Applying Rough Sets Theory to Corporate Credit Ratings

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Applying Rough Sets Theory to Corporate Credit Ratings

Tien-Chin Wang,Ying-Hsiu Chen

Abstract—Risk assessment and credit rating are primary criteria to investigate the repayment ability of borrower for financial institution. The amount of corporate bond has increased rapidly in recent years. Bond market in Taiwan has also developed actively. Bond market is thus an indispensable risk index for developing the credit rating mechanism. This study utilizes the rough sets theory and the financial ratios of credit evaluation of TCRI as criteria. Using the semiconductor industry of Taiwan stock market as models, this research finds out several important reference factors that sway enterprise credit rating. The credit rating evaluating criteria are grouped into the following three kinds: good, probably good, probably bad. Results of this study show that the interest expense ratio, debt ratio, receives months, sale months play important roles for overall assessment of enterprises.

Index Terms—Corporate Credit Ratings, Rough Sets, Taiwan Corporate Credit Risk Index (TCRI).

I.Introduction

Risk assessment and credit rating are primary criteria for investigating the repayment ability of a borrower to a financial institution. The amount of corporate bonds has increased rapidly in recent years. The bond market in Taiwan has also developed actively,but the corporate credit line of a company is often higher.

When a customerbreaks a contract, the loss is alsoserious. Therefore, the bank must incorporate better risk management to maintain its corporate credit line and lower the risk of financial loss incurred through broken contracts. The bond market is thus an indispensable risk index for developing the credit rating mechanism.

At present, the most pervasive way ofanalyze of bank credit isthe “5P” principle, a factor of borrowed money (People), fund use factor (Purpose), refund source factor (Payment), the creditor's rights guarantee (Protection), and factor of vision of the future (Perspective). An alternative is using the “5C” principle as the standard of credit rating, which is character, capital, capacity, collateral and condition. Its purpose and appraisal essential factor has the same stead with the 5P principle.

Credit ratings of enterprises are vague and uncertain. Therefore, this study utilizes the rough sets theory (RST)proceeds to in corporate credit rating. RST represents a different mathematicalapproach to vague and uncertain data.Using the semiconductor industry of the Taiwan stock market as a model,the attribute result of the Taiwan Corporate Credit Risk Index (TCRI) is used to analyze and extract the important factors that influence enterprise credit ratings. Classify the credit rating results and determine which enterprises belong to low risk and claim investments. The findings in the research will be the reference materials of the bank in their credit rating decision.

II.Literature Review

This study utilizes the rough sets theory to analyze the attributes of corporate credit ratings. In literature review, section 2.1, 2.2 and 2.3 discuss the meaning of credit ratings, related criteria of research and empirical application result. Section 2.4 focuses on the applications of rough sets.

2.1.Credit Ratings

Credit rating is an estimate of credit condition or the ability to pay debt. Financial institution follows the certain procedure, using the statistical method to lay down a number of rating standards which accesses an enterprise’s credit situation and gives an overall default risk assessment. Getting each credit attribute gives the quantification, and calculates its points and rating. According to the rating the quality of credit is decided [1], [2]. In addition, when this credit intensity changes, a financial institution can promptly make the suitable revision to the credit rank, to reflect as present the credit quality.

2.2.The related criterion of corporate credit ratings

The credit-rating system, currently operated for mid- and small- scaled business units in Taiwan, consists of three main categories: Financial Conditions (FC), General Management (GM), as well as Characters and Perspectives (CP). Credit rating has been implemented for several years in foreign countries, however, the mechanism of credit rating in Taiwan is limited to Taiwan Ratings Corporation and TEJ (Taiwan Economic Journal Co. Ltd.) to establish more complete databases.

Taiwan Ratings Corporation encompasses two basic components its corporate rating methodology: business risk analysis and financial risk analysis. Each corporate rating analysis begins with an assessment of the company's environment. Factors assessed include industry prospects for growth, stability, or decline, and the pattern of business cycles. Financial risk is portrayed largely through quantitative means, particularly by using financial ratios. Analytical adjustments are made to better portray reality.

TCRI (Taiwan Corporate Credit Risk Index) is a corporate credit rating system, which was developed by TEJ. The main risk assessment factors include: profitability, security, activity and scale. Each factor has several representative financial ratios. TCRI assesses risk by first obtaining basic rank by the financial material that estimates a basic synthesis score by 10 financial values and the ratio (Table 1), then determines a preliminary basic rank. The next rating depends on the risk and the scale obtains the threshold rank which is, finally decided by TCRI using the non-quantification factor.

TABLE 1

Taiwan Corporate Credit Risk Index

Risk Assessment Factor / Representative Financial ratio
Profitability / Return on Equity (ROE)
Operating Profit (OP)
Return on Asset (ROA)
Security / quick ratio
interest expense ratio
debt ratio
Activity / receives months
sale months
Scale / operating income
total assets

Formula: ROE = recurring income discounted / average net value; OP = operating revenue / operating income; ROA = EBIT /average asset; quick ratio= quick asset /current liabilities; interest expense ratio = interest expense / operating income; debt ratio = total debt / shareholders' equity; receives months = 12/(operating income/average tab); sale months = 12/(cost of operating /average inventory).

Taiwan Ratings Corporation concentrates primarily on the financial negotiable securities industry due to the general industry lacking sufficient credit ratings. In addition, TEJ develops the TCRI implementation by using public information appraise the credit risk. The information is obtained conveniently; furthermore TCRI aids this study by applying rough sets theory to corporate credit rating. Based on above reason this study adopt TCRI as the evaluate criteria.

2.3.Empirical application result of corporate credit rating

The bank must have better risk management policies for assessing to corporate credit lines, in order to lower the risk that the bank takes on loans. Zimmermann and Zysno [3] consider that there are many fuzzy characteristics in the decision-making process, thus, they proposed the use of fuzzy method expression evaluate criteria. Su and Tsai [4] combine the traditional finance condition and the fuzzy set theory, relying on the triangle membership function and standard fuzzy rating value to establish a ranking. Chen and Chiou [5] proposed using the fuzzy integral, a fuzzy approach for rating business credit for commercial loans. The proposed approach uses fuzzy sets (fuzzy numbers) to describe the criteria so that the final credit-rating results can reveal the changes in credit information.

2.4.Application of Rough Sets

The rough set theory has proved to be very useful in practice, as is clear from the record of many previous real-life applications. RST may solve the general basic problem, for example, to make the attribute simplification, to find the hidden data pattern, as well as account for the decision-making rule [6], [7].

In particular, the rough sets approach has found interesting applications in medicine [8], pharmacology, business, banking, market research [9], engineering design, meteorology, vibration analysis, switching function, conflict analysis, image processing, voice recognition, concurrent system analysis, decision analysis, character recognition, and other fields[10].

III.Rough Set Theory (RST)

The rough sets theory was proposed by Pawlak in 1982 [6] to deal with uncertain and fuzzy materials and to simplify knowledge. In the rough sets theory, humans use their general knowledge to classify the world around them as abstract or concrete. Everything is classified according to its characteristics, and those with nearly identical characteristics may be put into the same group. This is called indiscernible relation, denoted as and is the basis of rough sets theory.

One of the main advantages of rough set theory is that it does not need any preliminary or additional information about data. The main problems that can be approached using rough sets theory include data reduction, discovery of data dependencies, estimation of data significance, generation of decision algorithms from data, approximate classification of data, discovery of patterns in data and discovery of cause-effect relationships [10].The following is the concept of rough sets theory [11], [12].

3.1.Information Systems

Knowledge can be finished by the information systems, the basic composition of an information system is the set of objects which are to be studied. The knowledge of these objects is described by their attributes and attribute values. The information system is defined as follows:

(1)

whereU is the universe, a finite non-empty set of objects, , and A is the set of attributes. Each attribute(attributebelonging to the considered set of attributes A) defines an information function:

(2)

where is the set of values of, called the domain of attribute. In all attributes, there are decision attributes and condition attributes.

3.2.Indiscernible relation

For every set of attributes, an indiscernible relation is defined in the following way: two objects, and , are indiscernible by the set of attributes B in A, if for every.The equivalence class of is called the elementary set in B because it represents the smallest discernible groups of objects. For any element of A, the equivalence class of in relationis represented as.

3.3.Upper and Lower approximations

The rough sets approach to data analysis hinges on two basic concepts, namely the lower and the upper approximations of a set, referring to: the elements that doubtlessly belong to the set, and the elements that possibly belong to the set. The definition is shown as follows:

Let X denote the subset of elements of the universe U, the lower approximation of X in B, denoted as , is defined as the union of all these elementary sets which are contained in X.More formally:

(3)

The above statement is to be read as: the lower approximation of the set X is a set of objects, which belong to the elementary sets contained in X (in the space B), is called the lower approximation of the set X in B.

The upper approximation of the set X, denoted as, is the union of these elementary sets, which have a non-empty intersection with X:

(4)

The above statement is to be read as: the upper approximation of the set X is a set of objects, which belong to the elementary sets that have a non-empty intersection with X, is called the upper approximation of the set X in B.

The differenceis called a boundary of X in U.

(5)

3.4.Core and reduct of attributes

The concepts of core and reduct are two very important concepts of the rough sets theory. If the set of attributes is dependent, one can be interested in finding all possible minimal subsets of attributes. These lead to the same number of elementary sets as the whole set of attributes (reducts) in finding the set of all indispensable attributes (core).

Simplification of the information system can be used to recognize some values of attributes which are not necessary for the system. For example, some attributes which are redundant can be deleted or be filtered by means of the simplification procedures. If, , then the attributeis dispensable, otherwise,is indispensable in A. In other words, if after deleting the attribute, the number of elementary sets in the information system is the same, then it concludes that attributeis dispensable.

Hence, the simplification can contain the minimal subsets of independent attributes, which ensure they can represent the whole set. The core is the necessary element for representing knowledge or rules, and is the common part of all reducts. The researcher uses the discernibility matrix to compute the values of reducts and core.

IV.Case Study

Risk assessment and credit rating are primary criteria to investigate the repayment ability of the borrower to the financial institution. However, credit rating of an enterprise is vague and uncertain. Therefore, a researcher can utilize the characteristic of RST to deal with vague and imprecise data, and proceed to analysis of corporate credit rating.

This study utilizes the financial ratios of credit evaluation of TCRI as criteria. Using the semiconductor industry of the Taiwan stock market as a model, this research discovers several important reference factors that sway enterprise credit rating. This research classifies the credit rating results, and determines which enterprise really belongs to low risk and claim investment. The findings in the research will be the reference materials of the bank in their credit rating decision.

4.1.Subjects

This study takes 16 listed companies in the Semiconductor Industry of Taiwan as research subjects, which are used to calculate corporate credit rating including: United Microelectronics Corp., Advanced Semiconductor Engineering, Inc., Siliconware Precision Ind. Co., Ltd., Orient Semiconductor Electronics Ltd., Taiwan Semiconductor Manufacturing Company, Ltd., Macronix International Co., Ltd., Mosel Vitelic Inc., Winbond Electronics Corp., Silicon Integrated Systems Corp., VIA Technologies, Inc., Sunplus Technology Co., Ltd., Nanya Technology Corp., Weltrend Semiconductor, Inc., King Yuan Electronics Co., Ltd., Mediatek Incorporation, Novatek Microelectronics Corp.,etc.

4.2.The Data

This research takes 11 financial ratios of enterprise credit risk assessment of TEJ as criteria. The attributes are Return on Equity (ROE) (), Operating Profit (OP)(), Return on Asset (ROA) (), quick ratio(),interest expense ratio(),debt ratio(),receives months(),sale months(),operating income(),total assets(), all of the ten attributes belong to the condition attribute. Another attribute is TCRI () which belongs to the decision attribute.

The application starts with an appropriate discretization of the information system by translating the values of the quantitative attributesand of the decision attribute {} into qualitative terms (Table 2). The condition attributes and decision attribute are coded into three qualitative terms, such as: good, medium and bad. The results of this evaluation are show as Table 2, where G, M, and B denote “Good”, “Medium”, and “Bad”, respectively.

TABLE 2

The results of three measurements performed for 16 objects

F
E / / / / / / / / / / /
1 / B / B / B / B / G / G / G / G / B / G / G
2 / B / B / B / B / G / G / G / M / B / B / G
3 / B / B / B / B / G / G / G / M / B / B / G
4 / G / M / M / B / G / B / G / M / B / B / B
5 / B / M / M / M / G / G / M / M / G / G / G
6 / M / G / M / B / G / M / G / B / B / B / M
7 / G / M / G / B / G / G / B / M / B / B / B
8 / B / B / B / B / G / G / M / M / B / B / M
9 / B / B / B / B / M / G / M / M / B / B / M
10 / B / B / M / B / G / G / G / B / B / B / M
11 / B / B / B / B / G / M / G / M / B / B / G
12 / B / B / B / B / B / G / G / B / B / B / M
13 / B / B / B / G / G / M / B / G / B / B / M
14 / B / B / B / B / G / G / M / B / B / B / M
15 / G / G / G / M / G / M / M / G / B / B / G
16 / G / B / M / B / G / G / G / G / B / B / G

F: financial rate; E: enterprise

4.3.Analysis and results

Sixteen enterprises with eleven attributes are evaluates in this paper. Using the terminology of the rough sets theory, this data set can be considered as an information system, where universe U and attributes A correspond to the set of objects and to the set of variables, respectively:

, there are 10 condition attributes and one decision attribute {}.

The information functionfor this system is presented in Table 2. The domains of the particular attributes are:

This study checks the attributes(), if the TRCI of the enterprises are “Good”, this represents that the enterprise keep the better ability of repayment. According to Table 2, the enterprises 1, 2, 3, 5, 11, 15 and 16 are “Good”, we denote the set as. We combine the enterprises which have the same evaluation results in the attribute B. The results are shown that there are fifteen elementary sets.

Using Equation (3), the lower approximation of X is,which represent enterprises 2, 3 that certainly belong to the set of “Good” corporate rating. Using Equation (4), the upper approximation of X is, which represent enterprises 1, 2, 3, 5, 11, 15, 16, and could belong to the set of “Good” corporate rating. Using Equation (5), the boundary of X is,which represents enterprises 1, 5, 11, 15, 16, of uncertain membership to the set of “Good” corporate rating.

Concerning the core and reduct attributes, we consider the subsets of A and compute the numbers of elementary sets. Finding that and have the same number of elementary sets as B, and are minimal subsets of B we conclude that the two subsets are the reduct of B.

The core of B, defined by, are, the four attributes, , , , which have great influence on overall assessments.

This study according to the decision attribute find that the overall assessments is a good enterprise as the first step, then using RST as further analysis, therefore, the same enterprise will not appear in this study but obtain a different credit rating.

V.Conclusions

Risk assessment and credit rating are primary criteria used to investigate the repayment ability of a borrower to a financial institution. The bank must have better risk management ability to access corporate credit lines, in order to lower the risk that the bank makes on loans. Because of the credit rating of an enterprise is vague and uncertain. This study applies another analysis method─rough sets theory (RST)─to determine the corporate credit ratings. The purpose of this study is to utilize the characteristics of RST to deal with vague and imprecise data, which is used corporate credit rating.

This study utilizes the financial ratios of credit evaluation of TCRI as criteria. Sixteen enterprises with eleven attributes are evaluated in this paper. The credit rating evaluating criteria are grouped into the following three kinds: certainly, could, uncertain belong to the set of “Good” corporate rating; enterprises 2, 3 certainly belong to the set of “Good” corporate rating. Results of this study show that the interest expense ratio, debt ratio, receives months, sale months play important roles in the overall assessment of enterprises.