Contributions to Economics For further volumes: http://www.springer.com/series/1262 Martin Hibbeln Risk Management in Credit Portfolios Concentration Risk and Basel II Dr. Martin Hibbeln Technische Universita¨t Braunschweig Institute of Finance Carl-Friedrich-Gauß-Faculty Abt-Jerusalem-Str. 7 38106 Braunschweig Germany [email protected] ISSN 1431-1933 ISBN 978-3-7908-2606-7 e-ISBN 978-3-7908-2607-4 DOI 10.1007/978-3-7908-2607-4 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010934306 # Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: SPi Publisher Services Printed on acid-free paper Physica‐Verlag is a brand of Springer‐Verlag Berlin Heidelberg Springer‐Verlag is a part of Springer Science+Business Media (www.springer.com) Foreword Over the last 10 years, there has hardly been a topic that has occupied the credit sector more than the appropriate determination of the capital backing of credit risk positions. Even after the adoption of the capital requirements by the Basel Committee on Banking Supervision “Basel II” in June 2004, the great relevance of this topic is still present because many types of banking risk are not taken into account. The importance of such risk types is also recognized within the framework of Basel II. According to Pillar 2, “there are three main areas that might be particularly suited to treatment: risks considered under Pillar 1 that are not fully captured by the Pillar 1 process (e.g. credit concentration risk); those factors not taken into account by the Pillar 1 process (e.g. interest rate risk in the banking book, business and strategic risk); and factors external to the bank (e.g. business cycle effects)”. In this context especially the consideration of concentration risks is a very important task since concentration risks in mortgage banks can be seen as one relevant cause of the financial crisis. Against this background, Martin Hibbeln has set himself the targets of analyzing concentration risks in detail and of consistently integrating concentration risks into the Basel II model. First, the author deals with regulatory principles of the European Banking Supervision, which have to be considered in the framework of concen- tration risk measurement. In addition, he focuses on the question whether or not credit concentrations stemming from bank specialization have a risk increasing effect. The subsequent theoretical analysis takes the Asymptotic Single Risk Factor (ASRF) framework of Gordy as a starting point since this environment underlies the Internal Ratings-Based (IRB) Approach of Basel II. For the purpose of extending this model, Martin Hibbeln addresses two types of concentration risk: name con- centrations and sector concentrations. With regard to name concentrations, he determines credit portfolio sizes for different portfolio structures that lead to a violation of the assumptions of the ASRF model. The results are of great practical relevance since on this basis a bank is able to identify concentration risks in their credit portfolios. He also analyzes available granularity adjustments concerning their suitability for the measurement of name concentrations. With respect to sector v vi Foreword concentrations, Martin Hibbeln modifies existing approaches to measuring concen- tration risks in order to consistently extend the Basel II framework. He shows how to implement the approaches for practical application and gives a detailed analysis with regard to measurement accuracy and runtime of the procedures. Again, the results are of practical importance since the analysis shows in detail which procedure shall be implemented. Furthermore, he analyzes the adequacy of the non-coherent risk measure Value-at-Risk (VaR), which is often criticized in the literature. For this purpose, all studies in question are undertaken by the use of the coherent measure Expected Shortfall (ES), as well. Surprisingly, the respective results do not show significant differences and consequently, the use of the VaR seems to be unproblematic when determining risk concentrations. All in all, this book deals with a relevant topic within the framework of credit risk management. In this context the author succeeds impressively in connecting theoretical results and practical applications, which in turn implies the book to be suitable for academics as well as practitioners. Against this background, I wish this innovative and inventive work the high degree of attention it undoubtedly deserves due to its quality. Braunschweig, Germany Marc Gu¨rtler April 2010 Preface This monograph was written while I was a research associate at the Institute of Finance at the Technische Universita¨t Braunschweig. It was accepted as my doctoral thesis by the Carl-Friedrich-Gauß-Faculty of the Technische Universita¨t Braunschweig in March 2010. At this point I would like to thank all those who have contributed to the success of this work and who have made the time of my dissertation project very exciting and enjoyable. First of all, my thanks go out to my supervisor, Prof. Dr. Marc Gu¨rtler. Our recurrent technical and non-technical discussions, our sporty competitions as well as the necessary academic freedom I was given were of great importance for the development of this work and for the excellent working atmosphere. Furthermore, I want to thank Prof. Dr. Gernot Sieg for serving as a reviewer for my doctoral thesis and for the quick preparation of the referee report. I would also like to thank the entire team of the Institute of Finance. During my dissertation project, I could especially benefit from numerous discussions and cooperative publications with Dr. Dirk Heithecker, Dipl.-Math. Oec. Sven Olboeter, and Dipl.-Math. Oec. Clemens Vo¨hringer. Moreover, I am particularly grateful to Dipl.-Math. Oec. Franziska Becker, Dipl.-Math. Oec. Julia Stolpe, and Dipl.-Math. Oec. Christine Winkelvos for many inspiring and enjoyable discussions about various topics – mostly not explicitly related to this monograph – during my time as a research associate and partly already during my studies. In addition, I want to thank Silvia Nitschke for the perfect organization of the institute. A special thanks goes to Dr. Kathryn Viemann. During my studies and my doctoral work, she was a great sparring partner and always able to encourage and motivate me. Representative for the team of central risk management of the VW Bank GmbH, I would like to thank Dipl.-Math. Oec. Stefan Ehlers and Dr. Antje Henne of the LGD-team for the excellent collaboration during my 2-years lasting participation in the Basel II project. There I had the opportunity to convince myself that theoretical knowledge about credit risk modeling can easily be put into banking practice. Many thanks also go to Oliver Bredtmann, M.Sc., Dipl.-Wirt.-Inf. Markus Weinmann, and Anne Gottschall, B.A., for their patience in checking earlier versions of this monograph and improving my writing style in English. vii viii Preface Last but not least, I want to express my thanks to my family, who has always supported and encouraged me, and especially to my parents, Ingeborg and Gert Hibbeln. It was them who never tired of answering me thousands of “How does it work?”- and “Why?”-questions when I was a child, and I am certain that they have a great part in sparking my scientific curiosity, which finally resulted in this doctoral thesis. Thank you for everything! Braunschweig, Germany Martin Hibbeln April 2010 Contents 1 Introduction ................................................................ 1 1.1 Problem Definition and Objectives of This Work ...................... 1 1.2 Course of Investigation ................................................. 2 2 Credit Risk Measurement in the Context of Basel II ................... 5 2.1 Banking Supervision and Basel II ...................................... 5 2.2 Measures of Risk in Credit Portfolios .................................. 8 2.2.1 Risk Parameters and Expected Loss .............................. 8 2.2.2 Value at Risk, Tail Conditional Expectation, and Expected Shortfall .......................................... 11 2.2.3 Coherency of Risk Measures ................................... 16 2.2.4 Estimation and Statistical Errors of VaR and ES .............. 22 2.3 The Unconditional Probability of Default Within the Asset Value Model of Merton ................................................ 25 2.4 The Conditional Probability of Default Within the One-Factor Model of Vasicek ...................................................... 28 2.5 Measuring Credit Risk in Homogeneous Portfolios with the Vasicek Model ............................................... 31 2.6 Measuring Credit Risk in Heterogeneous