風(fēng)險(xiǎn)管理與金融機(jī)構(gòu)課件Ch14

RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CreditRisk:EstimatingDefaultProbabilitiesChapter14

1RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CreditRatings(90)IntheS&P/Fitchratingsystem,AAAisthebestrating.AfterthatcomesAA,A,BBB,BB,B,andCCCThecorrespondingMoody’sratingsareAaa,Aa,A,Baa,Ba,B,andCaaBondswithratingsofBBB(orBaa)andaboveareconsideredtobe“investmentgrade”Mostbankshavetheirowninternalratingssystemsforborrowers2RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009Altman’sZ-score(Manufacturingcompanies)page291X1=WorkingCapital/TotalAssetsX2=RetainedEarnings/TotalAssetsX3=EBIT/TotalAssetsX4=MarketValueofEquity/BookValueofLiabilitiesX5=Sales/TotalAssets

Z=1.2X1+1.4X2+3.3X3+0.6X4+0.99X5 IftheZ>3.0defaultisunlikely;if2.7<Z<3.0weshouldbeonalert.If1.8<Z<2.7thereisamoderatechanceofdefault;ifZ<1.8thereisahighchanceofdefault3RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009EstimatingDefaultProbabilitiesAlternatives:UsehistoricaldataUsebondpricesorassetswapsUseCDSspreadsUseMerton’smodel

4RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009HistoricalDataHistoricaldataprovidedbyratingagenciescanbeusedtoestimatetheprobabilityofdefault5RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CumulativeAverageDefaultRates%(1970-2007,Moody’s)

Table14.1,page2926RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009InterpretationThetableshowstheprobabilityofdefaultforcompaniesstartingwithaparticularcreditratingAcompanywithaninitialcreditratingofBaahasaprobabilityof0.170%ofdefaultingbytheendofthefirstyear,0.478%bytheendofthesecondyear,andsoon7RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009DoDefaultProbabilitiesIncreasewithTime?ForacompanythatstartswithagoodcreditratingdefaultprobabilitiestendtoincreasewithtimeForacompanythatstartswithapoorcreditratingdefaultprobabilitiestendtodecreasewithtime8RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009DefaultIntensityvsUnconditionalDefaultProbabilityThedefaultintensityorhazardrateistheprobabilityofdefaultconditionalonnoearlierdefaultTheunconditionaldefaultprobabilityistheprobabilityofdefaultasseenattimezeroWhatarethedefaultintensitiesandunconditionaldefaultprobabilitiesfromtheMoody’stableforaCaaratecompanyinthethirdyear?9RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009RecoveryRate Therecoveryrateforabondisusuallydefinedasthepriceofthebondimmediatelyafterdefaultasapercentofitsfacevalue10RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009RecoveryRates;Moody’s:1982to2007

(Table14.2,page293)11RecoveryRatesDependonDefaultRatesMoody’sbestfitestimateforthe1982to2007periodis AveRecoveryRate=59.33?3.06×SpecGradeDefaultRateR2ofregressionisabout0.5

R2ofregressionwasabout0.5.RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull200912RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CreditDefaultSwaps(page294)

Buyeroftheinstrumentacquiresprotectionfromtheselleragainstadefaultbyaparticularcompanyorcountry(thereferenceentity)Example:Buyerpaysapremiumof90bpsperyearfor$100millionof5-yearprotectionagainstcompanyXPremiumisknownasthecreditdefaultspread.ItispaidforlifeofcontractoruntildefaultIfthereisadefault,thebuyerhastherighttosellbondswithafacevalueof$100millionissuedbycompanyXfor$100million(Severalbondsmaybedeliverable)13RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CDSStructure(Figure14.1,page294)

DefaultProtectionBuyer,ADefaultProtectionSeller,B90bpsperyearPayoffifthereisadefaultbyreferenceentity=100(1-R)Recoveryrate,R,istheratioofthevalueofthebondissuedbyreferenceentityimmediatelyafterdefaulttothefacevalueofthebond14RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009OtherDetailsPaymentsareusuallymadequarterlyinarrearsIntheeventofdefaultthereisafinalaccrualpaymentbythebuyerSettlementcanbespecifiedasdeliveryofthebondsorincash(severalbondsareusuallydeliverable)Supposepaymentsaremadequarterlyintheexamplejustconsidered.Whatarethecashflowsifthereisadefaultafter3yearsand1monthandrecoveryrateis40%?15RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009AttractionsoftheCDSMarketAllowscreditriskstobetradedinthesamewayasmarketrisksCanbeusedtotransfercreditriskstoathirdpartyCanbeusedtodiversifycreditrisks16RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CreditIndices(98)CDXIG:equallyweightedportfolioof125investmentgradeNorthAmericancompaniesiTraxx:equallyweightedportfolioof125investmentgradeEuropeancompaniesIfthefive-yearCDSindexisbid165offer166itmeansthataportfolioof125CDSsontheCDXcompaniescanbeboughtfor166bpspercompany,e.g.,$800,000of5-yearprotectiononeachnamecouldbepurchasedfor$1,660,000peryear.Whenacompanydefaultstheannualpaymentisreducedby1/125.17RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CreditDefaultSwapsandBondYields(page298)Portfolioconsistingofa5-yearparyieldcorporatebondthatprovidesayieldof6%andalongpositionina5-yearCDScosting100basispointsperyearis(approximately)alongpositioninarisklessinstrumentpaying5%peryearWhatarearbitrageopportunitiesinthissituationisrisk-freerateis4.5%?Whatifitis5.5%?18Risk-freeRateTherisk-freerateusedbybondtraderswhenquotingcreditspreadsistheTreasuryrateTherisk-freerateusedinthecreditmarketsistheLIBOR/swaprateRiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull200919AssetSwapsAssetswapsareusedbythemarketasanestimateofthebondyieldrelativetoLIBORThepresentvalueoftheassetswapspreadisthepresentvalueofthecostofdefaultRiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull200920RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009AssetSwaps(page299)Supposeassetswapspreadforaparticularcorporatebondis150basispointsOnesidepayscouponsonthebond;theotherpaysLIBOR+150basispoints.ThecouponsonthebondarepaidregardlessofwhetherthereisadefaultInadditionthereisaninitialexchangeofcashreflectingthedifferencebetweenthebondpriceand$100ThePVoftheassetswapspreadistheamountbywhichthepriceofthecorporatebondisexceededbythepriceofasimilarrisk-freebondwhentheLIBOR/swapcurveisusedfordiscounting21RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009UsingCDSPricestoPredictDefaultProbabilities Averagedefaultintensityoverlifeofbondis approximately wheresisthespreadofthebond’syieldovertherisk-freerateandRistherecoveryrate22RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009MoreExactCalculationforBonds(page262)Supposethatafiveyearcorporatebondpaysacouponof6%perannum(semiannually).Theyieldis7%withcontinuouscompoundingandtheyieldonasimilarrisk-freebondis5%(withcontinuouscompounding)Theexpectedlossfromdefaultsis8.738.ThiscanbecalculatedasthePVofassetswapspreadsorasthedifferencebetweenthemarketpriceofthebondanditsrisk-freepriceSupposethattheunconditionalprobabilityofdefaultisQperyearandthatdefaultsalwayshappenhalfwaythroughayear(immediatelybeforeacouponpayment).23RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CalculationsTime(yrs)DefProbRecoveryAmountRisk-freeValueLossDiscountFactorPVofExpLoss0.5Q40106.7366.730.975365.08Q1.5Q40105.9765.970.927761.20Q2.5Q40105.1765.170.882557.52Q3.5Q40104.3464.340.839554.01Q4.5Q40103.4663.460.798550.67QTotal288.48Q24RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009CalculationscontinuedWeset288.48Q=8.738togetQ=3.03%ThisanalysiscanbeextendedtoallowdefaultstotakeplacemorefrequentlyWithseveralbondswecanusemoreparameterstodescribethedefaultprobabilitydistribution25RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009RealWorldvsRisk-NeutralDefaultProbabilities

Thedefaultprobabilitiesbackedoutofbondpricesorcreditdefaultswapspreadsarerisk-neutraldefaultprobabilitiesThedefaultprobabilitiesbackedoutofhistoricaldataarereal-worlddefaultprobabilities26RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009AComparisonCalculate7-yeardefaultintensitiesfromtheMoody’sdata(1970-2007).Thesearerealworlddefaultprobabilities)UseMerrillLynchdata(1996-2007)toestimateaverage7-yeardefaultintensitiesfrombondprices(thesearerisk-neutraldefaultintensities)Assumearisk-freerateequaltothe7-yearswaprateminus10basispoints27RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009RealWorldvsRiskNeutralDefaultProbabilities(7yearaverages)Table14.4,page30428RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009RiskPremiumsEarnedByBondTraders(Table14.5,page304)29RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009PossibleReasonsforTheseResults

(Thethirdreasonisthemostimportant)CorporatebondsarerelativelyilliquidThesubjectivedefaultprobabilitiesofbondtradersmaybemuchhigherthantheestimatesfromMoody’shistoricaldataBondsdonotdefaultindependentlyofeachother.Thisleadstosystematicriskthatcannotbediversifiedaway.Bondreturnsarehighlyskewedwithlimitedupside.Thenon-systematicriskisdifficulttodiversifyawayandmaybepricedbythemarket30RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009WhichWorldShouldWeUse?Weshoulduserisk-neutralestimatesforvaluingcreditderivativesandestimatingthepresentvalueofthecostofdefaultWeshoulduserealworldestimatesforcalculatingcreditVaRandscenarioanalysis31RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009Merton’sModel(Section14.8,pages307-309)Merton’smodelregardstheequityasanoptionontheassetsofthefirmInasimplesituationtheequityvalueismax(VT–D,0) whereVTisthevalueofthefirmandD

isthedebtrepaymentrequired32RiskManagementandFinancialInstitutions2e,Chapter14,Copyright?JohnC.Hull2009Equityvs.AssetsAnoptionpricingmodelenablesthevalueofthefirm’sequitytoday,E0,toberelatedtothevalueofitsassetstoday,V0,andthevolatilityofits