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Fuzzy Logic in Credit Rating

**Faculty Contributor** : Jayadev M., Associate Professor

**Student Contributors** : Rajakishore Behera and Kiran Kumar K

Banks, particularly in India, have to make credit assessments on insufficient data, which reduces the applicability of current models. This article suggests a model based on Fuzzy Logic which can work with minimal data to give more accurate credit ratings. Designing this model involves identifying the attributes that affect credibility, modelling this data as inputs and eventually developing a rule based inference engine to assess credit risk. Preliminary analysis of the model outputs confirms the advantages of the Fuzzy Logic model over the current models.

A key characteristic of a developed economy is the easy availability of credit, both for the companies as well as consumers. With the growth of the Indian economy and the appetite of the Indian consumer to spend, the market for credit has expanded rapidly. With credit expansion, there also comes the need for a sound and robust credit assessment system. Banks use credit assessments to decide whether borrowers will be able to meet their loan obligations. The credit score helps in determining the risk associated with a customer while granting a loan. However, in India, credit assessment is often based on insufficient data.

Many of the current credit scoring models use the Altman Model^{1} in some form or the other. This model while being simple to use, has problems relating to the availability of data and multi-collinearity of variables. A viable credit rating model should be able to give an accurate picture of the assessee based on minimal data. One such model is Expert Systems wherein a borrower is assessed on the basis of knowledge gained from previous experiences. Fuzzy Logic^{2} , an extension of Expert Systems, is a form of multi-valued logic derived from Fuzzy Set theory to deal with reasoning that is approximate rather than precise. Research on credit risk management has shown that models based on Fuzzy Logic can yield more accurate predictions of credit risk than the traditional multivariate model^{3} . This article explains an attempt to develop a simple Fuzzy rule based model for analysing the credit worthiness of a company in the Indian context.

## Designing the Credit Assessment Model

The design of the Fuzzy Logic Credit Rating System involves the following steps:

- Identification of attributes which affect credibility
- Input modelling of the attributes by giving appropriate weights and quantification of the same
- Development of a rule based inference engine and expert system

Exhibit 1 shows the design approach of the model.

* Exhibit 1* The Design Approach of the Fuzzy Logic Credit Rating Model
## Selecting Inputs to the Credit Rating Model

The first step in developing the model is to decide on the input parameters. To get an accurate credit rating, both quantitative financial data and qualitative data are required. Due to lack of availability of qualitative data, only quantitative data is taken into consideration . The following seven ratios are selected as input parameters.

- Working Capital/Total Asset ratio
- Earnings Before Interest and Tax(EBIT)/Total Asset(TA) ratio
- Equity (E)/Debt (D)ratio
- Sales (S)/Total Asset ratio
- Current ratio
- Interest Coverage ratio
- Operating margin

In order to develop the fuzzy inference system of credit management, the seven parameters were divided into four groups as illustrated in Exhibit 2. This is done to simplify the model and pool measurements which give the same inference. The working capital to total assets and EBIT to total assets ratios are grouped together since both of them indicate the ability of a company to manage its short term liability and yet give returns. Operating margin and sales/total asset turnover measure the profitability of a company, hence they are combined into one inference system. The interest coverage ratio and debt to equity measure the ability of a company to meet its long term debt obligations.

* Exhibit 2* Grouping of Input Parameters
## Developing the Fuzzy Inference System

Fuzzy inference is the process of mapping from a given input to an output using fuzzy logic. The mapping then provides a basis on which decisions can be made, or patterns discerned. An inference engine / system is the software code which processes the rules, cases, objects or other types of knowledge and expertise based on the facts of a given situation. The inference engine used is Mamdani^{4} type for the entire rule based engine with centroid algorithm for Defuzzification.

### Modelling the Inputs

In modelling the inputs for the fuzzy inference engine, since some attributes may be psychographic in nature, the input variables are divided into various categories. Here, all inputs are divided into three categories “low”, “medium” and “high” based on the probability of default calculated from the existing data. This process is called Fuzzification. To establish levels of correlation between the parameter groups and the credit worthiness of a company, joint probabilities of default were calculated (using MATLAB software), and a joint probability matrix was created.

For example the probability of default when the working capital to total assets ratio and EBIT to total assets ratio are taken into account at different levels viz. low, medium or high is shown in Exhibit 3.

* Exhibit 3* Mapping Probability of Default using One Group of Input Parameters
Similarly, a total of 49 matrices are generated and the probabilities are used from them in forming the rules for the model. Based on the rules of the matrix, the output of the four inference systems (corresponding to the four models shown in Exhibit 2) are used to evaluate the bad loans prediction. Since none of the inference systems individually have high accuracy, the output of the four inference systems is fed as an input to the new fuzzy model.

### Analyzing the Model Output

The final output of the Fuzzy model is a quantitative value. Before the accuracy of the score so obtained can be predicted, the cut off range needed to be defined. Since the data used to develop this model is a training data set, the cut off range is obtained through trial and error. Any company which scores less than point 0.6 is taken as a defaulter company and any company with a score greater than 0.4 is taken as a non-defaulter company. Exhibit 4 gives a summary of the results.

* Exhibit 4* Scores from the Fuzzy Logic Model Identifying Defaulter and Non Defaulter Companies
## Practical Application and Scope of the Fuzzy Logic Model

The model has some drawbacks in that it does not take into consideration qualitative data. It is also not a self learning model. The unavailability of data other than that used as the learning set and possibility of the training data set not being accurate (because the market value of the firms is not known precisely in valuation of its assets) are other drawbacks.

The Fuzzy Logic model is easier to understand and can incorporate new knowledge easily.

Despite drawbacks in the model developed here, the Fuzzy Logic model has advantages over the current systems based on the Altman model. The Fuzzy Logic model is easier to understand and can incorporate new knowledge easily. To illustrate, in India, since most of the knowledge is tacitly available only with the banks, this simple model can be used to generate uniformity across various branches of the same bank. Unlike the statistical models, Fuzzy Logic models are easier to interpret and they retain the experts’ knowledge with them. Hence sharing of knowledge becomes easier. Since Fuzzy Logic models do not follow any distribution, one can obtain accurate ratings even with a small set of data as compared to statistical methods.

Further, Fuzzy Logic models can be integrated with neural networks resulting in a better model with higher prediction accuracy. The scope of the model increases when one incorporates qualitative data the system. Furthermore, instead of using Fuzzy Logic as a standalone model, one can also use it as a module in credit rating. The problem of credit scoring i.e. rating of retail customers can be probed further as also the use of Artificial Intelligence techniques to make the model self learning.

## Conclusion

Plenty of literature exists about the predictive power of Fuzzy Logic systems over other methods of credit rating and Fuzzy systems have found practical application in many cases^{5}. The simple model developed here, with only financial parameters as inputs, gave results which were more accurate than models based on Multi Discriminant analysis, such as the Altman model. This shows that Fuzzy Logic models have an inherent advantage because of their ability to take care of the fuzziness or ambiguity in the system. Other advantages include easy interpretability and scope for integration with other systems such as neural networks for higher accuracy. Also, this credit rating model has immense significance in the Indian scenario, where the availability of data about borrowers is a problem.

#### Authors

** Jayadev M. ** is an Associate Professor in the Finance and Control area at IIM Bangalore. He holds a Doctor of Philosophy (PhD) and a M. Phil from Osmania University, Hyderabad. He is also an associate member of Indian Institute of Bankers. He can be reached at
jayadevm@iimb.ernet.in

** Kiran Kumar K ** (PGP 2007-09) holds a bachelors degree in Mechanical Engineering from NIT Warangal. He can be reached at kirank07@iimb.ernet.in

** Rajakishore Behera ** (PGP 2007-09) holds a bachelors degree in Mechanical Engineering from NIT Trichy. He can be reached at rajakishoreb07@iimb.ernet.in

#### Keywords

Financial Services, Credit Rating, Model, Finance and Control, Fuzzy Logic, Banking

#### References

- Bankruptcy Prediction Models, bankruptcyaction.com/insolart1.htm. Last accessed on March 10, 2010.
- Fuzzy Logic, Stanford Encyclopaedia of Philosophy, http://plato.stanford.edu/entries/logic-fuzzy. Last accessed on March 10, 2010.
- Bo Huang et al (Bo Huan, G Qing-Pu Zhang, Yun-Quan Hu, ‘Research on Credit Risk Management of the State-owned Commercial Bank’, Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005) constructed a fuzzy neural network model for the Commercial Bank of China. The results concluded that the model can reduce the credit risk of the bank with better predictions than the traditional multivariate model. Many other papers show a similar improvement in the prediction accuracy.
- Mamdani’s method, eMathTeacher: Mamdani's Fuzzy Inference Method, Universidad Politécnica de Madrid © 2009, http://www.dma.fi.upm.es/java/fuzzy/fuzzyinf/mamdani_en.htm, Last accessed on Feb 15, 2010
- Fuzzy Logic Applications for Banking and Loans, http://artificialintelligence.suite101.com/article.cfm/fuzzy_logic_applications_for_banking_and_loans, Last accessed on Feb 15, 2010