贷款组合信用风险管理.ppt

CREDITRISKOFLOANPORTFOLIOS FromSaundersandCornett I Introduction Creditriskofaloan asset portfolioshouldtakeintoaccountboththeconcentrationriskandthebenefitfromloanportfoliodiversification Portfoliocreditriskcanbeusedtosetmaximumloanconcentrationlimitsforcertainbusinessorborrowingsectors TheFDICImprovementActof1991requiresbankregulatorstoincorporatecreditconcentrationriskintotheirevaluationofbankinsolvencyrisk I Introduction Bankswillbeallowedtousetheirown internal models suchasCreditMetricsandCreditRisk andKMV sPortfolioManager tocalculatetheircapitalrequirementsagainstinsolvencyriskfromexcessiveloanconcentrations TheNationalAssociationofInsuranceCommissioners NAIC hasdevelopedlimitsfordifferenttypesofassetsandborrowersininsurers portfolios aso calledpigeonholeapproach II SimpleModelsofLoanConcentrationRisk 1 MigrationAnalysis LendingofficerstrackS P Moody s ortheirowninternalcreditratingsofcertainpoolsofloansorcertainsectors Ifthecreditratingsofanumberofborrowersinasectororratingclassdeclinefasterthanhasbeenhistoricallyexperienced thenlendingtothatsectororclasswillbecurtailed II SimpleModelsofLoanConcentrationRisk TABLE AHypotheticalRatingMigrationorTransitionMatrixRiskGradeatEndofYear 123Default Riskgradeat1 85 10 04 01Beginningof2 12 83 03 02Year3 03 13 80 04 II SimpleModelsofLoanConcentrationRisk Aloanmigrationmatrix ortransitionmatrix seekstoreflectthehistoricexperienceofapoolofloansintermsoftheircredit ratingmigrationovertime Assuch itcanbeusedasabenchmarkagainstwhichthecreditmigrationpatternsofanynewpoolofloanscanbecompared E g Forgrade2loans historically12percenthavebeenupgradedto1 83percenthaveremainedat2 3percenthavebeendowngradedto3 and2percenthavedefaultedbytheendoftheyear II SimpleModelsofLoanConcentrationRisk SupposethattheFIisevaluatingthecreditriskofitscurrentportfolioofloansofgrade2ratedborrowersandthatoverthelastfewyearsamuchhigherpercentage say 5percent ofloanshasbeendowngradedto3andahigherpercentage say 3percent hasdefaultedthanisimpliedbythehistorictransitionmatrix TheFImaythenseektorestrictitssupplyoflower qualityloans e g thoserated2and3 concentratingmoreofitsportfolioongrade1loans II SimpleModelsofLoanConcentrationRisk 2 SettingExternalLimits Formanagementtosetsomeexternallimitsonthemaximumamountofloansthatcanbemadetoanindividualborrowerorsector E g supposemanagementisunwillingtopermitlossesexceeding10percentofanFI scapitaltoaparticularsector Ifitisestimatedthattheamountlostperdollarofdefaultedloansinthissectoris50cents thenthemaximumloanstoasingleborrowerasapercentofcapital definedastheconcentrationlimit is II SimpleModelsofLoanConcentrationRisk Concentrationlimit Maximumlossasapercentofcapital 1 Lossrate 10 1 5 20 Bankregulatorsinrecentyearshavelimitedloanconcentrationstoindividualborrowerstoamaximumof10percentofabank scapital III LoanPortfolioDiversificationandModernPortfolioTheory MPT TheFImanagercancomputetheexpectedreturn RP andrisk P2 onaportfolioofassetsasRP XiRi P2 Xi2 i2 XiXj ij i jIfmanyloanshavenegativedefaultcovariancesorcorrelations thesumoftheindividualcreditrisksofloansviewedindependentlywilloverestimatetheriskofthewholeportfolio FIscantakeadvantageofthelawoflargenumbersintheirinvestmentdecisions III LoanPortfolioDiversificationandModernPortfolioTheory MPT KMVPortfolioManagerModel Anymodelthatseekstoestimateanefficientfrontierforloansandthustheoptimalorbestproportions Xi inwhichtoholdloansmadetodifferentborrowersneedstodetermineandmeasurethreethings 1 theexpectedreturnonaloantoborroweri Ri 2 theriskofaloantoborroweri i and3 thecorrelationofdefaultrisksbetweenloansmadetoborrowersiandj ij III LoanPortfolioDiversificationandModernPortfolioTheory MPT KMVmeasureseachoftheseasfollows Ri AISi E Li AISi EDFi LGDi i ULi Di LGDi EDFi 1 EDFi 1 2 LGDiwhereAIS All in spread Annualfeesearnedontheloan TheannualspreadbetweentheloanratepaidbytheborrowerandtheFI scostoffunds Theexpectedlossontheloan E Li E Li TheExpectedLoss Theexpectedprobabilityoftheborrowerdefaultingoverthenextyearoritsexpecteddefaultfrequency EDFi TheamountlostbytheFIiftheborrowerdefaults thelossgivendefaultorLGDi III LoanPortfolioDiversificationandModernPortfolioTheory MPT ReturnontheLoan Ri Measuredbytheso calledannualall in spread AIS whichmeasuresannualfeesearnedontheloanbytheFIplustheannualspreadbetweentheloanratepaidbytheborrowerandtheFI scostoffunds Deductedfromthisistheexpectedlossontheloan E Li Thisexpectedloss E Li isequaltotheproductoftheexpectedprobabilityoftheborrowerdefaultingoverthenextyear oritsexpecteddefaultfrequency EDFi timestheamountlostbytheFIiftheborrowerdefaults thelossgivendefaultorLGDi III LoanPortfolioDiversificationandModernPortfolioTheory MPT RiskoftheLoan i Theriskoftheloanreflectsthevolatilityoftheloan sdefaultrate Di arounditsexpectedvaluetimestheamountlostgivendefault LGDi TheproductofthevolatilityofthedefaultrateandtheLGDiscalledtheunexpectedlossontheloan ULi andisameasureoftheloan sriskor i Tomeasurethevolatilityofthedefaultrate assumethatloanscaneitherdefaultorrepay nodefault thendefaultsare binomially distributed andthestandarddeviationofthedefaultratefortheithborrower Di isequaltothesquarerootoftheprobabilityofdefaulttimes1minustheprobabilityofdefault EDF 1 EDF 1 2 III LoanPortfolioDiversificationandModernPortfolioTheory MPT CorrelationofLoanDefaults ij Tomeasuretheunobservabledefaultriskcorrelationbetweenanytwoborrowers theKMVPortfolioManagermodelusesthesystematicreturncomponentsofthestockorequityreturnsofthetwoborrowersandcalculatesacorrelationthatisbasedonthehistoricalcomovementbetweenthosereturns AccordingtoKMV defaultcorrelationstendtobelowandliebetween 002and 15 Thismakesintuitivesense Forexample whatistheprobabilitythatbothIBMandGeneralMotorswillgobankruptatthesametime Forbothfirms theirassetvalueswouldhavetofallbelowtheirdebtvaluesatthesametimeoverthenextyear III LoanPortfolioDiversificationandModernPortfolioTheory MPT AnumberoflargebanksareusingtheKMVmodel andothersimilarmodels toactivelymanagetheirloanportfolios Nevertheless somebanksarereluctanttousesuchmodelsifitinvolvessellingortradingloansmadetotheirlong termcustomers Intheviewofsomebankers activeportfoliomanagementharmsthelong termrelationshipsbankershavebuiltupwiththeircustomers Asaresult gainsfromdiversificationhavetobeoffsetagainstlossofreputation IV PartialApplicationsofPortfolioTheory LoanVolume BasedModels Table AllocationoftheLoanPortfoliotoDifferentSectorNationalBankABankB Realestate10 15 10 C I607525Individuals15555Others15510 IV PartialApplicationsofPortfolioTheory Tocalculatetheextenttowhicheachbankdeviatesfromthenationalbenchmark weusethestandarddeviationofbankA sandbankB sloanallocationsfromthenationalbenchmark Wecalculatetherelativemeasureofloanallocationdeviationas Xij Xi 2 1 2 j N IV PartialApplicationsofPortfolioTheory BankBdeviatessignificantlyfromthenationalbenchmarkduetoitsheavyconcentrationinindividualloans ThestandarddeviationsimplyprovidesamanagerwithameasureofthedegreetowhichanFI sloanportfoliocompositiondeviatesfromthenationalaverageorbenchmark ThispartialuseofmodemportfoliotheoryprovidesanFImanagerwithafeelfortherelativedegreeofloanconcentrationcarriedintheassetportfolio IV PartialApplicationsofPortfolioTheory TABLE MeasuresofLoanAllocationDeviationfromtheNationalBenchmarkPortfolio BankABankB X1j X1 2 05 2 0025 0 2 0 X2j X2 2 15 2 0225 05 2 0025 X3j X3 2 10 2 01 4 2 16 X4j X4 2 10 2 01 05 2 0025 Xjj Xi 2 045 285 A 10 61 B 26 69 IV PartialApplicationsofPortfolioTheory LoanLossRatio BasedModels Thismodelinvolvesestimatingthesystematicloanlossriskofaparticularsectorrelativetotheloanlossriskofabank stotalloanportfolio Thissystematicloanlosscanbeestimatedbyrunningatimeseriesregressionofquarterlylossesoftheithsector slossrateonthequarterlylossrateofabank stotalloans Sectorallossesintheithsector Loanstotheithsector TotalLoanLosses TotalLoans IV PartialApplicationsofPortfolioTheory Where measuresthesystematiclosssensitivityoftheithsectorloans Theimplicationofthismodelisthatsectorswithlower scouldhavehigherconcentrationlimitsthanhigh sectors sincelow loansectorrisks loanlosses arelesssystematic thatis aremorediversifiableinaportfoliosense IV PartialApplicationsofPortfolioTheory RegulatoryModels Themethodadoptedislargelysubjectiveandisbasedonexaminerdiscretion Thereaso