad 6.6666667 1.06896552 Classif ication error 0.3409091(type I) 0.23664122(typ e II) Average error 0.2628571 With the result compared with that of training samples, make a contrast research upon the current scoring method the testing result is better not only in bad person s ratio in the former two classes in multiple-class, but also in the average error in two-class. This shows that the model has a preferable application foreground. How to select appropriate classifying value to get different classes will be based on the stratagems and the business demand of the bank. This can be represented by the credit criteria that bank have selected, strict or lenient. Bank will consider the default rate and the classification error synthetically, that is, based on the risk, set different credit grades, and make out the corresponding credit amount. The comprehensive score presented in this paper will realize the compounding classes under the different default rate and misclassifying rate conveniently. 4. A Comparison Study that one big commercial bank is using in China. The first class means the good credit and will grant the credit to the applicants, and the other class means the bad credit and will refuse the application. The clique value of the bank is 110, which is the lowest score that can grant the credit to the applicants. We get 199 records that belong to the first class and 151 records to the other in the 350 samples by the 110-clique value. To make a reasonable contrast, we classify two classes which have the same records in each class, that is, 199 records in class 1 meaning the good credit class, the other 151 means the bad credit and will refuse their applications. The class comprehensive score is 0.06 now, bigger than 0.06 belongs to the class 1, and the others to the class 2, table 7 shows the detail contrast. We use the test samples which include 350 records to cost of granting credit to a high-risk applicant is Table 7 results contrast with two methods significantly greater than that of denying credit to a good >=110 <110 Total >0.06 risk <0.06 applicant. Therefore, the bank will concentrate more on type I error, and requires a small error rate. The type I 1(good cr edit) 2(bad credit) 1(good credit) 2(bad credit) error of our method is 27.27%, reducing about 40% to dit 160 102 262 173 87 the bank s result which is 44.32%. If we take a higher it 39 49 88 24 64 clique value, the type I error will decrease sharply as we 199 151 350 can 199 see from the multiple-class 151 classification, which is error 0.4432(typ e I) 0.3893(type II) 0.2727(type outlined I) in 0.3321(type table 3. This I) contrast of results shows that our ror 0.4029 method 0.3171 has a better effect in practice of credit card risk management. We have the average error 31.71%, much lower than the bank s 40.29%. It is generally believed that the

5. Summary and conclusions We present an improved method which is applicable to Chinese commercial banks. It has the following characteristics: (1) Index coefficients are given only based on sample data, thus the objectivity is guaranteed. (2) It is able to adjust the scoring function dynamically if needed, hence has a good adaptability to the population drift phenomenon, etc.. (3) The default rate is increasing monotonously with the decreasing of the score. The banks can set different grades according to the strategy and business with the relationship of score and default rate in order to control the credit card risk. meets the requirement of credit card risk management, and the The primary results of our method manifest that it test result indicated that it has a good application foreground. The demonstration test shows that it is superior to the current method used in Chinese commercial banks. We hope to get better results through more logical data pretreatment and more suitable sample scale selecting etc. Credit scoring and its applications, Society for Industrial and Applied Mathematics, Philadelphia, 2002. [3] He Xiaoqun, Modern statistical methods and applications, Ren Ming University of China Publishing Company, 1998. (in Chinese) [4] Liu Xianyong, SPSS 10.0 -- The statistical soft and its application. National Defence Industry Press, 2002. (in Chinese) [5] Zhang Wei, Li yushuang. The overview of the credit risk in commercial bank, the Jounal of Management Science, 1998.9. (in Chinese) [7] Ba Shusong. The risk management function and effects of credit scoring system to commercial band, Congqing Finance, 2001.6. (in Chinese) [8] A Chinese commercial bank. Personal credit scoring criterion and personal credit grade. (in Chinese) [9] Zhang Aiming, etc.. The PCA based prediction model and demonstration research in public companies financial failure. Journal of financial research, 2001.3 (in Chinese) 6. Acknowledgements This research is partly supported by the President Fund of Chinese Academy of Sciences (CAS). The authors are gradeful to Profs. Ji Lei, Chi Hong, Chen Jianming and other colleagues in the Working Group of Financial and Management Science, of the Institute of policy and Management, CAS, for their helpful advices in writing this paper. References [1] Thomas, Lyn, A survey of credit and behavioral scoring: forecasting financial risk of lending to customers, International Journal of Forecasting, Vol. 16, p149-172, 2000. [2] Thomas.Lyn, David.Eldelman and Jonathan.Crook,