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1、CREDIT RISK OF LOAN PORTFOLIOS FromSaundersandCornettI.IntroductionnCreditriskofaloan(asset)portfolioshouldtakeintoaccountboththeconcentrationriskandthebenefitfromloanportfoliodiversification.nPortfoliocreditriskcanbeusedtosetmaximumloanconcentrationlimitsforcertainbusinessorborrowingsectors.nTheFDI
2、CImprovementActof1991requiresbankregulatorstoincorporatecreditconcentrationriskintotheirevaluationofbankinsolvencyrisk.I.IntroductionnBankswillbeallowedtousetheirowninternalmodels,suchasCreditMetricsandCreditRisk+andKMVsPortfolioManager,tocalculatetheircapitalrequirementsagainstinsolvencyriskfromexc
3、essiveloanconcentrations.nTheNationalAssociationofInsuranceCommissioners(NAIC)hasdevelopedlimitsfordifferenttypesofassetsandborrowersininsurersportfolios-aso-calledpigeonholeapproach.II.Simple Models of Loan Concentration Riskn1.Migration Analysis:LendingofficerstrackS&P,Moodys,ortheirowninternalcre
4、ditratingsofcertainpoolsofloansorcertainsectors.Ifthecreditratingsofanumberofborrowersinasectororratingclassdeclinefasterthanhasbeenhistoricallyexperienced,thenlendingtothatsectororclasswillbecurtailed.II.Simple Models of Loan Concentration RisknTABLE:AHypotheticalRatingMigrationorTransitionMatrixRi
5、skGradeatEndofYearn_n123Defaultn_nRiskgradeat1.85.10.04.01nBeginningof2.12.83.03.02nYear3.03.13.80.04n_II.Simple Models of Loan Concentration RisknAloanmigrationmatrix(ortransitionmatrix)seekstoreflectthehistoricexperienceofapoolofloansintermsoftheircredit-ratingmigrationovertime.Assuch,itcanbeuseda
6、sabenchmarkagainstwhichthecreditmigrationpatternsofanynewpoolofloanscanbecompared.nE.g.:Forgrade2loans,historically12percenthavebeenupgradedto1,83percenthaveremainedat2,3percenthavebeendowngradedto3,and2percenthavedefaultedbytheendoftheyear.II.Simple Models of Loan Concentration RisknSupposethattheF
7、Iisevaluatingthecreditriskofitscurrentportfolioofloansofgrade2ratedborrowersandthatoverthelastfewyearsamuchhigherpercentage(say,5percent)ofloanshasbeendowngradedto3andahigherpercentage(say,3percent)hasdefaultedthanisimpliedbythehistorictransitionmatrix.TheFImaythenseektorestrictitssupplyoflower-qual
8、ityloans(e.g.,thoserated2and3),concentratingmoreofitsportfolioongrade1loans.II.Simple Models of Loan Concentration Riskn2.Setting External Limits:Formanagementtosetsomeexternallimitsonthemaximumamountofloansthatcanbemadetoanindividualborrowerorsector.nE.g.,supposemanagementisunwillingtopermitlossese
9、xceeding10percentofanFIscapitaltoaparticularsector.Ifitisestimatedthattheamountlostperdollarofdefaultedloansinthissectoris50cents,thenthemaximumloanstoasingleborrowerasapercentofcapital,definedastheconcentrationlimit,isII.Simple Models of Loan Concentration RisknConcentrationlimit=Maximumlossasanper
10、centofcapital*(1/Lossnrate)n=10%*1/.5n=20%nBankregulatorsinrecentyearshavelimitedloanconcentrationstoindividualborrowerstoamaximumof10percentofabankscapital.III.Loan Portfolio Diversification and Modern Portfolio Theory(MPT)nTheFImanagercancomputetheexpectedreturn(RP)andrisk(P2)onaportfolioofassetsa
11、snRP=XiRinP2=Xi2i2+XiXjijijnIfmanyloanshavenegativedefaultcovariancesorcorrelations,thesumoftheindividualcreditrisksofloansviewedindependentlywilloverestimatetheriskofthewholeportfolio.FIscantakeadvantageofthelawoflargenumbersintheirinvestmentdecisions.III.Loan Portfolio Diversification and Modern P
12、ortfolio Theory(MPT)nKMV Portfolio Manager Model:nAnymodelthatseekstoestimateanefficientfrontierforloansandthustheoptimalorbestproportions(Xi)inwhichtoholdloansmadetodifferentborrowersneedstodetermineandmeasurethreethings:n1.theexpectedreturnonaloantoborroweri(Ri),n2.theriskofaloantoborroweri(i),and
13、n3.thecorrelationofdefaultrisksbetweenloansmadetoborrowersiandj(ij).III.Loan Portfolio Diversification and Modern Portfolio Theory(MPT)nKMVmeasureseachoftheseasfollows:nRi=AISi-E(Li)=AISi-EDFi*LGDini=ULi=Di*LGDi=EDFi(1-EDFi)1/2*LGDiwherenAIS=All-in-spread=Annualfeesearnedontheloan+Theannualspreadbet
14、weentheloanratepaidbytheborrowerandtheFIscostoffunds-TheexpectedlossontheloanE(Li).nE(Li)=TheExpectedLoss=(Theexpectedprobabilityoftheborrowerdefaultingoverthenextyearoritsexpecteddefaultfrequency(EDFi)*(TheamountlostbytheFIiftheborrowerdefaultsthelossgivendefaultorLGDi).III.Loan Portfolio Diversifi
15、cation and Modern Portfolio Theory(MPT)nReturnontheLoan(Ri):nMeasuredbytheso-calledannualall-in-spread(AIS),whichmeasuresannualfeesearnedontheloanbytheFIplustheannualspreadbetweentheloanratepaidbytheborrowerandtheFIscostoffunds.DeductedfromthisistheexpectedlossontheloanE(Li).nThisexpectedlossE(Li)is
16、equaltotheproductoftheexpectedprobabilityoftheborrowerdefaultingoverthenextyear,oritsexpecteddefaultfrequency(EDFi)timestheamountlostbytheFIiftheborrowerdefaultsthelossgivendefaultorLGDi.III.Loan Portfolio Diversification and Modern Portfolio Theory(MPT)nRiskoftheLoan(i):nTheriskoftheloanreflectsthe
17、volatilityoftheloansdefaultrate(Di)arounditsexpectedvaluetimestheamountlostgivendefault(LGDi).nTheproductofthevolatilityofthedefaultrateandtheLGDiscalledtheunexpectedlossontheloan(ULi)andisameasureoftheloansriskori.nTomeasurethevolatilityofthedefaultrate,assumethatloanscaneitherdefaultorrepay(nodefa
18、ult);thendefaultsarebinomiallydistributed,andthestandarddeviationofthedefaultratefortheithborrower(Di)isequaltothesquarerootoftheprobabilityofdefaulttimes1minustheprobabilityofdefault(EDF)*(1-EDF)1/2.III.Loan Portfolio Diversification and Modern Portfolio Theory(MPT)nCorrelationofLoanDefaults(ij):nT
19、omeasuretheunobservabledefaultriskcorrelationbetweenanytwoborrowers,theKMVPortfolioManagermodelusesthesystematicreturncomponentsofthestockorequityreturnsofthetwoborrowersandcalculatesacorrelationthatisbasedonthehistoricalcomovementbetweenthosereturns.nAccordingtoKMV,defaultcorrelationstendtobelowand
20、liebetween.002and.15.Thismakesintuitivesense.Forexample,whatistheprobabilitythatbothIBMandGeneralMotorswillgobankruptatthesametime?Forbothfirms,theirassetvalueswouldhavetofallbelowtheirdebtvaluesatthesametimeoverthenextyear!III.Loan Portfolio Diversification and Modern Portfolio Theory(MPT)nAnumbero
21、flargebanksareusingtheKMVmodel(andothersimilarmodels)toactivelymanagetheirloanportfolios.Nevertheless,somebanksarereluctanttousesuchmodelsifitinvolvessellingortradingloansmadetotheirlong-termcustomers.Intheviewofsomebankers,activeportfoliomanagementharmsthelong-termrelationshipsbankershavebuiltupwit
22、htheircustomers.Asaresult,gainsfromdiversificationhavetobeoffsetagainstlossofreputation.IV.Partial Applications of Portfolio TheorynLoan Volume-Based Models:nTable:AllocationoftheLoanPortfoliotoDifferentSectornNationalBankABankBn_nRealestate10%15%10%nC&I607525nIndividuals15555nOthers15510n_IV.Partia
23、l Applications of Portfolio TheorynTocalculatetheextenttowhicheachbankdeviatesfromthenationalbenchmark,weusethestandarddeviationofbankAsandbankBsloanallocationsfromthenationalbenchmark.nWecalculatetherelativemeasureofloanallocationdeviationasn(Xij-Xi)21/2nj=-nNIV.Partial Applications of Portfolio Th
24、eorynBankBdeviatessignificantlyfromthenationalbenchmarkduetoitsheavyconcentrationinindividualloans.nThestandarddeviationsimplyprovidesamanagerwithameasureofthedegreetowhichanFIsloanportfoliocompositiondeviatesfromthenationalaverageorbenchmark.nThispartialuseofmodemportfoliotheoryprovidesanFImanagerw
25、ithafeelfortherelativedegreeofloanconcentrationcarriedintheassetportfolio.IV.Partial Applications of Portfolio TheorynTABLE:MeasuresofLoanAllocationDeviationfromtheNationalBenchmarkPortfolion_nBankABankBn_n(X1j-X1)2(.05)2=.0025(0)2=0n(X2j-X2)2(.15)2=.0225(.05)2=.0025n(X3j-X3)2(-.10)2=.01(.4)2=.16n(X
26、4j-X4)2(-.10)2=.01(-.05)2=.0025n_ _n(Xjj-Xi)2=.045=.285nA=10.61%B=26.69%n_IV.Partial Applications of Portfolio TheorynLoan Loss Ratio-Based Models:nThismodelinvolvesestimatingthesystematicloanlossriskofaparticularsectorrelativetotheloanlossriskofabankstotalloanportfolio.Thissystematicloanlosscanbees
27、timatedbyrunningatimeseriesregressionofquarterlylossesoftheithsectorslossrateonthequarterlylossrateofabankstotalloans:n(Sectorallossesintheithsector/Loanstotheithsector)=+(TotalLoanLosses/TotalLoans)IV.Partial Applications of Portfolio TheorynWheremeasuresthesystematiclosssensitivityoftheithsectorlo
28、ans.nTheimplicationofthismodelisthatsectorswithlowerscouldhavehigherconcentrationlimitsthanhighsectors-sincelowloansectorrisks(loanlosses)arelesssystematic,thatis,aremorediversifiableinaportfoliosense.IV.Partial Applications of Portfolio TheorynRegulatory Models:nThemethodadoptedislargelysubjectivea
29、ndisbasedonexaminerdiscretion.Thereasonsgivenforrejectingthemoretechnicalmodelsarethat(1)currentmethodsforidentifyingconcentrationriskarenotsufficientlyadvancedtojustifytheiruseandn(2)insufficientdataareavailabletoestimatemorequantitative-typemodels,althoughthedevelopmentofmodelslikeKMV,aswellasCred
30、itMetricsandCreditRisk+,maymakebankregulatorschangetheirminds.IV.Partial Applications of Portfolio TheorynLifeandproperty-casualtyinsuranceregulatorshavealsobeenconcernedwithexcessiveindustrysectorandborrowerconcentrations.nThesegeneraldiversificationlimitsaresetat3percentforlife-healthinsurersand5p
31、ercentforproperty-casualtyinsurersimplyingthatlife-healthcompaniesmustholdsecuritiesofaminimumof33differentissuers,whileforPCcompaniestheminimumis20.nTherationaleforsuchasimplerulecomesfrommodernportfoliotheory,whichshowsthatequalinvestmentsacrossapproximately15ormorestockscanprovidesignificantgainsfromdiversification.