2025年FRM二级真题汇编

2025年FRM二级真题汇编考试时间：______分钟总分：______分姓名：______第一部分金融市场与产品1.Considerastockportfolioconsistingofthreeassets:AssetAwithabetaof1.2,AssetBwithabetaof0.8,andAssetCwithabetaof1.5.Theportfolioweightsare40%inAssetA,35%inAssetB,and25%inAssetC.Iftherisk-freerateis2%andtheexpectedmarketreturnis8%,calculatetheexpectedreturnoftheportfoliousingtheCapitalAssetPricingModel(CAPM).Pleaseshowyourcalculationsclearly.2.Acorporatebondhasafacevalueof$1,000,acouponrateof5%paidsemi-annually,and7yearstomaturity.Thebondiscurrentlytradingatapriceof$980.Whatistheyieldtomaturity(YTM)ofthebond?Youmayuseapproximationmethodsifnecessary,butjustifyyourapproach.3.Describethekeydifferencesbetweenaforwardcontractandafuturescontract.Inyouranswer,coveraspectssuchasstandardization,clearingmechanism,marking-to-market,andpotentialfordefault.4.AninvestorbuysacalloptiononStockXwithastrikepriceof$50andapremiumof$3.Thestockcurrentlytradesat$48.TheinvestoralsobuysaputoptiononStockXwithastrikepriceof$45andapremiumof$2.Calculatethemaximumlossandthebreak-evenpointforthisstraddlestrategy.Explainthepotentialprofitandtheunderlyingstrategy.第二部分风险度量与管理5.Abankcalculatesa1-day99%confidencelevelValueatRisk(VaR)foritstradingportfoliotobe$5million.Theportfoliomanagerbelievesthatthetrue10-dayVaRisapproximatelythe1-dayVaRmultipliedbythesquarerootof10.However,themanagerisconcernedaboutthepotentialfortailriskandestimatesthetaillosscoefficient(K)tobe2.5(i.e.,the99.9%confidencelevel).Usingthebank's1-dayVaRestimate,calculatethe10-dayVaRincorporatingthetaillosscoefficient.Discusstheassumptionsandlimitationsofthiscalculation.6.Explaintheconceptofbeta(β)inthecontextofmarketrisk.Howisbetausedbyportfoliomanagersforriskassessmentandassetallocation?Discussthelimitationsofusingbetaasasolemeasureofrisk.7.Aportfolioconsistsofthefollowingpositions:*100sharesofStockY,price$60,beta1.1*500sharesofStockZ,price$40,beta0.9*Shortpositionof200sharesofStockW,price$25,beta1.3Therisk-freerateis1.5%.Theexpectedreturnsforthemarketare10%.Calculatetheportfolio'sbetaanditsexpectedreturnaccordingtotheCAPM.8.Describethemaincomponentsofacomprehensiveriskmanagementframeworkforafinancialinstitution.Discusstheroleofriskappetite,risklimits,andriskreportingwithinthisframework.第三部分信用风险9.ExplainthedifferencebetweenProbabilityofDefault(PD),LossGivenDefault(LGD),andExposureatDefault(EAD)inthecontextofcreditrisk.HowarethesethreeparametersusedtocalculateExpectedCreditLosses(ECL)?10.AcompanyhasaPDof2%,anLGDof40%,andanEADequalto100%oftheoutstandingloanbalance.Theaverageoutstandingloanbalanceforthiscompanyis$50million.CalculatetheExpectedCreditLoss(ECL)forthisportfoliosegment.11.Discussthekeyassumptionsandlimitationsofthestandardcreditriskmodels(e.g.,internalratings-basedmodels)usedbybanks.Whyareback-testingproceduresimportantforthesemodels?12.WhatisaCreditDefaultSwap(CDS)?ExplaintherolesoftheProtectionBuyer,ProtectionSeller,andtheCreditReferenceEntity(CREF)inaCDStransaction.DiscussthemainusesofCDSandthetypesofcreditriskitcantransfer.第四部分操作风险13.DefineoperationalriskaspertheBaselAccords.Provideexamplesofdifferenttypesofoperationalrisksthatafinancialinstitutionmightface.14.Explainthedifferencebetweenlossdatacollection(LOCC)andlosseventanalysis.Howdoeslossdatacontributetooperationalriskmanagementandcapitalcalculation?15.Discusstheroleofinternalcontrolsinmitigatingoperationalrisk.Provideexamplesofeffectiveinternalcontrolsindifferentareasofabank(e.g.,tradeprocessing,fraudprevention).16.AbankisassessingitsoperationalriskcapitalbasedontheBasicIndicatorMethod(BIM).Thetotalrevenuegeneratedbythebankoverthepreviousthreeyears(includinginterestincome,feeandcommissionincome)is$10billion.CalculatetheoperationalriskcapitalrequiredundertheBIM,assumingariskfactorof15%.第五部分流动性风险与压力测试17.ExplaintheconceptofLiquidityCoverageRatio(LCR).WhatassetsareincludedintheHigh-QualityLiquidAssets(HQLA)basket,andwhatistheminimumrequiredLCRratioaccordingtoBaselIII?18.Describethedifferencebetweenstaticanddynamicliquiditystresstesting.Whatarethekeyconsiderationswhendesigningadynamicliquiditystresstestforabank?19.Abank'scurrentLevel1liquidityassetsamountto$200billion.ItsNetStableFundingRatio(NSFR)is95%,anditsrequiredNSFRratiois100%.Ifthebank'stotalexposuretouncentralizedcounterpartiesis$300billion,calculateitsNSFR.DiscussthesignificanceoftheNSFRratio.20.Abankexperiencesasuddenwithdrawalofdepositsduetomarketpanic.Itscurrentassetsare$800billion,ofwhich$200billionareconsideredhighlyliquid(meetingLCRrequirements).Itstotalliabilitiesare$900billion,including$500billionofshort-termwholesalefunding.Thebankneedstomeeta30-dayliquidityrequirementof$400billion.Evaluatethebank'sliquiditypositionbasedontheLCRandNSFRconcepts,anddiscusspotentialmeasuresthebankcouldtake.第六部分道德与专业准则21.Ariskmanagerdiscoversthatacolleaguehasbeenmanipulatingriskreportstopresentamorefavorablepictureofthebank'sriskprofile,potentiallymisleadingseniormanagementandregulators.Discusstheethicaldilemmafacedbytheriskmanager.WhataretheprofessionalobligationsoftheriskmanageraccordingtotheGARPCodeofConduct,andwhatstepsshouldthemanagertake?22.Explaintheimportanceoftransparencyanddisclosureinriskmanagementpractices.Provideexamplesofhowtransparencycanbenefitafinancialinstitutionanditsstakeholders.23.Describetheconceptof"conflictofinterest"inthecontextofariskmanagementfunction.Howcanfinancialinstitutionsmanageconflictsofinteresttoensureobjectiveriskassessmentanddecision-making?24.Aportfoliomanagerisconsideringtakingonasecondjobthatcouldpotentiallyinvolvemanaginginvestmentsforacompetitor.Discusswhetherthissituationcreatesaconflictofinterest,andexplaintherelevantethicalconsiderationsbasedonprofessionalconductstandards.试卷答案第一部分金融市场与产品1.计算过程：*资产A贡献的预期回报=40%*(8%-2%)=0.4*6%=2.4%*资产B贡献的预期回报=35%*(8%-2%)=0.35*6%=2.1%*资产C贡献的预期回报=25%*(8%-2%)=0.25*6%=1.5%*投资组合预期回报=2.4%+2.1%+1.5%=6.0%*或者，使用加权平均贝塔：*投资组合贝塔=(1.2*0.4)+(0.8*0.35)+(1.5*0.25)=0.48+0.28+0.375=1.135*投资组合预期回报=无风险率+投资组合贝塔*(市场预期回报-无风险率)*投资组合预期回报=2%+1.135*(8%-2%)=2%+1.135*6%=2%+6.81%=8.81%2.计算过程(近似法)：*平均债券收益率=(面值-当前价格+年利息总和)/[(面值+当前价格)/2*剩余年数]*年利息总和=$1,000*5%*2=$50(半年付一次)*近似年收益率=($1,000-$980+$50)/[($1,000+$980)/2*7]=$70/($9980/2*7)=$70/($4990*7)=$70/$34,930≈0.001997or0.1997%*半年收益率≈0.1997%/2=0.09985%*年收益率(近似)≈0.09985%*2=0.1997%or19.97%(Note:Thisisaroughapproximation;afinancialcalculatororiterativemethodwouldyield5.07%exactly.Thepromptallowsapproximation).3.关键区别：*标准化：Futuresarestandardizedandtradedonexchanges;forwardsarecustomizedandtradedover-the-counter(OTC).*清算机制：Futureshaveaclearinghousethatguaranteescontracts;forwardsinvolvecounterpartycreditriskbetweenthetwoparties.*保证金与盯市：Futuresrequireinitialandmaintenancemarginswithdailymarking-to-market;forwardstypicallyhavenoinitialmarginrequirementandaresettledonlyatmaturity.*违约风险：Futureshavelowercounterpartyriskduetotheclearinghouse;forwardshavehighercounterpartyrisk(riskofdefaultbythecounterparty).4.计算：*最大损失=(最低股价-最低执行价)*头寸数量+(执行价+支付的期权金)*头寸数量*最低股价=$45(putstrike-putpremium=$45-$2=$43)*最大损失=($43-$45)*1+($50+$3)*1=-$2+$53=$51(ifstockgoesto$45orlower)*或者，考虑更可能的最低价$45(putstrike)，损失来自put金：$2*更正思路：Thestraddleinvolvesbuyingbothacallandaputwiththesamestrike($50)andexpiration.Themaximumlossoccursifthestockpriceisexactlyatthestrikepriceatexpiration,makingbothoptionsworthless.*MaximumLoss=CostofCall+CostofPut=$3+$2=$5pershare.*Break-evenpoints:*Above:StrikePrice+TotalPremium=$50+$5=$55*Below:StrikePrice-TotalPremium=$50-$5=$45*PotentialProfit:Theoreticallyunlimitedprofitabove$55andunlimitedprofitbelow$45(minusthetotalpremiumpaid).Profit=StockPrice-StrikePrice-TotalPremium(ifprice>strike+premium)orStrikePrice-StockPrice-TotalPremium(ifprice<strike-premium).*Strategy:Astraddleisaneutralstrategy(regardingpricedirection)thatprofitsfromsignificantpricemovementineitherdirection,butincursahighpremiumcost.第二部分风险度量与管理5.计算：*1-day99%VaR=$5M*1-day99.9%VaR(K*1-day99%VaR)=2.5*$5M=$12.5M*10-dayVaR(usingsimplescaling)=1-day99.9%VaR*sqrt(10)=$12.5M*sqrt(10)≈$12.5M*3.162=$39.525M*解析思路：Thiscalculationassumesthatreturnsarenormallydistributedandindependentoverthedays.Itusesthe99.9%confidencelevelVaR(whichcorrespondstothe2.5standarddeviationstaillosscoefficientK)asthebasisfor10-dayVaR,scalingbythesquarerootoftime.ItincorporatesthetailriskcoefficientKdirectlyintothe1-dayVaRestimatebeforescaling.Limitationsincludemodelrisk(normalityassumption),taildependency(returnsmightbecorrelatedintails),andtheassumptionthatvolatilityscaleslinearlywithtime.6.概念与用途：*概念：Betameasuresthevolatilityofanassetorportfolioinrelationtotheoverallmarket(typicallyrepresentedbyamarketindex).Itquantifiesthesystematicrisk(marketrisk)ofaninvestment.*用途：*RiskAssessment:Abeta>1indicateshighervolatilitythanthemarket;beta<1indicateslowervolatility.Betahelpsassesstheriskcontributionofanassettoaportfolio.*AssetAllocation:Portfoliomanagersusebetatobalancetheoverallmarketriskexposureofaportfoliobycombiningassetswithdifferentbetas.*局限性：*Historicaldatareliance:Betaisbackward-lookingandmaynotpredictfutureperformance.*Linearrelationship:Betaassumesalinearrelationshipbetweenassetreturnsandmarketreturns,whichmaynothold.*Marketdefinition:Thechoiceofmarketindexaffectsthebetacalculation.*Timesensitivity:Betacanchangeovertime.*Ignoresidiosyncraticrisk:Betaonlymeasuresmarketrisk,notunsystematicriskspecifictotheasset.7.计算：*PortfolioBeta:*Beta(Portfolio)=(W_A*Beta_A)+(W_B*Beta_B)+(W_C*Beta_C)*Beta(Portfolio)=(0.40*1.1)+(0.35*0.9)+(0.25*-1.3)*Beta(Portfolio)=0.44+0.315-0.325=0.43*PortfolioExpectedReturn(usingCAPM):*E(R_P)=R_f+Beta(P)*[E(R_M)-R_f]*E(R_P)=1.5%+0.43*(10%-1.5%)*E(R_P)=1.5%+0.43*8.5%*E(R_P)=1.5%+3.655%*E(R_P)=5.155%8.风险管理框架组成：*组成部分：Riskgovernance(roles,responsibilities),riskmanagementpoliciesandprocedures,riskidentificationandassessment,riskmitigationstrategies(hedging,control),riskmonitoringandreporting,riskculture,riskappetiteandlimits.*角色：*风险偏好(RiskAppetite):Definesthelevelandtypeofrisktheinstitutioniswillingtotaketoachieveitsobjectives,oftenexpressedqualitativelyorquantitativelyfordifferentrisktypes.*风险限额(RiskLimits):Specificnumericalconstraintsonexposuresorriskmeasures(e.g.,VaRlimit,creditconcentrationlimit)derivedfromtheriskappetite,usedtocontrolrisk-taking.*风险报告(RiskReporting):Communicatesriskexposures,limitsbreaches,losses,andemergingriskstomanagementandtheboard,providingtransparencyandsupportingdecision-making.第三部分信用风险9.定义与关系：*PD:ProbabilityofDefault-Thelikelihoodthataborrowerwillfailtomeettheircontractualobligations(e.g.,defaultonaloan).*LGD:LossGivenDefault-Thefractionofaloan'sexposurethatislostiftheborrowerdefaults.Itdependsonrecoveryefforts.*EAD:ExposureatDefault-Thetotalamountofcreditexposureassociatedwithasingleborroweratthetimeofdefault.Itcanbethefulloutstandingbalanceorafractionifcollateralexists.*关系：ECL=PD*LGD*EAD.Theseparameterstogetherquantifytheexpectedfinancialimpactofdefaults.10.计算：*ECL=PD*LGD*EAD*ECL=2%*40%*$50,000,000*ECL=0.02*0.40*$50,000,000*ECL=0.008*$50,000,000=$400,00011.模型假设与局限：*假设：Standardmodels(IBMs)oftenassumenormalityofdefaultprobabilities,correlationbetweenratings,andlinearlossgivendefault.Theyrelyonsignificantinternaldata.*局限：*Modelrisk:Assumptionsmaybeviolated(e.g.,extremeevents,ratingmigrationdifficulties).*Dataquality:Relianceoninternaldatacanbesubjectiveorinsufficient.*Ratingaccuracy:Internalratingsmaynotperfectlypredictactualdefaults.*Complexity:Modelscanbecomplexanddifficulttoimplementandunderstand.*回溯测试(Back-testing):Importantforvalidatingmodelaccuracy.Itcomparesmodel-predictedlossesagainstactuallossesoveraperiod.Ithelpsassessmodelperformance,identifyflaws,calibrateparameters,andensurethemodel'spredictivepowerandcompliancewithregulatoryrequirements.12.CDS定义与角色：*定义：ACreditDefaultSwap(CDS)isafinancialderivativecontractthatprovidesprotectionagainstthedefaultofadebtobligation(thereferenceentity).Oneparty(buyer)paysapremiumtotheotherparty(seller)inexchangeforcompensationiftheCDSreferenceentitydefaults.*角色：*保护买方(ProtectionBuyer):Theentityseekinginsuranceagainstthedefaultofthereferenceentity.Theypaythepremium.*保护卖方(ProtectionSeller):Theentityprovidingthedefaultinsurance.Theyreceivethepremiumandpaythebuyerifadefaultoccurs.*参考实体(CREF-CreditReferenceEntity):TheentitywhosedebtisbeinginsuredbytheCDS.*用途：Creditrisktransfer(shiftingdefaultrisk),hedgingexistingexposures,speculatingoncreditevents,facilitatingtrading.*类型：Single-nameCDS(protectingoneentity),IndexCDS(protectingabasketofentities).第四部分操作风险13.定义与类型：*定义(巴塞尔)：Operationalriskistheriskoflossresultingfrominadequateorfailedinternalprocesses,people,systems,orfromexternalevents.(AsperBaselAccords,specificallyBCBS239).*类型：Internalfraud,externalfraud,systemfailures,businessdisruptionevents(naturaldisasters,poweroutages),humanerror,processfailures,transactionprocessingerrors,legalrisks(breachesoflaw),reputationalrisk(oftenaconsequence).14.LOCC与损失事件分析：*损失数据收集(LOCC-LossDataCollection):Thesystematicprocessofcollecting,validating,andmaintaininginternallossdatarelatedtooperationalincidentsthatresultedinafinancialloss.It'saboutcapturingthe*data*.*损失事件分析(LossEventAnalysis):Theprocessofinvestigatingspecificoperationallosseventstounderstandtherootcauses,determinethelossamount,assesstheadequacyofcontrols,andidentifyopportunitiesforimprovement.It'saboutanalyzingthe*events*.*贡献：Lossdata(collectedviaLOCC)isessentialforcalculatingregulatoryoperationalriskcapital(AdvancedMeasurementApproaches-AMAs),understandinglosspatterns,identifyingkeylossdrivers,informingriskmanagementstrategies,andimprovingcontrols.15.内部控制作用与示例：*作用：Internalcontrolsarepoliciesandproceduresdesignedtoprovidereasonableassuranceregardingthereliabilityoffinancialreporting,theeffectivenessandefficiencyofoperations,andcompliancewithapplicablelawsandregulations.Theyhelpmitigateoperationalriskbypreventingerrors,fraud,anddisruptions.*示例：*贸易处理：Automatedreconciliationbetweentradeentriesandsettlements,segregationofduties(e.g.,tradingexecutionvs.posting),approvalworkflowsforlargetrades.*欺诈预防：Transactionmonitoringsystemsforunusualpatterns,backgroundchecksforemployees,clearpoliciesforhandlingsuspiciousactivity.16.BIM计算：*OperationalRiskCapital(BIM)=15%*TotalRevenue(3-yearaverage)*TotalRevenue=$10billion*OperationalRiskCapital=15%*$10,000,000,000=$1,500,000,000第五部分流动性风险与压力测试17.LCR定义与要求：*定义：TheLiquidityCoverageRatio(LCR)measuresabank'sabilitytomeetitsshort-termliquidityneedsduringperiodsofmarketstressbyholdinghighlyliquidassets.ItensuressufficientHigh-QualityLiquidAssets(HQLA)tocoveroutflowsovera30-dayperiod.*HQLA资产：Cash,centralbankreserves,governmentbonds(domesticandforeign)withhighcreditqualityandshortmaturity(<1year),high-qualitycorporatebondsmeetingspecificcriteria.*要求：TheminimumLCRratiomandatedbyBaselIIIistypically100%.18.静态与动态压力测试：*静态压力测试：Assumesthatthebank'sbalancesheetstructure(assets,liabilities,flows)remainsfixedduringthestressperiod,exceptfortheshockapplied(e.g.,apercentagedropinassetvaluesorincreaseinfundingcosts).Simplerbutlessrealisticasitignoresinternaladjustments.*动态压力测试：Simulateshowthebank'sbalancesheetevolvesovertimeduringastressscenario.Considersinternalresponseslikeassetsales,liabilitymanagement(e.g.,accessingcentralbankfacilities,issuebonds),depositoutflows,andfundingadjustments.Morecomplexbutprovidesamorerealisticassessmentofliquidityresilienceandmanagementactions.19.NSFR计算：*NSFR=(AvailableStableFunding/RequiredStableFunding)*100%*AvailableStableFunding=Level1LiquidityAssets+NSFR*(TotalExposuretoUncentralizedCounterparties)*$200billion+NSFR*$300billion*NSFR=[$200billion+NSFR*$300billion]/(NSFR*$300billion)*100%*NSFR=$200/NSFR*$300+$300*NSFR=$60/NSFR+$300*NSFR^2=$60+$300*NSFR*NSFR^2-300*NSFR-$60=0*SolvingthisquadraticequationforNSFR(usingquadraticformulaorcalculator,ensuringpositivesolution):*NSFR≈0.199or199%*TheNSFRratioisapproximately199%.Therequiredratiois100%.20.流动性评估与措施：*评估：*LCR:HQLA=$200billion.RequiredLCR=100%*$400billion(30-dayneed)=$400billion.CurrentHQLA($200B)isfarbelowtherequirement.ThebankhasasevereliquidityshortfallbasedonLCR.*NSFR:AvailableStableFunding=$200B+199%*$300B≈$200B+$597B=$797B.RequiredStableFunding=100%*$900B=$900B.NSFRisbelow100%(approx88.5%),indicatingpotentialfutureliquiditystrain.*措施：Thebankurgentlyneedstoincreaseitshighlyliquidassets(e.g.,sellotherassets,borrowfromcentralbank),securestablefunding(e.g.,issuelong-termdebt,entercentralbankfacilities),manageliabilities(reduceshort-termwholesalefunding,potentiallyincreasecoredeposits),andimplementcontingencyfundingplans.第六部分道德与专业准则21.伦理困境与步骤：*困境：Theriskmanagerfacesaconflictbetweenpersonalintegrity/ethicsandpotentialjobsecurityorloyaltytothecolleague.Reportingcouldleadtonegativeconsequencesforthecolleagueandpotentiallythemanager.Notreportingcompromisesethicalstandardsandpotentiallyallowssignificantrisktotheinstitution.*义务与步骤(GARPCode):Themanagerhasadutytoacthonestlyandwithintegrity(Principle1),maintainprofessionalcompetence(Principle2),andupholdprofessionalstandards(Principle3).Steps:1.Verifytheinformationindependentlyifpossible.2.Reporttheissuetoadirectsupervisorif