CC BY
22
UDK 65.012.26 Tian Qiuli,
lecturer, East China Jiaotong University
THE APPLICATION OF THE LOGISTIC MODEL ON THE ANALYSIS OF CREDIT RISK MEASUREMENT OF THE MINOR ENTERPRISE
Abstract. The recent financial crisis requires more on the analysis of credit risk. Concerning the minor enterprise, this paper analyzes several models in qualitative term, and examines the prediction effect of Logistic model, which gives a conclusion that Logistic model is well fit for the analysis of credit risk of minor enterprise.
Keywords: logistic model, minor enterprise, credit risk measurement.
Preface
As the sub-prime crisis in the whole world broken out, evaluation of enterprises' credit is brought forward as an important issue. The difficulty in financing makes the credit risk evaluation and measurement of minor enterprises' a great problem to both minor enterprises and bank. Therefore, measurement of minor enterprises' credit is becoming a popular topic.
By now, throughout the artificial expert system and subjective analysis phase, univariate analysis phase, multivariable analysis phase, credit risk modeling was brought forward firstly by Horrigan (1966). Multivariate regression model was used to evaluate the credit risk of enterprises by West (1970), Pogue and Soldfsky (1969), and factor analysis and discriminant analysis was used to predict the credit rate of bonds by Pinches and Mingo (1983).
As the development of research, many researchers tried to improve the statistical methods to evaluate credit risk. A lot of non-parametric methods are involved in the credit risk evaluation, such as Ordered Probit analysis, cluster analysis, Unordered Lo-git, discriminant analysis and linear analysis. Edering-ton (1985), Gentry (1987) compared the prediction effect of each method to find the best one. Neural network model was also developed in recent years to analyze the credit risk.
Domestic researches were concentrated on the credit risk evaluation of public companies and the default evaluation of commercial bank customers. The
accuracy of prediction of different methods was also compared by Huang Xiaoyu (1988), Guo xiangzhao and Li Zhikuan (1995), Guan Qihai and Feng Zong-xian (2004). Xie Chi and Xu Guoxia (2006) compared the difference of Credit Metrics model and CPV model to find a better model for the commercial bank credit risk management.
1. Comparison of several credit risk measurement models
Till now, there has been no maturity model on credit risk measurement in the global around. Each credit risk measurement way and model in common use has both advantages and disadvantages.
Generally speaking, the traditional credit risk analysis and credit rating methods are simple and easy, and are not so strict to data. However, these two ways are subjective, and results vary as the variety of rating organizations and experts. The fairness of rating results is also doubtful.
Multivariate analysis method is effective in finding financial ratios used for discrimination of performance of enterprises. However, this method is useful under the hypothesis that variables are normally distributed, which is not correct for most financial ratios, and this method assumes a linear relationship between variables and credit risk, which restrict the explanatory ability of variables. In this way, multiva-riate analysis method is true to companies with rich financial data, i.e. enterprises with a certain scale or on maturity development stage, but is not good for the minor enterprises.
KMV model is suitable to the credit risk evaluation of quoted company, and basically, this model is a static model. In other words, this model hypothesizes that once the debt structure of enterprises is determined by the managers, it will never change in the future. This hypothesis is false to most enterprises, especially minor enterprises, whose capital gearing changes over periods as the development. Apparently,
ИРКУТСКИМ государственный университет путей сообщения
KMV model is not suitable to the credit risk management of domestic minor enterprises.
Neural network model is benefit to human factor with weakened weighting, is fault tolerant, and is good in handling complicated non-linear relationships. But a good neural network model costs great works and times. Generally speaking, neural network model is used for the evaluation after the credit granting, for example, the extension of credit line in the latter, but is less used for credit evaluation in the earlier. Now the application of neural network model in domestic credit risk management is still being researched.
The hypothesis on CreditMetric Model that the credit rating transition probability is regular under the same economic environment and different macroscopic states results in deviation of evaluation results: when the economic is better, the default probability from CreditMetric Model is higher than the realistic default probability, but if the economic is worse, the default probability from this model is lower. In 1997, as modification of credit rating transition probability, the CreditPortfolio View is brought forward by McKinsey. However, it is wanted to be improved bea-cause of the more complicated operation and worse stability.
Traditional linear statistic model is based on the hypothesis of the linear relationship between credit risk and related financial information, which does not restrict Logistic model. Also default probability of the next period of enterprise can be predicted from Logistic model. Compared with Multivariate analysis method, Logistic model is more flexible and compared with other credit risk models, such as KMV, neural network, CreditMetrics and so on, Logistic regression model is relatively simple and can be better explained in economics. Therefore, logistic regression model owns better practicability and is suitable to the calculation of default probability of various enterprises with a certain financial data.
In all, Logistic model will be better used in the credit risk measurement of minor enterprises in our country. Therefore, this paper will go to further empirical analysis of the measurement effect of Logistic model with financial data of minor enterprises.
2. Selection of samples and determination of financial indices
2.1. Definition of minor enterprises
The latest standard of minor enterprises in our country is from "Announcement on interim regulations on standards of minor enterprises" published in Feb, 19th, 2003, which applies to industry, construction, transportation and post, wholesale and retail, hotels and catering services. According to the interim
regulations, the standards of minor enterprises are as follows, see table 1. This paper distinguishes minor enterprises accordingly when getting data.
Table 1
The standards of minor enterprises
Industries/indices Population Sales Total
of (million assets
employees RMB) (million RMB)
industry Less than Less than Less than
2000 300 400
construction Less than Less than Less than
3000 300 400
wholesale and retail Less than 500 Less than 150 /
transportation and post Less than 3000 Less than 300 /
hotels and catering Less than Less than /
services 800 150
Source: "Announcement on interim regulations on standards of minor enterprises", published in Feb 19th, 2003.
2.2. Determination of samples
Due to the insufficient and unavailable information, it's difficult for the default customers in domestic banks to be researched directly, therefore, the financial information of quoted companies will be substituted in this paper. The ST shares will be treated as default samples, while others will be treated as not-default samples. Now that the proportion of default samples to not-default samples falls short of accepted standards, the natural selection methods will be used to assign the proportion of default samples and not-default samples in this paper, i.e. all the samples available will be selected.
In this paper, all the minor enterprises of industry, construction, transportation and post, wholesale and retail, hotels and catering services listed in Shenzhen and Shanghai stock market will be selected as learning set. Financial data in the year of 2005, 2006 and 2007 are selected at the same time, and after removing the missing and error values, totally 133 default samples and 254 not-default samples are selected. Data are from CCER.
2.3. The selection and determination of financial indices
Referring to prior research, 33 indices are selected initially, as a representation of profitability, solvency, efficiency, growth ability and capital structure of enterprises. Then, the method of "the optical choice of credit factors of linear Logit score model under strict control" is used to select financial indices, in which method the financial ratios of least contribution are removed one by one. At last, 16 financial indices are chosen: Return on equity, Total assets
Системный анализ. Моделирование. Транспорт. Энергетика. Строительство
growth rate, Growth rate of core business revenue, Current ratio, Quick ratio, Ratio of cash to current liabilities, Ratio of cash to total liabilities, Assets turnover, Return on total assets, Ratio of profit to cost, Time interest earned ratio, Ratio of revenue to liabilities, Ratio of long-term liabilities to total liabilities, Debt to tangible assets ratio, Cash assets ratio, Operating margins.
2.4. Factor analysis to financial ratios
As requirement to models, the independent variables should not be independent from each other and not be multi-collinear. If the independent variables entering into models are strongly related, the reliability and consistency can not be ensured. In this way, the factor analysis is provided at first in this paper, in order to eliminate the relevance of financial ratios and reduce the dimensions of variables.
The test of relevance of 16 financial ratios shows that, the KMO value of samples is 0,741, and in the Bartlett sphere test, the significance probability of %2 is 0,000 which is less than 1 %, which represents that data are related and samples are proper for the factor analysis.
After the factor analysis, results tells that, there are 6 factors which characteristic root is more than 1, explain 83,261 % of total variation. The loading
scores of rotated factors are shown in table 2.
Factors are renamed more meaningfully, according to the meaning of the first three ratios of largest loading scores on a certain factor, so that the regression results can be explained better. From loading scores of ratios on factors in table 2, we can get that:
Factor 1 has greatest effect on Quick ratio, Current ratio, Ratio of cash to total liabilities, Ratio of revenue to liabilities, Debt to tangible assets ratio and Ratio of cash to current liabilities, which represent the solvency of enterprises. It is named as solvency factor.
Factor 2 has better influence on Operating margins and Ratio of profit to cost, which represent the quality of profitability of enterprises, named as quality of profitability factor.
Factor 3 influences Assets turnover and Cash assets ratio in a great way, representing the earning on assets, and is named as earning on assets factor.
There is great effect of factor 4 on Time interest earned ratio, Return on total assets and Return on equity, which represent the total profitability of enterprises, and factor 4 is renamed as financial performance factor.
Factor 5 affects Ratio of long-term liabilities to total liabilities greatly, which represent the debt structure of enterprises, and is renamed as debt structure factor.
Table 2
Loading scores of rotated factors
FACTORS
1 2 3 4 5 6
Quick ratio .897 .089 .065 -.030 .317 -.066
Current ratio .889 .073 .087 -.033 .324 -.072
Ratio of cash to total liabilities .873 .068 .181 .024 -.163 .000
Ratio of revenue to liabilities .833 .041 .092 .060 -.317 .128
Debt to tangible assets ratio .828 .002 -.079 .031 -.168 .098
Ratio of cash to current liabilities .805 .119 .124 -.037 .404 -.115
Operating margins .058 .921 .055 .084 .055 .048
Ratio of profit to cost .163 .867 .123 .080 .226 .041
Assets turnover .096 -.022 .879 .017 -.122 -.056
Cash assets ratio .445 .125 .654 .059 .009 -.157
Total assets growth rate -.094 .174 .645 .090 .173 .395
Time interest earned ratio -.015 -.001 -.062 .828 -.127 -.153
Return on total assets .038 .187 .173 .819 .070 .119
Return on equity .000 -.360 .065 .418 .411 .388
Ratio of long-term liabilities to total liabilities .050 .318 -.055 -.067 .748 -.125
Growth rate of core business revenue .026 .059 -.013 -.049 -.124 .808
ИРКУТСКИМ государственный университет путей сообщения
For factor 6, Growth rate of core business revenue is influenced greatly. Additionally, the loading score of Total assets growth rate on factor 6 is 0,395, more than 0,3. Considering the economic meaning of this ratio, it is assigned to factor 6. These two ratios represent the growth of business, so factor 6 is named as growth factor.
Factors all of the above represent the assets, debts structure, growth ability, profitability, solvency and financial performance of enterprises respectively, which in total is a full appraisal of financial.
3. Logistic regression analysis
3.1. Introduction of Logistic regression
As a non-lienar discrimiant method, the function of Logistic model is like
f (x) =--,
(p0
1 + e
where xi is the independent variable, i.e. discriminant factors;
P is regression coefficient, obtained from the regression;
n
P0 + x is the scores of enterprises' cre-
¿=1
dit;
f (x) e [0,l] is the default probability.
3.2. Setting variables and determining the critical value
When analysis with Logistic regression model, default or not is set as dependent variable, 6 factors got earlier is set as independent variables, and Forward Stepwise (conditional) method is adopted to distinguish the factors significantly influencing the samples with the ones not significantly influencing the samples.
Dependent variables of two states are required to be transferred to be 0 and 1, therefore, in order to explain the results of regression, default samples are valued as 1, while not-default samples are valued as 0. For the Logistic model, 0,647 is chosen as a critical value, i.e. only when f (x) is larger than 0,647, the enterprise is distinguished as default company.
3.3. Analysis of regression results
Table 3 shows the result of Logistic regression, from which default probability (P) can be calculated as:
f (x) = ■
1
i+e
,(1.214+2.2291 + 0.8562 + 0.5503-0.4774 + 0.7025-1.0336
Table 3
Parameters in Logistic model
Factors B S.E. Wald Df Sig. Exp(B)
Factor 1 2.229 .529 17.727 1 .000 9.287
Factor 2 .856 .156 30.218 1 .000 2.355
Factor 3 .550 .140 15.317 1 .000 1.733
Factor 4 -.477 .210 5.147 1 .023 .621
Factor 5 .702 .248 7.977 1 .005 2.017
Factor 6 -1.033 .264 15.307 1 .000 .356
constant 1.214 .187 41.912 1 .000 3.365
Factor of the most influence to default or not of enterprises is solvency factor, whose Exp(B) is 9,287, entering into regression equation in step 2. It can be easily found that, due to the small scale and weak intangible assets, minor enterprises get little credit from financing institutions. Once enterprises can't repay debt in time, financing institutions will ask for the paying back the borrowing one by one, which is a vicious circle, and turn to the bankrupt of enterprises. This result is in accordance with the realistic.
The quality of profitability factor has significant influence to the default or not of enterprises. Its Exp(B) is 2,335, and enters into the regression equation in step 1. The amount of profit to the sales of enterprises and the cost to get profit influence the operation of minor enterprises greatly. As tiny funds and small earnings enterprises, whether the sales bring adequate profit and whether cost can be controlled, apparently has great influence. The financial position factor entering into regression equation in step 3 also stresses this phenomenon. This factor also explains the operating feature of minor enterprises.
The Exp(B) of debt factor is 2,017, also has great influence to the default of enterprises. In other words, whether there is an adequate debt structure or not it is very important to the credit of enterprises. The scale of assets is small to minor enterprises, which means large long-term debt can cause the moral hazard. Once the debt fails to be repaid, minor enterprises tend to turn to bankruptcy to escape debts repayment. This result is the same to prior research results.
From the analysis above, we can find that, the result from the Logistic regression model is coincidence with the real operating situations, and regression results can be explained well.
3.4. The test of prediction effectiveness
The prediction effectiveness is tested using financial data of 2008, with 35 default samples and 85 not-default samples. The factor values of testing samples are calculated with the coefficient matrix got from the factor analysis. Putting factor values into the Logistic regression model, the prediction result of test samples can be got.
Системный анализ. Моделирование. Транспорт. Энергетика. Строительство
Table 4 gives the test result of model to learning samples and testing samples. From it we can conclude that model has a quite high accuracy rate to learning model, which demonstrates that the variables set and model design is good and valuable in application. Meanwhile, model has good prediction effectiveness to testing samples, with the total accuracy rate of 75,8 %, which proves that Logistic can distinguish default enterprises and not-default enterprises well.
Table 4
Prediction result of learning samples and testing samples from discriminant model
samples Learning samples Testin g samples
ST share Not- default share Accuracy rate ST share Not- default share Accuracy rate
STshare Not- default share Total 92 20 41 234 69,9 92.1 84.2 22 16 13 69 62,9 81,1 75,8
To annotate: the critical value is 0,647
Conclusion
After qualitative and quantitative analysis, the conclusion can be got that Logistic model is able to provide good prediction when measuring the credit risk of minor enterprises, and can be well applied. In another way, there is also limitation of the analysis in this paper.
First of all, the enterprises are limited to quoted companies in the quantitative analysis due to the unavailability of other companies' financial data. In fact, most of the minor enterprises are not quoted companies, and the financial statements are not disclosure. This may result in the weak typicality of research.
Second of all, due to the limit of samples amount, only samples of industry, construction, transportation and post, wholesale and retail, hotels and catering services are selected, but not all industries.
Meanwhile, the financial factors are the only variables
considered, with industries variable and other macroe-
conomic variables ignored.
REFERENCES
1. Altman, E. I. Haldeman, G. & Narayanan, P. ZETA Analysis: A New Model to Identify the Bankruptcy Risk of Corporations [J]. Journal of Banking and Finance, 1977(18): 29-54
2. Michel, C., G., Dan and M., Robert, A Comparative Analysis of Current Credit Risk Models[J]. Journal of Banking and Finance, Vol.24, pp.59-117,2000.
3. West, R. R. An alternative approach to predicting corporate bond ratings [J]. Journal of Accounting Research, 1970, Spring: 118-127
4. Han Gang. A Study on Credit Risk Measurement Methods in Foreign Countries and Its Applicability in China [J]. Studies of International Finance, 2008(3): 43-47
5. Bo Yiyi. The application of Logistic model on the credit risk management of listed companies[J]. Economic & Trade Update, 2008(6): 148-149
6. Tian Qiuli. Research on the financial ratios predicting enterprises' default - analysis base on the inter-industry difference [D]. Master Thesis. Zhejiang University, 2004
7. Liu Xuebo. Research on Modern Measurement Model of Credit Risk and Application in China Bank of KMV Model [D]. Master Thesis. Ocean University of China, 2007
8. Wu Zhouyu. Overview of modern measurement models of credit risk [J]. China Economist, 2007(3): 16-17
9. Liu Hengyu, Lian Jianping. Appraisal of main credit risk models based on statistic analysis [J]. Commercial Times, 2008(16): 66-68
