2025年FRM考試備考資料考試時間：______分鐘總分：______分姓名：______PartI1.Describethefundamentaldifferencebetweensystematicriskandunsystematicriskinthecontextofinvestmentportfolios.Explainhowdiversificationaffectstheoverallriskprofileofaportfolio.2.Aportfolioconsistsoftwoassets,AandB.AssetAhasanexpectedreturnof12%andastandarddeviationof18%.AssetBhasanexpectedreturnof8%andastandarddeviationof10%.ThecorrelationcoefficientbetweenthereturnsofassetsAandBis0.4.TheweightsofassetsAandBintheportfolioare60%and40%,respectively.Calculatetheexpectedreturnandthestandarddeviationoftheportfolio.3.ExplaintheconceptofValueatRisk(VaR).DescribethelimitationsofVaRasariskmeasureanddiscusstwoalternativeriskmeasuresthatcanprovideadditionalinsights.4.Abankisrequiredtoholdacapitalbuffertocoverpotentiallosses.ExplaintheconceptoftheBaselIIIcapitaladequacyframework.DescribethetwomaincomponentsofregulatorycapitalunderBaselIIIandtheirpurposes.5.Definetheterm"creditdefaultswap(CDS)".ExplainhowaCDScanbeusedforcreditriskmanagementanddescribethemainpartiesinvolvedinaCDStransaction.PartII6.DescribethekeyassumptionsoftheCapitalAssetPricingModel(CAPM).ExplainhowtheCAPMcanbeusedtoestimatetheexpectedreturnofanasset.DiscussonemajorcriticismoftheCAPM.7.Acompanyisevaluatinganewprojectwiththefollowingcashflows:Initialinvestmentof$1,000,000,cashinflowsof$300,000attheendofeachyearfor5years.Thecompany'scostofcapitalis10%.CalculatetheNetPresentValue(NPV)oftheproject.ShouldthecompanyaccepttheprojectbasedontheNPVcriterion?8.Explainthedifferencebetweenaforwardcontractandafuturescontract.Describethemaincharacteristicsofeachcontractanddiscusstheroleofmarking-to-marketinfuturestrading.9.Aportfoliomanagerusesafactormodeltoexplainthereturnsofastock.Themodelis:R_i=R_f+β_g*(R_m-R_f)+ε_i,whereR_iisthereturnofstocki,R_fistherisk-freerate,R_misthereturnofthemarketportfolio,β_gisthestock'ssensitivitytothemarketfactor,andε_iistheerrorterm.Explainthemeaningofeachcomponentinthemodel.Whatistheexpectedreturnofstockiiftherisk-freerateis2%,themarketreturnis10%,andβ_gis1.2?10.Discussthemainsourcesofoperationalriskinafinancialinstitution.Describetwodifferentmethodsusedtomeasureoperationalriskcapital.Explainthechallengesinmeasuringoperationalrisk.11.Explaintheconceptofliquidityrisk.Describetwotypesofliquidityriskthatabankmayface.Howcanbanksmanagetheirliquidityriskexposure?12.Acompanyhasabondoutstandingwithafacevalueof$1,000,acouponrateof5%,and5yearstomaturity.Themarketinterestrateforsimilarbondsis6%.Calculatethecurrentpriceofthebondusingthepresentvalueformula.Whatwillhappentothepriceofthebondifthemarketinterestratedecreasesto4%?13.Discusstheroleofregulatoryoversightinpromotingfinancialstability.Provideanexampleofaregulatoryrequirementthataimstoenhancethestabilityofthefinancialsystem.14.ExplainhowMonteCarlosimulationcanbeusedtoestimatetheValueatRisk(VaR)foraportfolioofassets.DescribethemainstepsinvolvedinimplementingaMonteCarloVaRsimulation.15.Afinancialinstitutionusesaninternalrating-based(IRB)approachtocalculatecreditriskcapital.TheinstitutionestimatestheProbabilityofDefault(PD)foraspecificloantobe3%,theLossGivenDefault(LGD)tobe50%,andtheExposureatDefault(EAD)tobe$1,000,000.CalculatetheExpectedCreditLoss(ECL)forthisloan.試卷答案PartI1.Systematicrisk,alsoknownasmarketrisk,affectsallassetsinthemarketandcannotbeeliminatedthroughdiversification.Itiscausedbyfactorssuchaseconomicrecessions,politicalevents,andchangesininterestrates.Unsystematicrisk,alsoknownasspecificoridiosyncraticrisk,isuniquetoindividualassetsorindustriesandcanbereducedthroughdiversification.Bycombiningassetsthatarenotperfectlycorrelated,theoverallvolatilityofaportfoliocanbelowered.Diversificationsmoothsoutthereturnsofaportfoliobyoffsettinglossesinsomeassetswithgainsinothers,thusreducingtheimpactofunsystematicrisk.2.ExpectedReturn(E(Rp))=w_A*E(R_A)+w_B*E(R_B)=0.60*12%+0.40*8%=7.2%+3.2%=10.4%.Variance(σ_p^2)=w_A^2*σ_A^2+w_B^2*σ_B^2+2*w_A*w_B*σ_A*σ_B*ρ_{AB}=(0.60)^2*(0.18)^2+(0.40)^2*(0.10)^2+2*0.60*0.40*0.18*0.10*0.4=0.4056*0.0324+0.16*0.01+2*0.60*0.40*0.18*0.10*0.4=0.01308424+0.0016+0.003168=0.01785224StandardDeviation(σ_p)=sqrt(0.01785224)≈0.1336or13.36%.3.VaRisastatisticalmeasurethatquantifiesthepotentiallossinvalueofaportfoliooveradefinedperiodforagivenconfidenceinterval.Forexample,a1-day95%VaRof$1millionmeansthatthereisa95%probabilitythattheportfoliowillnotlosemorethan$1millionoverthenextday.LimitationsofVaRinclude:itdoesnotmeasurethemagnitudeoflossesbeyondtheVaRthreshold(tailrisk),itassumesnormaldistributionofreturns(whichmaynotholdinreality),anditcanbemanipulatedbychoosingappropriatetimehorizonsandconfidencelevels.Twoalternativeriskmeasuresare:ConditionalValueatRisk(CVaR),whichestimatestheexpectedlossgiventhatalossexceedstheVaRthreshold,providingabettermeasureoftailrisk;andExpectedShortfall(ES),whichisessentiallythesameasCVaRandisnowtheregulatorystandardforoperationalriskinEurope.4.TheBaselIIIcapitaladequacyframeworkisasetofregulationsestablishedbytheBaselCommitteeonBankingSupervisiontoenhancethestabilityofthebankingsectorbyincreasingcapitalrequirementsandimprovingriskmanagementpractices.ThetwomaincomponentsofregulatorycapitalunderBaselIIIare:CommonEquityTier1(CET1)capital,whichincludescommonstockandretainedearnings,representingthehighestqualitycapital;andTier1capital,whichalsoincludessubordinateddebtwithalongmaturityandhighlossabsorbency.CET1capitalispreferredbyregulatorsduetoitshigherqualityandissubjecttostricterrequirementsregardingitsminimumamountandcomposition.5.ACreditDefaultSwap(CDS)isafinancialderivativecontractthatprovidesprotectionagainstthedefaultofadebtobligation,suchasabondorloan.Thecontractinvolvesthreemainparties:theprotectionbuyer,whopaysapremiumtotheprotectionsellerinexchangeforprotectionagainstdefault;theprotectionseller,whoreceivesthepremiumandagreestocompensatethebuyerforlossesresultingfromacreditevent(suchasdefaultorbankruptcy);andthereferenceentity,whichistheentitywhosecreditworthinessisbeinginsured.TheCDScanbeusedforcreditriskmanagementbyallowinginvestorstotransfercreditrisk,hedgeexistingpositions,orspeculateonthecreditqualityofthereferenceentity.PartII6.TheCapitalAssetPricingModel(CAPM)isatheoreticalmodelthatdescribestherelationshipbetweensystematicriskandexpectedreturnforassets,particularlystocks.ThekeyassumptionsoftheCAPMinclude:investorsarerationalandrisk-averse,marketsareefficient,therearenotransactioncostsortaxes,allinvestorshavethesametimehorizonandriskpreferences,andallinvestorshaveaccesstothesameinformation.TheCAPMcanbeusedtoestimatetheexpectedreturnofanassetusingtheformula:E(R_i)=R_f+β_i*(E(R_m)-R_f),whereE(R_i)istheexpectedreturnoftheasset,R_fistherisk-freerate,β_iistheasset'sbetacoefficient,andE(R_m)istheexpectedreturnofthemarketportfolio.AmajorcriticismoftheCAPMisitsunrealisticassumptions,suchasmarketefficiencyandidenticalinvestorpreferences,whichmaynotholdinreal-worldmarkets.7.NPV=-InitialInvestment+Σ[CashInflow/(1+r)^t],whereristhediscountrateandtisthetimeperiod.NPV=-$1,000,000+$300,000/(1+0.10)^1+$300,000/(1+0.10)^2+$300,000/(1+0.10)^3+$300,000/(1+0.10)^4+$300,000/(1+0.10)^5NPV=-$1,000,000+$300,000/1.10+$300,000/1.21+$300,000/1.331+$300,000/1.4641+$300,000/1.61051NPV=-$1,000,000+$272,727.27+$247,933.88+$226,978.99+$204,904.05+$186,276.40NPV=-$1,000,000+$1,138,911.59NPV≈$138,911.59.SincetheNPVispositive,thecompanyshouldaccepttheprojectbasedontheNPVcriterion,asitisexpectedtoaddvaluetothecompany.8.Aforwardcontractisacustomized,privateagreementbetweentwopartiestobuyorsellanassetatapredeterminedpriceonafuturedate.Itisnottradedonanexchangeandissubjecttocounterpartyrisk.Afuturescontractisastandardized,exchange-tradedcontractthatobligatesthebuyertopurchaseandthesellertosellanassetatapredeterminedpriceonafuturedate.Futurescontractshavestandardizedterms,aremarked-to-marketdaily,andrequireinitialandvariationmargindeposits.Themaindifferenceliesintheircustomization(forwardvs.standardized),tradingvenue(OTCvs.exchange),andriskmanagementfeatures(counterpartyriskvs.clearinghouseguaranteeanddailymarking-to-market).9.InthefactormodelR_i=R_f+β_g*(R_m-R_f)+ε_i:R_iisthereturnofstocki,representingtheactualreturnofthestock.R_fistherisk-freerate,representingthereturnonaninvestmentwithzerorisk.R_misthereturnofthemarketportfolio,representingthereturnoftheoverallmarket.β_gisthestock'ssensitivitytothemarketfactor,alsoknownasthestock'sbeta,measuringhowmuchthestock'sreturnreactstochangesinthemarketreturn.ε_iistheerrorterm,representingtheportionofthestock'sreturnthatcannotbeexplainedbythemarketfactorandisduetootherfactorsorrandomevents.TheexpectedreturnofstockiiscalculatedasE(R_i)=R_f+β_g*E(R_m-R_f).IfR_fis2%,R_mis10%,andβ_gis1.2,thenE(R_i)=2%+1.2*(10%-2%)=2%+1.2*8%=2%+9.6%=11.6%.10.Operationalriskreferstotheriskoflossresultingfrominadequateorfailedinternalprocesses,people,systems,orfromexternalevents.Mainsourcesofoperationalriskinclude:humanerror(e.g.,mistakesbyemployees),systemfailures(e.g.,IToutages),fraud(e.g.,internalorexternaltheft),externalevents(e.g.,naturaldisasters,terroristattacks),andlegalandcomplianceissues.Twodifferentmethodsusedtomeasureoperationalriskcapitalare:BasicIndicatorMethod(BIM),whichcalculatesoperationalriskcapitalasapercentageoftheinstitution'stotaloperationalincome,andAdvancedMeasurementApproach(AMA),whichallowsinstitutionstousemoresophisticatedmodels(e.g.,InternalMeasurementofExpectedLosses-IMEL,andInternalMeasurementofUnexpectedLosses-IMUL)tocalculateoperationalriskcapitalbasedontheirspecificoperationalriskprofile.Challengesinmeasuringoperationalriskincludethedifficultyinidentifyingandquantifyingallpotentialoperationalriskevents,thelackofhistoricaldataforcertaintypesofrisks,andthecomplexityofmodelinginterdependenciesbetweendifferentoperationalrisksources.11.Liquidityriskistheriskthatafinancialinstitutionwillbeunabletomeetitsfinancialobligationsastheyfalldue,eitherbecauseitcannotexititsinvestmentsatareasonablepriceorbecauseitdoesnothavesufficientliquidassets.Twotypesofliquidityriskare:Fundingliquidityrisk,whichistheriskthattheinstitutionwillnothavesufficientfundstomeetitsshort-termobligations,suchascustomerwithdrawalsorinterbankborrowings;andMarketliquidityrisk,whichistheriskthattheinstitutionwillnotbeabletosellassetsquicklyenoughatafairmarketprice,potentiallyleadingtosignificantlosses.Banksmanagetheirliquidityriskexposurethroughvariousstrategies,includingholdingsufficientlevelsofliquidassets(e.g.,cash,governmentbonds),maintainingaccesstofundingsources(e.g.,interbankmarkets,centralbankfacilities),implementingrobustliquidityriskmanagementframeworks,conductingregularliquiditystresstests,andsettingliquidityrisklimitsandtriggers.12.CurrentPriceoftheBond=Σ[CouponPayment/(1+r)^t]+FaceValue/(1+r)^n,whereristhemarketinterestrate,tisthetimeperiod,nisthenumberofyearstomaturity,andCouponPayment=FaceValue*CouponRate.CouponPayment=$1,000*5%=$50.Price=$50/(1+0.06)^1+$50/(1+0.06)^2+$50/(1+0.06)^3+$50/(1+0.06)^4+$50/(1+0.06)^5+$1,000/(1+0.06)^5Price=$50/1.06+$50/1.1236+$50/1.1910+$50/1.2625+$50/1.3382+$1,000/1.3382Price=$47.17+$44.50+$41.98+$39.60+$37.36+$747.26Price≈$1,068.87.Ifthemarketinterestratedecreasesto4%,thepriceofthebondwillincrease.Price=$50/(1+0.04)^1+$50/(1+0.04)^2+$50/(1+0.04)^3+$50/(1+0.04)^4+$50/(1+0.04)^5+$1,000/(1+0.04)^5Price=$50/1.04+$50/1.0816+$50/1.1249+$50/1.1704+$50/1.2167+$1,000/1.2167Price=$47.62+$46.25+$44.45+$42.74+$41.09+$821.93Price≈$1,193.08.Thepriceincreasesfromapproximately$1,068.87to$1,193.08asthemarketinterestratedecreasesfrom6%to4%.13.Regulatoryoversightplaysacrucialroleinpromotingfinancialstabilitybyestablishingrulesandregulationsthataimtopreventsystemicrisks,ensurethesolvencyandliquidityoffinancialinstitutions,andprotectconsumers.AnexampleofaregulatoryrequirementthataimstoenhancethestabilityofthefinancialsystemistheimplementationofBaselIIIcapitaladequacystandards.BaselIIIrequiresbankstoholdhigherlevelsofcapital,particularlycommonequityTier1(CET1)capital,whichisthem