FRM真题答案

94.ThejointprobabilitydistributionofrandomvariablesXandYisgivenbyf(x,y)=kxyforx=1,2,3,y=1,2,3,andkisapositiveconstant.WhatistheprobabilitythatX+Ywillexceed5?a.1/9b.1/4c.1/36d.Cannotbedetermined95.Whichofthefollowingisnotanapproachfordetectingstyledriftofhedgefunds?a.Performanceattributionb.Peergroupcomparisonc.Cashflowanalysisd.Communicationwithfundmanager96.Tohedgeagainstfuture,unanticipated,andsignificantincreasesinborrowingrates,whichofthefollowingalternativesoffersthegreatestflexibilityfortheborrower?a.Interestratecollarb.Fixedforfloatingswapc.Callswaptiond.Interestratefloor97.Assumethetruedistributionofreturnsisleptokurtotic.IfweassumenormalitywhenwecalculatetheVaR,thenwhichofthefollowingstatementsistrue:a.The95%VaRisoverstated.b.The95%VaRisunderstated.c.The95%VaRisappropriate.d.WecannotstatetherelationshipbetweenthetrueVaRandthecalculatedVaR.Thenextthreequestionsusethefollowingdata:98.Aportfolioconsistsoftwobonds.Thecredit-VaRisdefinedasthemaximumlossduetodefaultsataconfidencelevelof98%overaone-yearhorizon.Theprobabilityofjointdefaultofthetwobondsis1.27%,andthedefaultcorrelationis30%.BondValueoneyearforwardOneyearcumulativedefaultprobabilityRecoveryrateB1=USD1,000,0003%60%B2=USD600,0005%40%Whatistheexpectedcreditlossoftheportfolio?a.USD0b.USD9,652c.USD20,348d.USD30,00098.Whatisyourbestestimateofthecredit-VaRforthisportfolioofbondsbasedonthedistributionoflossesduetodefaults?a.USD570,000b.USD400,000c.USD360,000d.USD370,00099.Inthepreviousquestion,youestimatedaVaRthatcorrespondstotheVaRobtainedfromCreditRisk+.SupposethatinsteadyouwantedtoestimatetheVaRusingtheCreditMetricsapproach.Ifyouweregivenalladditionaldatalistedbelow,whichdatawouldyounotneedtoestimatetheCreditMetrics-Stylecredit-VaR?a.Volatilityoffirmvalueforeachissuerb.Transitionmatrixfordowngradesandupgradesinadditiontodefaultprobabilitiesc.Ternstructureofcreditspreadsandinterestratesd.Promisedcouponpaymentsandmaturity101.Giventheinformationprovidedinthetablebelow,whatistheriskbudget,atthe99%confidencelevelofthefollowingCHFmillionequallyweightedinvestmentportfolio?AssetExpectedReturnVolatilityCorrelationStocksBondsStocks24.00%18%10.1Bonds15.00%6%0.11a.CHF20.97millionb.CHF13.98millionc.CHF27.96milliond.CHF22.77million102.TheChiefRiskOfficer(CRO)ofanexportingfirmisattemptingtoestimatethefirm’sone-yearcashflowatrisk.WhichofthefollowingissuesdescribesanapproachthatisirrelevanttothetasktotheCRO?a.Becausecashflowatriskisgenerallyestimatedoveraquarteroroverayear,itisnecessarytoforecastthefuturevaluesofriskfactors.b.Totheextentthatthefirm’sincomefromexportsisbestapproximatedbyarealoptionbecausethefirmdoesnothavetoexportwhenthepriceoftheforeigncurrencyisunexpectedlylow,theCROcanuseoptionanalysisanddoesnothavetoworryaboutforecastingexchangerates.c.Aparametricapproachcanbeusedifexposurestoforeignexchangeriskfactorsarelinear,iftherearenootherriskfactors,andifexchangeratechangesarenormallydistributed.d.UsingaMonteCarloapproachwillhelptheCROifthefirm’sforeigncurrencyincomeisanonlinearfunctionofexchangerates.103.AsinglestockhasapriceofUSD10andacurrentdailyvolatilityof2%.Usingthedelta-normalmethod,theVaRatthe95%confidencelevelofalongat-the-moneycallonthisstockoveraone-dayholdingperiodisapproximatelya.USD1.645b.USD0.16c.USD0.33d.USD0.23104.Yourbankisusingtheinternalmodelsapproachtoestimateitsgeneralmarketriskcharge.Themultiplicationfactor‘k’,setbytheregulator,is3andbanksareallowedtousethesquarerootruletoscaledailyVaR.Thepreviousday’sone-dayVaRestimateisEUR3million,andtheaverageofthedailyVaRoverthelast60daysisEUR2million.Giventheaboveinformation,whatwillbethemarketriskchargeforyourbank?a.EUR9.49millionb.EUR28.46millionc.EUR6.32milliond.EUR18.97million105.AportfoliomanagerhasabondpositionworthUSD100million.Thepositionhasamodifieddurationofeightyearsandaconvexityof150years.Assumethatthetermstructureisflat.Byhowmuchdoesthevalueofthepositionchangeifinterestratesincreaseby25basispoints?a.USD-2,046,875b.USD-2,187,500c.USD-1,953,125d.USD-1,906,250106.Supposeyouareholding100WheelbarrowCompanyshareswithacurrentpriceofUSD50.Thedailyhistoricalmeanandvolatilityofthereturnofthestockis1%and2%,respectively.Thebid-askspreadofthestockvariesovertime.Thedailyhistoricalmeanandvolatilityofthespreadis0.5%and1%,respectively.Calculatethedailyliquidity-adjustedVaR(LVaR)at99%confidencelevel(boththereturnandspreadofthestockarenormallydistributed):a.USD254b.USD229c.USD325d.USD275107.Considerthefollowingpotentialoperationalrisks.Duetoaroguetrader,weestimatethatoverone-yearperiodthereisa10%chancewecouldloseanywherebetweenEUR0andEUR100million(equalprobabilityforallpointswithinthatrangeand0probabilityofanylossesoutsidethatrange).Duetomodelrisk,weestimatethatoveraone-yearperiodthereisa20%chancethatwewillloseEUR25millionnormallydistributedwithastandarddeviationofEUR5million.Whichofthefollowingstatementsistrue?a.Theexpectedlossfromaroguetraderislessthantheexpectedlossfrommodelrisk.b.Theexpectedlossfromaroguetraderisgreaterthantheexpectedlossfrommodelrisk.c.Themaximumunexpectedlossfromaroguetrader