2025年CFA二级重点习题集

2025年CFA二级重点习题集考试时间：______分钟总分：______分姓名：______Instructions:PleaseanswerallquestionsbasedontheconceptsandstandardscoveredintheCFALevelIIcurriculum.Showall必要的calculationsandprovidelogical,well-supportedreasoningforyouranswers,especiallyforessayandproblemquestions.EssayQuestions(Pleaseprovidecomprehensiveanswerswithdetailedexplanationsandrelevantexampleswhereapplicable.)1.Aportfoliomanagerisconsideringaddingastocktoanexistingportfolio.Thestockhasabetaof1.2relativetothemarket.Themanagerusesamulti-factormodelwithmarketrisk(MKT),size(SMB),andvalue(HML)factorstoevaluatestocks.Thestockhasanestimatedalphaof0.5%,SMBfactorsensitivityof0.8,andHMLfactorsensitivityof-0.3.Themarketriskpremiumisexpectedtobe6%,andthefactorriskpremiumsforSMBandHMLareestimatedat5%and-3%,respectively.Assumetherisk-freerateis2%.Calculatetheexpectedreturnonthisstockaccordingtothemulti-factormodel.Discusswhetherthestockappearstobefairlyvalued,overvalued,orundervaluedbasedonitsalpha,andexplaintheimplicationsfortheportfoliomanager'sdecision.2.Youareanalyzingtwobonds,BondAandBondB.Bothbondshaveafacevalueof$1,000andpaysemi-annualcoupons.BondAhasacouponrateof5%,ayieldtomaturity(YTM)of5%,andmaturesin10years.BondBhasacouponrateof4%,aYTMof5%,andalsomaturesin10years.Explaintherelationshipbetweenthedurationofthesetwobonds.CalculatetheMacaulaydurationandmodifieddurationofBondA.AssumingtheYTMremainsunchanged,estimatethepercentagechangeinthepriceofBondAifthemarketyieldincreasesby100basispoints.DiscusstheprimarydifferencesininterestrateriskbetweenBondAandBondB.3.Acompanyisevaluatinganewprojectthatrequiresaninitialinvestmentof$1million.Theprojectisexpectedtogeneratecashinflowsof$400,000attheendofeachyearfor4years.ThecompanyusesaWACCof10%todiscountcashflows.TheCFOsuggestsusingapaybackperiodof3yearsasadecisioncriterion.TheCIOarguesthatthepaybackperiodistoosimplisticandsuggestsusingtheNetPresentValue(NPV)methodinstead.CalculatethepaybackperiodfortheprojectandtheNPV.DiscussthelimitationsofthepaybackperiodasadecisiontoolandexplainwhytheNPVmethodisgenerallyconsideredsuperiorforcapitalbudgetingdecisions.Whatqualitativefactorsmightthecompanyconsiderinadditiontothequantitativeresults?4.Describethekeydifferencesbetweenacalloptionandaputoption.Explaintheconceptofaput-callparityrelationshipforEuropeanoptionsonnon-dividendpayingstocks.Assumethefollowingpricesforanon-dividendpayingstock:currentstockprice=$100,priceofa6-monthEuropeancalloptionwithastrikepriceof$95=$14,priceofa6-monthEuropeanputoptionwithastrikepriceof$95=$6.Therisk-freeratefor6monthsis2%.Usingput-callparity,calculatethetheoreticalpriceofa6-monthEuropeancalloptionwithastrikepriceof$100.Discusstheimplicationsifthecalculatedtheoreticalpricediffersfromthemarketpriceofthe$100strikecalloption.ProblemQuestions(Pleaseprovidedetailedcalculations,includingallformulasusedandnumericalsteps,andaclearconclusionbasedonyourresults.)1.Aninvestorholdsaportfolioconsistingofthreestocks:StockX,StockY,andStockZ.Theportfolioweights,expectedreturns,andstandarddeviationsareasfollows:*StockX:Weight=40%,ExpectedReturn=12%,StandardDeviation=15%*StockY:Weight=35%,ExpectedReturn=10%,StandardDeviation=20%*StockZ:Weight=25%,ExpectedReturn=14%,StandardDeviation=25%Thecorrelationcoefficientsbetweenthestocksare:Corr(X,Y)=0.4,Corr(X,Z)=0.2,andCorr(Y,Z)=0.6.Calculatetheexpectedreturnandthestandarddeviationoftheportfolio.Discusshowthecorrelationsbetweenthestocksaffecttheportfolio'soverallrisk.2.Youareanalyzingacompany'sfinancialstatementsandhavecalculatedthefollowingdataforthisyearandlastyear:*Sales:$500million(Year1),$600million(Year2)*CostofGoodsSold:$300million(Year1),$360million(Year2)*GrossProfit:$200million(Year1),$240million(Year2)*OperatingIncome(EBIT):$60million(Year1),$90million(Year2)*InterestExpense:$10million(Year1),$15million(Year2)*IncomeBeforeTax:$50million(Year1),$75million(Year2)*TaxExpense(TaxRate=30%):$15million(Year1),$22.5million(Year2)*NetIncome:$35million(Year1),$52.5million(Year2)Calculatethefollowingratiosforbothyears:GrossProfitMargin,OperatingProfitMargin(EBITMargin),NetProfitMargin,ReturnonAssets(ROA)assumingtotalassetsare$800millionatthebeginningofYear1and$900millionatthebeginningofYear2,andReturnonEquity(ROE)assumingtotalequityis$250millionatthebeginningofYear1and$300millionatthebeginningofYear2.Analyzethecompany'sprofitabilitytrendsoverthetwo-yearperiod.3.Aninvestorisconsideringbuyinga5-yearEuropeanputoptiononanon-dividendpayingstockwithastrikepriceof$50.Thecurrentstockpriceis$55.Theoptionhasamarketpriceof$3.Therisk-freeratefor1yearis2%,for2yearsis2.5%,for3yearsis3%,for4yearsis3.5%,andfor5yearsis4%.Usingtheput-callparityrelationship,calculatethetheoreticalpriceofa5-yearEuropeancalloptiononthesamestockwithastrikepriceof$50.Assumetherearenotransactioncosts.Explainwhethertheputoptionappearstobeoverpriced,underpriced,orfairlypricedrelativetothetheoreticalpriceimpliedbyput-callparity.Discussthefactorsthatcouldcauseadiscrepancybetweenthemarketpriceandthetheoreticalprice.4.Youaremanaginga$10millionportfolio.Youareconsideringaddinganewstock,StockW,whichhasanexpectedreturnof15%andastandarddeviationof30%.Thecurrentportfoliohasanexpectedreturnof12%andastandarddeviationof18%.Thecorrelationcoefficientbetweentheportfolio(excludingStockW)andStockWis0.3.a.Calculatetheexpectedreturnandthestandarddeviationofthenewportfolioifyouinvest10%ofthetotalportfolioinStockW.b.Calculatetheexpectedreturnandthestandarddeviationofthenewportfolioifyouinvest20%ofthetotalportfolioinStockW.c.Basedonyourcalculations,discusstheimpactofaddingStockWtotheportfoliointermsofbothexpectedreturnandrisk(standarddeviation).DoesStockWappeartobeagooddiversificationcandidatefortheexistingportfolio?Ethics(SituationalQuestion)Aportfoliomanagerisresponsibleformanagingtwoseparateportfolios,PortfolioAandPortfolioB,fortwodifferentclients.ClientAisalargeinstitutionalinvestor,andClientBisahigh-net-worthindividual.Duringaconference,theportfoliomanagerlearnsthatacompetitorisabouttoannouncepotentiallynegativeinformationaboutanindustrysectorthatheavilyinfluencesbothPortfolioA(ClientAholdsasignificantposition)andPortfolioB(ClientBisheavilyinvested).Theportfoliomanager'sfirmhasnotyetreceivedthisinformationofficially,buttheportfoliomanagerhashearditthroughareliablesourceattheconference.a.Describethepotentialconflictsofinterestthattheportfoliomanagerfacesinthissituation.b.WhatstepsshouldtheportfoliomanagertaketocomplywiththeCFAInstituteCodeandStandardsofProfessionalConduct,specificallyStandardIII(A)–LoyaltytoClientsandProfessors,StandardIII(B)–ObjectivityandIndependence,andStandardIV(A)–Professionalism,inthisscenario?Explainthereasoningbehindyouractions.试卷答案EssayQuestions1.ExpectedReturn(Multi-FactorModel):ExpectedReturn=Risk-FreeRate+Beta*(MarketRiskPremium)+SMBSensitivity*(SMBRiskPremium)+HMLSensitivity*(HMLRiskPremium)ExpectedReturn=2%+1.2*(6%)+0.8*(5%)+(-0.3)*(-3%)ExpectedReturn=2%+7.2%+4%+0.9%ExpectedReturn=14.1%AnalysisofAlpha:Thestock'salphais0.5%.Sincethecalculatedexpectedreturnusingthemulti-factormodelis14.1%,andthemodel'sexpectedreturnbasedonriskfactorsaloneis(2%+1.2*6%+0.8*5%+(-0.3)*(-3%))=14.1%,thealphaof0.5%representstheexcessreturnthestockgeneratesafteradjustingforitsfactorexposures.Apositivealphasuggeststhestockisgeneratingreturnsabovewhatwouldbepredictedbythemulti-factormodel,indicatingitmightbeundervaluedaccordingtothismethodology.Theportfoliomanagershouldconsideraddingthestockiftheybelievethisexcessreturnissustainable.2.DurationRelationship&Calculations(BondA):*Relationship:BondAhasahighercouponrate(5%)thanBondB(4%).ForbondswiththesamematurityandYTM,thebondwiththehighercouponratewillhaveashorterduration.Thisisbecauseahigherproportionofitstotalcashflowscomesearlier(coupons),reducingtheweightedaveragetimeuntilcashflowreceipt.*MacaulayDuration(BondA):Usingtheformula:MD=[Σ(t*CFt/(1+YTM)^t)]/PVWherePV=[Σ(CFt/(1+YTM)^t)]andCFt=CouponPayment=0.05*1000/2=$25(semi-annual)PV=[25/(1.025)^1+25/(1.025)^2+...+25/(1.025)^20+1000/(1.025)^20]PV≈$926.40(Usingfinancialcalculatororspreadsheet)MD=[(1*25/1.025)+(2*25/1.025^2)+...+(20*25/1.025^20)+(20*1000/1.025^20)]/926.40MD≈[24.39+47.67+...+37.90+615.50]/926.40MD≈372.08/926.40MD≈4.009years(approximately8.02semi-annualperiods)*ModifiedDuration(BondA):MD=MacaulayDuration/(1+YTM/n)MD=4.009/(1+0.05/2)MD=4.009/1.025MD≈3.907years(approximately7.81semi-annualperiods)*PriceChangeEstimation:%ΔPrice≈-MD*%ΔYTM%ΔYTM=100basispoints=1%=0.01%ΔPrice≈-3.907*0.01%ΔPrice≈-0.3907or-39.07basispointsInterestRateRiskDifferences:BondAhaslowerdurationandthuslowerinterestratesensitivitycomparedtoBondB.ThismeansitspricewilldecreasebyasmallerpercentageforagivenincreaseinYTM.BondB,withitslowercoupon,hasmoreofitsvaluedependentonthefinalprincipalpayment,makingitmoresensitivetointerestratechanges.3.Payback&NPVCalculations&Analysis:*PaybackPeriod:CumulativeCashInflows:Year0:-$1M;Year1:$0;Year2:$400k;Year3:$800k;Year4:$1.2M.Theinitialinvestmentof$1MisrecoveredbetweenYear3andYear4.Specifically,$1M-$800k(endofYear3)=$200kremaining.The$400kreceivedinYear4recoversthisremainingamount.PaybackPeriod=3years+($200k/$400k)=3+0.5=3.5years.*NPVCalculation:NPV=Σ[CFt/(1+WACC)^t]-InitialInvestmentNPV=[400k/(1.10)^1]+[400k/(1.10)^2]+[400k/(1.10)^3]+[400k/(1.10)^4]-1,000kNPV=[400k/1.10]+[400k/1.21]+[400k/1.331]+[400k/1.4641]-1,000kNPV=363.64+330.58+300.53+273.21-1,000NPV=$1,267.96-$1,000NPV=$267.96*Analysis:Thepaybackperiodis3.5years.WhiletheCFOmightpreferprojects回收资金快，itignoresthetimevalueofmoneyandcashflowsoccurringafterthepaybackperiod.TheNPVispositiveat$267.96,indicatingthattheprojectisexpectedtoaddvaluetothecompany.ThisistheprimaryadvantageoftheNPVmethod;itconsidersallcashflowsovertheproject'slife,discountsthemtotheirpresentvalue,andprovidesadirectmeasureoftheexpectedincreaseinwealth.ApositiveNPVsuggeststheproject'sreturnexceedsthecostofcapital.Qualitativefactorsincludeprojectstrategicfit,managementexperience,marketcompetition,technologicalrisks,andpotentialenvironmentalimpact.4.OptionConcepts&Put-CallParity:*Differences:Acalloptiongivestheholdertheright(butnotobligation)tobuytheunderlyingstockataspecifiedstrikeprice(K)beforeoronaspecifiedexpirationdate.Aputoptiongivestheholdertheright(butnotobligation)toselltheunderlyingstockataspecifiedstrikeprice(K)beforeoronaspecifiedexpirationdate.Calloptionsaretypicallyboughtbybullishinvestors,whileputoptionsaretypicallyboughtbybearishinvestorsorusedforhedging.*Put-CallParity(Non-DividendStock):C+K*e^(-rT)=P+S0WhereC=CallPrice,P=PutPrice,S0=StockPrice,K=StrikePrice,r=Risk-FreeRate,T=TimetoExpiration.RearrangingfortheCallPrice(C):C=P+S0-K*e^(-rT)C=$6+$100-$95*e^(-0.02*0.5)C=$6+$100-$95*e^(-0.01)C=$6+$100-$95*(1/e^0.01)C=$6+$100-$95*(1/1.01005)C=$6+$100-$95*0.99005C=$6+$100-$94.05475C=$11.94525*Marketvs.TheoreticalPrice:Thetheoreticalpriceofthe$100strikecalloptionisapproximately$11.95.Sincethemarketpriceisgivenas$14,theputoptionappearstobeunderpricedrelativetotheput-callparityrelationship,assumingnotransactioncostsandnoarbitrageopportunityexists.Thissuggestsanopportunitymightexistforatradertopotentiallybuytheunderpricedcalloptionandselltheoverpricedputoption(orviceversa)tolockinarisk-freeprofit,althoughtransactioncostswouldlikelyeliminatethisopportunityinpractice.Factorscausingdiscrepanciesincludemarketliquidity,investorsentiment,transactioncosts,modelimperfections,andearlyexercisepossibilities(notapplicableforEuropeanoptions).ProblemQuestions1.PortfolioExpectedReturn&StandardDeviation:*ExpectedReturn(E(Rp)):E(Rp)=wX*E(RX)+wY*E(RY)+wZ*E(RZ)E(Rp)=0.40*12%+0.35*10%+0.25*14%E(Rp)=4.8%+3.5%+3.5%E(Rp)=12.8%*PortfolioVariance(σp²):σp²=wX²*σX²+wY²*σY²+wZ²*σZ²+2*wX*wY*σX*σY*ρXY+2*wX*wZ*σX*σZ*ρXZ+2*wY*wZ*σY*σZ*ρYZσp²=(0.40)²*(0.15)²+(0.35)²*(0.20)²+(0.25)²*(0.25)²+2*(0.40*0.35*0.15*0.20*0.4)+2*(0.40*0.25*0.15*0.25*0.2)+2*(0.35*0.25*0.20*0.25*0.6)σp²=0.16*0.0225+0.1225*0.04+0.0625*0.0625+2*0.04*0.15*0.20*0.4+2*0.10*0.15*0.25*0.2+2*0.0875*0.20*0.25*0.6σp²=0.0036+0.0049+0.0039+0.0048+0.0015+0.0105σp²=0.0292*PortfolioStandardDeviation(σp):σp=√σp²=√0.0292≈0.1709or17.09%*ImpactofCorrelations:Thecorrelationsbetweenthestocks(rXY=0.4,rXZ=0.2,rYZ=0.6)influencetheportfolio'soverallrisk(standarddeviation).Theportfoliovarianceformulashowsthatpositivecorrelationsaddtotheportfoliorisk,whilenegativecorrelationssubtractfromit.Inthisportfolio,thehighestcorrelationisbetweenStockYandStockZ(0.6),andthelowestisbetweenStockXandStockZ(0.2).Theaveragecorrelationisaround0.4.Sincenonearestronglynegative,theportfolioriskismoderate.Thediversificationbenefitsarelimitedbutexist,primarilyduetothelowercorrelationbetweenXandZ(0.2).Ifcorrelationswerehigher,theportfolioriskwouldbegreater;ifsomewerenegative,theriskcouldbelower.2.FinancialRatiosCalculation&Analysis:*Year1:GrossProfitMargin=(GrossProfit/Sales)*100=(200/500)*100=40.0%OperatingProfitMargin=(EBIT/Sales)*100=(60/500)*100=12.0%NetProfitMargin=(NetIncome/Sales)*100=(35/500)*100=7.0%ROA=NetIncome/AverageTotalAssets=35/[(800+900)/2]=35/850≈4.12%ROE=NetIncome/AverageTotalEquity=35/[(250+300)/2]=35/275≈12.73%*Year2:GrossProfitMargin=(240/600)*100=40.0%OperatingProfitMargin=(90/600)*100=15.0%NetProfitMargin=(52.5/600)*100=8.75%ROA=52.5/[(900+1000)/2]=52.5/950≈5.53%ROE=52.5/[(300+350)/2]=52.5/325≈16.15%*Analysis:*TheGrossProfitMarginisconsistentat40.0%forbothyears,indicatingstablecostofgoodssoldrelativetosales.*TheOperatingProfitMarginincreasedsignificantlyfrom12.0%to15.0%inYear2.Thissuggestsimprovedoperationalefficiencyorbettercostcontrol.*TheNetProfitMarginalsoincreasedfrom7.0%to8.75%inYear2,showingthattheimprovementsinoperatingprofittranslatedintohigherbottom-lineprofitability.*ReturnonAssets(ROA)improvedfrom4.12%to5.53%,indicatingthatthecompanyisgeneratingmoreprofitperdollarofassetsduetoeitherhighernetincomeormoreefficientassetutilization.*ReturnonEquity(ROE)sawasubstantialincreasefrom12.73%to16.15%.Thissignificantrisecouldbeduetothehighernetprofitmarginorpotentiallyhigherfinancialleverage(debt/equityratioincreasedfrom(800-250)/(250)=2to(1000-350)/(350)≈2.29,assumingdebtremainedconstantrelativetoequitychanges–checkcalculation:Year1Debt=800-250=550;Year2Debt=1000-350=650;ChangeinDebt=100;ChangeinEquity=100;Leverageincreased).Thestrongprofitabilitygrowthisapositivesignforshareholders.3.OptionPricing&Arbitrage:*TheoreticalCallPrice(UsingPut-CallParity):C=P+S0-K*e^(-rT)C=$6+$55-$50*e^(-0.04*1)C=$6+$55-$50*e^(-0.04)C=$6+$55-$50*(1/e^0.04)C=$6+$55-$50*(1/1.04081)C=$6+$55-$50*0.95946C=$6+$55-$47.973C=$51.027TheoreticalCallPrice≈$51.03*Marketvs.TheoreticalPrice:Themarketpriceofthecalloptionis$3,whilethetheoreticalpricebasedonput-callparityisapproximately$51.03.Themarketpriceissignificantlylowerthanthetheoreticalprice.*Under/Overpriced:Thecalloptionisheavilyunderpricedrelativetotheput-callparityrelationship,assumingnotransactioncosts.Ifnoarbitrageopportunityexists,thislargediscrepancysuggestsanerrorinpricingormarketconditionsnotcapturedbythesimplemodel.*FactorsCausingDiscrepancy:Possiblefactorsincludemodelimperfections(put-callparityassumesnodividends,constantvolatility,notransactioncosts,Europeanexercise),marketliquidityissues(thinmarketforoneoftheoptions),largebid-askspreads,investorsentimentorbehavior,orpresenceofarbitrageurswhowouldnormallystepintocorrectsuchlargepricedeviations,unlessconstraintsliketransactioncostspreventthem.4.PortfolioManagementCalculations:*a.10%InvestmentinStockW:*NewPortfolioValue:$10M*(1-0.10)+WInvested=$9M+$1M=$10M*NewWeights:PortionofW=10%;RemainingPortfolio=90%*E(Rp_new):E(Rp_new)=wRem*E(RRem)+wW*E(RW)E(Rp_new)=0.90*12%+0.10*15%E(Rp_new)=10.8%+1.5%E(Rp_new)=12.3%*σp_new²:σp_new²=wRem²*σRem²+wW²*σW²+2*wRem*wW*σRem*σW*ρRemWσp_new²=(0.90)²*(0.18)²+(0.10)²*(0.30)²+2*(0.90*0.10*0.18*0.30*0.3)σp_new²=0.81*0.0324+0.01*0.09+2*0.09*0.18*0.3σp_new²=0.026284+0.0009+0.00972σp_new²=0.037904*σp_new:σp_new=√0.037904≈0.1947or19.47%*b.20%InvestmentinStockW:*NewPortfolioValue:$10M*(1-0.20)+WInvested=$8M+$2M=$10M*NewWeights:PortionofW=20%;RemainingPortfolio=80%*E(Rp_new):E(Rp_new)=0.80*12%+0.20*15%E(Rp_new)=9.6%+3.0%E(Rp_new)=12.6%*σp_new²:σp_new²=(0.80)²*(0.18)²+(0.20)²*(0.30)²+2*(0.80*0.20*0.18*0.30*0.3)σp_new²=0.64*0.0324+0.04*0.09+2*0.16*0.18*0.30σp_new²=0.020736+0.0036+0.01728σp_new²=0.041616*σp_new:σp_new=√0.041616≈0.2040or20.40%*c.ImpactAnalysis:*ExpectedReturn:AddingStockWincreasestheportfolio'sexpectedreturnfromtheoriginal12%to12.3%(10%inW)andfurtherto12.6%(20%inW).ThisindicatesStockWhasahigherexpectedreturnthantheexistingportfolio(12%),makingitanattractiveadditionintermsofreturnpotential.*Risk(StandardDeviation):AddingStockWinitially*decreases*theportfolio'sstandarddeviation(risk)from18%to19.47%(10%inW)andthenincreasesitslightlyto20.40%(20%inW)comparedtotheoriginal18%.TheriskdecreasesbecauseStockWhasalowerstandarddeviation(30%)thantheportfolio(18%)andacorrelationofonly0.3withtheexistingportfolio,suggestingdiversificationbenefits.Theslightincreaseinriskat20%allocationmightindicatethatthediversificationbenefitsarediminishingorthatthestock'scharacteristicsbecomelessfavorableathigherweights.Overall,StockWappearstobeagooddiversificationcandidatebecauseitoffershigherexpectedreturnwithonlyaslightincrease(orevenadecrease)inriskcomparedtotheoriginalportfolio,demonstratingpositivealpha(E(RW)>E(Rp_old))andlowercorrelation(ρRemW=0.3<1).Ethics1.ConflictsofInterest:Theportfoliomanagerfacesasignificantconflictofinterest.ClientA'sportfolioisheavilyimpactedbytheupcomingnegativeinformationinthesector,whileClientBisalsosignificantlyinvested.Themanagerpossessesmaterial,non-publicinformation(thecompetitor'spotentialannouncement)beforeitbecomespublic.Thisinformationcouldmovethemarket,andthemanager'sknowledgeofitcouldpotentiallyinfluenceinvestmen