Petr Jakubík and Christian Schmieder: Stress Testing Credit Risk: Is the Czech Republic Different from Germany?
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WORKING PAPER SERIES 9
WORKING PAPER SERIES
Stress Testing Credit Risk: Is the Czech Republic Different from Germany?
Petr Jakubík Christian Schmieder
9/2008
CNB WORKING PAPER SERIES The Working Paper Series of the Czech National Bank (CNB) is intended to disseminate the results of the CNB’s research projects as well as the other research activities of both the staff of the CNB and collaborating outside contributor, including invited speakers. The Series aims to present original research contributions relevant to central banks. It is refereed internationally. The referee process is managed by the CNB Research Department. The working papers are circulated to stimulate discussion. The views expressed are those of the authors and do not necessarily reflect the official views of the CNB. Printed and distributed by the Czech National Bank. Available at http://www.cnb.cz.
Reviewed by: Miroslav Singer Vladimír Pikora Christoph Memmel
Project Coordinator: Michal Hlaváček
© Czech National Bank, December 2008 Petr Jakubík, Christian Schmieder
(Czech National Bank) (Next Finance) (Deutsche Bundesbank)
Stress Testing Credit Risk: Is the Czech Republic Different from Germany?
Petr Jakubík and Christian Schmieder *
Abstract This study deals with credit risk modelling and stress testing within the context of a Merton-type one-factor model. We analyse the corporate and household sectors of the Czech Republic and Germany to find determining variables of credit risk in both countries. We find that a set of similar variables explains corporate credit risk in both countries despite substantial differences in the default rate pattern. This does not apply to households, where further research seems to be necessary. Next, we establish a framework for the stress testing of credit risk. We use a country specific stress scenario that shocks macroeconomic variables with medium severity. The test results in credit risk increasing by more than 100% in the Czech Republic and by roughly 40% in Germany. The two outcomes are not fully comparable since the shocks are calibrated according to the historical development of the time series considered and the size of the shocks for the Czech Republic was driven by the transformation period.
JEL Codes: Keywords:
G21, G28, G33. Credit risk, credit risk modelling, stress testing.
* Petr Jakubík, Czech National Bank and Institute of Economic Studies, Charles University in Prague (e-mail:
[email protected]); Christian Schmieder, Deutsche Bundesbank and European Investment Bank (e-mail:
[email protected]). This work was supported by Czech National Bank Research Project No. C2/07. The data analysis for this paper was generated using Base SAS and SAS/STAT software, Version 9.1.3. of the SAS System for Windows. Copyright © 2002-2003 SAS Institute Inc. SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc., Cary, NC, USA. The findings, interpretations and conclusions expressed in this paper are entirely those of the authors and do not represent the views of any of the authors’ institutions. We thank Miroslav Singer, Michal Hlaváček, Vladimír Pikora, Jan Frait, Kateřina Šmídková, Thilo Liebig, Christoph Memmel and Pierre Tychon for their valuable comments and support. The financial support provided for this project by the Czech National Bank is gratefully acknowledged.
2 Petr Jakubík and Christian Schmieder
Nontechnical Summary This study deals with two major aspects of credit risk, namely its measurement and management. We seek to measure credit risk on the ‘macro’ level by investigating the two major elements of non-bank credit in economies: corporate credit and household credit. For that purpose, we use a relatively simple credit model whereby credit losses can be explained by the development of key macroeconomic factors such as GDP growth and inflation. Accordingly, we estimate separate models for corporate credit and household credit. Next, we make use of these models to predict potential future levels of credit losses for firms and households, commonly known as stress testing. The outcome of these forecasts on a macro level is then used for predicting a stress scenario of a typical bank credit portfolio. In this way, the study takes a comprehensive view of credit risk. The analysis is carried out for two countries, Germany and the Czech Republic. The application of the method to two countries is the key contribution of this study. The main questions are as follows. ¾ Which factors are the most important macroeconomic drivers of credit risk? ¾ Are they the same for the two (very different) economies? ¾ How vulnerable are these two economies and banks in economic stress periods? Why are these questions relevant? The recent financial crisis originated mainly from severe problems in the US household credit sector (the so-called US subprime crisis). It adds one more chapter to the history of past financial crises which have been caused primarily by an accumulation of non-bank credit losses, be it corporate or household debt. It is striking that despite the awareness that credit risk is the most important threat to financial stability, the complexity of this risk type is so high that crisis prevention remains a key challenge for the future. This results particularly from the increasing complexity of financial markets and their international dimensions, which requires worldwide cooperation. This is the purpose of this study, namely to add insights to the important subject of financial stability. It thus contributes to the recent recommendations issued in April 2008 by a key international forum for fostering financial stability, the Financial Stability Forum, which recommends a strengthening of authorities’ responsiveness to risks and an improvement of stresstesting practices and capital planning processes by banks. We use a common indicator to explain credit risk, namely non-performing loans. We find that our model is useful for explaining credit risk for firm debt and that similar macroeconomic variables explain the corporate default rates of the Czech Republic and Germany. Given their different cyclical patterns, this is a surprising outcome. For household debt, our model is less useful for both countries, which leaves some challenges for future research. Afterwards, we assess how future recessions could influence corporate credit and household credit losses by referring to historical stress scenarios. We use the macroeconomic situation at the end of 2006 and predict an economic downturn for 2007 for both countries. We use stress levels of similar severity for both countries from a historical perspective, including the last decade, and find that even relatively light stress can lead to a substantial increase in the corporate default rate
Stress Testing Credit Risk: Is the Czech Republic Different from Germany? 3 (more than 100% for the Czech Republic; up to 40% for Germany). As a caveat, the sensitivity of the corporate sector default rates for the Czech Republic was driven by the high volatility of macroeconomic indicators during the transition period of the late 1990s, so the results have to be interpreted carefully. For households, sensitivity to the macroeconomic environment is less pronounced, unlike what the recent US subprime crisis might suggest, and seems to confirm the observation that the financial crisis has not had a considerable effect on the Czech and German household sector so far. In the last step, the stress scenarios for the economies are applied to a hypothetical, but realistic average credit portfolio that could be held by a Czech or German bank. The credit risk models for both countries employ similar variables and the size of the shocks is calibrated according to the past development of the given time series. It is clearly shown that macroeconomic shocks can significantly increase the portfolio risk measured by the Basel II regulatory IRB minimum capital requirements in both countries. The methods and procedure presented in this study can be used by regulatory bodies to be able to take measures to safeguard financial stability. For banks, the framework elaborated may contribute to the introduction of Basel II-type micro stress testing. In any case, future research is needed on the highly complex issues discussed in this paper.
4 Petr Jakubík and Christian Schmieder
1. Introduction In quantitative terms, credit risk is the most important risk in banking books. This has recently been shown clearly again in the US subprime crisis. Moreover, the crisis occurred despite various improvements in credit risk management, for example progress in the field of credit risk analysis applied by banks on the portfolio level – spurred by Basel II1 – as well as the increasing availability of a wide range of instruments that make credit risk more liquid, for example securitisation and credit derivatives. Hence, credit risk remains a major threat to financial stability in the globalised financial world, where cross-border contagion of crises particularly threatens countries with weak banking sectors. Credit risk analysis for the financial sector as a whole can be seen as a crucial means of preventing financial instability. This can be realised by means of a regular robustness test on a country’s banking sector against credit risk, for example by means of stress tests carried out by supervisory bodies and central banks, providing hints for detecting financial system fragility.2 Within the framework of credit risk modelling and stress testing, this study investigates and compares two countries, a new EU member state – the Czech Republic – and the largest EU economy – Germany. We seek to provide answers to various questions, notably: which macroeconomic variables are the most important for explaining credit risk; whether there are country-specific differences; and what impact unfavourable macroeconomic circumstances can have on the macro and micro (portfolio) level. The data employed in this study cover a period of eight years from 1998 to 2006 for the Czech Republic and twelve years from 1994 to 2006 for Germany. The investigated time period covers multiple periods of severe macroeconomic stress, namely the consequences of the Asian crisis in 1997 and the Russian crisis in 1998, as well as the crisis in the financial markets after 11 September 2001. When it comes to credit risk analysis for the Central and Eastern European transition economies (and also for many other transformation economies and developing countries), a key limitation is the availability of data, as the time series are usually (still) relatively short and have various structural breaks. Accordingly, the data in this study were selected very carefully to prevent misinterpretation.3 In order to arrive at a meaningful comparison between the Czech Republic and Germany, equivalent data was sought. We investigate both the corporate sector and the household sector and find that credit risk for corporates can be modelled based on similar macroeconomic variables for both countries, despite fundamental differences in the default rate (time) pattern. Credit risk modelling for the household sector turns out to be more challenging for both countries, as there are apparently other variables than solely economic ones explaining the default rate pattern. These findings do, in general, confirm previous studies.
1
See BCBS (2006), European Commission (2006) and the national transpositions of Basel II. The importance of this mission is underlined, for example, by the fact that the Basel Committee on Banking Supervision has mandated a working group of the Research Task Force to further investigate stress testing. 3 We draw on the findings of the analysis carried out by Jakubík (2007a and 2007b). 2
Stress Testing Credit Risk: Is the Czech Republic Different from Germany? 5 In the second step, we use the outcome of our credit risk modelling for macro stress testing purposes. In the third step, we translate the outcome of the macro stress tests into a Basel II-type micro stress test of a hypothetical, but realistic, credit portfolio. We find that the impact of the macroeconomic shocks we study is substantially higher in the Czech Republic than in Germany, on both the macro and micro levels. For a stress test of medium severity, we find an increase in aggregate corporate default rates of more than 100% and a rise in the Basel II internal ratingsbased (IRB4) minimum capital requirements on the credit portfolio level of up to 60% in the Czech case within one year. The figures for Germany are an increase in corporate default rates of 40% and an augmentation of the IRB minimum capital requirements of roughly 30% for the same credit portfolio. For the household sectors of both countries, the impact is much less pronounced compared to corporates, with a higher impact in the German case, but the outcome is less robust and therefore has to be interpreted carefully. Our contribution to the literature is two-fold: first, we provide a comprehensive framework for stress testing; second, we directly compare a new EU member state with one of the large “old” EU economies. While there is no directly comparable study in the literature, we confirm the finding of previous studies that stress events have a more material effect in less developed economies. The paper is organised as follows. Section 2 provides an overview of related studies. Section 3 describes the model used to analyse credit risk for the corporate and household sectors. In Section 4, the underlying data are presented. Next, the corporate and household models are calibrated for the Czech Republic and Germany in sections 5 and 6 respectively. Section 7 is devoted to stress testing. Finally, section 8 provides conclusions.
2. Related Literature A key motivation for this study originates from the Basel II framework, concluded in 2006, which seeks to provide a more meaningful framework for the solvency of financial institutions and financial stability compared to the previous Basel Accord dating back to 1988.5 Within this framework, our focus is on the investigation of business cycle effects on the aggregate default rate of corporates and households and the link to banks’ capital requirements. Various studies have been carried out in this domain. On the micro level, a comprehensive survey of the literature dealing with cyclical effects on the major credit risk parameters, namely the probability of default (PD), loss given default (LGD) and the exposure at default (EAD), has been provided by Allen and Saunders (2004). Accordingly, all three credit risk parameters are found to be highly exposed to cyclical effects, implying a considerable impact on portfolio credit risk and capital requirements.6 In a recent study carried out by Düllmann et al. (2008), this has also been demonstrated to hold true for credit correlations. 4
Credit Portfolio Risk in this study is measured based on the Basel II minimum capital requirements, which closely resemble the Credit Value-at-Risk figures. We refer to the internal ratings-based (IRB) approach – see BCBS (2006), para. 272. 5 Another important catalyst for stress testing was the Financial Sector Assessment Program (FSAP) of the International Monetary Fund (IMF) and the World Bank initiated in the late 1990s. 6 The study by Catarineu-Rabell et al. (2003), for example, was an early one to show that the choice of a Pointin-Time (PIT) rating system can evoke procyclicality of capital requirements, whereas Through-the-Cycle (TTC) rating systems are more neutral. Through a comparison of PIT rating systems and TTC systems, Löffler (2004)
6 Petr Jakubík and Christian Schmieder While most of the numerous studies on the cyclicality of portfolio credit risk have been carried out for developed countries, the outcome that capital requirements vary strongly with the economic cycle and are driven by a complex interaction of different credit risk parameters does also hold true for developing countries, although pertinent empirical evidence remains more limited to date. Vallés (2006), for example, finds that the implementation of a through-the-cycle (TTC) rating system in emerging countries would be very difficult due to the high volatility of credit risk, indicating that portfolio credit risk might fluctuate even more strongly than in the developed world. Despite the numerous contributions on how credit risk parameters fluctuate over the business cycle, stress testing of (real) credit portfolios remains relatively limited to date, particularly due to the limited data that is publicly available. Among the few contributions are Peura and Jokivuolle (2004) and Rösch and Scheule (2007). There is a wide range of research on the macroeconomic perspective of credit risk. The seminal question is how to model the aggregated credit risk of an economy or specific sectors such as corporates and households. Various approaches have been followed in the literature, such as applying econometric analysis on a firm-specific level including macroeconomic variables (Bunn and Redwood 2003) and using multi-factor credit portfolio models. A seminal model in the latter context was proposed by Wilson (1997a, 1997b), known as Credit Portfolio ViewTM, which has been used for macro stress testing by Virolainen (2004), for example. In terms of the dependent variable, macro stress tests have typically been analysed based on loan loss provisions (LLPs) or non-performing loans (NPLs). A recent review of different modelling methodologies has been provided by Sorge and Virolainen (2006). Various macroeconomic variables have been found to be relevant as drivers of credit risk, the main drivers for corporate credit risk being GDP growth and interest rates (Virolainen, 2004). Other relevant variables were corporate indebtedness, inflation, industrial production, real wages, the stock index and the oil price (Virolainen, 2004). For the household sector, empirical evidence is more limited, with unemployment and interest rates being among the most relevant variables referred to. Stress testing is commonly used by central banks and regulatory bodies to identify vulnerabilities of the financial sector overall or to determine specific risks for individual institutions.7 This can generally be realised in a top-down manner or by referring to a bottom-up framework.8 Sorge and finds that the differences are mainly driven by cyclical components of default risk. Bangia et al. (2002) and Trück and Rachev (2005), for example, have shown that there is a substantial impact of default probabilities and rating transitions on portfolio credit risk. 7 Macro stress tests are also carried out by the regulatory bodies of the two countries analysed in this study, the Czech National Bank and the Deutsche Bundesbank. In the Czech case, the stress testing framework has been gradually elaborated since 2004 by Čihák (2004) and Čihák et al. (2007). Based on a forecast of the macroeconomic environment in terms of historical worst-case scenarios, credit risk models as developed by Jakubík (2007) are applied. The Deutsche Bundesbank takes a two-step approach: besides using aggregate data available in the central bank to analyse financial stability (top-down approach), it also uses information collected from single institutions via a survey (bottom-up approach) (Deutsche Bundesbank, 2007). In the first case, which is similar to the current study, the Bundesbank uses a macro module to define macroeconomic stress events via macroeconomic variables, which are then fed into a microeconomic module (the so-called banking module) to assess which banks would run into difficulties (Deutsche Bundesbank, 2007, p. 106f.). 8 For an overview of stress tests applied by German banks, see Deutsche Bundesbank (2004) and Deutsche Bundesbank (2007).
Stress Testing Credit Risk: Is the Czech Republic Different from Germany? 7 Virolainen (2006) provide a literature overview of analytical approaches to macro stress tests and apply these models to the case of Finland (see also Jones et al., 2004, and Sorge, 2004). Boss et al. (2006) give an overview of the stress testing framework followed by the Austrian central bank. The rationale is to explain industry-specific default rates by means of macroeconomic risk factor changes in order to be able to apply industry sector-specific stress tests. Credit risk models with macroeconomic variables are also employed in stress test exercises carried out by the Bank of England. Within this framework, Pain (2003) found an empirical relationship between banks’ loan loss provisions and macroeconomic indicators such as GDP growth, real interest rates, credit growth and the concentration of the domestic loan portfolio. For the new EU member states, studies remain more limited. Overall, previous studies find that a relatively limited number of macroeconomic factors permit credit risk for the corporate sector to be explained in a meaningful way, including at times of financial turbulence.9
3 Credit Risk Modelling with Macroeconomic Variables In this study, we refer to the loaded one-factor credit risk model, which is also the basis for calculating the Basel II capital requirements for credit risk (Gordy, 2003). To explain credit risk, the idea is to model the aggregated credit risk conditional on the macroeconomic environment, whereby the model becomes a quasi multi-factor model while keeping its conceptual simplicity. The one-factor model has been employed for credit risk modelling by several authors, for example Hamerle et al. (2004), Rösch (2005) and Jakubík (2007). Unlike linear models, this relatively simple non-linear model better captures the highly complex relationships of economies, which are hardly linear in the real world. Subsequently, the basic cornerstones of the model and the ways it will be used for credit risk modelling are outlined. A random variable with a standard normal distribution is assumed for the standardised logarithmic asset returns of firm i at time t:
Rit = ρ Ft + 1 − ρU it
(1)
where Rit denotes the logarithmic asset return for each firm i of an economy at time t, and Ft corresponds to the logarithmic asset return of the economy at time t, which is assumed to be a random variable with a standard normal distribution. This variable represents the part of the asset return which is not firm-specific and can thus denote the general economic conditions for the profitability and creditworthiness of firms in the economy. Uit denotes the firm-specific asset return, which is again assumed to be random with a standard normal distribution. The two random variables are assumed to be serially independent. The portion of risk that is systematic is defined by ρi , the correlation of the firm’s asset return with the systematic factor Ft. Given these assumptions, the logarithmic asset return of firm i at time t is also standard normally distributed. The model is based on the Merton model, according to which a default occurs if the return on a firm’s assets falls below a certain barrier T, the default threshold. Formally,
P (Yit = 1) = P( Rit < T ) , 9
See Borio et al. (2001), for example.
(2)
8 Petr Jakubík and Christian Schmieder where Y denotes a binary random variable with two potential states, borrower i defaults (1), or does not default (0), at time t and T is the default threshold. In order to model aggregate credit risk by means of different macroeconomic indicators, it is further assumed – unlike in the case of Gordy’s Basel II one-factor-model (Gordy, 2003) – that the value of the default threshold T depends on the economic cycle. This is modelled by taking a linear combination of macroeconomic variables (xjt) to represent the value of the default threshold T. The final form of the macroeconomic one-factor credit risk model used in this study is shown in equation (3), where Ψ denotes the distribution function of the standard normal distribution that represents the impact of changes in the macroeconomic indicators, β0 is a constant and βj are the coefficients of the macroeconomic variables, xjt: K
K
j =1
j =1
pit = P( Rit < T ) = P( ρ Ft + 1 − ρU it < β 0 + ∑ β j x jt ) = Ψ (β 0 + ∑ β j x jt )
(3)
The default probability conditional on the realisation Ft of a random unobservable factor representing the state of the economy at time t corresponding to the default probability (3) is given by formula (4). K
pi ( f t ) = P(U it
