2025年CFA考试专项练习

2025年CFA考试专项练习考试时间：______分钟总分：______分姓名：______试卷内容1.Aninvestorisconsideringaddingastocktotheirportfolio.Thestockhasanexpectedreturnof12%andastandarddeviationof20%.Theportfoliocurrentlyconsistsof10stockswithanexpectedreturnof10%andastandarddeviationof15%.Thecorrelationcoefficientbetweenthenewstockandtheexistingportfoliois0.3.Whatistheexpectedreturnandstandarddeviationoftheportfolioafteraddingthestock?2.Acompany'sstockiscurrentlytradingat$50pershare.Thecompanyisexpectedtopayadividendof$2persharenextyear,andtherequiredrateofreturnforthestockis10%.Usingtheconstantgrowthmodel,whatistheimpliedgrowthrateofdividends?3.Aportfoliomanagerisconstructingaportfoliousingtwoassets.AssetAhasanexpectedreturnof8%andastandarddeviationof10%.AssetBhasanexpectedreturnof12%andastandarddeviationof14%.Thecorrelationcoefficientbetweenthetwoassetsis0.4.Whatistheminimumpossiblestandarddeviationoftheportfolio?4.Thefollowingdatarepresentsthemonthlyreturnsoftwostocksoverthepastyear:StockA:5%,-2%,3%,7%,1%,-1%,4%,6%,0%,2%StockB:3%,1%,-3%,4%,2%,0%,5%,1%,-2%,3%CalculatetheSharperatioforeachstockiftherisk-freerateis1%permonth.5.Acompanyhasadebt-to-equityratioof0.6.Thecostofdebtis5%andthecostofequityis12%.Ifthecompany'staxrateis30%,whatistheweightedaveragecostofcapital(WACC)?6.Explainthedifferencebetweensystematicriskandunsystematicrisk.Provideanexampleofeach.7.Astockhasabetaof1.5.Themarketriskpremiumis8%.Iftherisk-freerateis2%,whatistheexpectedreturnofthestockaccordingtothecapitalassetpricingmodel(CAPM)?8.DescribetheEfficientMarketHypothesis(EMH).Whatarethethreeformsofmarketefficiency?9.Acompanyisconsideringinvestinginanewproject.Theprojectrequiresaninitialinvestmentof$1,000,000andisexpectedtogeneratecashflowsof$300,000peryearfor5years.Iftherequiredrateofreturnfortheprojectis10%,whatisthenetpresentvalue(NPV)oftheproject?10.Whatarethethreemaintypesofrisksassociatedwithfixedincomesecurities?Explaineachtypebriefly.11.Abondhasafacevalueof$1,000,acouponrateof5%,andamaturityof10years.Ifthemarketinterestrateis6%,whatisthepriceofthebond?12.Compareandcontrastthefeaturesofacalloptionandaputoption.13.Aninvestorisconsideringinvestinginamutualfundthatchargesa2%loadfeeandhasanexpenseratioof1.5%.Thefund'sportfolioiscurrentlyvaluedat$10million,andtheinvestorwantstoinvest$50,000.Howmuchofthe$50,000willactuallybeinvestedinthefund'sportfolioaftertheloadfeeisdeducted?14.Whataretheprimarydifferencesbetweenpassiveandactiveinvestmentmanagementstrategies?15.Explaintheconceptofarbitrage.Provideanexampleofapotentialarbitrageopportunityintheforeignexchangemarket.16.Acompanyisevaluatingtwodifferentprojects.ProjectAhasaninternalrateofreturn(IRR)of12%andapaybackperiodof3years.ProjectBhasanIRRof10%andapaybackperiodof2years.Ifthecompany'srequiredrateofreturnis8%,whichprojectshouldbeaccepted?Explainyourreasoning.17.Describethedifferentstagesoftheinvestmentlifecycle.Whatarethekeyactivitiesinvolvedineachstage?18.Whataretheprimaryresponsibilitiesofaportfoliomanager?19.Explaintheconceptofdiversification.Howdoesdiversificationhelpreduceportfoliorisk?20.Aportfolioconsistsofthreeassetswiththefollowingweightsandexpectedreturns:Asset1:40%,12%Asset2:30%,10%Asset3:30%,14%Whatistheexpectedreturnoftheportfolio?21.Acompany'sstockhasabetaof1.2.Themarketreturnisexpectedtobe10%nextyear,andtherisk-freerateis2%.UsingtheCapitalAssetPricingModel(CAPM),whatistherequiredreturnforthestock?22.Abondwithafacevalueof$1,000andacouponrateof6%paysinterestsemi-annually.Ifthebondhasamaturityof5yearsandthemarketinterestrateis5%,whatisthepriceofthebond?23.Aninvestorbuysacalloptionwithastrikepriceof$50forapremiumof$2.Thestockpriceatexpirationis$60.Whatistheinvestor'sprofitorloss?24.Whatisthedifferencebetweenaprimarymarketandasecondarymarket?25.Describetheroleoffinancialintermediariesinthefinancialsystem.试卷答案1.ExpectedReturn:(0.1*10%)+(0.9*12%)=10%+10.8%=20.8%StandardDeviation:sqrt[(0.1^2*15^2)+(0.9^2*20^2)+(2*0.1*0.9*15*20*0.3)]=sqrt[22.5+324+81]=sqrt[427.5]≈20.68%2.ImpliedGrowthRate(g):P0=D1/(ke-g)=>$50=$2/(0.10-g)=>0.10-g=0.04=>g=0.06or6%3.MinimumStandardDeviation:Useweightsthatminimizevariance.wA^2*σA^2+wB^2*σB^2+2*wA*wB*σA*σB*ρAB.Tominimize,setwA=σB^2/(σA^2+σB^2)andwB=σA^2/(σA^2+σB^2).wA=14^2/(10^2+14^2)=196/296≈0.6612.wB=10^2/(10^2+14^2)=100/296≈0.3388.MinSD=sqrt[(0.6612^2*10^2)+(0.3388^2*14^2)+(2*0.6612*0.3388*10*14*0.4)]=sqrt[44.0+16.2+39.9]=sqrt[100.1]≈10.00%4.StockA:*MeanReturn=(5-2+3+7+1-1+4+6+0+2)/10=23/10=2.3%*Variance=[(5-2.3)^2+(-2-2.3)^2+...+(2-2.3)^2]/10=29.61/10=2.961*SD=sqrt(2.961)≈1.721%*ExcessReturn=2.3%-1%=1.3%*SharpeRatio=1.3%/1.721%≈0.757StockB:*MeanReturn=(3+1-3+4+2+0+5+1-2+3)/10=13/10=1.3%*Variance=[(3-1.3)^2+(1-1.3)^2+...+(3-1.3)^2]/10=23.69/10=2.369*SD=sqrt(2.369)≈1.539%*ExcessReturn=1.3%-1%=0.3%*SharpeRatio=0.3%/1.539%≈0.1955.WACC=(E/V*Re)+(D/V*Rd*(1-Tc))*E/V=1/(1+0.6)=1/1.6=0.625*D/V=0.6/1.6=0.375*WACC=(0.625*12%)+(0.375*5%*(1-0.3))=7.5%+(0.375*5%*0.7)=7.5%+1.3125%=8.8125%6.SystematicRisk:Riskthataffectsallassetsinthemarket,causedbymacroeconomicfactors(e.g.,inflation,interestrates).Itcannotbediversifiedaway.Example:Asuddenincreaseininterestratesaffectstheentirestockmarket.UnsystematicRisk:Riskspecifictoanindividualcompanyorindustry.Itcanbereducedthroughdiversification.Example:Acompanyfacingaproductrecall.7.ExpectedReturn=Rf+Beta*(RM-Rf)*ExpectedReturn=2%+1.5*(8%)=2%+12%=14%8.EfficientMarketHypothesis(EMH):Thetheorythatfinancialmarketsareefficient,meaningthatassetpricesreflectallavailableinformation.Pricesadjustrapidlytonewinformation,makingitimpossibletoconsistentlyachievereturnsabovethemarketaveragewithouttakingonadditionalrisk.FormsofMarketEfficiency:*WeakForm:Pricereflectsallpasttradinginformation(pricemovementsarerandom).Technicalanalysiscannotconsistentlygenerateexcessreturns.*Semi-StrongForm:Pricereflectsallpubliclyavailableinformation(pastprices,financialstatements,news).Fundamentalanalysiscannotconsistentlygenerateexcessreturns.*StrongForm:Pricereflectsallinformation,bothpublicandprivate(insiderinformation).Noonecanconsistentlyachieveexcessreturns,evenwithinsideinformation.9.NPV=Σ[CFt/(1+r)^t]-InitialInvestment*NPV=[$300,000/(1+0.10)^1]+[$300,000/(1+0.10)^2]+...+[$300,000/(1+0.10)^5]-$1,000,000*NPV=$300,000*[1/(1.10)+1/(1.10)^2+...+1/(1.10)^5]*NPV=$300,000*[PVIFA(10%,5)]*PVIFA(10%,5)=[1-(1+0.10)^-5]/0.10=[1-0.62092]/0.10=0.37908/0.10=3.7908*NPV=$300,000*3.7908-$1,000,000=$1,137,240-$1,000,000=$137,24010.TypesofRisksassociatedwithFixedIncomeSecurities:*CreditRisk(DefaultRisk):Theriskthattheissuerwillfailtomaketimelyprincipalorinterestpayments.*InterestRateRisk:Theriskthatchangesinmarketinterestrateswillnegativelyaffectthebond'sprice.Bondpricesandyieldsmoveinversely.*ReinvestmentRisk:Theriskthatfuturecashflows(interestpaymentsorprincipalrepayment)willneedtobereinvestedatalowerratethantheoriginalinvestmentyield.11.Price=[C*(1-(1+r)^-n)]/r+F/(1+r)^n*Price=[($1,000*5%)*(1-(1+0.06)^-10)]/0.06+$1,000/(1+0.06)^10*Price=[$50*(1-0.55839)]/0.06+$1,000/1.79085*Price=[$50*0.44161]/0.06+$558.39*Price=$22.0805/0.06+$558.39=$368.01+$558.39=$926.4012.CallOption:Givestheholdertheright,butnottheobligation,tobuyanunderlyingassetataspecifiedstrikepricebeforeoronaspecifiedexpirationdate.Writerincursobligationtosell.PutOption:Givestheholdertheright,butnottheobligation,tosellanunderlyingassetataspecifiedstrikepricebeforeoronaspecifiedexpirationdate.Writerincursobligationtobuy.*Similarities:Botharederivatives,havestrikeprice,expirationdate,andinvolveanunderlyingasset.Bothderivetheirvaluefromthepriceoftheunderlying.*Differences:Callgivestherightto*buy*,Putgivestherightto*sell*.Callbuyerprofitsifunderlyingpricerises,Putbuyerprofitsifunderlyingpricefalls.13.LoadFee=$50,000*2%=$1,000AmountInvested=$50,000-$1,000=$49,00014.PassiveManagement:Aimstoreplicateamarketindexbyholdingthesamesecuritiesinthesameproportionsastheindex.Aimstomatchmarketreturn,lowcosts,lowturnover.Example:IndexmutualfundorETF.ActiveManagement:Aimstooutperformthemarketbenchmarkbyselectingspecificsecuritiesortimingmarketmovements.Requiresactiveresearch,highercosts,higherturnover.Example:Fundmanageractivelybuyingandsellingstocks.15.Arbitrage:Thesimultaneousbuyingandsellingofanassettoprofitfromapricedifferencebetweentwoormoremarketsorfromapricedifferencebetweentworelatedassets.Example:IfEUR/USDis$1.10inNewYorkand$1.12inLondon,simultaneouslybuyEURinNYandsellEURinLondon,lockingina$0.02profitperEUR(ignoringtransactioncosts).16.UsingIRR:ProjectA(12%)>RequiredRate(8%),ProjectB(10%)>RequiredRate(8%).BothprojectshavepositiveNPVbasedontheirIRRsbeinggreaterthantherequiredrate.Ifmutuallyexclusive,choosetheonewiththehigherIRR.Ifindependent,bothcanbeaccepted.UsingPaybackPeriod:PaybackPeriodmeasuresliquidity/earlyrecoveryofinvestment.Shorterisgenerallypreferred.ProjectB(2years)<ProjectA(3years).However,paybackperioddoesnotconsidercashflowsafterthepaybackperiodorthetimevalueofmoney.Decision:BasedonIRR(whichconsidersallcashflowsandtimevalueofmoney)andassumingtheprojectsareindependent,bothshouldbeaccepted.Iftheyaremutuallyexclusive,ProjectAischosenbasedonthehigherIRR.17.StagesoftheInvestmentLifeCycle:*InvestmentPlanning:Definingfinancialgoals,risktolerance,timehorizon,andestablishinganinvestmentpolicystatement.Gatheringinformation.*InvestmentImplementation:Selectingspecificinvestments(stocks,bonds,funds,etc.)basedontheinvestmentpolicystatementandconstructingtheportfolio.Executingtrades.*InvestmentMonitoring&Rebalancing:Periodicallyreviewingtheportfolio'sperformance,comparingittobenchmarks,assessingchangesintheinvestor'ssituationormarketconditions,andmakingadjustments(sellinghigh,buyinglow)tobringtheportfoliobackinlinewiththeoriginalassetallocationtargets.18.PrimaryResponsibilitiesofaPortfolioManager:*Settinginvestmentobjectivesandpoliciesbasedonclientneeds.*Conductingresearchandanalysisofmarkets,sectors,andindividualsecurities.*Constructingandmanagingtheinvestmentportfolio.*Monitoringportfolioperformanceagainstbenchmarks.*Revisingtheinvestmentstrategyasneeded.*Communicatingwithclients,providingreports,andexplaininginvestmentdecisions.*Adheringtoethicalstandardsandregulations.19.Diversification:Spreadinginvestmentsacrossvariousassetsthatarenotperfectlycorrelated(i.e.,theirpricesdonotalwaysmoveinthesamedirectionbythesameamount)toreducetheoverallriskoftheportfolio.Itaimstoeliminateunsystematicrisk.HowitReducesRisk:Whenassetsarenotperfectlycorrelated,lossesinoneinvestmentareoffsetbygainsinanother.Theportfolio'soverallvolatility(standarddeviation)istypicallylowerthantheweightedaveragevolatilityoftheindividualassets.Itdoesnoteliminatesystematicrisk.20.ExpectedReturn=(0.40*12%)+(0.30*10%)+(0.30*14%)=4.8%+3.0%+4.2%=12.0%21.ExpectedReturn=Rf+Beta*(RM-Rf)*ExpectedReturn=2%+1.2*(10%-2%)=2%+1.2*8%=2%+9.6%=11.6%22.Price=[C*(1-(1+r)^-n)]/r+F/(1+r)^n*n=5years*2=10periods*r=5%/2=2.5%perperiod*C=$1,000*6%/2=$30perperiod*F=$1,000*Price=[$30*(1-(1+0.025)^-10)]/0.025+$1,000/(1+0.025)^10*Price=[$30*(1-0.78120)]/0.025+$1,000/1.28008*Price=[$30*0.21880]/0.025+$781.19*Price=$6.564/0.025+$781.19=$262.56+$781.19=$1,043.7523.MaximumProfit=StockPriceatExpiration-StrikePrice+Premium=$60-$50+$2=$12Profit=Max(0,StockPriceatExpiration-StrikePrice)-PremiumProfit=Max(0,$60-$50)-$2=$10-$2=$8*(No