2025CFA考試真題解析考試時(shí)間：______分鐘總分：______分姓名：______注意：以下題目均為假設(shè)性題目，用于模擬分析，不代表真實(shí)的CFA考試內(nèi)容、難度或形式。作答時(shí)請(qǐng)仔細(xì)閱讀題目要求。1.Aninvestmentmanagerisevaluatingtwoportfoliosforpotentialinclusioninaclient'sdiversifiedportfolio.PortfolioAhasanexpectedreturnof12%andastandarddeviationof15%.PortfolioBhasanexpectedreturnof8%andastandarddeviationof10%.ThecorrelationcoefficientbetweenthereturnsofPortfolioAandPortfolioBis0.4.Basedonthisinformation,whichofthefollowingstatementsismostlikelycorrectregardingtheriskandreturnofcombiningthesetwoportfolios?2.AcompanyreportsthefollowingfinancialdatafortheyearendedDecember31,2023:*SalesRevenue:$500million*CostofGoodsSold:$300million*GrossProfit:$200million*OperatingExpenses:$100million(includingdepreciationof$20million)*InterestExpense:$15million*IncomeTaxExpense:$25million*PreferredDividends:$10millionThecompany'ssharesoutstandingare50million.Whatistheearningspershare(EPS)fortheyearendedDecember31,2023?3.Astockcurrentlytradesat$50pershare.Thecompanyisexpectedtopayadividendof$2pershareattheendoftheyear(D1=$2).Therequiredrateofreturnonthestockis10%.UsingtheDividendDiscountModel(DDM)withconstantgrowth,whatistheimpliedgrowthrateofdividends(g)?4.Whichofthefollowingstatementsbestdescribestherelationshipbetweentheyieldtomaturity(YTM)andthepriceofabond?5.AninvestorisconsideringbuyingacalloptiononStockXwithastrikepriceof$60andapremiumof$4pershare.ThecurrentmarketpriceofStockXis$55.Whatisthemaximumlosstheinvestorcouldincuriftheybuythiscalloptionandholdituntilexpiration?6.ThespotexchangerateforUSD/EURis0.90.Theone-yearforwardexchangerateforUSD/EURis0.88.Assumingnoarbitrageopportunitiesexist,whatistheimpliedannualinterestratedifferentialbetweentheUSandtheEurozone?7.Aportfoliomanagerusesafactormodeltoexplainthereturnsofastock.Themodelis:Ri=Rf+βi*(RM-Rf)+eiWhere:*Ri=Returnonstocki*Rf=Risk-freerate*βi=Betaofstocki*RM=Returnonthemarketportfolio*ei=ErrortermThemanagergathersthefollowingdataforStockX:*AveragereturnofStockX(Ri)=15%*Risk-freerate(Rf)=5%*Averagereturnofthemarketportfolio(RM)=10%*BetaofStockX(βi)=1.2WhatistheestimatedreturnofStockXaccordingtothisfactormodel?8.Whichofthefollowingisgenerallyconsideredahigherriskforacompanycomparedtoitsbusinessrisk?9.Anindividualisevaluatingtwodifferentinvestmentoptions.OptionAoffersaguaranteedreturnof6%peryearfor5years.OptionBoffersareturnthatisdependentontheperformanceofaspecificindustryindex.Historically,theindustryindexhasprovidedanaveragereturnof10%peryearwithastandarddeviationof15%.AssumingthereturnsofOptionBarenormallydistributed,whatistheapproximateprobabilitythatOptionBwillprovideareturnlowerthanOptionA'sguaranteedreturnof6%inanygivenyear?10.Afinancialadvisorisconstructingaportfolioforaclientwithahighrisktolerance.Theclientwantstoinvestinsmall-capstocks.Whichofthefollowingcharacteristicsismostlikelyassociatedwithsmall-capstocks?11.Thebalancesheetofacompanyshowscurrentassetsof$200millionandcurrentliabilitiesof$100million.Thelong-termassetsare$400millionandthelong-termliabilitiesare$250million.Whatisthecompany'sdebt-to-equityratio?12.Aprojectrequiresaninitialinvestmentof$1millionandisexpectedtogeneratecashinflowsof$400,000attheendofeachyearfor4years.Therequiredrateofreturnfortheprojectis10%.WhatistheNetPresentValue(NPV)oftheproject?13.WhichofthefollowingstatementsregardingtheEfficientMarketHypothesis(EMH)ismostaccurate?14.Acompanyisevaluatingthepurchaseofanewmachine.Themachinecosts$500,000andhasanexpectedusefullifeof5years.Thecompanyusesstraight-linedepreciation.Attheendof5years,themachineisexpectedtohaveasalvagevalueof$50,000.Whatistheannualdepreciationexpenseforthemachine?15.WhichofthefollowingisacomponentoftheWeightedAverageCostofCapital(WACC)?16.Aninvestorholdsaportfolioconsistingof60%stocksand40%bonds.Theexpectedreturnofthestockportionis12%,andtheexpectedreturnofthebondportionis6%.Whatistheexpectedreturnoftheoverallportfolio?17.Abondwithafacevalueof$1,000paysanannualcouponof5%.Thebondhas10yearstomaturity.Ifthemarketrequiredrateofreturnforsimilarbondsis6%,whatistheapproximatepriceofthebond?18.WhichofthefollowingregulatorybodiesisprimarilyresponsibleforoverseeingtheinvestmentmanagementindustryintheUnitedStates?19.Amutualfundhasassetsof$500millionandliabilitiesof$50million.Thefundhas10millionsharesoutstanding.Whatisthenetassetvalue(NAV)pershareofthemutualfund?20.Whichofthefollowinginvestmentstrategiesismostlikelytoresultinthehighestpotentialreturnsbutalsothehighestpotentialrisks?試卷答案1.Therisk(standarddeviation)ofaportfolioisinfluencedbytheindividualassets'risks,theirweights,andthecovariance(orcorrelation)betweenthem.Combiningnegativelycorrelatedassets(likeacorrelationof0.4)canreducetheoverallportfoliorisk.GivenPortfolioBhasalowerstandarddeviation(10%vs15%),andtheyaresomewhatnegativelycorrelated,combiningthemcouldpotentiallylowertheportfolio'soverallvolatilitycomparedtoholdingeitherportfolioalone,assumingappropriateweights.WhilePortfolioAoffersahigherreturn,itshigherriskmightbeoffsetbythediversificationbenefitwhencombinedwithPortfolioB.Therefore,themostlikelycorrectstatementisthatcombiningthetwoportfolioscouldpotentiallylowertheoverallportfolioriskcomparedtoholdingonlyoneoftheindividualportfolios,especiallygiventhenegativecorrelation.2.EarningsPerShare(EPS)iscalculatedasNetIncomeavailabletocommonshareholdersdividedbytheaveragenumberofcommonsharesoutstandingduringtheperiod.*CalculateNetIncome:SalesRevenue-CostofGoodsSold-OperatingExpenses-InterestExpense-IncomeTaxExpense$500million-$300million-$100million-$15million-$25million=$60million*CalculateNetIncomeavailabletocommonshareholders:NetIncome-PreferredDividends$60million-$10million=$50million*CalculateEPS:NetIncomeavailabletocommonshareholders/Sharesoutstanding$50million/50millionshares=$1pershare3.UsingtheDividendDiscountModel(DDM)withconstantgrowth:StockPrice(P0)=D1/(k-g)Where:*P0=Currentstockprice=$50*D1=Dividendattheendoftheyear=$2*k=Requiredrateofreturn=10%or0.10*g=ImpliedgrowthrateofdividendsRearrangetheformulatosolveforg:g=D1/P0-kg=$2/$50-0.10g=0.04-0.10g=-0.06or-6%Thenegativegrowthratesuggeststhestockispotentiallyovervaluedbasedonthismodel,ortherequiredrateofreturnisveryhighrelativetotheexpecteddividendanditsgrowth.4.Forastandardfixed-ratebond,thereisaninverserelationshipbetweenthebond'spriceanditsyieldtomaturity(YTM).Whenmarketinterestratesriseabovethebond'scouponrate,thebond'spricefallstomakeitsYTMcompetitivewithnewissues.Conversely,whenmarketinterestratesfallbelowthebond'scouponrate,thebond'spricerisesbecauseitoffersahigherreturnthannewlyissuedbonds.Therefore,astheyieldtomaturityincreases,thepriceofthebonddecreases.5.Themaximumlossforabuyerofacalloptionoccursifthestockpriceatexpirationislessthanorequaltothestrikeprice.Inthiscase,thecalloptionwouldbeoutofthemoney,anditsvalueatexpirationwouldbe$0.Thelossincurredbytheinvestoristhepremiumpaidfortheoption.MaximumLoss=Premiumpaid=$4pershare6.Theinterestratedifferentialcanbeapproximatedusingtheforwardexchangerateandthespotexchangerate.Theformulais:(ForwardRate/SpotRate)^(1/n)-1Wherenisthenumberofyears.(0.88/0.90)^(1/1)-1=0.9778-1=-0.0222or-2.22%ThenegativedifferentialsuggeststheinterestrateintheUSisimpliedtobelowerthantheinterestrateintheEurozonebyapproximately2.22%peryear,basedontheforwardexchangerate.7.Plugthegivenvaluesintothefactormodelformula:Ri=Rf+βi*(RM-Rf)+ei15%=5%+1.2*(RM-5%)+ei15%=5%+1.2*RM-1.2*5%+ei15%=5%+1.2*RM-6%+ei15%=-1%+1.2*RM+ei15%+1%=1.2*RM+ei16%=1.2*RM+eiTheestimatedreturn(Ri)accordingtothemodelis16%,assumingtheerrorterm(ei)iszerooraveragedoutovertheperiodbeingestimated.8.Financialriskreferstotheriskrelatedtothecompany'sfinancingdecisions,primarilytheuseofdebt.Businessriskreferstotheriskinherentinthecompany'soperationsandcompetitiveenvironment,suchasmarketdemand,coststructure,andcompetition.Leverage(usingdebt)magnifiesboththepotentialreturnsandthepotentiallossesforthecompany.Therefore,financialriskisgenerallyconsideredhigherthanbusinessriskbecauseitdirectlyimpactsthecompany'ssolvencyandtheriskfacedbyequityholders,potentiallyleadingtofinancialdistressorbankruptcyifthecompanycannotmeetitsdebtobligations.9.TofindtheprobabilitythatOptionBreturnslessthanOptionA'sguaranteed6%,weneedtostandardizethevalueusingtheZ-scoreformulaforanormaldistribution:Z=(X-μ)/σWhere:*X=OptionA'sreturn=6%*μ=MeanreturnofOptionB=10%*σ=StandarddeviationofOptionB=15%Z=(6-10)/15Z=-4/15Z≈-0.2667Usingstandardnormaldistributiontablesoracalculator,findtheprobabilitycorrespondingtoZ=-0.2667.ThecumulativeprobabilityforZ=-0.27(approximately)isabout0.3936.Therefore,theprobabilitythatOptionBreturnslowerthan6%isapproximately39.36%.10.Small-capstocksarestocksofcompanieswithrelativelysmallmarketcapitalizations.Thesecompaniesareoftencharacterizedbyhighergrowthpotentialbutalsofacegreaterfinancialuncertaintiesandoperationalchallengescomparedtolarge-capstocks.Theytypicallyreinvestmoreearningsforgrowthratherthanpayingdividends.Therefore,highervolatility,potentiallyhighergrowthprospects,butalsohigherrisk(includingliquidityriskandbusinessrisk)aremostlikelyassociatedwithsmall-capstocks.11.Thedebt-to-equityratioiscalculatedasTotalLiabilitiesdividedbyShareholders'Equity.*CalculateShareholders'Equity:TotalAssets-TotalLiabilities($200million+$400million)-($100million+$250million)=$600million-$350million=$250million*CalculateDebt-to-EquityRatio:TotalLiabilities/Shareholders'Equity($100million+$250million)/$250million=$350million/$250million=1.4or140%12.Calculatethepresentvalueofeachcashinflowusingthepresentvalueof$1factor(PVIF)for10%:*PVIF(10%,Year1)=1/(1+0.10)^1=1/1.10≈0.9091*PVIF(10%,Year2)=1/(1+0.10)^2=1/1.21≈0.8264*PVIF(10%,Year3)=1/(1+0.10)^3=1/1.331≈0.7513*PVIF(10%,Year4)=1/(1+0.10)^4=1/1.4641≈0.6830*CalculatePVofeachcashinflow:$400,000*PVIFYear1:$400,000*0.9091=$363,640Year2:$400,000*0.8264=$330,560Year3:$400,000*0.7513=$300,520Year4:$400,000*0.6830=$273,200*Sumthepresentvaluesofthecashinflows:$363,640+$330,560+$300,520+$273,200=$1,267,920*CalculateNPV:PVofcashinflows-InitialinvestmentNPV=$1,267,920-$1,000,000=$267,92013.TheEfficientMarketHypothesis(EMH)suggeststhatfinancialmarketsareefficient,andassetpricesreflectallavailableinformation.Inanefficientmarket,itisimpossibletoconsistentlyachievereturnsabovethemarketaveragewithouttakingonadditionalrisk,asallknowninformationisalreadypricedintotheasset.Therefore,themostaccuratestatementisthatinanefficientmarket,allknowninformationisalreadyreflectedinthepriceoftheasset.14.Straight-linedepreciationiscalculatedbydividingthedepreciablebase(Cost-SalvageValue)bytheusefullifeoftheasset.*Cost=$500,000*SalvageValue=$50,000*UsefulLife=5years*DepreciableBase=Cost-SalvageValue=$500,000-$50,000=$450,000*AnnualDepreciationExpense=DepreciableBase/UsefulLife$450,000/5years=$90,000peryear15.TheWeightedAverageCostofCapital(WACC)istheaverageratethatacompanyisexpectedtopaytofinanceitsassets.Itiscalculatedastheweightedaverageofthecostsofallsourcesofcapital,includingequity,debt,andpreferredstock,wheretheweightsaretheproportionsofeachsourceinthecompany'scapitalstructure.Therefore,thecostofequityisacomponentoftheWACC.16.Theexpectedreturnofaportfolioistheweightedaverageoftheexpectedreturnsoftheindividualassetsintheportfolio.*Weightofstocks=60%or0.60*Expectedreturnofstocks=12%or0.12*Weightofbonds=40%or0.40*Expectedreturnofbonds=6%or0.06*Expectedreturnofportfolio(E(Rp))=(Weightofstocks*E(Rstocks))+(Weightofbonds*E(Rbonds))*E(Rp)=(0.60*0.12)+(0.40*0.06)*E(Rp)=0.072+0.024*E(Rp)=0.096or9.6%17.Calculatethepresentvalueoftheannualcouponpaymentsandthepresentvalueofthefacevalue(paidatmaturity)usingthepresentvalueofanannuityfactor(PVIFA)andthepresentvalueof$1factor(PVIF)for6%over10years.*AnnualCouponPayment=5%*$1,000=$50*PVIFA(6%,10years)=[1-(1+0.06)^-10]/0.06≈[1-0.5584]/0.06≈5.5824*PVofCouponPayments=$50*PVIFA(6%,10)=$50*5.5824=$279.12*PVIF(6%,10years)=1/(1+0.06)^10≈1/1.7908≈0.5584*PVofFaceValue=$1,000*PV