Credit Risk Evaluation Modeling – Analysis – Management INAUGURAL-DISSERTATION ZUR ERLANGUNG DER WÜRDE EINES DOKTORS DER WIRTSCHAFTSWISSENSCHAFTEN DER WIRTSCHAFTSWISSENSCHAFTLICHEN FAKULTÄT DER RUPRECHT-KARLS-UNIVERSITÄT HEIDELBERG VORGELEGT VON UWE WEHRSPOHN AUS EPPINGEN HEIDELBERG, JULI 2002 This monography is available in e-book-format at http://www.risk-and-evaluation.com. This monography was accepted as a doctoral thesis at the faculty of economics at Heidelberg University, Ger- many. © 2002 Center for Risk & Evaluation GmbH & Co. KG Berwanger Straße 4 D-75031 Eppingen www.risk-and-evaluation.com 2 Acknowledgements My thanks are due to Prof. Dr. Hans Gersbach for lively discussions and many ideas that con- tributed essentially to the success of this thesis. Among the many people who provided valuable feedback I would particularly like to thank Prof. Dr. Eva Terberger, Dr. Jürgen Prahl, Philipp Schenk, Stefan Lange, Bernard de Wit, Jean-Michel Bouhours, Frank Romeike, Jörg Düsterhaus and many colleagues at banks and consulting companies for countless suggestions and remarks. They assisted me in creating the awareness of technical, mathematical and economical problems which helped me to formulate and realize the standards that render credit risk models valuable and efficient in banks and financial institutions. Further, I gratefully acknowledge the profound support from Gertrud Lieblein and Computer Sciences Corporation – CSC Ploenzke AG that made this research project possible. My heartfelt thank also goes to my wife Petra for her steady encouragement to pursue this extensive scientific work. Uwe Wehrspohn 3 Introduction In the 1990ies, credit risk has become the major concern of risk managers in financial institu- tions and of regulators. This has various reasons: • Although market risk is much better researched, the larger part of banks’ economic capital is generally used for credit risk. The sophistication of traditional standard methods of measurement, analysis, and management of credit risk might, there- fore, not be in line with its significance. • Triggered by the liberalization and integration of the European market, new chan- nels of distribution through e-banking, financial disintermediation, and the en- trance of insurance companies and investment funds in the market, the competitive pressure upon financial institutions has increased and led to decreasing credit mar- gins1. At the same time, the number of bankruptcies of companies stagnated or in- creased2 in most European countries, leading to a post-war record of insolvencies in 2001 in Germany3. • A great number of insolvencies and restructuring activities of banks were influ- enced by prior bankruptcies of creditors. In the German market, prominent exam- ples are the Bankgesellschaft Berlin (2001), the Gontard-MetallBank (2002), the Schmidtbank (2001), and many mergers among regional banks4 to avoid insol- vency or a shut down by regulatory authorities. The thesis contributes to the evaluation and development of credit risk management methods. First, it offers an in-depth analysis of the well-known credit risk models Credit Metrics (JP Morgan), Credit Risk+ (Credit Suisse First Boston), Credit Portfolio View (McKinsey & Company) and the Vasicek-Kealhofer-model5 (KMV Corporation). Second, we develop the Credit Risk Evaluation model6 as an alternative risk model that overcomes a variety of defi- ciencies of the existing approaches. Third, we provide a series of new results about homoge- nous portfolios in Credit Metrics, the KMV model and the CRE model that allow to better 1 Bundesbank (2001). 2 Creditreform (2002), p. 4. 3 Creditreform (2002), p. 16. 4 Between 1993 and 2000 1,000 out of 2,800 Volks- und Raiffeisenbanken and 142 out of 717 savings banks ceased to exist in Germany (Bundesbank 2001, p. 59). All of them merged with other banks so that factual insolvency could be avoided in all cases. Note that shortage of regulatory capital in consequence of credit losses was not the reason for all of these mergers. Many of them were motivated to achieve cost reduction and were carried out for other reasons. 5 We refer to the Vasicek-Kealhofer-model also as the KMV model. 6 Credit Risk Evaluation model is a trademark of the Center for Risk & Evaluation GmbH & Co. KG, Heidelberg. We re- fer to the Credit Risk Evaluation model also as the CRE model. 4 understand and compare the models and to see the impact of modeling assumptions on the reported portfolio risk. Fourth, the thesis covers all methodological steps that are necessary to quantify, to analyze and to improve the credit risk and the risk adjusted return of a bank port- folio. Conceptually, the work follows the risk management process that comprises three major as- pects: the modeling process of the credit risk from the individual client to the portfolio (the qualitative aspect), the quantification of portfolio risk and risk contributions to portfolio risk as well as the analysis of portfolio risk structures (the quantitative aspect), and, finally, meth- ods to improve portfolio risk and its risk adjusted profitability (the management aspect). The modeling process The modeling process includes the identification, mathematical description and estimation of influence factors on credit risk. On the level of the single client these are the definitions of default7 and other credit events8, the estimation of default probabilities9, the calculation of credit exposures10 and the estimation of losses given default11. On the portfolio level, depend- encies and interactions of clients need to be modeled12. The assessment of the risk models is predominantly an analysis of the modeling decisions taken and of the estimation techniques applied. We show that all of the four models have con- siderable conceptual problems that may lead to an invalid estimation, analysis and pricing of portfolio risk. In particular, we identify that the techniques applied for the estimation of default probabilities and related inputs cause systematic errors in Credit Risk+13 and Credit Portfolio View14 if certain very strict requirements on the amount of available data are not met even if model assumptions are assumed to hold. If data is sparse, both models are prone to underestimate default probabilities and in turn portfolio risk. For Credit Metrics and the KMV model, it is shown that both models lead to correct results if they are correctly specified. The concept of dependence that is common to both models – called the normal correlation model – can easily be generalized by choosing a non-normal 7 See section I.A. 8 I.e. of rating transitions, see sections I.B.4, I.B.6.c)(4), I.B.7. 9 See section I.B. 10 Section I.C. 11 Section I.D. 12 See Section II.A. 13 Section I.B.5 14 Section I.B.6 5 distribution for joint asset returns. As one of the main results, we prove for homogenous port- folios that the normal correlation model is precisely the risk minimal among of all possible generalizations of this concept of dependence. This implies that even if the basic concept of dependence is correctly specified, Credit Metrics and the Vasicek-Kealhofer model systemati- cally underestimate portfolio risk if there is any deviation from the normal distribution of as- set returns. Credit Risk+ has one special problem regarding the aggregation of portfolio risk15. It is the only model whose authors intend to avoid computer simulations to calculate portfolio risk and attain an analytical solution for the portfolio loss distribution. For this reason, the authors choose a Poisson approximation of the distribution of the number of defaulting credits in a portfolio segment. As a consequence each segment contains an infinite number of credits. This hidden assumption may lead to a significant overestimation of risk in small segments, e.g. when the segment of very large exposures in a bank portfolio is considered that is usually quite small. Thus, Credit Risk+ is particularly suited for very large and homogenous portfo- lios. However, at high percentiles, the reported portfolio losses even always exceed the total portfolio exposure. With the Credit Risk Evaluation model, we present a risk model that avoids these pitfalls and integrates a comprehensive set of influence factors on an individual client’s risk and on the portfolio risk. In particular, the CRE model captures influences on default probabilities and dependencies such as the level of country risk, business cycle effects, sector correlations and individual dependencies between clients. This leads to an unbiased and more realistic estima- tion of portfolio risk16. The CRE model also differs from the other models with respect to the architecture, which is modular in contrast to the monolithic design in other models. This means that the corner- stones of credit risk modeling such as the description of clients’ default probabilities, expo- sures, losses given default, and dependencies are designed as building blocks that interact in certain ways, but the methods in each module can be exchanged and adjusted separately. This architecture has the advantage that, by choosing appropriate methods in each component, the overall model may be flexibly adapted to the type and quality of the available data and to the structure of the portfolio to be analyzed. 15 Section II.A.3.a) 16 Sections I.B.7 and II.A.2 6 For instance, if the portfolio is large and if sufficiently long histories of default data are avail- able, business cycle effects on default probabilities can be assessed in the CRE model. Other- wise, more simple methods to estimate default can be applied such as long term averages of default frequencies etc. Similarly, country risk typically is one of the major drivers of portfo- lio risk of internationally operating banks. In turn, these banks should use a risk model that can capture its effect17. Regional banks, on the other hand, might not have any exposures on an international scale and, therefore, may well ignore country risk. Moreover, an object-oriented software implementation of the model can directly follow its conceptual layout.