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Contributions to Economics Forfurthervolumes: http://www.springer.com/series/1262 Martin Hibbeln Risk Management in Credit Portfolios Concentration Risk and Basel II Dr.MartinHibbeln TechnischeUniversita¨tBraunschweig InstituteofFinance Carl-Friedrich-Gauß-Faculty Abt-Jerusalem-Str.7 38106Braunschweig Germany [email protected] ISSN1431-1933 ISBN978-3-7908-2606-7 e-ISBN978-3-7908-2607-4 DOI10.1007/978-3-7908-2607-4 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2010934306 #Springer-VerlagBerlinHeidelberg2010 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective lawsandregulationsandthereforefreeforgeneraluse. Coverdesign:SPiPublisherServices Printedonacid-freepaper Physica‐VerlagisabrandofSpringer‐VerlagBerlinHeidelberg Springer‐VerlagisapartofSpringerScience+BusinessMedia(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 CommitteeonBankingSupervision“BaselII”inJune2004,thegreatrelevanceof this topic is still present because many types of banking risk are not taken into account.Theimportanceofsuchrisktypesisalsorecognizedwithintheframework 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 takenintoaccountbythePillar1process(e.g.interestrateriskinthebankingbook, 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 veryimportanttasksinceconcentrationrisksinmortgagebankscanbeseenasone relevantcauseofthefinancialcrisis. Againstthisbackground,MartinHibbelnhassethimselfthetargetsofanalyzing concentrationrisksindetailandofconsistentlyintegratingconcentrationrisksinto theBaselIImodel.First,theauthordealswithregulatoryprinciplesoftheEuropean Banking Supervision, which have to be considered in the framework of concentration risk measurement. In addition, he focuses on the question whether or not credit concentrations stemming from bank specialization have a risk increasing effect.ThesubsequenttheoreticalanalysistakestheAsymptoticSingleRiskFactor (ASRF)frameworkofGordyasastartingpointsincethisenvironmentunderliesthe Internal Ratings-Based (IRB) Approach of Basel II. For the purpose of extending this model, Martin Hibbeln addresses two types of concentration risk: name concentrations and sector concentrations. With regard to name concentrations, he determines credit portfolio sizes for different portfolio structures that lead to a violationoftheassumptionsoftheASRFmodel.Theresultsareofgreatpractical relevance since on this basis a bank is able to identify concentration risks intheir credit portfolios. He also analyzes available granularity adjustments concerning theirsuitabilityforthemeasurementofnameconcentrations.Withrespecttosector v vi Foreword concentrations,MartinHibbelnmodifiesexistingapproachestomeasuringconcen- 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 whichprocedureshallbeimplemented.Furthermore,heanalyzes theadequacyof thenon-coherentriskmeasureValue-at-Risk(VaR),whichisoftencriticizedinthe literature.Forthispurpose,allstudiesinquestionareundertakenbytheuseofthe coherent measure Expected Shortfall (ES), as well. Surprisingly, the respective results do not show significant differences and consequently, the use of the VaR seemstobeunproblematicwhendeterminingriskconcentrations. 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 andpracticalapplications, which inturn implies the book tobe suitableforacademicsaswellaspractitioners.Againstthisbackground,Iwishthis innovativeandinventiveworkthehighdegreeofattentionitundoubtedlydeserves duetoitsquality. Braunschweig,Germany MarcGu¨rtler April2010 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 BraunschweiginMarch2010.AtthispointIwouldliketothankallthosewhohave contributed to the success of this work and who have made the time of my dissertationprojectveryexcitingandenjoyable. First of all, my thanks go out to my supervisor, Prof. Dr. Marc Gu¨rtler. Our recurrenttechnical andnon-technical discussions,oursportycompetitions aswell as the necessary academic freedom I was given were of great importance for the developmentofthisworkandfortheexcellentworkingatmosphere.Furthermore, I want to thank Prof. Dr. Gernot Sieg for serving as a reviewer for my doctoral thesisandforthequickpreparationoftherefereereport. IwouldalsoliketothanktheentireteamoftheInstituteofFinance.Duringmy dissertation project, I could especially benefit from numerous discussions and cooperativepublicationswithDr.DirkHeithecker,Dipl.-Math.Oec.SvenOlboeter, and Dipl.-Math. Oec. Clemens Vo¨hringer. Moreover, I am particularly gratefulto Dipl.-Math.Oec.FranziskaBecker,Dipl.-Math.Oec.JuliaStolpe,andDipl.-Math. Oec. Christine Winkelvos for many inspiring and enjoyable discussions about various topics –mostlynotexplicitlyrelatedtothismonograph–duringmytime asaresearchassociateandpartlyalreadyduringmystudies.Inaddition,Iwantto thankSilviaNitschkefortheperfectorganizationoftheinstitute.Aspecialthanks goestoDr.KathrynViemann.Duringmystudiesandmydoctoralwork,shewasa greatsparringpartnerandalwaysabletoencourageandmotivateme. RepresentativefortheteamofcentralriskmanagementoftheVWBankGmbH, I would like to thank Dipl.-Math. Oec. Stefan Ehlers and Dr. Antje Henne of the LGD-teamfortheexcellentcollaborationduringmy2-yearslastingparticipationin theBaselIIproject.ThereIhadtheopportunitytoconvincemyselfthattheoretical knowledgeaboutcreditriskmodelingcaneasilybeputintobankingpractice. 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 versionsofthismonographandimprovingmywritingstyleinEnglish. 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.Itwasthemwhonevertiredofansweringmethousandsof“Howdoesit work?”-and“Why?”-questionswhenIwasachild,andIamcertainthattheyhavea greatpartinsparkingmyscientificcuriosity,whichfinallyresultedinthisdoctoral thesis.Thankyouforeverything! Braunschweig,Germany MartinHibbeln April2010 Contents 1 Introduction ................................................................ 1 1.1 ProblemDefinitionandObjectivesofThisWork ...................... 1 1.2 CourseofInvestigation ................................................. 2 2 CreditRiskMeasurementintheContextofBaselII ................... 5 2.1 BankingSupervisionandBaselII ...................................... 5 2.2 MeasuresofRiskinCreditPortfolios .................................. 8 2.2.1 RiskParametersandExpectedLoss .............................. 8 2.2.2 ValueatRisk,TailConditionalExpectation, andExpectedShortfall .......................................... 11 2.2.3 CoherencyofRiskMeasures ................................... 16 2.2.4 EstimationandStatisticalErrorsofVaRandES .............. 22 2.3 TheUnconditionalProbabilityofDefaultWithintheAsset ValueModelofMerton ................................................ 25 2.4 TheConditionalProbabilityofDefaultWithintheOne-Factor ModelofVasicek ...................................................... 28 2.5 MeasuringCreditRiskinHomogeneousPortfolios withtheVasicekModel ............................................... 31 2.6 MeasuringCreditRiskinHeterogeneousPortfolios withtheASRFModelofGordy ....................................... 35 2.7 MeasuringCreditRiskWithintheIRBApproach ofBaselII .............................................................. 39 2.8 Appendix ............................................................... 43 3 ConcentrationRiskinCreditPortfoliosandItsTreatment UnderBaselII ............................................................. 57 3.1 TypesofConcentrationRisk .......................................... 57 3.2 IncurrenceandRelevanceofConcentrationRisk ..................... 59 3.3 MeasurementandManagementofConcentrationRisk ............... 62 ix x Contents 3.4 HeuristicApproachesfortheMeasurement ofConcentrationRisk ................................................. 67 3.5 ReviewoftheLiteratureonModel-BasedApproaches ofConcentrationRiskMeasurement .................................. 70 4 Model-BasedMeasurementofNameConcentrationRisk inCreditPortfolios ........................................................ 73 4.1 FundamentalsandResearchQuestionsonName ConcentrationRisk .................................................... 73 4.2 MeasurementofNameConcentrationUsingtheRisk MeasureValueatRisk ................................................. 75 4.2.1 ConsideringNameConcentrationwiththeGranularity Adjustment ...................................................... 75 4.2.2 NumericalAnalysisoftheVaR-BasedGranularity Adjustment ...................................................... 87 4.3 MeasurementofNameConcentrationUsingtheRiskMeasure ExpectedShortfall .................................................... 103 4.3.1 AdjustingforCoherencybyParameterization oftheConfidenceLevel ....................................... 103 4.3.2 ConsideringNameConcentrationwiththeGranularity Adjustment ..................................................... 108 4.3.3 MomentMatchingProcedureforStochasticLGDs ........... 114 4.3.4 NumericalAnalysisoftheES-BasedGranularity Adjustment ..................................................... 121 4.4 InterimResult ......................................................... 134 4.5 Appendix .............................................................. 136 5 Model-BasedMeasurementofSectorConcentration RiskinCreditPortfolios ................................................. 183 5.1 FundamentalsandResearchQuestionsonSector ConcentrationRisk ................................................... 183 5.2 IncorporationofSectorConcentrationsUsingMulti-Factor Models ................................................................ 185 5.2.1 StructureofMulti-FactorModelsandBaselII-Consistent ParameterizationThroughaCorrelationMatching Procedure ...................................................... 185 5.2.2 AccountingforSectorConcentrationswiththe ModelofPykhtin .............................................. 190 5.2.3 AccountingforSectorConcentrationswiththe ModelofCespedes,Herrero,KreininandRosen ............. 197 5.2.4 AccountingforSectorConcentrationswiththe ModelofDu¨llmann ............................................ 202