2016年5月frm二級模擬考試一題目

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2016年5月FRM二級（一Anystisreviewingabondforinvestmentpurposes.Thebondisexpectedtohaveadefaultprobabilityof2%,withanexpectedlossof80bpsintheeventofdefault.Iftheitsexpectedreturntomatchtherisk-freerate?Ariskmanagerispricinga10-yearcalloptionon10-yearTreasuryusingasuccessfullytestedpricingmodel.Currentinterestratevolatilityishighandtheriskmanagerisconcernedabouttheeffectthismayhaveonshort-termrateswhenpricingtheoption.Whichofthefollowingactionswouldbestaddressthepotentialfornegativeshort-terminterestratestoariseinthemodel?Whenshort-termratesarenegative,theriskmanageradjuststherisk-neutralMelvinBrownmanagesalongportfolioofdebtandequityinvestmentsforaninsurancecompanyandhasbeentryingtoimplementanewriskmanagementprogrambasedonestimatingandreportingthedailyvalueatrisk(VaR)foreaanager’sportfolio.Browniswritingareporttogainsupportforhisproposal.IfBrowndeterminesthatdailyVaR(10%)forhisportfolioisequalto$20,000,whichofthefollowingstatementsshouldheincludinginhisreport?Computationally,delta-normalVaRismorecomplexthanstandarddeviationbuteasiertointerpretfromariskmanagement.VaRwasdevelopedspecificallyforthepurposeofmeasuringtheeconomic金程教 Therateparameterintheexponentialdistributionmeasurestherateatwhichittakesaneventtooccur.Inthecontextofwaitingforacompanytodefault,therateparameterisknownasthehazardrateandindicatestherateatwhichdefaultwillarrive.Whichofthefollowingstatementsabouthazardrates(i.e.defaultintensity)iscorrectassumingaconstantdefaultintensityof0.2?Trackingerrorisdefinedasthestandarddeviationofthedifferencebetweenthereturnsonaportfolioandthebenarkportfolio.Usingonlyinformationratiosallowriskonentire(firm)portfoliostobeTheoptimalweightsoftheallocationstovariousfundmanagers(ofafirm)donotnecessarilyhavetosumtoone.schemeacrossactivefundmanagersofafirm.AfirmusesVaRtoestimatetheprobabilityoflosses.However,managementisconcernedthattheestimationprocessgivesequalweighttoallobservations.Therefore,alternativeapproachesareconsidered.Whichofthefollowingstatementsaccuraydescribesanreturnswithvolatility-adjustedreturns.IIINeitherInor金程教 Theannualmeanandvolatilityofaportfolioare10%and40%,respectively.ThecurrentvalueoftheportfolioisGBP100,000.Howdoesthe1-year95%VaRthatiscalculatedusinganormaldistributionassumption(normalVaR)comparewiththe1-year95%VaRRiskaggregation isoneofthechallenging areaswithintheeconomic andmakingcertainchoicesinaggregatingthoserisktypes.Classificationbyrisktypes(market,credit,operational,andbusiness)maybeapproximateandpronetoerror.Forexample,thedefinitionsofrisktypesmaydifferacrossbanksorwithinagivenbank,whichcomplicatestheaggregationprocess.Mostbanksbeginbyaggregatingriskintosilosbyrisk-typeacrosstheentirebank.Otherbankspreferusingbusinessunitsilos,whileotherscombinebothapproaches.Whichofthefollowingstatementsregardingriskaggregationiscorrect?versustheweightedaverageofthetwoseparateportfolios.Asimplesummationmethodofriskaggregationaddstogetherindividualcapitalcomponents,differentiatesbetweenrisktypes,andproducesunequalweighting.Avariance-covariancematrixriskaggregationmethodsummarizestheinterdependenciesacrossrisktypesandprovidesaflexibleframeworkforrecognizingdiversificationbenefits.distributionsintoajointprobabilitydistributionthroughcopulafunctions.GraysonBallentine,anystwithPlatinumConsultants,is yzingtheeconomicmargin.Afterthemargintransaction,thetotalassetsonthefulleconomicbalancesheetandtheleverageratioareclosestto: 金程教 A.B.C.D.Ariskystiscomparingtheuseofparametricandnon-parametricapproachesforcalculatingVaRandisconcernedaboutsomeofthecharacteristicspresentinthelossdata.Whichofthefollowing wouldmakeparametricapproachesthefavoredmethodtouse?AsaresultofthenewBaselstandards,everybankmustnowcalculateexplicitcapitalchargestocoveroperationalriskusingoneofthreeapproaches:thebasicindicatorapproach(BIA),thestandardizedapproach(SA),andtheadvancedmeasurementapproach(AMA).Howmanyofthefollowingstatementsaretruewithrespecttotheseoperationalriskapproaches?TheAMAallowsabanktobuilditsownoperationalriskmodelandmeasurementsystemcomparabletomarketriskstandards.Basel’s1996Amendmentallowsmoresophisticatedbankswithwell-establishedriskmanagementfunctionstouseaninternalmodel-basedapproach(IMA)forsettingmarketriskcapital.Mostlargebankspreferredtousetheinternalmodel-basedapproachbecauseitbetterreflectedthebenefitsofdiversificationandledtolowercapitalrequirements.Aboutthiscapitalchargeformarketriskundertheinternalmodelsapproach(IMA),including2009revisionstotheoriginalAmendment,eachofthefollowing金程教 Thevalue-at-risk(VaR)measureusedintheinternalmodel-basedapproachiscalculatedwitha10-daytimehorizonanda99.0%confidencelevel;andregulatorsVaRmultipliedbythesquarerootoften;i.e.,10-day99.0%VaR=one-day99.0%Thecapitalrequirementisequaltomax[VaR(t–1),m(c)×VaR(avg)]+SRC,whereVaR(t–1)isthepreviousday’svalueatrisk,andVaR(avg)istheaveragevalueatriskoverthepast60daysThecapitalrequirementaddstwoterms:value-at-risk(VaR)andspecificriskcharge(SCR).Inacorporatebondsecurity,forexample,thecreditriskiscapturedbytheVaRtermandtheinterestrateriskiscapturesbytheSRCterm.bankmustjustifytheomissionofanyriskfactorsthatareotherwiseusedinpricingrepresentedasF,U,andS,respectively.SubordinateddebtcanberepresentedbyalongcallwithexercisepriceofFandshortcallwithexercisepriceofU.firmisnotindistress.Anystisexaminingasampleofreturndata.Asa step,the ystconstructaplotofthedataasshownbelow.金程教 Afirm’sfinancialplanningdepartmentreportsthataproject’sproposedrisk-adjustedthefirm’sequitybetais1.3.Useadjustedrisk-adjustedreturnoncapital(ARAROC)todeterminewhetherornottheprojectshouldbeaccepted.Thisfirmshould:ystBarbaraconstructedaninterestratetreewithmonthlytimesteps,where(t)=1/12.Thecurrentshort-termrateis3%.Hertermstructuremodelassumesanannualbasispointvolatilityof200basispointswithanannual(lambda)driftof50basispoints.Shedrift.Hereisherratetree:金程教 Whatistheun-displayedmissingvalueatnode[2.0];i.e.,therateinthetreenottherealizedprocess?HarrisonMichaels,FRM,anystatHudsonRiskytics,isdiscussingthedefaultsensitivitiesofequity,mezzanine,andseniortranchesandmakesthefollowingIIINeitherInorUnderthelossdistributionapproach(LDA),Girlingsaysthestepistomodelfrequency.Thenextstep(Step#2)istomodelseverity:“Thenextstepinmodelingexpectedoperationalrisklossesistodeterminethelikelysizeofaneventgiventhefactthataneventhasoccurred.Thisistheseverityofanevent.Unlikefrequency,severityneednotbeaninteger,butcanfallanywherealongacontinuum.Whenalossoccursitmightbe$1.50oritmightbe$133,892.25oranyothervalue.Theseveritydistributionestablishestheprobabilityofaneventoccurrin erawiderangeofvalues,fromzerotovery,verylargelosses.”AccordingtoGirling,eachofthefollowingstatementsistrueabouttheseveritydistributionexceptwhichisfalse?Regulatorstakeakeeninterestinhowwelltheselecteddistribution金程教 Inadditionto“goodnessoffit,”asuitableseveritymodelshouldprobablymeetthefollowingcriteria:realistic,well-specified,flexible,andsimple.Whicheverdistributionisselected,theprobabilitydensityfunctionforseveritywillhavelight(thin)tailsandwillalsobeskewedtotheleft.Themostcommonandleastcomplexapproachtomodelingseverityistousealognormaldistribution,althoughlowfrequencylossesmayfitbettertootheroptionssuchasGeneralizedGamma,TransformedBeta,GeneralizedPareto,orWeibull.Theriskmanagementgroupestimatesthe1-day99%VaRonalong-only,large-capequityportfoliousingavarietyofapproaches.AdailyriskreportshowsthefollowingSupposemeanreversionexistsforavariablewithavalueof30attimeperiodt–1.Assumethatthelong-runmeanvalueforthisvariableis40andignorethestochastictermincludedinmostregressionsoffinancialdata.Whatistheexpectedchangeinvalueof4 ens,Inc.,(J ens)frequentlyentersintoderivativestradeswithitscounterparties.WhichofthefollowingterminationeventswouldJ ensmostlikelyfindbeneficialifitwantedtomaintaintheabilitytoterminateatradeatpre-specifiedfuturedates?金程教 oneyear.Whichofthefollowinginequalitiesmostaccurayreflectstheconvexityeffectforthis2-yearbondusingJensen’sinequalityformula?clustering;i.e.,timedependencywhichviolatesanassumptionthatthelossesareindependentandidenticallydistributed(i.i.d.).Whichisthebestapproach,POTEV?TheclusteringisnotrelevantandyoucanuseeitherPOTorGEV:unlikeandinfact,anticipatesclustering.effectshouldbemitigated.NeitherGEVnorPOTcanbeused;thereisnocurrentlyknownmethodfordealingwithno.d.dataunderEVT.Youproposetocomputetheexpectedshortfall(ES)ofapositionbyemployingextreme(blockaapproach)distribution.YourcolleagueFredobjectswiththefollowingEVTis ortheother.Weare“stuckwith”GEVPDduetosmallsamples.Asthesamplesizeincreases,thecentrallimittheorem(CLT)justifiesanormaldistributionfortheextremelosstail.金程教 Tofiteitherdistribution(GDPorGEV),weneedtospecifybothascaleandatailparameter,buttherearenoknownmethodsforestimatingtheseparameterswithhistoricaldata.totheir(mostly)asymptoticnatureandpaucityofdata.Ahedgefundisconsideringtakingpositionsinvarioustranchesofacollateralizeddebtobligation(CDO).Thefund’schiefeconomistpredictsthatthedefaultprobabilitywilldecreasesignificantlyandthatthedefaultcorrelationwillincrease.BasedonthisTheannualreturnsoftwoassets,X(i)andY(i),areshownbelowforthefiveyearsfrom2010to2013.ThereturnshavebeensortedwithrespecttoX(i);forexample,in2010X(i)aaonitslltfrsottrisReturnisReturnof金程教 nearesttotheKendall’stau?exceptwhichisnot?TheGaussiancopulahaslowtaildependencewhichisaweaknessbecausedependencies(includingcorrelations)increaseinacrisis.tocalibrateCDOtrancheswithasinglecorrelationmodel.TheGaussiancopulaisprincipallystaticandconsequentlyallowsonlylimitedriskmanagement;i.e.,thereisnostochasticprocessforthecriticalunderlyingvariables’defaultintensityanddefaultcorrelation.TheGaussiancopulaislimitedtomarketriskapplicationsbecauseitrequires(n*n)pairwisecorrelationparameters,whichisnaturaltoacovariancematrix,butincreditriskthereisnotheoreticalwaytoassumethesevalueswhentheyarepairwisedefaultcorrelations.bytheBaselCommittee.Giventhefollowinginformation,whatisthebank’snetstablefundingratio?金程教 Whichofthefollowingstatementsregardingfrictionsinthesecuritizationofsubprimemortgagesiscorrect?Thearrangerwilltypicallyhaveaninformationadvantageovertheoriginatorwithregardtothequalityoftheloanssecuritized.cancreateanincentivefortheoriginatortocollaboratewiththeborrowerinfilingfalseloanapplications.Themajorcreditratingagenciesarepaidbyinvestorsfortheirratingserviceofmortgage-backedsecurities,andthiscreatesapotentialofinterest.TheuseofescrowaccountsforinsuranceandtaxpaymentseliminatestheriskofWithrespecttotherisk-freerate,LIBOR,andtheovernightindexedswap(OIS)rate,considerthefollowingfivestatements:therisk-freerateisU.S.Treasurybills,notesandbonds.Followingthecreditcrisis,bankshaveabandonedLIBORastherisk-freeratefornon-collateralizedtransactions.Three-monthLIBORrateisnormallyhigherthanthethree-monthOISratebecausetheremoreriskinmakingasinglethree-monthloantoacreditworthybankthanaseriesofovernightloanstocreditworthybanks.LIBORistherateofinterestatwhichAA-ratedbanksborrowforperiodsupto12monthsfromotherbanks.III,IVandVareComputingVaRonaPortfoliocontainingaverylargenumberofpositionscanbesimplifiedbymapthesepositionstoasmallernumberofelementaryriskfactors.Whichofthefollowingmapswouldbeadequate?金程教 Eachpositioninacorporatebondportfolioismappedonthebondwiththeclosestmaturityamongasetofernmentbonds.ernmentbondspayingregularcouponsaremappedonzero-couponernmentApositioninthestockmarketindexismappedonapositioninastockwithinthatGriffinRiehlisariskmanageratBluegrassBankandTrust,asmall,independentcommercialbankinKentucky.RiehlhasrecentlyreadtheBaselCommitteeonBanking mendationsforsoundoperationalmanagementandwouldlketoputbythecommittee.Whichofthefollowingisnotoneofthethreecommon“l(fā)inesofdefense”suggestedbytheBaselCommitteeforoperationalriskernance? reviewsofoperational risksandriskmanagementUsingtheVasicekmodel,assumeacurrentshort-termrateof6.2%andanannual oftheinterestrateprocessof2.5%.Alsoassumethatthelong-runmean-revertinglevelis13.2%withaspeedofadjustmentof0.4.WithinabinomialA.B.C.D.A2-yearcreditdefaultswap(CDS)specifyingphysicaldeliverydefaultsatoftwoyears.Ifthereferenceassetisa$200million,8.0%ABCcorporatebond,andtheCDSspreadis125basispoints,thebuyeroftheCDSwill:金程教 AtraderobservesaquoteforStockDUY,andthemidpointofitscurrentbestbidandbestaskpricesisCAD45.DUYhasanestimateddailyreturnvolatilityof0.38%andaveragebid-askspreadofCAD0.1.Usingtheconstantspreadapproachona20,000shareestimatedliquidity-adjusted,1-day95%VaR?CADCADCADCADModelriskistheriskassociatedwithtryingtocaptureanobservedphenomenonusingafinancialmodel.Models,bytheirveryconstruction,areflawedinstrumentsandcannotpossiblycapturethefullscopeoffactorsnecessarytoexplainthedynamicrelationshipsweobserve.Itisbettertoaskoneselfwhatiswrongwiththemodelratherthanglossingoverpotentialerrorsinconstruction.Importantsourcesofmodelriskincludeincorrect calibration,programmingerrors,anddataproblems.Whichofthefollowingstatementsisdistribution,whereasanormaldistributionrepresentsamoreaccurateunderlyingstochasticprocess.Multipleusersofthecapitalassetpricingmodel(CAPM)mayincorporatedifferentmeasuresofbeta.Thisisanexampleofincorrectmodelspecification.Useofoutdatedmodelinputparametersmeasuredwitherrororbaseduponinappropriatesampleperiodsisanexampleofincorrectmodelapplication.exampleofincorrectmodelapplication.JasonConnor,FRM,isahedgefundmanagerwhoisexplainingimpliedvolatilityforcurrencyoptionstojuniorysts.WhichofthefollowingstatementsbestcompleteshisThereisagreaterchanceofextremepricemovementsthanpredictedbyalognormaldistribution.Therearenoarbitrageopportunitiesunlesstheimpliedvolatilityversusstrike金程教 $10million(i.e.,ifclosedoutimmediay,Bwouldowe$10milliontoA);replacementvalueforBwithrespecttoC=$10million;replacementvalueforCwithrespecttoA=$10million.Ifthesepositionswereimmediaynovatedtocentralcounterpartywithhavea$10millionexposuretothecentralcounterparty.CounterpartyexposuresamongA,BandCareeacheliminatedtozero;andeachwillhavezeroexposuretothecentralcounterparty.centralcounterparty.hecbculftexhecbculftexltionof123456789theVaRmodelthatisbeingbacktested?IIerror.modeliscorrect.CanzoneInternationalBankcarries$3.0billioninLevel1assetsplus$2.0billioninLevel"lessstable"deposits(liabilities)of$80.0billionwithanaveragerun-offrate(factor)of10%;expectedcashinflowsare$10.0billion.PleasenoteperBaselIII:金程教 haircutundertheLCRthestockofHQLALevel2assets(comprisingLevel2AassetsandanyLevel2Bassetspermittedbythesupervisor)canbeincludedinthestockofHQLA,subjecttotherequirementthattheycomprisenomorethan40%oftheoverallstockafterhaircutshavebeenDefinition:Totalnetcashoutflowsoverthenext30calendardays=Totalexpectedcashoutflow-Min{totalexpectedcashinflows;75%oftotalexpectedcashoutflows}that6.0defaultsperyearistheaverageinaPoissonprocess(distribution),whatistheprobabilitythatthenextmunicipaldefaultwilloccurwithinonemonth?金程教 AninvestorhassolddefaultprotectiononthemosiortrancheofaCDO.Ifthedefaultisunchanged,theinvestor’sposition:Willneithergainnorlosevalue,sinceonlyexpecteddefaultlossesmatterandcorrelationdoesnotaffectexpecteddefaultlosses.Caneitherincreaseordecrease,dependingonthepricingmodelusedandthemarketconditions.AsuWaliaisaseniorystworkingforasellsidecompanypreparingresearchreportsrisktothefirm’sassets,whichheexpectswillbenefitequityholderstothedetrimentofdebtholders.WhichofthefollowingconceptsbestdescribesthescenarioinWalia’sAdverseRiskABCD Withtheinformationprovided,whatisthemostappropriatecreditriskmitigationtechniqueinthiscase?金程教 IncreaseDuringtherecentcreditcrisis,subprimemortgagesreceivedpressurefromupwardmovementsininterestrates,alongwiththeimpossibilityformostoftheseborrowerstorefinance.Asaresult,manysubprimeborrowersallowedtheirreducedvaluehomestobetakenoverbythelender.AllofthefollowingstatementsdescribetheeffectsubprimeThedefaultsinthelowertrancheswerehighbutdidnotaffectseniortrancheGiventheinformationbelow,whatistheliquidity-adjustedVaRatthe95%confidenceBid-askspreadA.B.C.D.payingafixed8.5%(i.e.,350bpsoverLIBORflatat5%).金程教 ThereisneverayearinwhicheitherthejuniororseniorbondsarepaidtheirfullBothbondholders(seniorandjunior)realizealloftheirinterestpaymentsinthebothbondholders).Juniorbondholdersufferinterestpaymentshortfallsandaprincipalshortfall,butseniorbondholdersreceivealloftheirinterestandexperiencenoprincipalshortfall.Bothbondholdersrealizealloftheirinterestpayments,infull,andgetbacktheentiretyoftheirprincipal.TheRAROCis15%,therisk-freerateis3%,themarketreturnis16%,andtheequitybetais1.50.WhatistheadjustedRAROC(ARAROC),andshouldtheprojectbeInOctober2007,theBaselCommitteereleasedguidelinesfortreatingincrementaldefaultriskinthetradingbook.Later,inlightoftheglobalfinancialcrisis(GFC),theCommitteeexpandedthescopeofthecapitalchargeintothemore passingincrementalriskcharge(IRC).WhichofthefollowingwasmostnearlythemotivationfortheexpandedcoverageoftheIRC?Lossesduetoidiosyncraticfactors,notsystematicfactors,includingbasisrisk金程教 wideningspreadsand/orlossofliquidity.LossesonsecuritizedproductsduetooperationalriskincludinglegalandcontractThevaluationagentisthepartycallingfordeliveryorreturnofcollateralandthusmusthandleallcalculations;i.e.,calculationofcreditexposure,marketvalueofpostedcollateral,uncollateralizedexposure,andthedeliveryorreturnamountAcounterpartywhopostsadividend-payingassetascollateral(i.e.,the"giver"ofcollateral)forfeitsalldividendsasthereceiverimmediay estheeconomicownerofthecollateralabovethethreshold,onlytheincrementalexposurewillbecollateralizedAnindependentiseffectivelyanegativethresholdandistypicallyheldasacushionagainst“gaprisk;”i.e.,theriskthatatransaction'smarketvaluemaygapsubstantiallyandquicklyWhichofthefollowingmeasuresaremostlikelytobeusedbyasecuritizedproductbackedbystudentloans?Singlemonthlymortality(SMM),constantprepaymentrate(CPR),andPublicSecuritiesAssociation(PSA).Weightedaveragelife(WAL),weightedaveragematurity(WAM),andweightedaveragecoupon(WAC).Whichofthefollowingsubprimecharacteristicsprovidedirectprotectionforsenior金程教 firmvolatility,andinterestrates(i.e.,thedebtvalueincreasesasthesefactorsTheseniordebthasnegativeexposurestodebtmaturity,firmvolatility,andinterestrates(i.e.,theseniordebtvaluedecreasesasthesefactorsincrease).Thesubordinateddebthaspositiveexposurestodebtmaturity,firmvolatility,andinterestrates(i.e.,thesubordinateddealueincreasesasthesefactorsincrease).Theseniordebthaspositiveexposurestodebtmaturity,firmvolatility,andrates(i.e.,theseniordebtvalueincreasesasthesefactorsincrease).Thesubordinateddebthasnegativeexposurestodebtmaturity,firmvolatility,andinterestrates(i.e.,thesubordinateddealuedecreasesasthesefactorsincrease).Boththeseniordebtandsubordinateddebthavenegativeexposurestomaturity,firmvolatility,andinterestrates(i.e.,thedebtvaluedecreasesasthesefactorsincrease).vvUSD621USD740 o金程教 andthebetaofAssetAwithrespecttotheportfolio,beta(A,P),equals0.520.andthebetaofAssetBwithrespecttotheportfolio,beta(B,P),equals1.480.andtheportfolio,rho(A,P),isequalto0.647.ThecorrelationbetweenAssetBandtheportfolio,rho(B,P),isequalto0.9213.arenormallydistributed)riskunderBaselII(orBaselIII).Thebankhasthreebusinesslinesandeachbusinesslinecontributesone-thirdtowardthetotalgross e.Foragiventotalgross whichbusinessmixwillproducethelargestcapitalcharge?PublicEmployeeRetirementFund(PERF)has$600millioninassetsand$600millioninliabilities,foracurrentsurplusofzero.Theannualexpectedreturnonassetsis8.0%with18.0%volatilityperannum;theannualexpectedreturnonliabilitiesis6.0%with14.0%volatilityperannum.Botharenormallydistributed.Thecorrelationbetweenassetsandliabilitiesis0.60.Whatisthe95%absolutesurplusatrisk(absoluteSaR);i.e.,theworstexpectedshortfall,orlossrelativetocurrentsurplusofzero,with95%confidence?Theinterestratetreebelowshowsthetrueprocessforaone-yearinterestrate.金程教 currentone-yearspotrateis7.0%.Nextyear,investorsexpecttheone-yearratetoeitherincreaseto10.0%ordropto4.0%,withequalprobabilityofanincreaseordrop.Inthesubsequentyear(Year2),investorssimilarlyexpectthefutureone-yearratetoagainknownprocess,thepriceofa$1,000partwo-yearzero-couponbondwouldbe$874.13;usmodifythisandinsteadassumethatinvestorsarerisk-averse:theywouldpreferacertain7.0%returntoanexpected7.0%returnwithvolatility.Consequently,letusassumeinvestorsrequire(charge)ariskpremiumof90basispoints.Comparedtotherisk-neutralpriceof$874.13,whatisthechangeinpriceduetotheintroductionoftherisk0%recoveryrateissuedbyCompanyA.Thebondiscurrentlytradingat80%offacevalue.Assumingtheexcessspreadonlycapturescreditriskandthattherisk-freerateis5%perannum,therisk-neutral1-yearprobabilityofdefaultonCompanyAisclosesttowhichofthefollowing?Copulaenablesthestructuresofcorrelationbetweenvariablestobecalculatedseparayfromtheirmarginaldistributions.金程教 Correlationcanbeausefulmeasureoftherelationshipbetweenvariablesdrawnfromadistributionwithoutadefinedvariance.Correlationisagoodmeasureofdependencewhenthemeasuredvariablesaredistributedasmultivariateelliptical.Itowns20%ofthestockofacompany.MajorInvestment’sriskmanagerisconcernedthat,intheeventtheentirepositionneedstobesold,itsizewouldaffectthemarketprice.Hisestimateofthepriceelasticityofdemandis-0.5.WhatistheincreaseinMajorInvestments’Value-at-Riskestimateforthispositionifaliquidityadjustmentismade?TheMertonmodelandtheMoody’sKMVusedifferentapproachestodeterminetheprobabilityofdefault.WhichofthefollowingisconsistentwithMoody’sKMVmodel?Thehistoricalfrequencyofdefaultforcorporatebondshasbeen6%.UpdatingthiswithAltman’sZ-scoreysiswouldprovideaprobabilityofdefaultthatissomewhatdifferentthan6%. todefault is1.96and,historically, 1.2%offirmswiththischaracterizationhavedefaulted,sothereisa1.2%probabilityofdefault.Youaretative likelytoexperienceanextremeeventthanbefore.Basedontheinformationprovidedbyyourboss,tomodelthefrequencyandseverityofextremeevents,whichofthefollowingdistributionswouldbemostappropriatetouse?金程教 Poisson Poisson TheCEOofMerlionHoldings,alargediversifiedconglomerate,iskeentoenhanceshareholdervalueusinganenterpriseriskmanagementframework.Youareaskedtoassistseniormanagementtofyandmanagetherisk-returntradeofffortheentirefirm.Specifically,theCEOwantstoknowwhichriskstoretainandwhichriskstolayoffthefollowingstatementsis/arecorrect?hecontextofthemarginalimpactoftheprojectonthefirm’stotalrisk.Supposeaportfoliohasavalueof$1,000,000with50independentcreditpositions.Eachofthecreditshasadefaultprobabilityof2%andarecoveryrateof0%.Thecreditportfoliohasadefaultcorrelationequalto0.Thenumberofdefaultsisbinomiallydistributedandthe95thpercentileofthenumberofdefaultsis3.WhatisthecreditvalueapproachtocreditriskinBaselIIandBaselIII,except:Theriskweightfunctionestimatesa99.9%confidentone-yearhorizoncredit金程教 UL=WCL–ELincludeamaturityadjustment.thebanks’owninternalestimates.Currencyoptionsexhibitvolatilitysbecausetheat-the-moneyoptionshavehigherimpliedvolatilitythanaway-from-the-moneyoptions.impliedvolatility.Relativetocurrencytraders,itappearsthatequitytraders’expectationsofextremepricemovementsaremoreasymmetric.Giventheexpectedexposure(EE),theneachofthefollowingisthereforeplausible,exceptwhichisnottrue?LineA,onlybecausetheEEisunimodal(withonepeak),isalsotheumpotentialfutureexposure(umPFE).LineBistheexpectedpositiveexposure(EPE),oftencalledthe"loanequivalent,"andisasinglenumberbecauseitistheaverageoftheexpectedexposuresoverthetimehorizon.LineCistheeffectiveexpectedpositiveexposure(EEPE),andisasingle金程教 Arecentlypublishedarticleonissueswithvalueatrisk(VaR)estimatesincludedthefollowingstatements.Statement1:DifferencesintheuseofconfidenceintervalsandtimehorizoncancausesignificantvariabilityinVaRestimatesasthereislackofuniformityinpractice.Statement2: