MCDM 2006, Chania, Greece, June 19-23, 2006

MULTI CRITERIA CREDIT RATING (MCCR): A CREDIT RATING ASSIGNMENT PROCESS FOR ITALIAN ENTERPRISES ACCORDING TO BASEL II Francesca Bernè1, Mattia Ciprian2, Maurizio Fanni3, Daria Marassi1, Valentino Pediroda2 1

Eu-ra Europe Rating S.p.A L.go Don Francesco Bonifacio, 1 34125 Trieste, Italy e-mail: [email protected] [email protected]

2

Dipartimento di Ingegneria Meccanica Università degli Studi di Trieste via Valerio 10 34127 Trieste, Italy e-mail: [email protected] [email protected]

3

Dipartimento di Economia e Tecnica Aziendale Università degli Studi di Trieste Piazzale Europa 1 34127 Trieste, Italy e-mail: [email protected]

Keywords: Basel II, probability of default, statistical analysis, Multi Criteria Decision Making, rating Summary: A Multi Criteria Decision Making Model has been applied to solve the credit rating assignment process following Basel II guidelines. In order to select the input parameters, the integration of three different statistical methods has been employed. The model has been tested on a database that is representative of the Italian companies system. 1. Introduction to Basel II, a credit rating assignment process and probability of default Credit risk affects virtually every financial contract. Therefore the measurement, pricing and management of credit risk has received much attention from practitioners who have a strong interest in accurately pricing and managing this kind of risk and from financial economists who have much to learn from the way such risk is priced in the market, and from bank authorities who need to design minimum capital requirements that correctly reflect the credit risk of banks’ loan portfolios. Following the work of the Basel Committee on Banking Supervision to reform the capital adequacy framework by introducing risksensitive capital requirements, significant attention has been devoted to the subject of credit risk measurement by the international regulatory, academic and banking communities. The agreement called “International Convergence of Capital Measurement and Capital Standards” and known as “Basel II”, the last version of which was published in June 2004, will be applied on a consolidated basis to internationally active banks from January 1, 2007. According to Basel II, banks should have a process for assessing their overall capital adequacy in relation to their risk profile and a strategy for maintaining their capital levels. All material risks faced by the bank should be evaluated as part of the capital assessment process, in particular: a) credit risk; b) operational risk which is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events; c) market risk; d) interest rate risk in the banking book; e) liquidity risk; f) other risks. The Committee proposes to give banks a choice between two broad methodologies for calculating their capital requirements for credit risk. One will be to measure credit risk in a standardised manner, supported by external credit assessments (by external agencies called ECAI - External Credit Assessment Institution). The second methodology, which is subject to explicit approval of bank authorities, would allow banks to use their Internal Ratings Systems (IRS) for credit risk. Two different IRS can be utilized: a) FIRBA (Foundation Internal Rating Approach); b) AIRBA (Advanced Internal Rating Based Approach). Three main variables affect the credit risk of a financial asset: (i) the probability of default (PD); (ii) the loss given default (LGD) which is equal to one minus the recovery rate in the event of default (RR); (iii) the exposure at default (EAD); (iv) the maturity (M).

Credit risk literature has given particular attention to the estimation of the first component, probability of default, which includes credit rating assignment processes with adequate models and methodologies. What is credit rating? Credit rating is an opinion of the general creditworthiness of an obligor (issuer rating), or the creditworthiness of an obligor in respect of a specific debt security or other financial obligation (issue rating), based on relevant risk factors. A different probability of default (within one year, two years and three years) is associated with each credit rating category (indicated by symbols: traditional AAA to D). In the view of an agency, the rating process for an issuer-company includes the estimate of the financial risk profile through the analysis of financial statement data and off balance-sheet items. The first phase finishes with the assignment of a fundamental credit rating which consists of the evaluation of the financial and economic equilibrium of the company, and its flows (cash flow, working capital flow, etc.) and represents an essential aspect for vulnerability assessment, a prerequisite for corporate rating and credit rating for credit institutions. In the second phase, the valuation is not limited to an examination of various financial measures. Proper assessment of credit quality for an industrial company involves a thorough review of business fundamentals (qualitative factors analysis), including industrial prospects for growth, markets and products, competitive environment, management, corporate governance, innovation and development, strength and weakness factors, etc. The combination of fundamental rating and the qualitative elements is the so called corporate credit rating. In addition to these factors, a bank analyzes data for evaluation of its relationship with a company and the relationship of a company with the overall banking system (doubtful loans, substandard loan, etc.). Furthermore, according to Basel II, a default for a credit institution is considered to have occurred with regard to a particular obligor when either or both of the two following events have taken place: a) the bank considers that the obligor is unlikely to pay its credit obligations to the banking group in full, without recourse by the bank to actions such as realising security (if held); b) the obligor is overdue more than 90 days (in the case of Italy, for a transition period of 5 years, 180 days) on any material credit obligation to the banking group. With regard to a rating agency, default is related to defining a serious pathological condition for an issuer-enterprise. According to uncertainty and risk theory, at present, a company is evaluated as a financial assets portfolio, affected by: (i) operating risk which represents the uncertainty of its expected results; (ii) financial risk if the company is levered; (iii) a default risk which depends on the incapacity of the company to reach the trade-off between operating and financial risks and their adequate returns. If this equilibrium is not maintained (which means that if operating and financial risks increase the returns decrease) the company value decreases, competitive advantage losses emerge, and different vulnerability and distress grades occur. This paper discusses one model for assessing distress of industrial companies, using financial statement data, developed by Eu-Ra Europe Rating S.p.A., a spin-off of the Ph.D. in Corporate Finance (Department of Economics and Management, University of Trieste, Italy) in collaboration with Department of Mechanical Engineering, University of Trieste, Italy. The evidence is related to Italian industrial enterprises. It is not intended for the finance, insurance, and real estate sectors. Specifically, a set of financial and economic ratios is analyzed in a corporate bankruptcy prediction with the purpose of creating a fundamental credit rating model. In general, ratios measuring profitability, liquidity, and solvency appears as the most significant indicators (see Appendix 1). Most standard texts on financial statement analysis discuss ratios that characterize various aspects of a firm’s performance. While each of these ratios may provide important alternative perspectives of a firm’s condition, the main questions for our purpose are: which ratios are most important in detecting bankruptcy potential? And which methods can be applied? 2 Current Theory of default prediction by numerical methods The use of numerical methodologies to evaluate the default risk of a company is a well-known problem in Finance and Statistical sciences. The modern era of commercial default prediction really begins with the work of Beaver and Altman in the late 1960s. Beaver (1967), with univariate analysis, found that a number of indicators could discriminate between matched samples of failed and non-failed firms for as long as five years prior to failure. The most interesting examples for the definition of a numerical model for the default prediction is the Zscores method of Altman (Altman, 1968) which, starting from the financial ratios of the companies, calculates a multivariate discriminant model to divide the companies in

two categories: bankrupt or non-bankrupt. The discriminant function, of the formula Z = V1X1 + V2X2 +…+ VnXn, transforms the individual variable values to a single discriminant score, or z value, which is then used to classify the object where: X1, X2, . . ., Xn = discriminant coefficients, and V1, V2,, . . ., Vn = independent variables The advantage of this methodology is the simplicity of the analytical form, with direct correlations between the input parameters (financial ratios) and the discriminant score. A common criticism of this method is that it is depends on financial environment (Country or economic sector). One of the advantage of the Zscores methodology is the demonstration of the necessity to have a numerical method to derive the probability of default. Starting from the Altman ideas, new statistical theories have been developed, based on the conditional probability or machine learning. From a mathematical point of view the problem of determining a model for the default probability becomes: Let x denote our vector of explanatory variables (financial ratios), let the random variable Y ∈ {0, 1} indicate default (Y = 1) or survival (Y = 0) over some fixed time interval from the observation of x ∈ Rd. We seek the conditional probability measure p(y|x) = Prob(Y = 1|x). To solve this problem, many different numerical methodologies have been developed: Neural Networks (Rojas, 1996), Support Vector Machines (Cortez, 1995), and the classic Logit and Probit models (Hastie, 2002). These methods tend to optimize a likelihood function, in order to find the best matching between the numerical model and the known database. The advantage is that the discriminant coefficients of the model are not user defined but they are automatically determinated by the optimization algorithm. One new important method, based on machine learning, is the Maximum Expected Utility Principle (MEU) developed at the Standard & Poor's Risk Solutions Group (Friedman, 2003a b c). This model has a clear economic interpretation and it measures the performance in economic terms. The main idea is to seek a probability measure that maximizes the out-of-sample expected utility of an investor who chooses his investment strategy so as to maximize his expected utility under the model he believes to be efficient. The Group of authors demonstrates how this new numerical method outperforms the Logit and Probit methodology, since it takes into consideration the interactions between the financial rations in order to obtain a better approximation of the real probability of default. In the papers the authors present an iterative model to determinate the most default predictive financial ratios for avoiding the arbitrariness in the input variables choice. Another default risk predictor is RiskCalcTM (RiskCalcTM for private, 2000) used by Moody’s. This model is based on the Merton model (Merton, 1973) in which the firm's future asset value has a probability distribution characterized by its expected value and standard deviation. The method defines a “distance to default” which is the distance in standard deviations between the expected value of assets and the value of liabilities at time T. The greater the value of the firm and the smaller its volatility, then the lower is the probability of default. The authors demonstrate how the Merton methodology outperforms the Zscores model using the well-known CAP index of accuracy, reaching a value of 0.54 when Zscores reaches 0.45. The disadvantage of the methods based on statistical theory or machine learning is the necessity to have an accurate and complete database of the companies, data that could be difficult to assemble, especially considering the data of the companies which experienced bankruptcy in the past. In this paper an accurate, automatic methodology based on the combination of different numerical models has been developed, in order to improve the usability of the default risk predictor with an interesting connection between financial theory and new statistical methods. The basic idea is to reduce the importance of the database in order to extend the default risk estimation. 3. Why MCDM? The increasing complexity of financial problems over the past decades has driven analysts to develop and adopt more sophisticated quantitative analysis techniques. Furthermore, in the last years, is growing the opinion that the criteria to guide financial decisions has to be multidimensional (Ciprian et al. 2006, Zopounidis & Doumpos 2002 a).

This is the reason why mathematical models have replaced verbal models (Spronk, Steuer,& Zopounidis, 2005). Financial institutions as well as firms acknowledge the multi-dimensional nature of financial decision problems and the implication “is that there may be an attempt to redefine the analytical tools used to solve problems; for example, goal programming and multi-criteria decision making”, according to Bhaskar (Bhaskar, 1983, p. 616). Institutions and firms often use optimization and statistical software packages even though many of these are not specifically designed for financial decision making problems. Examples of such programs are the CGX system, the BANKS system, the BANKADVISER system, the INVEX system, the FINEVA system, the FINCLAS system, the INVESTOR system, etc. (Spronk et al., 2005). The use of mathematics and operational research approach in Finance began in the 50’s with the introduction of Markowitz’s portfolio theory (Markowitz, 1950). Since then many researchers and practitioners have made their contribution. With our study, we would like to illustrate how multidimensional approaches may be useful to solve a financial problem: the individual creditworthiness. The core of MCCR (Multi Criteria Credit Rating) developed by Eu-Ra Europe Rating S.p.A. is a MCDM algorithm proposed by J.B. Yang and P. Sen (Sen & Yang, 1998, pp. 75-97): CODASID. This method attempts to generate a clear preference order for alternative designs through a concordance analysis (extending the original analysis of ELECTRE (Roy, 1996)) and a discordance analysis by similarity to ideal designs, deriving from the TOPSIS method (Hwang & Yoon, 1981) the basic idea of which is to define such a distance measure for each feasible design from given reference design. The basic concept is that the best action should have the shortest distance from an ideal design and the greatest from a negative ideal design. Due to its multidimensional nature, the model is able to examine all of the data inputs together, rather than on a field-by-field basis that traditional statistical models use. The power to examine all of the data together allows investigation and understanding of the financial health of each enterprise and that gives the models their predictive power. This is how analysts and practitioners work: identifying complex patterns within sets of data. 4. Database description In this section we discuss the selection of data for the development of Multi Criteria Credit Rating (MCCR). The statistical representation and the quality of the underlying data is one of the most important drivers of the performance of any kind of model. An extensive database developed by Eu-Ra Europe Rating is used. This database includes annual financial statements of about 225,000 private firms operating in industrial sectors and in all Italian regions (company size: annual sales revenue equal to or greater than Euro 500,000) over the previous eight years. The data cover over 30% of all Italian private companies required to draw up annual financial statement under Italian law (D.Lgs. 129/91) and represent about 80% of sales revenue generated in Italy by private industrial companies (finance, insurance, and real estate sectors are not included). Furthermore a distressed group of companies that filed a bankruptcy petition under Italian Bankruptcy Law from 2002 through 2004 was involved. The financial statement data are processed applying the Fund Accounting (Flow and Fund Analysis, Fanni, 2000) methodology, which underlines company strength and weakness factors and its possible pathologies. In particular it offers drivers to evaluate financial and economics equilibrium of a company and drivers for the cash flow analysis. The same methodology is able to give warning ratios on the financial statement which does not meet on system request standards. A representative stratify sample of private Italian companies, according to territorial distribution and to the economic sectors and to the company size, is extracted from the database. The representative sample includes around 106,000 private companies, for which the annual financial information over the three years are analyzed (period 2002 - 2004). This represents more than 314,000 yearly observations. The sample represents about 88% of Italian private firms (size in terms of sales revenues: greater than Euro 1 million). Furthermore, to assemble the representative sample the database was cleaned to ensure good data. For example, excluded financial statements from Eu-Ra database based on plausibility checks of particular positions in financial statements (e.g. assets less than zero) or where the financial statement covered a period of less than twelve months. The companies included in the training set have been classified according to their main business lines. Each sector shows a characteristic that distinguishes it from the other economic sectors. The objective of

this classification is to ensure that the assessment of each company included in the sample is appropriate, considering the main risks and trends in the industry under examination. In order to create adequate sector groups, starting from the ATECO classification (Italian industries standard issued by ISTAT - Italian Statistical Office) cluster analysis is used. Cluster analysis proceeds in this way: first, a number of ratios from the financial statements database, which characterizes each industry, are identified. Next the similarity between industries are examined by considering the difference between the ratio average value using k-mean techniques. Finally, an analytical review of the cluster analysis results was carried out, in order to ensure accuracy. According on this methodology, 37 industrial clusters were created: this each firm (composed database) is classified following this classification. 5 Statistical analysis of predictive power of the financial ratios default and the selection of variables for the model All statistical models of default use data such as firm-specific income and balance sheet statements to predict the probability of future financial distress of a firm. The selection of variables and their transformation are often the most important part of modeling default risk. All the steps described in the following section have been applied to each of 37 industrial clusters as a representative sample of Italian companies. About 80 financial ratios were calculated for each company. In order to avoid redundancy, these ratios were processed, excluding those that are highly statistically correlated, either directly or inversely. This means that, in case of high correlation of two ratios, the one that is considered to have a lower relation with default status has been excluded. To understand the importance of financial ratios in terms of bankruptcy predictive power, three different methods are used: T-Student parameter, Self Organizing Maps and Default Frequency. By combining these three different methodologies, which show different aspects of the predictive power of each factor, it has been possible to identify the level of importance to be attached to each credit factor.

5.1 T-Student Analysis T-Student parameter is used to define whether the difference between two sets is genuine or not (Press, 1989). By applying the concept of standard error, the conventional statistic for measuring the significance of a difference of means is termed Student’s t. The entire database of companies is divided in two sets: bankrupt and non bankrupt, and whether a financial ratio is important in the two set divisions has to be understood. In numerical terms:

∑ (x sD = t=

− xone ) + ∑ (xi − xtwo ) 2

i

one

two

N1 + N 2 − 2

2

1 1 + N N 2 1

(1)

x one − xtwo sD

where N1 and N2 are the number of companies in the two sets, mean(xone) and mean(xtwo) are the means of the financial ratios for the two sets. If the t parameter is high the means are different and the financial ratio is significant for default prediction. The t-Student parameter for each financial ratio and for each industrial cluster in order to compute has been calculated the default predictivity of the ratio. 5.2 Default Frequency It is important when considering which ratios to include in a model to have prior expectation of how they will be related to default. This relationship is shown clearly by Default Frequency: i.e. the frequency where a firm has defaulted over a given period. An example of Default Frequency is depicted in Figure 1: the x-axis shows the percentile in which a particular ratio value lies and the y-axis shows the default frequency observed for firms with ratios in that percentile. For example, it can be seen from Figure1 that

EBITDA interest coverage ratio has lower values that are associated with higher default rates. It is also evident from Figure 2 that the Current Assets Growth Rate ratio has no relation with default.

Figure 1 Default Frequency for a financial ratio (EBITDA interest coverage ratio) with high correlation with default.

Figure 2 - Default Frequency for a financial ratio (Current Assets Growth Rate) with no correlation with default.

5.3 Self-Organizing Maps The visualization of the interaction between financial ratios and default is one important point for improving the performance of a default probability estimation. The financial analyst can obtain considerable information about the direct control of the relations between the input and output parameter of the default model. This is an important field in data mining and different methodologies have been developed: clustering, Principal Component Analysis, and Self-Organizing Maps. The Self-Organizing Map (SOM) (Kohonen, 2001) is an unsupervised neural network algorithm that projects high-dimensional data onto a two-dimensional map. The projection preserves the topology of the data so that similar data items will be mapped to nearby locations on the map. This allows the user to identify clusters, i.e. large groupings of a certain type of input pattern. Further examination may then reveal what features the members of a cluster have in common. Since its invention by Finnish Professor Teuvo Kohonen in the early 1980s (Kohonen, 1982), more than 4,000 research articles have been

published on the algorithm (Ojia, 2002), its visualization and application. The maps comprehensively visualize natural groupings and relations in the data and have been successfully applied in a broad spectrum of research areas ranging from speech recognition to financial analysis. The Self-Organizing Map belongs to the class of unsupervised and competitive learning algorithms. It is a sheet-like neural network, with nodes arranged as a regular, usually two-dimensional grid. Each node is directly associated with a weight vector. The items in the input data set are considered to be in a vector format. If n is the dimension of the input space, then every node on the map grid holds an n-dimensional vector of weights. The basic principle is to adjust these weight vectors until the map represents visualization of the input data set. Since the number of map nodes is usually significantly smaller than the number of items in the dataset, it is obvious to say that it is impossible to represent every input item from the data space on the map. Rather, the objective is to achieve a configuration in which the distribution of the data is reflected and the most important metric relations are preserved. In particular, the importance is in obtaining a correlation between the similarity of items in the dataset and the distance between their most similar representatives on the map. In other words, items that are similar in the input space should map to nearby nodes on the grid. By running the Self-Organizing Maps on the companies’ database and by using the value 0 for nonbankrupt companies and value 1 for bankrupt companies, it is possible to visualize the correlation between financial ratios and default (Figure 3).

Figure 3 - Use of the Self Organizing maps; upper: map for default (red) – no default (blue), bottom-left: map for Return on investment ratio (ROI – Operating income/Total assets), bottom-right: map for Operating income interest coverage ratio (Interest expenses/Operating income).

From the maps the direct correlation between default and ROI is evident. In fact, with high value of the ROI ratio there are no companies in default. The correlation is different for the Operating income interest coverage ratio: in the cluster characterized by default there are companies with high and low values of this ratio. It is clear how the use of Self-Organizing Maps may complete the information extracted by the tstudent parameter and the Default Frequency, thus helping the financial analyst to use in the numerical default probability model those financial ratios which have more predictive power over default. Furthermore, SOMs permit the financial analyst to measure critical values (dangerous, pathological, adequate, very good, etc..) for each ratio, which are used in the following steps described below.

6. Fuzzy-MCDM As Achille Messac wrote in 1996 about physical optimization, “the decision maker has substantive knowledge and often clear objectives, regarding aspects of the problem at hand, that can be articulated in physically meaningful terms (e.g. a Return On Investment of 10% is desirable; 8%, tolerable; and 5%, unacceptable)”. Following that idea, there has been developed by us a methodology for studying, comprehending and analyzing every balance sheet and income statement data collected. MCCR uses about ten inputs: these are not financial ratios but a transformation of them: a function of the likelihood of default that each ratio carries. The financial analyst expresses preferences with respect to each factor using a scale between 0 and 1.8 as shown in Figure 4. The value of the ratio under consideration is on the horizontal axis, and the function that will be minimized for that metric, the classfunction, is on the vertical axis and represents the degree of penalty that has to be assigned to each factor when it has a value in a given range; i.e. the higher the transform value, the worse the ratio.

Figure 4 - Fuzzy approach for ROE (Return on equity – Net income/ Equity)

Unlike Messac, who considers only expert judgements, we define the class-functions by combining the information arising out of several data mining methods such as Self-Organizing Maps (SOM), statistical parameters (t-Student, mean, variance, median, standard deviation, percentile, etc. for each industry cluster), Default Frequencies. The full amount of information is reviewed by an expert analyst, using economic logic (meaning of financial ratio). It is clear that the result of this investigation is a vector of penalty values; we will ask the model to minimize each quantity. As noted about, we reach a rating evaluation, then a classification based on the solvency of the company by using a MCDM algorithm that deals with “outranking relations” and by using pairwise comparisons among alternatives under each of the criteria separately. In order to carry this out some reference profiles have been introduced, as well explained in Zopounidis & Doumpos 2002 b. Those reference profiles, named “pivot firms”, are defined as vectors of individual profiles for each criterion and depict the 18 Eu-Ra credit rating classes: i.e. each pivot firm is a penalized firm for each of the 18 rating classes, following the traditional standards of rating agencies. Another input required by CODASID, in addition to the matrix containing the factors to be explored during the decision procedure, is a vector of weights expressing the relative importance of one attribute with respect to the others. The relative weight vectors of the elements has been calculated by grouping the variables according to their own categories, by establishing their hierarchy in the context of the problem and by formulating a pairwise comparison matrix for elements at each level of the hierarchy and, finally, by applying the Analytic Hierarchy Process (AHP) method (Saaty 1980, Saaty & Vargas 2000). 7. Results MCCR is the means of assigning fundamental credit rating to each company under examination, according to Eu-Ra rating categories in line with international standards of rating agencies (AAA, AA, A, BBB+, BBB, BBB-, BB+, BB, BB-, B+, B, B-, CCC+, CCC, CCC-, CC and D). The following figure (Figure 5)

shows fundamental rating distribution for a sample of Italian enterprises for the period 2002-2004 on a yearly base (about 130,000 companies for each year belonging to all industrial sectors). Rating distribution 30,00% 25,00% 20,00% 15,00% 10,00% 5,00% 0,00% AAA

AA

A

BBB

BB

B

CCC

CC

C

D

2002 0,00% 1,57% 5,23% 14,42% 20,04% 26,38% 18,36% 13,43% 0,56% 0,01% 2003 0,00% 1,09% 4,26% 13,81% 20,21% 27,07% 19,47% 13,49% 0,59% 0,01% 2004 0,00% 1,32% 4,92% 14,06% 19,59% 26,74% 18,80% 13,65% 0,91% 0,01%

Figure 5 - Fundamental Rating distribution on a yearly base (period 2002-2004).

The cumulative accuracy ratio (CAP) summarises the power curve for a model on a data set, and compares this with that of the perfect and random model. The cumulative accuracy ratio measures the area under the power curve for a model and compares this with the area under the perfect and random models, as shown in Figure 6, below. Thus the perfect model would have an accuracy ratio of 100%, and the random model would have an accuracy ratio of 0%. When comparing the performance of two models on a data set, the more powerful model on that data set will have a higher accuracy ratio. Figure 6 shows the cumulative accuracy ratio (CAP) for Italian companies belonging to the wholesale sector, applying MCCR this ratio reaches a value of 0.63 in comparison with 0.6 obtained by using Zscores and Moody’s model.

Figure 6 - Cumulative Accuracy Profile (CAP) plot.

Conclusions By combining modern numerical data mining with Multi Criteria Decision Making Algorithm and with Corporate Finance theory, a model has been developed in order to assess distress of industrial companies according to Basel II guidelines. The evidence was related to Italian industrial enterprises and took into consideration the situation of the Italian economy both from a micro and macro perspective. Care has been given to how financial ratios are related to default by using three different methodologies: T- Student, Default Frequency, Self Organizing Maps.

The advantages of the MCCR may be summarized as follows: (i) the method is not only based on statistical analysis but is a coherent and adequate integration of financial and corporate logic and modern numerical methods (ii) the model allows flexibility and accuracy for evaluation of companies belonging to different economic sectors (iii) Fuzzy logic is applied to include qualitative concepts (according to Corporate Finance theory and practice) in quantitative models (MCDM). The model has been tested on the Eu-Ra database that is representative of the Italian companies system. From the credit rating distribution on a yearly base and from the accuracy ratio reached by MCCR, the model performance is comparable with the principal default models used by Rating Agencies. Appendix 1 Solvency ratios Cash flow ratio

Leverage Debt to equity Total assets/Total liabilities Gearing Retained earnings/Total assets Total assets/Current liabilities Current

Interest coverage Profitability and economic equilibrium ratios ROI ROE ROS Interest expenses/Operating income Sales/Total assets

Financial Meaning indicates the company’s ability to cover total liabilities with the yearly cash flow from operating activities. The higher the ratio, the better the firm’s ability to carry its total debt. measures the level of total liabilities of the company in comparison with equity. indicates the level of total debt of the company (excluding trade accounts payable). indicates company’s solvency. The company shows a level of deficit when the value of this ratio is under one unit. indicates the level of net debt of the company in comparison with equity indicates the level of covering of total assets with retained earnings. Retained earnings represent the undistributed earnings of a company consisting of the net income for all past periods minus the dividends that have been declared represents the level of total assets over current liabilities

indicate the equilibrium between short-term investment and financing. The traditional distinction between current assets and liabilities is based on maturity of less than one year. The levels assumed from these ratios depend on the sector in which the company operates. Indicate the ability of the company to cover interest expenses through the economic margins (EBITDA and EBIT) and through the cash flow from operating activities

measures the profitability of company investments without regard to the way the investment is financed. measures the profitability of the equity. indicates the profitability of the sales. indicates the incidence of interest expenses over operating income.

indicates the investments turnover with regard to sales. The level assumed from the ratio depends on the sector in which the company operates

Table 1: Main financial ratios and meanings

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MULTI CRITERIA CREDIT RATING (MCCR): A CREDIT RATING ASSIGNMENT PROCESS FOR ITALIAN ENTERPRISES ACCORDING TO BASEL II Francesca Bernè1, Mattia Ciprian2, Maurizio Fanni3, Daria Marassi1, Valentino Pediroda2 1

Eu-ra Europe Rating S.p.A L.go Don Francesco Bonifacio, 1 34125 Trieste, Italy e-mail: [email protected] [email protected]

2

Dipartimento di Ingegneria Meccanica Università degli Studi di Trieste via Valerio 10 34127 Trieste, Italy e-mail: [email protected] [email protected]

3

Dipartimento di Economia e Tecnica Aziendale Università degli Studi di Trieste Piazzale Europa 1 34127 Trieste, Italy e-mail: [email protected]

Keywords: Basel II, probability of default, statistical analysis, Multi Criteria Decision Making, rating Summary: A Multi Criteria Decision Making Model has been applied to solve the credit rating assignment process following Basel II guidelines. In order to select the input parameters, the integration of three different statistical methods has been employed. The model has been tested on a database that is representative of the Italian companies system. 1. Introduction to Basel II, a credit rating assignment process and probability of default Credit risk affects virtually every financial contract. Therefore the measurement, pricing and management of credit risk has received much attention from practitioners who have a strong interest in accurately pricing and managing this kind of risk and from financial economists who have much to learn from the way such risk is priced in the market, and from bank authorities who need to design minimum capital requirements that correctly reflect the credit risk of banks’ loan portfolios. Following the work of the Basel Committee on Banking Supervision to reform the capital adequacy framework by introducing risksensitive capital requirements, significant attention has been devoted to the subject of credit risk measurement by the international regulatory, academic and banking communities. The agreement called “International Convergence of Capital Measurement and Capital Standards” and known as “Basel II”, the last version of which was published in June 2004, will be applied on a consolidated basis to internationally active banks from January 1, 2007. According to Basel II, banks should have a process for assessing their overall capital adequacy in relation to their risk profile and a strategy for maintaining their capital levels. All material risks faced by the bank should be evaluated as part of the capital assessment process, in particular: a) credit risk; b) operational risk which is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events; c) market risk; d) interest rate risk in the banking book; e) liquidity risk; f) other risks. The Committee proposes to give banks a choice between two broad methodologies for calculating their capital requirements for credit risk. One will be to measure credit risk in a standardised manner, supported by external credit assessments (by external agencies called ECAI - External Credit Assessment Institution). The second methodology, which is subject to explicit approval of bank authorities, would allow banks to use their Internal Ratings Systems (IRS) for credit risk. Two different IRS can be utilized: a) FIRBA (Foundation Internal Rating Approach); b) AIRBA (Advanced Internal Rating Based Approach). Three main variables affect the credit risk of a financial asset: (i) the probability of default (PD); (ii) the loss given default (LGD) which is equal to one minus the recovery rate in the event of default (RR); (iii) the exposure at default (EAD); (iv) the maturity (M).

Credit risk literature has given particular attention to the estimation of the first component, probability of default, which includes credit rating assignment processes with adequate models and methodologies. What is credit rating? Credit rating is an opinion of the general creditworthiness of an obligor (issuer rating), or the creditworthiness of an obligor in respect of a specific debt security or other financial obligation (issue rating), based on relevant risk factors. A different probability of default (within one year, two years and three years) is associated with each credit rating category (indicated by symbols: traditional AAA to D). In the view of an agency, the rating process for an issuer-company includes the estimate of the financial risk profile through the analysis of financial statement data and off balance-sheet items. The first phase finishes with the assignment of a fundamental credit rating which consists of the evaluation of the financial and economic equilibrium of the company, and its flows (cash flow, working capital flow, etc.) and represents an essential aspect for vulnerability assessment, a prerequisite for corporate rating and credit rating for credit institutions. In the second phase, the valuation is not limited to an examination of various financial measures. Proper assessment of credit quality for an industrial company involves a thorough review of business fundamentals (qualitative factors analysis), including industrial prospects for growth, markets and products, competitive environment, management, corporate governance, innovation and development, strength and weakness factors, etc. The combination of fundamental rating and the qualitative elements is the so called corporate credit rating. In addition to these factors, a bank analyzes data for evaluation of its relationship with a company and the relationship of a company with the overall banking system (doubtful loans, substandard loan, etc.). Furthermore, according to Basel II, a default for a credit institution is considered to have occurred with regard to a particular obligor when either or both of the two following events have taken place: a) the bank considers that the obligor is unlikely to pay its credit obligations to the banking group in full, without recourse by the bank to actions such as realising security (if held); b) the obligor is overdue more than 90 days (in the case of Italy, for a transition period of 5 years, 180 days) on any material credit obligation to the banking group. With regard to a rating agency, default is related to defining a serious pathological condition for an issuer-enterprise. According to uncertainty and risk theory, at present, a company is evaluated as a financial assets portfolio, affected by: (i) operating risk which represents the uncertainty of its expected results; (ii) financial risk if the company is levered; (iii) a default risk which depends on the incapacity of the company to reach the trade-off between operating and financial risks and their adequate returns. If this equilibrium is not maintained (which means that if operating and financial risks increase the returns decrease) the company value decreases, competitive advantage losses emerge, and different vulnerability and distress grades occur. This paper discusses one model for assessing distress of industrial companies, using financial statement data, developed by Eu-Ra Europe Rating S.p.A., a spin-off of the Ph.D. in Corporate Finance (Department of Economics and Management, University of Trieste, Italy) in collaboration with Department of Mechanical Engineering, University of Trieste, Italy. The evidence is related to Italian industrial enterprises. It is not intended for the finance, insurance, and real estate sectors. Specifically, a set of financial and economic ratios is analyzed in a corporate bankruptcy prediction with the purpose of creating a fundamental credit rating model. In general, ratios measuring profitability, liquidity, and solvency appears as the most significant indicators (see Appendix 1). Most standard texts on financial statement analysis discuss ratios that characterize various aspects of a firm’s performance. While each of these ratios may provide important alternative perspectives of a firm’s condition, the main questions for our purpose are: which ratios are most important in detecting bankruptcy potential? And which methods can be applied? 2 Current Theory of default prediction by numerical methods The use of numerical methodologies to evaluate the default risk of a company is a well-known problem in Finance and Statistical sciences. The modern era of commercial default prediction really begins with the work of Beaver and Altman in the late 1960s. Beaver (1967), with univariate analysis, found that a number of indicators could discriminate between matched samples of failed and non-failed firms for as long as five years prior to failure. The most interesting examples for the definition of a numerical model for the default prediction is the Zscores method of Altman (Altman, 1968) which, starting from the financial ratios of the companies, calculates a multivariate discriminant model to divide the companies in

two categories: bankrupt or non-bankrupt. The discriminant function, of the formula Z = V1X1 + V2X2 +…+ VnXn, transforms the individual variable values to a single discriminant score, or z value, which is then used to classify the object where: X1, X2, . . ., Xn = discriminant coefficients, and V1, V2,, . . ., Vn = independent variables The advantage of this methodology is the simplicity of the analytical form, with direct correlations between the input parameters (financial ratios) and the discriminant score. A common criticism of this method is that it is depends on financial environment (Country or economic sector). One of the advantage of the Zscores methodology is the demonstration of the necessity to have a numerical method to derive the probability of default. Starting from the Altman ideas, new statistical theories have been developed, based on the conditional probability or machine learning. From a mathematical point of view the problem of determining a model for the default probability becomes: Let x denote our vector of explanatory variables (financial ratios), let the random variable Y ∈ {0, 1} indicate default (Y = 1) or survival (Y = 0) over some fixed time interval from the observation of x ∈ Rd. We seek the conditional probability measure p(y|x) = Prob(Y = 1|x). To solve this problem, many different numerical methodologies have been developed: Neural Networks (Rojas, 1996), Support Vector Machines (Cortez, 1995), and the classic Logit and Probit models (Hastie, 2002). These methods tend to optimize a likelihood function, in order to find the best matching between the numerical model and the known database. The advantage is that the discriminant coefficients of the model are not user defined but they are automatically determinated by the optimization algorithm. One new important method, based on machine learning, is the Maximum Expected Utility Principle (MEU) developed at the Standard & Poor's Risk Solutions Group (Friedman, 2003a b c). This model has a clear economic interpretation and it measures the performance in economic terms. The main idea is to seek a probability measure that maximizes the out-of-sample expected utility of an investor who chooses his investment strategy so as to maximize his expected utility under the model he believes to be efficient. The Group of authors demonstrates how this new numerical method outperforms the Logit and Probit methodology, since it takes into consideration the interactions between the financial rations in order to obtain a better approximation of the real probability of default. In the papers the authors present an iterative model to determinate the most default predictive financial ratios for avoiding the arbitrariness in the input variables choice. Another default risk predictor is RiskCalcTM (RiskCalcTM for private, 2000) used by Moody’s. This model is based on the Merton model (Merton, 1973) in which the firm's future asset value has a probability distribution characterized by its expected value and standard deviation. The method defines a “distance to default” which is the distance in standard deviations between the expected value of assets and the value of liabilities at time T. The greater the value of the firm and the smaller its volatility, then the lower is the probability of default. The authors demonstrate how the Merton methodology outperforms the Zscores model using the well-known CAP index of accuracy, reaching a value of 0.54 when Zscores reaches 0.45. The disadvantage of the methods based on statistical theory or machine learning is the necessity to have an accurate and complete database of the companies, data that could be difficult to assemble, especially considering the data of the companies which experienced bankruptcy in the past. In this paper an accurate, automatic methodology based on the combination of different numerical models has been developed, in order to improve the usability of the default risk predictor with an interesting connection between financial theory and new statistical methods. The basic idea is to reduce the importance of the database in order to extend the default risk estimation. 3. Why MCDM? The increasing complexity of financial problems over the past decades has driven analysts to develop and adopt more sophisticated quantitative analysis techniques. Furthermore, in the last years, is growing the opinion that the criteria to guide financial decisions has to be multidimensional (Ciprian et al. 2006, Zopounidis & Doumpos 2002 a).

This is the reason why mathematical models have replaced verbal models (Spronk, Steuer,& Zopounidis, 2005). Financial institutions as well as firms acknowledge the multi-dimensional nature of financial decision problems and the implication “is that there may be an attempt to redefine the analytical tools used to solve problems; for example, goal programming and multi-criteria decision making”, according to Bhaskar (Bhaskar, 1983, p. 616). Institutions and firms often use optimization and statistical software packages even though many of these are not specifically designed for financial decision making problems. Examples of such programs are the CGX system, the BANKS system, the BANKADVISER system, the INVEX system, the FINEVA system, the FINCLAS system, the INVESTOR system, etc. (Spronk et al., 2005). The use of mathematics and operational research approach in Finance began in the 50’s with the introduction of Markowitz’s portfolio theory (Markowitz, 1950). Since then many researchers and practitioners have made their contribution. With our study, we would like to illustrate how multidimensional approaches may be useful to solve a financial problem: the individual creditworthiness. The core of MCCR (Multi Criteria Credit Rating) developed by Eu-Ra Europe Rating S.p.A. is a MCDM algorithm proposed by J.B. Yang and P. Sen (Sen & Yang, 1998, pp. 75-97): CODASID. This method attempts to generate a clear preference order for alternative designs through a concordance analysis (extending the original analysis of ELECTRE (Roy, 1996)) and a discordance analysis by similarity to ideal designs, deriving from the TOPSIS method (Hwang & Yoon, 1981) the basic idea of which is to define such a distance measure for each feasible design from given reference design. The basic concept is that the best action should have the shortest distance from an ideal design and the greatest from a negative ideal design. Due to its multidimensional nature, the model is able to examine all of the data inputs together, rather than on a field-by-field basis that traditional statistical models use. The power to examine all of the data together allows investigation and understanding of the financial health of each enterprise and that gives the models their predictive power. This is how analysts and practitioners work: identifying complex patterns within sets of data. 4. Database description In this section we discuss the selection of data for the development of Multi Criteria Credit Rating (MCCR). The statistical representation and the quality of the underlying data is one of the most important drivers of the performance of any kind of model. An extensive database developed by Eu-Ra Europe Rating is used. This database includes annual financial statements of about 225,000 private firms operating in industrial sectors and in all Italian regions (company size: annual sales revenue equal to or greater than Euro 500,000) over the previous eight years. The data cover over 30% of all Italian private companies required to draw up annual financial statement under Italian law (D.Lgs. 129/91) and represent about 80% of sales revenue generated in Italy by private industrial companies (finance, insurance, and real estate sectors are not included). Furthermore a distressed group of companies that filed a bankruptcy petition under Italian Bankruptcy Law from 2002 through 2004 was involved. The financial statement data are processed applying the Fund Accounting (Flow and Fund Analysis, Fanni, 2000) methodology, which underlines company strength and weakness factors and its possible pathologies. In particular it offers drivers to evaluate financial and economics equilibrium of a company and drivers for the cash flow analysis. The same methodology is able to give warning ratios on the financial statement which does not meet on system request standards. A representative stratify sample of private Italian companies, according to territorial distribution and to the economic sectors and to the company size, is extracted from the database. The representative sample includes around 106,000 private companies, for which the annual financial information over the three years are analyzed (period 2002 - 2004). This represents more than 314,000 yearly observations. The sample represents about 88% of Italian private firms (size in terms of sales revenues: greater than Euro 1 million). Furthermore, to assemble the representative sample the database was cleaned to ensure good data. For example, excluded financial statements from Eu-Ra database based on plausibility checks of particular positions in financial statements (e.g. assets less than zero) or where the financial statement covered a period of less than twelve months. The companies included in the training set have been classified according to their main business lines. Each sector shows a characteristic that distinguishes it from the other economic sectors. The objective of

this classification is to ensure that the assessment of each company included in the sample is appropriate, considering the main risks and trends in the industry under examination. In order to create adequate sector groups, starting from the ATECO classification (Italian industries standard issued by ISTAT - Italian Statistical Office) cluster analysis is used. Cluster analysis proceeds in this way: first, a number of ratios from the financial statements database, which characterizes each industry, are identified. Next the similarity between industries are examined by considering the difference between the ratio average value using k-mean techniques. Finally, an analytical review of the cluster analysis results was carried out, in order to ensure accuracy. According on this methodology, 37 industrial clusters were created: this each firm (composed database) is classified following this classification. 5 Statistical analysis of predictive power of the financial ratios default and the selection of variables for the model All statistical models of default use data such as firm-specific income and balance sheet statements to predict the probability of future financial distress of a firm. The selection of variables and their transformation are often the most important part of modeling default risk. All the steps described in the following section have been applied to each of 37 industrial clusters as a representative sample of Italian companies. About 80 financial ratios were calculated for each company. In order to avoid redundancy, these ratios were processed, excluding those that are highly statistically correlated, either directly or inversely. This means that, in case of high correlation of two ratios, the one that is considered to have a lower relation with default status has been excluded. To understand the importance of financial ratios in terms of bankruptcy predictive power, three different methods are used: T-Student parameter, Self Organizing Maps and Default Frequency. By combining these three different methodologies, which show different aspects of the predictive power of each factor, it has been possible to identify the level of importance to be attached to each credit factor.

5.1 T-Student Analysis T-Student parameter is used to define whether the difference between two sets is genuine or not (Press, 1989). By applying the concept of standard error, the conventional statistic for measuring the significance of a difference of means is termed Student’s t. The entire database of companies is divided in two sets: bankrupt and non bankrupt, and whether a financial ratio is important in the two set divisions has to be understood. In numerical terms:

∑ (x sD = t=

− xone ) + ∑ (xi − xtwo ) 2

i

one

two

N1 + N 2 − 2

2

1 1 + N N 2 1

(1)

x one − xtwo sD

where N1 and N2 are the number of companies in the two sets, mean(xone) and mean(xtwo) are the means of the financial ratios for the two sets. If the t parameter is high the means are different and the financial ratio is significant for default prediction. The t-Student parameter for each financial ratio and for each industrial cluster in order to compute has been calculated the default predictivity of the ratio. 5.2 Default Frequency It is important when considering which ratios to include in a model to have prior expectation of how they will be related to default. This relationship is shown clearly by Default Frequency: i.e. the frequency where a firm has defaulted over a given period. An example of Default Frequency is depicted in Figure 1: the x-axis shows the percentile in which a particular ratio value lies and the y-axis shows the default frequency observed for firms with ratios in that percentile. For example, it can be seen from Figure1 that

EBITDA interest coverage ratio has lower values that are associated with higher default rates. It is also evident from Figure 2 that the Current Assets Growth Rate ratio has no relation with default.

Figure 1 Default Frequency for a financial ratio (EBITDA interest coverage ratio) with high correlation with default.

Figure 2 - Default Frequency for a financial ratio (Current Assets Growth Rate) with no correlation with default.

5.3 Self-Organizing Maps The visualization of the interaction between financial ratios and default is one important point for improving the performance of a default probability estimation. The financial analyst can obtain considerable information about the direct control of the relations between the input and output parameter of the default model. This is an important field in data mining and different methodologies have been developed: clustering, Principal Component Analysis, and Self-Organizing Maps. The Self-Organizing Map (SOM) (Kohonen, 2001) is an unsupervised neural network algorithm that projects high-dimensional data onto a two-dimensional map. The projection preserves the topology of the data so that similar data items will be mapped to nearby locations on the map. This allows the user to identify clusters, i.e. large groupings of a certain type of input pattern. Further examination may then reveal what features the members of a cluster have in common. Since its invention by Finnish Professor Teuvo Kohonen in the early 1980s (Kohonen, 1982), more than 4,000 research articles have been

published on the algorithm (Ojia, 2002), its visualization and application. The maps comprehensively visualize natural groupings and relations in the data and have been successfully applied in a broad spectrum of research areas ranging from speech recognition to financial analysis. The Self-Organizing Map belongs to the class of unsupervised and competitive learning algorithms. It is a sheet-like neural network, with nodes arranged as a regular, usually two-dimensional grid. Each node is directly associated with a weight vector. The items in the input data set are considered to be in a vector format. If n is the dimension of the input space, then every node on the map grid holds an n-dimensional vector of weights. The basic principle is to adjust these weight vectors until the map represents visualization of the input data set. Since the number of map nodes is usually significantly smaller than the number of items in the dataset, it is obvious to say that it is impossible to represent every input item from the data space on the map. Rather, the objective is to achieve a configuration in which the distribution of the data is reflected and the most important metric relations are preserved. In particular, the importance is in obtaining a correlation between the similarity of items in the dataset and the distance between their most similar representatives on the map. In other words, items that are similar in the input space should map to nearby nodes on the grid. By running the Self-Organizing Maps on the companies’ database and by using the value 0 for nonbankrupt companies and value 1 for bankrupt companies, it is possible to visualize the correlation between financial ratios and default (Figure 3).

Figure 3 - Use of the Self Organizing maps; upper: map for default (red) – no default (blue), bottom-left: map for Return on investment ratio (ROI – Operating income/Total assets), bottom-right: map for Operating income interest coverage ratio (Interest expenses/Operating income).

From the maps the direct correlation between default and ROI is evident. In fact, with high value of the ROI ratio there are no companies in default. The correlation is different for the Operating income interest coverage ratio: in the cluster characterized by default there are companies with high and low values of this ratio. It is clear how the use of Self-Organizing Maps may complete the information extracted by the tstudent parameter and the Default Frequency, thus helping the financial analyst to use in the numerical default probability model those financial ratios which have more predictive power over default. Furthermore, SOMs permit the financial analyst to measure critical values (dangerous, pathological, adequate, very good, etc..) for each ratio, which are used in the following steps described below.

6. Fuzzy-MCDM As Achille Messac wrote in 1996 about physical optimization, “the decision maker has substantive knowledge and often clear objectives, regarding aspects of the problem at hand, that can be articulated in physically meaningful terms (e.g. a Return On Investment of 10% is desirable; 8%, tolerable; and 5%, unacceptable)”. Following that idea, there has been developed by us a methodology for studying, comprehending and analyzing every balance sheet and income statement data collected. MCCR uses about ten inputs: these are not financial ratios but a transformation of them: a function of the likelihood of default that each ratio carries. The financial analyst expresses preferences with respect to each factor using a scale between 0 and 1.8 as shown in Figure 4. The value of the ratio under consideration is on the horizontal axis, and the function that will be minimized for that metric, the classfunction, is on the vertical axis and represents the degree of penalty that has to be assigned to each factor when it has a value in a given range; i.e. the higher the transform value, the worse the ratio.

Figure 4 - Fuzzy approach for ROE (Return on equity – Net income/ Equity)

Unlike Messac, who considers only expert judgements, we define the class-functions by combining the information arising out of several data mining methods such as Self-Organizing Maps (SOM), statistical parameters (t-Student, mean, variance, median, standard deviation, percentile, etc. for each industry cluster), Default Frequencies. The full amount of information is reviewed by an expert analyst, using economic logic (meaning of financial ratio). It is clear that the result of this investigation is a vector of penalty values; we will ask the model to minimize each quantity. As noted about, we reach a rating evaluation, then a classification based on the solvency of the company by using a MCDM algorithm that deals with “outranking relations” and by using pairwise comparisons among alternatives under each of the criteria separately. In order to carry this out some reference profiles have been introduced, as well explained in Zopounidis & Doumpos 2002 b. Those reference profiles, named “pivot firms”, are defined as vectors of individual profiles for each criterion and depict the 18 Eu-Ra credit rating classes: i.e. each pivot firm is a penalized firm for each of the 18 rating classes, following the traditional standards of rating agencies. Another input required by CODASID, in addition to the matrix containing the factors to be explored during the decision procedure, is a vector of weights expressing the relative importance of one attribute with respect to the others. The relative weight vectors of the elements has been calculated by grouping the variables according to their own categories, by establishing their hierarchy in the context of the problem and by formulating a pairwise comparison matrix for elements at each level of the hierarchy and, finally, by applying the Analytic Hierarchy Process (AHP) method (Saaty 1980, Saaty & Vargas 2000). 7. Results MCCR is the means of assigning fundamental credit rating to each company under examination, according to Eu-Ra rating categories in line with international standards of rating agencies (AAA, AA, A, BBB+, BBB, BBB-, BB+, BB, BB-, B+, B, B-, CCC+, CCC, CCC-, CC and D). The following figure (Figure 5)

shows fundamental rating distribution for a sample of Italian enterprises for the period 2002-2004 on a yearly base (about 130,000 companies for each year belonging to all industrial sectors). Rating distribution 30,00% 25,00% 20,00% 15,00% 10,00% 5,00% 0,00% AAA

AA

A

BBB

BB

B

CCC

CC

C

D

2002 0,00% 1,57% 5,23% 14,42% 20,04% 26,38% 18,36% 13,43% 0,56% 0,01% 2003 0,00% 1,09% 4,26% 13,81% 20,21% 27,07% 19,47% 13,49% 0,59% 0,01% 2004 0,00% 1,32% 4,92% 14,06% 19,59% 26,74% 18,80% 13,65% 0,91% 0,01%

Figure 5 - Fundamental Rating distribution on a yearly base (period 2002-2004).

The cumulative accuracy ratio (CAP) summarises the power curve for a model on a data set, and compares this with that of the perfect and random model. The cumulative accuracy ratio measures the area under the power curve for a model and compares this with the area under the perfect and random models, as shown in Figure 6, below. Thus the perfect model would have an accuracy ratio of 100%, and the random model would have an accuracy ratio of 0%. When comparing the performance of two models on a data set, the more powerful model on that data set will have a higher accuracy ratio. Figure 6 shows the cumulative accuracy ratio (CAP) for Italian companies belonging to the wholesale sector, applying MCCR this ratio reaches a value of 0.63 in comparison with 0.6 obtained by using Zscores and Moody’s model.

Figure 6 - Cumulative Accuracy Profile (CAP) plot.

Conclusions By combining modern numerical data mining with Multi Criteria Decision Making Algorithm and with Corporate Finance theory, a model has been developed in order to assess distress of industrial companies according to Basel II guidelines. The evidence was related to Italian industrial enterprises and took into consideration the situation of the Italian economy both from a micro and macro perspective. Care has been given to how financial ratios are related to default by using three different methodologies: T- Student, Default Frequency, Self Organizing Maps.

The advantages of the MCCR may be summarized as follows: (i) the method is not only based on statistical analysis but is a coherent and adequate integration of financial and corporate logic and modern numerical methods (ii) the model allows flexibility and accuracy for evaluation of companies belonging to different economic sectors (iii) Fuzzy logic is applied to include qualitative concepts (according to Corporate Finance theory and practice) in quantitative models (MCDM). The model has been tested on the Eu-Ra database that is representative of the Italian companies system. From the credit rating distribution on a yearly base and from the accuracy ratio reached by MCCR, the model performance is comparable with the principal default models used by Rating Agencies. Appendix 1 Solvency ratios Cash flow ratio

Leverage Debt to equity Total assets/Total liabilities Gearing Retained earnings/Total assets Total assets/Current liabilities Current

Interest coverage Profitability and economic equilibrium ratios ROI ROE ROS Interest expenses/Operating income Sales/Total assets

Financial Meaning indicates the company’s ability to cover total liabilities with the yearly cash flow from operating activities. The higher the ratio, the better the firm’s ability to carry its total debt. measures the level of total liabilities of the company in comparison with equity. indicates the level of total debt of the company (excluding trade accounts payable). indicates company’s solvency. The company shows a level of deficit when the value of this ratio is under one unit. indicates the level of net debt of the company in comparison with equity indicates the level of covering of total assets with retained earnings. Retained earnings represent the undistributed earnings of a company consisting of the net income for all past periods minus the dividends that have been declared represents the level of total assets over current liabilities

indicate the equilibrium between short-term investment and financing. The traditional distinction between current assets and liabilities is based on maturity of less than one year. The levels assumed from these ratios depend on the sector in which the company operates. Indicate the ability of the company to cover interest expenses through the economic margins (EBITDA and EBIT) and through the cash flow from operating activities

measures the profitability of company investments without regard to the way the investment is financed. measures the profitability of the equity. indicates the profitability of the sales. indicates the incidence of interest expenses over operating income.

indicates the investments turnover with regard to sales. The level assumed from the ratio depends on the sector in which the company operates

Table 1: Main financial ratios and meanings

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