Stress-testing German credit portfolios

The Journal of Risk Model Validation (27–45)

Volume 3/Number 3, Fall 2009

Stress-testing German credit portfolios Ferdinand Mager European Business School (EBS) International University, Schloß Reichartshausen, Rheingaustraße 1, 65375 Oestrich-Winkel, Germany; email: [email protected]

Christian Schmieder Deutsche Bundesbank and European Investment Bank, 100 boulevard Konrad Adenauer, L-2950 Luxembourg; email: [email protected]

This study deals with stress testing of realistic corporate credit portfolios of individual average small, medium and large banks in Germany. We apply stress tests of single and multiple credit risk parameters by using the internal ratings based (IRB) model and a model that additionally allows for variation of credit correlations. In a severe multiple-parameter stress scenario based on historical data, IRB minimum capital requirements increase by more than 80% with little difference between the credit portfolios. If stress testing is applied to correlation as well, the credit value-at-risk can increase by up to 300% and portfolio differences materialize.

1 INTRODUCTION Credit risk modeling and the management of banks’ credit portfolios have seen various advances over the last two decades, notably the move from a borrower level perspective to portfolio analysis. An important catalyst in credit risk management was Basel II, which has been applied, in effect, since January 2007.1 However, the recent financial and economic crisis has shown that credit risk portfolio management faces unsolved challenges, namely the ability to predict potential developments that have, so far, not been captured by state-of-the-art valueat-risk (VaR) models, for example sudden breakdowns in market mechanisms or violations in modeling assumptions. An important means to face this challenge is the application of micro prudential stress tests, which is also increasingly focused on by banks and supervisors (BCBS (2006)). This study deals with credit portfolio stress testing based on individual loan information. A fundamental prerequisite is to use real data. However, real data is often not available (eg, correlations) and, if it is, it is unlikely to be disclosed. This is why the empirical literature on stress testing portfolio credit risk (ie, taking The opinions in this paper do not necessarily reflect those the Deutsche Bundesbank or the European Investment Bank. 1 Basel II was approved in 2006 for the European Union. Other countries, especially the US, implemented the framework later or are seeking to implement it in the future.

27 © 2009 Incisive Media. Copying or distributing in print or electronic forms without written permission of Incisive Media is prohibited.

28

F. Mager and C. Schmieder

an explicit micro perspective) remains very limited, exceptions being Peura and Jokivuolle (2004) and Rösch and Scheule (2007). We compose three realistic credit portfolios, for small, medium and large German banks. Our analysis thereby reflects the German banking system, with its three-pillar structure and numerous small and medium banks (see Brunner et al (2004)). We apply stress tests of single and multiple credit risk parameters by using the Basel II internal ratings based (IRB) model as well as a simulation-based one-factor credit risk model that additionally allows for a variation of correlations. In a severe multiple-parameter scenario based on historical data, we find an increase of IRB minimum capital requirements of more than 80% with little difference between the credit portfolios. If stress testing is additionally applied to credit correlations, portfolio differences begin to materialize and the credit VaR may increase by up to 300%. This paper is organized as follows. In Section 2, we provide an overview of the data and the credit portfolios used for stress testing. Section 3 outlines the methods used for credit portfolio analysis and stress testing. In Section 4, we present the results. Section 5 concludes.

2 DATA This study is based on several databases, including balance sheet data of Deutsche Bundesbank, complemented with data from the German credit register, the German Statistical Office, Standard & Poor’s (S&P) and Moody’s KMV (MKMV). In this way, we seek to compose portfolio data that closely resembles that of German commercial banks, which has been confirmed based on comparisons with publicly available data on credit risk and the German credit register. An overview of our procedure and data is shown in Figure 1 (see page 29). Our main data source is the balance sheet database of Deutsche Bundesbank (1), which we use to derive probabilities of default (PDs). In the next step, we use credit register data and data from the German pension insurer (2) to ensure that the credit portfolios referred to (3) – namely a credit portfolio of a small German bank, of a medium-sized bank and of a larger one – are realistic. Finally, we make use of MKMV data to determine firm-size-dependent individual correlations (4). For the stress tests (6), historical data from the German Statistical Office and S&P (5) is used.

2.1 Balance sheet data In order to base our study on meaningful PDs, we make use of a study carried out by Gerke et al (2008). They benchmarked the data used for this study to the portfolio of the German Pension Fund, the so-called “Pensions-VersicherungsVerein” (PSVaG),2 whereby they are representative for Germany both in terms of 2 The PSVaG is the German counterpart to the Pension Benefit Guarantee Corporation in the US, and insures occupational pensions against bankruptcy. The PSVaG operates as a private mutual insurance association with compulsory membership for all firms running pension plans. In this way, the portfolio of the PSVaG is a cross-sectional representation of the German economy.

The Journal of Risk Model Validation


© 2009 Incisive Media. Copying or distributing in print or electronic forms without written permission of Incisive Media is prohibited.

Stress-testing German credit portfolios

FIGURE 1 Overview of empirical study and the respective data used.

(1) Balance sheet data: Probabilities of default (PD) (Gerke et al (2008))

(4) MKMV data: asset correlations for individual firms

(2) German credit register and portfolio of German pension insurer: Exposures

(3) Composition of credit portfolio (5) Historical data: German statistical office, S&P’s (6) Stress tests

level and in terms of the distribution. The PDs have been determined as annual default probabilities (PDi ) based on a cross-sectional calibration of a binary logistic regression model.3 The discriminatory power of the calibrated logit model (area under the receiver operating characteristic curve of 0.8181) has been found to be equivalent to other models being considered as being of high quality.4

2.2 Credit portfolio data For credit portfolio analysis and stress testing, we use the data of 6,298 firm observations from 2002. In terms of industrial and geographical sectors, this corporate credit portfolio (referred to as “Germany: Cross-Section”, PF0) has been found to constitute a cross-sectional portfolio of the German economy,5 which is used to compose three realistic bank portfolios as outlined below. 3 The model was estimated based on a representative subsample of PSVaG data, comprising

145,347 balance sheet datasets with 839 bankruptcies from 1989 to 2002. For further information see Gerke et al (2008). 4 For Moody’s RiskCalc model for Germany, for example, the area under the receiver operating characteristic curve yields 70.9%, which is lower than in the underlying study, but calculated outof-sample. For more information, see Escott et al (2001). The corresponding in-sample ratio can be expected to be similar to the model used in this study. 5 To verify this assumption, we also compared the industry sector distribution in the sample with findings of other studies, for example Düllmann and Masschelein (2006). Research Paper

www.thejournalofriskmodelvalidation.com © 2009 Incisive Media. Copying or distributing in print or electronic forms without written permission of Incisive Media is prohibited.

29

30

F. Mager and C. Schmieder

2.2.1 Credit risk parameters For the original sample (PF0), the firm’s one-year PDs range from 0.000007% to 16.7%. The exposure-weighted mean PD for this portfolio, 0.4% (see Table 1 on page 31), closely resembles the portfolio losses that have been observed by the PSVaG for this year, which indicates that the benchmarking was adequate to calibrate the level of the PDs to the German economy. The average PDs of the three bank portfolios range from 1.05% (Large bank portfolio) to 1.37% (Small bank portfolio), which is closely in line with default statistics provided by the Federal Statistical Office of Germany. The loss given defaults (LGD) are uniformly set to 45%, corresponding to the parameter value foreseen for senior unsecured debt under the Basel II Foundation IRB approach. The exposures at default (EADs) are determined by the size adjustment of the firm’s total assets, which are to reflect realistic credit exposures as further outlined below. The credit correlations are inferred from Düllmann et al (2008), who estimated the dynamic evolution of correlations of the asset values of European firms with a market index based on MKMV data. To make use of the data determined in that study, we proceeded in two steps. First, we determined a logarithmic fit function to link the MKMV asset values and asset correlations calculated by Düllmann et al (2008) for the respective year (see Table 5 on page 39).6 Next, we used the asset values in our portfolios to apply the fit function and to thereby determine individual asset correlations for each firm.7 In the case of the IRB model, we used the regulatory asset correlations based on PDs and a flat maturity of 2.5 years, the reference value for the Basel II Foundation IRB approach in most countries. 2.2.2 Credit portfolios We compose the three bank portfolios using two main assumptions. First, small banks tend to lend to small firms, medium banks to small and medium firms and large banks, in principle, to firms of all size groups. Second, we assume that the number of lenders increases with firm size8 and that larger firms increasingly have access to financing sources other than bank credit. Accordingly, the portfolios used in this study have been aligned with average German credit portfolios as shown in the German credit register (see also Gordy and Lütkebohmert (2007)). The portfolio characteristics of the three portfolios are shown in Table 1. For the portfolio of small banks (PF1), we assume that only small and medium enterprises are relevant (ie, firms with total sales of up to e50 million), yielding an overall 6 The fit function for 2001, which has been used to determine the asset correlations used for stress testing is: asset correlation = −0.1312 + 0.0227× LN (Total Assets). The total assets are in thousands of euro. 7 The asset correlations determined by Düllmann et al (2008) have been calculated directly from monthly MKMV asset values (and the respective asset returns) based on sliding windows of 24 months. 8 We use the results of Memmel et al (2007) and Schmieder et al (2009) to account for this.

The Journal of Risk Model Validation


© 2009 Incisive Media. Copying or distributing in print or electronic forms without written permission of Incisive Media is prohibited.

Research Paper

6,298 3,255 4,087 3,633

N 1.15 1.37 1.17 1.05

0.40 0.99 0.76 0.60

95 45 45 45

LGD (%) 9.07 6.65 8.78 9.94

Asset correlation (%) mean 20.87 12.15 15.02 16.75

Asset correlation (%) exposureweighted mean

0.0215 0.0148 0.0046 0.0018

Sample

NA 0.004–0.015 0.001–0.004