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12015年5月FRM一级真题1.Answer:BAcalendarspreadcanbecreatedbysellingaEuropeancalloptionwithacertainstrikepriceandbuyingalonger-maturityEuropeancalloptionwiththesamestrikeprice.Thereversecalendarspreadistheoppositewhichbuyashort-maturityoptionandsellalong-maturityoption.Theoriginalpositionisshort100MarchcallswithastrikepriceofUSD50andlong100AprilcallswithastrikepriceofUSD50.Therefore,itisacalendarspread.Abutterflyspreadinvolvespositionsinoptionswiththreedifferentstrikeprices.ItcanbecreatedbybuyingaEuropeancalloptionwitharelativelylowstrikepriceK1,buyingaEuropeancalloptionwitharelativelyhighstrikepriceK3,andsellingtwoEuropeancalloptionswithastrikepricethatishalfwaybetweenK1andK3.Thefinalpositionissellsthe100Aprilcalls(fromthegivendata,wecanguessthestrikepricewillbe50)andbuys50MarchcallswithastrikeatUSD30and50MarchcallswithastrikeatUSD70.2.Answer:ARi=E(Ri)+βi,GDP[GDP–E(GDP)]+βi,IR[IR–E(IR)]Ri=6%+[GDP–E(GDP)]–1.5×[IR–E(IR)]A:0.025B:0.0075C:-0.005D:0.01753.Answer:BTheGinicoefficientisusedtomeasuresocialinequalityonascaleofzerotoone,withzerobeingtotalequalityandonebeingtotalinequality.24.Answer:BSimulationone:Confidenceinterval=[μ–1.98×s/sqrt(100),μ+1.98×s/sqrt(100)]=[4.85–1.98×1.5/sqrt(100),4.85+1.98×1.5/sqrt(100)]=[4.55,5.15]Simulationtwo:Confidenceinterval=[μ–1.97×s/sqrt(400),μ+1.97×s/sqrt(400)]=[4.70,5.00]5.Answer:CAccordingtoGARPCodeofConduct:GARPMembersShallmakeadistinctionbetweenfactandopinioninthepresentationofanalysisandrecommendations.6.Answer:AAccordingto“AssessingCountryRisk”inValuationandRiskModels,riskanalysesshouldbe:Consistentandmadeusingrigorousframeworksthatallowforvalidcross-countrycomparisons.Concise,withtheconclusioneasytounderstand,butwithsufficientdetailtomakeitmeaningful.Informative,givingtheendusertherationalebehindanyassessmentwithoutany“blackboxes”thataredifficulttounderstand.Decisive,withaclearlydefinedpositiononprevailingcountryconditionsandfutureimplications.7.Answer:D3222221.121.081.131.071.15SampleMean1.1151SampleVariance1.121.111.081.111.131.111.071.111.151.110.001154SampleStandardDeviationsqrt0.001150.03408.Answer:CRatingagenciestypicallyreceivepaymentfromissuersfortheirratingservices.Theissuer-paymodelissometimesquestionedashavingthepotentialtodistorttheindependenceoftheratingprocess.9.Answer:CN=3,I/Y=4/2=2,PMT=1000×4.5%/2=22.5,FV=1000CPT:PV=1,007.2010.Answer:DThebolivarfuerte(VEF)lasttradedatUSD1=VEF6whiletheeconomistsestimatetheexchangeratenowwouldbeUSD1=VEF7.2275.ThereforeVEFdepreciated,andtheinflationrateofVenezuelahadahigherinflationratethantheUS.Atthebeginning,thecompanyhadequivalentofUSD50milliondenominatedinVEFwithUSD1=VEF6,whichisVEF300million.WithexchangerateofUSD1=VEF7.2275now,thecompanywilllossUSD8.5million.11.Answer:DAccordingto“PuttingVaRtoWork”inValuationandRiskModels,thefullrevaluationapproachusingavaluationexpressiontopricethederivativeattheVaRtailoftheunderlyingfactor.Thisapproachhasthegreatadvantageofaccuracy.Itdoesnotinvolveanyapproximations.However,thisapproachcanbecomputationallyveryburdensome.Thedelta-normalapproachinvolvesthedeltaapproximation,orthedelta-gammaapproximation.Theapproachisknownas“delta-normal”becausethelinear4approximationisoftenusedinconjunctionwithanormalityassumptionforthedistributionoffluctuationsintheunderlyingfactorvalue.Theapproachcanbeimplementedrelativelysimply.12.Answer:CAccordingto“OperationalRisk”inValuationandRiskModels,ascaleadjustmentshouldbemadetoexternaldata.Aftertheappropriatescaleadjustment,dataobtainedthroughsharingarrangementswithotherbankscanbemergedwiththebank’sowndatatoobtainalargersamplefordeterminingthelossseveritydistribution.13.Answer:CAccordingto“MeasuresofFinancialRisk”inValuationandRiskModels,ariskmeasureissaidtobecoherentifitsatisfiesthefollowingproperties:Monotonicity:Y≥X→ρ(Y)≤ρ(X)Subadditivity:ρ(X+Y)≤ρ(X)+ρ(Y)Positivehomogeneity:ρ(hX)=hρ(X)forh0Translationalinvariance:ρ(X+n)=ρ(X)–nforsomecertainamountn.VaRisnotcoherentasitisnotsubadditive,thereforeB,Disnotcorrect.ESistheaverageoftheworst100(1–α%)oflosses.ESiscoherent,thereforeCiscorrect,Aisnotcorrect.14.Answer:BVolumeisdefinedasthetotalofpurchasesorsalesduringatradingsession,notthetotalofpurchasesandsalescombined.Openinterestrepresentsatabulationofthetotalnumberoffuturescontractsinamarketthatremain“open”attheendofatradingsession,thatis,thosecontractsnotyetliquidatedeitherbyanoffsettingfuturesmarkettransactionorbydelivery.15.Answer:C5TBA(ToBeAnnounced)marketisaforwardmarketwithadeliveryoption.Justasinthecaseofthedeliveryoptioninnoteandbondfutures,theTBAsellerwillpickthecheapest-to-deliver(CTD)pool,thatis,thepoolthatisworththeleastsubjecttotheissuer,maturity,andcouponrequirements.16.Answer:DGiventhatthereturnsonthemarketindexaregreaterthanrisk-freerate,wecanconclude:E(RM)RF.E(RM)–RF0iiFiMFi,MMσERRβERR,βρσ17.Answer:DValuationandRiskModels:“PrinciplesforSoundStressTestingPracticesandSupervision”18.Answer:B62446250PX6C0.010.992.75%19.Answer:A0.045HedgeRatio0.90.810.051900N0.817720Sincethemanufacturerexpectstopurchaseinthreemonths,theyshouldbuythefuturescontracts.20.A