Factors that influence LGD for retail loans in financial

Sixth Brazilian Conference on Statistical Modelling in Insurance and Finance

Factors that influence LGD for retail loans in financial institutions Natália Cordeiro Zaniboni∗ Alcides Carlos de Ara´ ujo† ´ Alessandra de Avila Montini‡

Abstract The Basel regulations require attention to financial risks, in particular, credit risk. The capital required for credit risk consists of three components, including the loss given default (LGD). This study aimed to analyze the factors that influence the characteristics of LGD in the European financial institutions regarding retail loans, using the logistic regression model. The results suggest that the segment and exposure (EAD) affect the LGD. The model achieved an important result for the risk management studies, as it correctly classified 92% of the observations of high loss (LGD ≥ 50%). Keywords: Basel, Loss Given Default, Logistic Regression, Credit Risk Resumo A regula¸c˜ ao da Basiléia requer aten¸cão para os riscos financeiros, particularmente, o risco de crédito. O capital necessário para prote¸cão do risco de crédito consiste de três componentes, incluindo a perda em fun¸cão da inadimplência (LGD). O objetivo deste estudo é analisar os fatores que influenciam as caracter´ısticas do LGD em institui¸c˜ oes financeiras européias considerando empréstimos e utilizando o modelo de regrress˜ ao log´ıstica. Os resultados sugeriram que o segmento e a exposi¸cão (EAD) afetam o LGD. O modelo atingiu um resultado importante para a área de gestão de riscos, tendo classificado corretamente 92% das observa¸cões de altas perdas (LGD ≥ 50%). Keywords: Basiléia, Perda em fun¸cão da inadimplência, Regressão log´ıstica, Risco de Crédito

∗

Universidade de S˜ ao Paulo - FEA/USP; contato: [email protected] Universidade de S˜ ao Paulo - FEA/USP; contato: [email protected] ‡ Universidade de S˜ ao Paulo - FEA/USP; contato: [email protected] †


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Introduction

The risk associated with financial transactions is a widely studied subject throughout the financial system. In order to protect these system against the instability of the risks and prevent financial institutions from being exposed to high risks, an international committee of banking regulations and supervisory practices was established in 1974, the Basel Committee (Kapstein, 1994). The Basel II, known as the “International Convergence of Capital Measurement and Capital Standards: A Revised Framework”, first published in 1999 and completed in 2004, has as its main objective to standard the capital at risk from financial institutions, especially for credit risk (Santos, 2001) and consists of three pillars (BIS, 2004): 1. Minimum Capital Requirement (Pillar 1); 2. Supervisory Review Process (Pillar 2); 3. Market discipline (Pillar 3). The minimum capital required is the financial reserve required for financial institutions to cope with their risk exposures. This capital is composed by three risk components: PD (probability of default), LGD (loss given default) and EAD (exposure at default). The Basel committee suggests two approachs for calculating this capital: the standard approach, where the regulator itself provides the value of the risk components, and internal based approach, where the bank calculates its components based on its credit risk history and exposure characteristics, supervised by the local regulator. The Basel II presents the main definitions of the internal approach methodology (part 2, section III). In paragraph 252, the committee says that banks must develop methodologies and calculate their own estimates of PD (probability of default), LGD (loss given default) and EAD (exposure at default) for retail exposures. According Silva, Marins, and Neves (2008), the component LGD is the percentage of losses of a risk exposure at the time of default, which includes principal loss, the loss arising from opportunity costs and collection and recovery loss. Given the international requirements, the study aims to analyze characteristics and the factors that most influence the risk component LGD, considering the information available in Pilar 3 risk management reports of financial institutions. The first studies regarding the risk component LGD began in 1995, with Asarnow and Edwards (1995), and focused on LGD descriptive statistics, its distributions and factors that influence its variability. Latest research, starting in 2008, focused on LGD statistical models. This paper approach both subjects, and uses data from several financial institutions, most in Europe. A Logistic Regression model was ajusted for the LGD data, dividing the data in two groups: low LGD and high LGD, creating a binary responde variable. Several authors used this kind of approach to predict LGD. Belotti and Crook (2008) used logistic regression and obtained good results. Loterman et al. (2012) and Leow and Mues (2012) used binary models to predict LGD and found that this kind of model has better results in predicting LGD.

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2 2.1

Theoretical Framework Calculation of LGD

There are a few methodologies for the calculation of LGD. Chalupka and Kopecsni (2008) defined these as Market, Workout and Implied Market LGD. The Market LGD is calculated using the prices of marketable securities and loans after the default, the Workout LGD is calculated using the cash flow resulting from the recovery period, discounted to present value at the time of default and the Implied Market LGD is calculated using the prices of risky assets, but not yet in default, using a theoretical model of asset pricing. The most commonly used approach for calculation of LGD is the Workout LGD (Silva et al., 2008). According to Schuermann (2004), this is the most complex calculation, which involves some important decisions, such as the definition of the recovery time, the caution to appropriately include the costs of such recovery and the definition of the discount rate to calculate the present value of this flow. Workout LGD formula considering all losses given by Silva et al. (2008) is presented in equation (1). P ayments − Costs (1) EAD Where payments are indicated by the amount recovered after the default, the costs are the costs of recovery and EAD is the exposure at the time of the default. LGD = 1 −

2.2

Factors that influence LGD

Studies on LGD models began in the 90s, with Asarnow and Edwards (1995), who analyzed the behavior of the rate of loss during 24 years in the U.S. bank Citibank. They showed that there is a difference of the LGDs between commercial and industrial operations and structured operations (loans with greater monitoring are more structured and have greater governance). Operations with securities have average LGD of 12% and operations without securities have average LGD of 35%. Hurt and Felsovalyi (1998) developed a study similar to that of Asarnow and Edwards (1995), as they also analyzed the behavior of the rate of loss of Citibank, but it focuses on Latin America and covers 27 years of database. This study resulted in a calculation of LGD of 32%, and the exposure amount influence on LGD. Gupton, Gates, and Carty (2000), in a study conducted by Moody’s with 181 bank loans, indicated that the average of the LGDs of secured loans is 52% and the average LGD of unsecured loans is 69%. Gupton and Stein (2002) documented Mooody’s model for LGD, the LossCalc. It is a multivariate model developed with 1,800 securities, loans and preferred shares. They used factors grouped into four categories: type of debt and seniority, the company’s capital structure, industry indicators and macro-economic factors. Schuermann (2004) mentioned the distribution of two peaks of LGD using data from Moody’s financial securities, resulting in an average LGD of 40%, with the presence and quality of the security, the company’s industry, the degree of subordination of the bond and the economic situation are factors that influence on LGD. Querci (2005) studied the behavior of 15,827 loans at an Italian medium sized commercial bank and found that the LGD of retail loans has an average of 53.3%, while small and medium enterprises have an average of 48.4%. He also mentioned the distribution of two peaks of LGD data, and studied the following explanatory variables: place where the client lives, segment, type of loan, security, size of the recovery time (workout) and the

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client code. Only the client code successfully explains the variability of the LGD (this variable represents some characteristics of the client). Dermine and Carvalho (2006) developed a study with 371 credit operations of companies from a bank in Portugal, found an average LGD of 29% and showed that variables such as the loan amount, security and the company’s industry influence the LGD. The distribution of two peaks in this study was also verified. Belotti and Crook (2008) developed predictive models of LGD with credit card products in Britain. Variables such as length of relationship, income, number of credit cards, time at address, type of employment, credit or behavioral scores, debit balance and region of residence are variables that can influence the LGD value of the contract. Chalupka and Kopecsni (2008) studied losses of companies at default and the average of the LGD was 52%. It is also possible to observe the distribution with two peaks, and the exposure, recovery time, type of industry and company time are variables that can affect the loss of contracts. Belotti and Crook (2009) developed another study of predictive models of LGD with credit card products in Britain, adding macroeconomic variables to their previous study and found that, due to the period selected, it was not possible to prove that these macroeconomic variables influence the LGD just as the previously mentioned variables. Qi and Yang (2009) studied mortgage loans and showed that LGD can be explained by the percentage borrowed relative to the total value of the property, also called loanto-value, the depreciation of the property, the amount of the loan, the type of customer, the purpose of financing, if the property is used for housing and the time passed since the beginning of the loan. Silva et al. (2008) studied 9,557 operations registered in the SCR (Credit Information System of the Central Bank of Brazil) in the modalities: overdraft secured-check, current account overdraft and working capital. They also observed the distribution of two peaks of LGD, a mean of 47% and that the outstanding balance, the length of customer relationship, presence of security, customer size, rating, presence of renegotiations and the company’s industry sector affect the value of the LGD. The analysis of the LGD was also recommended, focusing on the segment of contracts (retail, specific financing and others). 2.3

Statistical Models for LGD

Belotti and Crook (2008) developed predictive LGD models for credit cards in Britain, and compared ordinary least squares regression with tobit regression and decision tree. OLS models are as good as tobit regression and decision tree. Bastos (2010) compared fractional regression and nonparametric regression tree using data on loans to small and medium enterprises from a bank of Portugal, and suggests that regression tree presented estimates closer to the true values when the workout time recovery are 12 to 24 months. Matuszyk et al. (2010) used decision tree to predict LGD for loans from a financial institution in the UK, covering a period from 1989 to 2004. The decision tree indicates a two stage modeling process: First LGD was reclassified as binary, where Yi = 0 if LGD ≤ 0 and Yi = 1 if LGD > 0, and a logistic regression model was used, identifying that exposure amount, history of payment delays, the time in which the client lives at the same address and if there is another loan applicant influence the binary variable. From this model’s response, if the loan is classified as LGD > 0, the value of LGD was predicted from a linear regression using historical payment delays, the client’s score, exposure amount and time to default as predictive variables. 4


Zhang and Thomas (2012) compared a linear regression model with survival analysis in predicting LGD for unsecured and credit cards loans from a financial institution in the UK, covering a period from 1987 to 2003. Linear regression obtained better results than survival analysis for both cases: where LGD was modeled directly and where a mixture of distributions was used as a two stage model similar to Matuszyk et al. (2010). Loterman et al. (2012) compared LGD modeling techniques. One stage techniques such as linear regression, beta regression, robust regression, ridge regression, splines regression, neural networks and regression tree, and two-stage models, that combine more than one technique, were compared. The study indicated that most of the LGD variability can not be explained, and nonlinear models, such as neural networks, achieve better results than more traditional linear models. Two-stage models that combine linear and nonlinear techniques also obtain good accuracy. Leow and Mues (2012) compared a two-stage model, which creates a logistic regression model for the probability of loss and a linear regression model to the severity of the loss, with a one stage linear regression model. The authors found that the two-stage model has better performance and accuracy in predicting LGD. 3 3.1

Methodology Data

According to Basel II, institutions must subject to a pillar called Market Discipline (Pillar 3) in which, under paragraph 809, market participants can access key information on capital, risk exposures, risk management processes and the capital adequacy of institutions. These institutions usually release an annual risk management report for the market. In this paper, we analyzed 12 risk management reports of financial institutions (Australia and New Zealand Banking Group, Barclays, Commonwealth, Credit Suisse, Danske Bank, Deutsche Bank, National Australian Bank, NIBC, RBS, Santander, SNS Bank’s and Westpac) from December/2008 to March/2011. The selected data refer to retail exposures of homogeneous risk groups. In accordance with paragraphs 401 and 402 of Basel II, each retail exposure must be allocated in a homogeneous risk group, which should provide risk differentiation, homogeneous exposures and allow accurate and consistent estimations of loss characteristics. It should also consider the characteristics of the borrower, the operation and default (BIS, 2004). The data base is composed of 214 homogeneous risk groups of credit loans from these 8 countries. PD, LGD, EAD (in thounsands of euros) and Basel segment classification were selected. Basel segment classification is defined by Basel II Accord, dividing loans as small and medium enterprise loans, residential mortgage loans, qualifying revolving retail exposures (such as credit cards) and other loans. 3.2

Logistic Regression

Since the purpose of this paper is to analyze the factors that influence the classification of loss given default and, consequently, the credit recovery, the binary logistic regression analysis is the most appropriate. We defined the binary variable as Yi = 1 for groups with LGD greater than or equal to 50%, that is, high loss and Yi = 0 for groups with LGD lower than 50%, that is, low loss. The model used to explain the probability of Yi = 1 is the binary logistic regression 5


model. The binary logistic regression relates a binary response variable with explanatory variables, which can be categorical, continuous or discrete. According to Hosmer and Lemeshow (2000) the ideal function to model binary cases is the logit function. The model estimates the probability of one of the binary responses, in this case we estimated the probability of high loss, which is presented in the equation 2. eβ0 +β1 x1 +β2 x2 +···+βk xk (2) 1 + eβ0 +β1 x1 +β2 x2 +···+βk xk Where B0 , B1 , . . ., βk are the model parameters related to the k explanatory variables, π(x) is the estimated probability of high-loss and xk is the k-th explanatory variable. π(x) =

4 4.1

Results Descriptive Statistics

Table 1 shows the distribution of homogeneous risk groups for the countries. The database consists of 214 groups of contracts arising from 8 countries. The groups were developed to be homogeneous with respect to the risk of retail exposures and were obtained from 12 financial institutions. Table 1: Distribution of groups for the countries Country

Number of Groups

%

Australia Scotland Denmark Spain Germany Netherlands Switzerland England Total

83 31 30 21 18 14 9 8 214

38.79% 14.49% 14.02% 9.81% 8.41% 6.54% 4.21% 3.74% 100.00%

Tables 2, 3 and 4 present the descriptive analysis of the LGD variables (%), EAD (million dollars) and PD (%) for each country used. Note that England is the country with the highest mean value of LGD, with the highest median of PD and highest minimum, mean value, median, maximum and standard deviation of exposure (EAD), indicating the highest risk among the countries analyzed. In addition, it presents the highest standard deviation of the LGD component. In the case of the PD component, England has the lowest coefficient of variation, the highest median, the highest minimum value and the lowest maximum value, indicating concentration and little discrimination of risk. In the case of component LGD (loss given default), Australia and Scotland have the highest means after England (approximately 50%). These countries also have the highest means of PD, indicating that the percentage of expected loss of these countries, represented by the PD multiplied by the LGD (BIS, 2004) are higher than the others. Netherlands is the country that indicates the lowest average of loss given default (LGD) and the lowest average of exposure at default (EAD), thus being one of the countries with the lowest risk compared with the others.

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Sixth Brazilian Conference on Statistical Modelling in Insurance and Finance Table 2: Descriptive Analysis of LGD (%) for the countries Country Australia Scotland Denmark Spain Germany Netherlands Switzerland England

Min. (%)

Average (%)

Median (%)

Max. (%)

S.D.(%)

C.V.

20.0% 1.9% 12.0% 13.0% 9.3% 8.2% 16.7% 14.9%

53.2% 50.8% 26.4% 39.4% 32.9% 13.2% 37.6% 60.6%

62.0% 70.6% 24.5% 39.3% 38.5% 9.8% 35.7% 67.4%

97.9% 100.0% 44.0% 79.5% 53.3% 36.7% 60.0% 97.1%

27.5% 29.1% 10.7% 24.3% 13.2% 7.7% 14.8% 30.5%

52% 57% 41% 62% 40% 59% 39% 50%

Table 3: Descriptive Analysis of Average PD (%) for the countries Country Australia Scotland Denmark Spain Germany Netherlands Switzerland England

Min. (%)

Average (%)

Median (%)

Max. (%)

S.D.(%)

C.V.

0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 2.3%

9.3% 9.9% 8.7% 6.2% 3.9% 5.4% 3.5% 5.1%

1.5% 1.6% 0.3% 0.8% 0.7% 1.2% 0.5% 4.8%

54.5% 58.6% 62.8% 35.5% 18.3% 32.3% 10.0% 8.5%

17.9% 19.3% 19.0% 11.3% 6.5% 9.2% 4.9% 2.6%

191% 195% 220% 183% 165% 170% 138% 50%

Table 5 shows the number of homogeneous risk groups by Basel Segment for each country, and note that the Netherlands only contains contracts of Real Estate Loans, England, Scotland and Australia have an approximately equal distribution of their contracts to all segments and Denmark, Spain, Germany, Netherlands and Switzerland do not have contracts classified as Small and Medium Enterprises. The measures of LGD, PD and EAD of England were obtained through the exploratory analysis of data provided in Table 6, which presents the 8 homogeneous risk groups of Barclays Bank, the only bank that generated a report of the operations in England. Note that the database contains a high exposure to real estate loans, and these exposures indicate the lowest risk, verified by the lowest mean of PD and LGD of this group. Figure 1 shows the distribution of LGD. Note the existence of two peaks, as noted in the literature, for example Schuermann (2004). Table 7 indicates that revolving credit agreements have higher average loss given default (LGD) and mortgage contracts have lower average loss given default (LGD). Table 4: Descriptive Analysis of EAD (US$ million) for the countries Country

Min.

Average

Median

Max.

S.D.

C.V.

Australia Scotland Denmark Spain Germany Netherlands Switzerland England

2 57 16 460 80 179 19,842

15,324 7,792 4,868 20,404 6,142 3,358 14,689 79,02

2,597 3,695 1,678 3,846 2,175 1,754 2,093 34,562

182,386 68,79 23,151 70,269 31,047 8,869 74,205 232,485

34,036 14,096 6,718 27,053 8,745 3,294 26,119 89,275

222% 181% 138% 133% 142% 98% 178% 113%

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Sixth Brazilian Conference on Statistical Modelling in Insurance and Finance Table 5: Number of Homogeneous Risk Groups by Basel Segment for each country Country

Real Estate Loans

Others

Revolving Credit

Small and Medium Enterprises

24 9 10 7 6 14 4 2 76

24 7 10 7 6 0 4 2 60

23 9 10 7 6 0 1 2 58

12 6 0 0 0 0 0 2 20

Australia Scotland Denmark Spain Germany Netherlands Switzerland England Total

Table 6: Homogeneous risk groups Bank

Date

Barclays Barclays Barclays Barclays Barclays Barclays Barclays Barclays

Dec/2009 Dec/2009 Dec/2009 Dec/2009 Dec/2010 Dec/2010 Dec/2010 Dec/2010

PD (%)

LGD (%)

EAD (US$ million)

Segment

6.87% 2.42% 3.88% 8.10% 8.49% 2.31% 2.78% 5.75%

61.8% 16.2% 85.1% 73.1% 57.2% 14.9% 79.6% 97.1%

21,489 210,682 46,69 22,433 20,784 232,486 57,753 19,842

Small and Medium Enterprises Real Estate Loans Revolving Credit Others Small and Medium Enterprises Real Estate Loans Revolving Credit Others

Figure 1: Distribution of LGD

4.2

Logistic Regression

By dividing the response variable, loss given default, into two groups using the cutoff in the LGD of 50%, it is possible to notice a greater amount of risk groups in the class of high loss (136 observations), and note also that the average PD is similar for these two groups. The average EAD is higher in groups with low loss. These data are presented in Table 8. Table 9 shows the number of homogeneous groups classified as high and low loss in each Basel segment classification. Most homogeneous risk groups classified as real estate loans obtained loss lower than 50%, indicating lower risk in this component. Note also that most homogeneous risk groups classified as revolving credit obtained loss greater than or equal to 50%, indicating the highest risk related to this component of all segment classifications available. To represent the categorized variable (segment) in a binary logistic regression, we 8

Sixth Brazilian Conference on Statistical Modelling in Insurance and Finance Table 7: Average LGD for each Basel segment Segment

Average LGD (%)

Real Estate Loans Revolving Credit Others Small and Medium Enterprises Total

17.0% 65.7% 54.6% 41.7% 43.0%

Table 8: Number of groups, average PD and exposure for the binary categories of LGD Class of LGD

PD (%)

N. of Observations

LGD < 50% LGD ≥ 50%

EAD (US$ million)

Average

Standard Deviation

Average

Standard Deviation

7.4% 8.8%

15.2% 17.0%

19,283 4,967

38,753 10,134

136 78

Table 9: Number of groups of each Basel segment for the binary categories of LGD

1

Class of LGD

N. of Observations

Real Estate Loans

Others

Revolving Credit

SME1

LGD < 50% LGD ≥50%

136 78

75 1

29 31

17 41

15 5

Small and Medium Enterprizes

created three dummy variables (indicators of 0 and 1 in case the observation presents the field observed) so that the small and medium enterprises segment is the reference class and receive the value 0 in the three dummies created , as shown in Table 10. Table 10: Dummy variables for the Basel segment classification Field

Real Estate Segment

Others Segment

Revolving Segment

Real Estate Loans Others Revolving Credit Small and Medium Enterprises

1 0 0 0

0 1 0 0

0 0 1 0

The indicators of exposure (EAD) and segment (real estate, others, revolving and SMEs) using a descriptive level of 10%, are determinants in the probability of high loss of the group. The indicator of average PD does not discriminate the loss very well (descriptive level higher than 0.10) and was excluded from the regression model. The values of the parameters and descriptive levels are presented in Table 11. Table 11: Parameters and descriptive level of the logistic regression Descriptive

Parameter Estimator

Descriptive Level

Intercept Average PD EAD (US$ million) Real Estate Segment Others Segment Revolving Segment SME Segment

-1.142600000 0.470400000 -0.000000475 -3.101800000 1.352900000 2.055800000 0.000000000

0.0309 0.6757 0.0922 0.0062 0.0207 0.0005 .

By excluding the variable Average PD, we noted that the variables EAD and Segments are still significant for the model. It is possible to notice, through the parameter of the 9


model, that the real estate segment is the least risky with regard to the high probability of loss, followed by loans to small and medium enterprises (SMEs), others and, finally, revolving credit. It is also evident that the greater the exposure (EAD) the lower the probability of high loss. These results are shown in Table 12. Table 12: Parameters of the logistic regression without the PD variable Descriptive

Parameter Estimator

Descriptive Level

Intercept EAD (US$ million) Real Estate Segment Others Segment Revolving Segment SME Segment

-1.096200000 -0.000000476 -3.110800000 1.345400000 2.046300000 0.000000000

0.0338 0.0911 0.0060 0.0213 0.0006 .

Table 13 shows the odds ratio for the variable segment. The ODDS indicate that the real estate segment is the least risky with regard to the probability of loss, followed by loans to small and medium enterprises, others and, finally, revolving credit. Revolving credit agreements present approximately seven times more chances of high-loss than the contracts of small and medium enterprises and other credit contracts present approximately four times more chances than contracts of small and medium enterprises. Table 13: ODDS Ratio of the Variable Segment Descriptive

ODDS Ratio

Real Estate Segment vs. SME Others Segment vs. SME Revolving Segment vs. SME

0.045 3.840 7.739

As previously mentioned, the logistic regression shows that groups with higher exposure are less likely to indicate high loss. This is due to the fact that the least risky segment, the real estate credit, indicates exposure values higher than the others. These two variables are not correlated as a whole (correlation of -0.20) but it is possible to notice that the average of the exposure to real estate credit is greater than the others. These results are shown in Table 14. Table 14: Exposure to real estate credit and other segments (US$ million) Descriptive

Average EAD (US$ million)

Real Estate Segment Others Segments

29,334 4,133

The cutoff point that maximizes the percentage of hits of the model is 50%, and with this cutoff point the model makes the correct prediction for 79% of the observations, and out of the groups that presented low loss, the model correctly classified 71% of the observations, and out of the groups that presented high loss, the model correctly classified 92% of the observations. The matrix that indicates the classifications resulting from the cutoff point 50% is shown in Table 15. In accordance with paragraph 444 of Basel II, internal models of loss should have a key role in risk management. Models built solely for purposes of Basel are not acceptable. This means that financial institutions that were analyzed in the study use their models for management, and this could be a possible variable to influence loss, because as institutions 10

Sixth Brazilian Conference on Statistical Modelling in Insurance and Finance Table 15: Matrix of assertiveness of the model Estimate

Performed Low Loss High Loss Total

Low Loss

High Loss

97 6 103

39 72 111

Total 136 78 214

use models in credit recovery, for instance, they could make this recovery more efficient and achieve a lower loss. 5

Conclusions and recommendations

The study found that the segment of the contract (real estate, revolving credit, others or small and medium enterprises) and the size of the exposure at the time of default (EAD) are variables that influence the probability of high loss given default (LGD), confirming results from Asarnow and Edwards (1995); Hurt and Felsovalyi (1998); Gupton et al. (2000); Schuermann (2004); Dermine and Carvalho (2006); Belotti and Crook (2008); Chalupka and Kopecsni (2008); Silva et al. (2008), especially regarding to the loan segment classification and its collateral. The variable probability of default (PD), for this database, did not affect the LGD. The logistic model correctly classified 92% of the observations of high loss given default (LGD ≥ 50%) and 79% of total observations. For further studies, we recommend a study on the influence of the use of models in loss management, as they are mandatory for the application of Basel. As institutions better differentiate their customers in credit recovery, for instance, they can make this recovery more efficient and achieve a lower loss.

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