ThE DEA METhOD IN MANAGING ThE CREDIT RISK OF COMPANIES

The subject of the present paper is a new procedure of forecasting credit risk to companies in the Polish economic environment. What favors the suggested approach is the fact that in Poland, unlike in western countries, the DEA method has not yet been implemented in assessing credit risk faced by companies. The research described in the paper has been conducted on the basis of comparing the proposed DEA method with the currently used procedures, namely the point method, discriminative analysis and linear regression. To verify and compare the efficiency of various methods of company credit risk estimation, the efficiency of the classification of companies has also been examined. The study has involved an analysed sample (a teaching sample) as well as a test sample which was not taken in model building. To conclude, the DEA method facilitates forecasting financial problems, including bankruptcy of companies, in Polish economic conditions, and its efficiency is comparable to or even greater than that of the approaches implemented so far.


introduction
Credit risk is inevitably linked with every bank's activities.It is one of the basic types of credit risk.It is understood mainly as the risk of default by a borrower with remaining interest rates and commissions.a competent credit risk management plays a major role in the process of bank administration.all operations undertaken by a bank, especially those involving loans, are meant to reduce that risk.Credit-scoring methods are believed to be one of the most accurate solutions facilitating the process of credit risk management.It is worth mentioning that the procedure of credit scoring has become more significant since the Basel Committee on Banking Supervision has published the guidelines of the New Basel Capital Accord, according to which credit scoring is one of the possible tools of assessing credit risk within internal ratings (Iwanicz-Drozdowska, 2005: 130, 150].The procedure of using the DEA method for credit scoring suggested in the article may prove an effective tool in solving the problems of credit risk assessment in Polish banks.

implementing DEA method in credit risk management
The DEA method was first introduced in 1978 by American economists Charnes, Cooper and rhodes.relying on the productivity concept formulated by G. Debreu (1951) and M.J. Farrel (1957), which defined efficiency measure as a quotient of singular input and singular output, they used it for a multidimensional situation in which there was more than one input as well as more than one output.applying this inference, they were able to propose a very practical system to measure efficiency.In the DEA method, efficiency is defined as follows (Gospodarowicz, 2002: 56 where: s -amount of outputs, m -amount of inputs, μ r -measure demonstrating of importance of each group of inputs, μ r , ν i -measure demonstrating the importance of each group of outputs. Using the DEA method, the efficiency of a variable is calculated in relation to other variables from a particular group.Effective variables within a particular group make the so-called efficiency curve (Figure 1).The efficiency of the other variables is calculated in relation to the curve defined through solving the issue of linear programming (using the DEA method).The efficiency curve is defined by variables in the form of inputs and outputs in a particular study of a given variable.In the DEA method, no prior knowledge of measurements is required because through the whole study the measure of the maximum efficiency of each variable is constantly calculated.
For the outcome where variables side with the efficiency curve (Figure 1), the coefficient is equal to 1.This demonstrates the technical efficiency of those variables.Correspondingly, if the variables fall below the efficiency curve, their coefficient is less than 1.This is a sufficient indication of the technical efficiency level.
The DEA analysis uses production units, called DMU (Decision Making Unit), as variables.DEA calculates a DMU's efficiency by determining the minimum possible inputs needed to capture a set of outputs or by determining the maximum possible outputs that can be generated from a given set of inputs.The efficient advertisers are set an efficiency score of one, while the inefficient advertisers' efficiency scores are less than one but greater than zero (Thomas, Barr, Cron, Slocum, 1998: 489).These assumptions are illustrated in Figure 2.
It is assumed that each production unit contains at least one input and one output.
the methodology of credit risk assessment the DEA method proposed in this article was prepared on the basis of litera-     -inputs: X 5 and X 6 , -outputs: X 1 , X 2 , X 3 and X 4 .
To calculate the technical efficiency indicator value of the firms, the CCR (constant scale effect) model was used.It was directed toward inputs with a search for the minimal value of the efficiency indicator that will possibly reduce the amount of input and result in an equal output of the study object.For this calculation, the optimal linear EMS 4 program was used.the efficiency indicator values for each firm in the study ranged from 0 to 1. the value of the efficiency indicator equal to 1 demonstrates the firm being effective, whereas the efficiency indicator value lower than 1 demonstrates that the firm has a possibility to improve the input and output relations, i. e. indicates the efficiency loss level.
In this part of the study, research was also aimed at finding the base point (cutoff Liquidity ratio = current assets / current liabilities X 5 Daily return indicator = (total assets*number of days) / (profit from sales and equals + other operation profits + financial profits) X 6 Total liabilities indicator = (total liabilities * 100) / total assets S o u r c e : author's study.
point) of the efficiency coefficient that will separate the solvent group of firms from the firms with a risk of delinquency.a good concept allowing for setting the right base point value, but also considering an incorrect object classification, was a study of interdependence between the value of incorrect classification and the value of the base point.In this approach, the optimal base point regulates the minimal entire cost of incorrect classification.Moreover, this concept permits a multivariant analysis, the optimal base point change due to an incorrect classification to Type I or II.
to show the entire cost of incorrect classification, the following formula was applied (Simak, 2000, pp. 94-95): where C 1 is the loss indicator Type I error, C 2 is the loss indictor Type II error, i(p) is the number of Type I errors, j(p) is the number of type II errors.
For the purpose of this study, C1 and C2 are equal to 0.6 and 0.03, respectively.
For the above-mentioned CCr model (constant scale effect) concentrated on inputs, the efficiency coefficient base value was verified for a year as well as two years before delinquency below 0.40.this indicates that 0.40 or a lower rank implies a high risk of defaulting, whereas 0.40 or a higher rank implies a low risk of defaulting.
The DEA classification efficiency is illustrated in Table 2.In addition, the DEA method results (table 2) were compared with the point method (MP) results as well as with the regressive linear (rl) results.Using the same material, the author was able to perform a reliable comparative analysis using statistical data.
Based on the classification results shown in Table 2, we can conclude that the efficiency of classifications I and II with  the use of the DEA method is similar to that of the discriminating analysis and a linear regression.stage 4: Approximation of DEA efficiency rate by linear regression the main purpose of this phase is an attempt to reduce the DEA method fallacy caused by the necessity of applying an optimal linear program for every study of a firm applying for a credit loan (Simak, 2000: 94-95).the suggested solution of this problem is the application of the regressive linear function which allows finding a correlation between the coefficient of the DEA method value and its effectiveness with defined inputs and outputs.In this case, the regressive linear function could be used as a linear estimation of the coefficient of the DEA method values, omitting an extensive process of the DEA method verification each time a new firm is applying for a credit.In other words, the regressive linear function could be used while determining the firm's credit risk level without going through the first three phases (Emel et al., 2003: 108-115).Accordingly, the regressive linear function was defined during the process of estimating the coefficient value of the DEA method efficiency.In the past, the coefficient values of the DEA method efficiency through a regressive linear function were treated as a dependent variable Y, and the defined input and output were noted as an operand X i (independent variable).the regressive linear function research was conducted employing the Statistica 6.0 program.When rating the value of the regressive linear function model, the level of significance α = 0.05 was established.
The final linear regression model formula is as follows: In general, the right model is not the one perfectly coordinated with empirical data, but the one where all the variables of independent X i and dependent Y are integrated.
to evaluate the effect of these variables, a parametric Student's t test is applied.the variable quantity determining the outcome in this test is shown in table 3.In this instance, the statistical quantity that relates to t takes into consideration the level of α = 0.05 with 93 degree where t α = 1.6614.The overall parametrical quantity is satisfied in a t t ≥ representa- tion where X 5 , X 1 and X 4 variables are imperative at the level of α = 0.01 or lower.
On the other hand, the parametrical F-Snedecora test is relevant for studying the financial indicator X i defined by its choice of changing variables.In reference to Table 3 Source: Self-study = 2.197 the H 0 theory is justified on none of the levels and can be rejected.
The coefficient R 2 indicates a correct application of the regressive linear function Y DEA .In the above analysis, the R 2 coefficient equals to 67% (Table 3) and indicates that the regressive linear Y DEA model has a 67% correlation with X i changing variables.
Summarizing the results of the above study (Table 3   stage 5: comparative analysis of the DEA method and of chosen methods of assessing credit risk of companies with the use of a test group to check and verify the accuracy and efficiency of the prognostic qualities of the above models, the statistical material (100 firms) was divided equally 1:1 in respect to two separate research samples: controlled and placebo groups.The efficiency rate of both groups' classification is presented in table 5.The classification results presented in Table 5 imply that the DEA method has superior prognostic indicators.It best minimizes type I errors where the classification efficiency was higher than 12% two years before delinquency and higher than 16% one year before delinquency.However, the general classification efficiency of the DEA method is similar to that of the method discrimination and linear regression analysis.

conclusions
the above analysis shows that a well reflected credit scoring model is reliable in differentiating a potentially high risk of default from a low risk of default clients.The DEA method correctly predicts the possible financial difficulties, including a company's bankruptcy risk, in the Polish economic situation.these results are com-parable with or even superior to the results obtained by other methods presently employed.
The study has confirmed the universal value of the DEA method in analysing a large spectrum of credit risk uncertainty.It not only measures efficiency in respect to the use of financial risk indicators, but also facilitates an accurate credit risk classifica-tion for corporations in the credit application process.
Due to the overall credit scoring success, it is safe to presume that this method will become a central tool in credit risk assessment for corporations and individual consumers.this credit scoring method is very dynamic, very promising, and continually developing.

Figure 3 .
Figure 3.The propossed method of assessing credit risk of companies by the DEA method S o u r c e : author's study.

Table 3 . Selected properties of the regressive linear function YDEA R 2 = 67%, F(6/93) = 31,46
, the statistical F-Snedecora result is equal to 31.46.The critical value of F* for the α = 0.05 level for 6 and 93 degrees is F * = 2.197.Based on F = 31,46 > F * = -test of essence: Student's t, F-Snedecora, determining the coefficient R 2 ) one can recognize that the choice of dependent variables in the regressive linear function Y DEA is accurate.Furthermore, all the regressive linear function Y DEA properties were statistically significant.The efficient classification results in table 4 in the regressive linear function Y DEA_2001-2002 do not differ considerably from the DEA method results shown in Stage 3 of this study, which means that equalization of the linear regression could be treated as a linear approximation of the coefficient of the efficiency value.