2025年CFA二級(jí)真題解析考試時(shí)間：______分鐘總分：______分姓名：______第一部分1.Acompanyisevaluatinganinvestmentprojectwithaninitialoutlayof$1,000,000.Theprojectisexpectedtogeneratecashinflowsof$300,000attheendofeachyearfor5years.Thecompany'sweightedaveragecostofcapital(WACC)is8%.UsingtheNetPresentValue(NPV)method,shouldthecompanyaccepttheprojectbasedonthecalculatedNPV?2.DescribethekeydifferencesbetweentheCapitalAssetPricingModel(CAPM)andtheFama-FrenchThree-FactorModelintermsoftheirassumptionsandthefactorstheyincorporatetoexplainassetreturns.3.Aportfoliomanagerisconstructingaportfoliousingthreestocks:StockAwithabetaof1.2,StockBwithabetaof0.8,andStockCwithabetaof1.5.Themanagerwantstheportfoliotohaveabetaof1.0.WhataretheproportionalinvestmentsinStocksA,B,andCthatthemanagershoulduse,assumingequalinvestmentamountsareinitiallyavailableforeachstockbeforerebalancing?4.Explaintheconceptofdurationinthecontextoffixed-incomesecurities.Howdoesdurationhelpinvestorsmanageinterestraterisk?5.DiscusstheprimaryadvantagesanddisadvantagesofusingtheDividendDiscountModel(DDM)forvaluingcommonstock.第二部分6.AcompanyreportedthefollowinginformationfortheyearendedDecember31,2022:*NetIncome:$500,000*DepreciationExpense:$100,000*AccountsReceivableIncrease:$30,000*AccountsPayableDecrease:$20,000*AccruedLiabilitiesIncrease:$40,000Calculatethecompany'sfreecashflow(FCF)fortheyear2022.7.Explainthedifferencebetweenhorizontalanalysisandverticalanalysisoffinancialstatements.Provideonepracticalapplicationforeachtypeofanalysis.8.Acompanyisconsideringissuingcallablebondswitha5%couponrate,10-yearmaturity,andacallpriceof105%.Thecurrentmarketinterestrateforsimilarnon-callablebondsis6%.Assumingthebondsarecallableonlyattheendofthefirstyear,whatistheyieldtocall(YTC)investorswouldexpectifthebondsarecalledattheendofthefirstyear?9.Describetheprocessofastocksplitandastockdividend.Whataretheprimaryeffectsofeachonacompany'sfinancialstatementsandashareholder'sownershippercentage?10.Compareandcontrasttheprimaryinvestmentobjectivesandriskprofilesofhedgefundsandprivateequityfunds.第三部分11.Aninvestorisconsideringbuyingacalloptionwithastrikepriceof$50andapremiumof$2.Theunderlyingstockcurrentlytradesat$48.Theinvestoralsoowns100sharesoftheunderlyingstock.Describethepotentialoutcomesandmaximumlossforthecalloptionstrategyknownasa"ProtectiveCall."12.Explaintheconceptofput-callparity.Whatarethekeycomponentsoftheput-callparityequationforEuropeanoptions?13.Acompanyisanalyzingapotentialinvestmentinanewmachine.Themachinecosts$500,000andhasanexpectedeconomiclifeof5yearswithnosalvagevalue.Themachineisexpectedtogenerateadditionalannualcashinflowsof$150,000.Thecompanyusesadiscountrateof10%forcapitalbudgetingdecisions.CalculatethePaybackPeriodandtheNetPresentValue(NPV)oftheinvestment.14.Discussthefactorsthatcancauseafirm'smarketvalueofequitytodifferfromitsbookvalueofequity.Provideexamplesofsituationswherethemarketvaluemightbesignificantlyhigherorlowerthanthebookvalue.15.Explainthedifferenttypesofmarketefficiencylevels(strongform,semi-strongform,weakform)andtheimplicationsofeachformforaninvestorattemptingtogenerateabnormalreturnsthroughsecurityanalysis.第四部分16.Describetheprimaryfunctionsoftheyieldcurveintermsofprovidinginformationaboutinterestratesandtheeconomy.Howcananinvertedyieldcurvebeinterpreted?17.Aportfolioconsistsof60%stocksand40%bonds.Theexpectedreturnandstandarddeviationofthestockportionare12%and20%,respectively.Theexpectedreturnandstandarddeviationofthebondportionare5%and8%,respectively.Thecorrelationcoefficientbetweenthereturnsofstocksandbondsis0.1.Calculatetheexpectedreturnandstandarddeviationoftheoverallportfolio.18.Explaintheconceptofoperatingleverage.Howdoesacompany'soperatingleverageaffectitsprofitabilityandriskprofile,particularlyinresponsetochangesinsalesvolume?19.Discussthevarioustypesofrisksassociatedwithforeigncurrencytranslationformultinationalcorporations.Whataresomecommonstrategiesusedtomitigatethesetranslationrisks?20.Comparetheinvestmentstrategiesandriskmanagementtechniquestypicallyemployedbymanagersoftraditionalmutualfundsversusexchange-tradedfunds(ETFs).---試卷答案第一部分1.CalculatetheNPVusingtheformula:NPV=Σ[CashInflow_t/(1+r)^t]-InitialOutlay,whereristheWACCandtistheyear.NPV=($300,000/1.08^1)+($300,000/1.08^2)+($300,000/1.08^3)+($300,000/1.08^4)+($300,000/1.08^5)-$1,000,000.NPV=$277,777.78+$256,578.95+$236,127.42+$218,643.56+$201,855.56-$1,000,000.NPV=$1,270,343.27-$1,000,000=$270,343.27.SincetheNPVispositive($270,343.27),thecompanyshouldaccepttheproject.2.CAPMassumesmarketsareefficient,investorsarerational,havehomogeneousexpectations,andonlycareaboutriskandreturn.Itusesonlythemarketriskpremium(Rm-Rf)andbeta(β)todetermineexpectedreturn:E(Ri)=Rf+βi(Rm-Rf).TheFama-FrenchmodelextendsCAPMbyaddingsize(SMB)andvalue(HML)factors,acknowledgingthatfactorsbeyondmarketriskcanexplainreturns.Ituses:E(Ri)=Rf+βi(MR)+βs(SMB)+βh(HML),whereMRismarketrisk,SMBissizefactor,andHMLisvaluefactor.3.Letinvestmentsbe$xforA,$xforB,and$xforC.Totalportfoliobeta=(x/AβA)+(x/BβB)+(x/CβC)=(x/1.2*1.2)+(x/0.8*0.8)+(x/1.5*1.5)=x+x+x=3x.Setthisequaltothetargetportfoliobeta:3x=1.0.Solveforx:x=1/3.Theproportionalinvestmentsare1/3forA,1/3forB,and1/3forC.Thismeanstheportfolioshouldbeequallyweightedamongthethreestockstoachieveabetaof1.0.4.Durationisameasureofthesensitivityoftheprice(value)ofafixed-incomesecuritytochangesininterestrates.Itprovidesanestimateofthepercentagechangeinpriceforagivenchangeinyield.TheformulaistypicallyMacaulaydurationorModifiedduration.Longerdurationmeanshigherpricevolatilityinresponsetointerestratechanges.Investorsusedurationtoestimateandmanagetheinterestrateriskexposureoftheirbondportfolios.Aportfoliomanagercanadjusttheweightedaveragedurationoftheportfoliotoalignwiththeirinterestrateoutlook.5.AdvantagesofDDM:Simple,theoreticallysoundifdividendsarepredictable,directlylinksvaluetocashflowsexpectedfromthestock.Disadvantages:Difficulttoforecastfuturedividendsaccurately,unsuitableforcompaniesthatdonotpaydividendsorhaveirregulardividendpolicies,highlysensitivetoinputassumptions(growthrate,discountrate),valuationcanbehighlyvariablebasedonchosenmodel(e.g.,constantgrowthmodel'sperpetuityassumption).第二部分6.FreeCashFlow(FCF)canbecalculatedasOperatingCashFlow(OCF)minusCapitalExpenditures(CapEx).OCF=NetIncome+Non-CashExpenses(Depreciation)+ChangesinWorkingCapital.ChangeinWorkingCapital=(ChangeinAR+ChangeinAccruedLiabilities)-ChangeinAP.OCF=$500,000+$100,000+($30,000+$40,000-$20,000)=$500,000+$100,000+$50,000=$650,000.AssumingnoinformationonCapExisprovidedbeyondthestandardincomestatementitems,FCF=OCF-CapEx.IfCapExisassumedtobeincludedintheinitialoutlayorisnotseparatelystated,thecalculationreliesontheprovideddata.AssumingstandardCapExisthemissingpiece,acompleteFCFneedsthatvalue.IfwestrictlyusethegivenOCFandnoexplicitCapEx,FCF=$650,000.However,typicallyCapExisneededforFCF.AssumingCapExisthemissinglink.Let'sreframethequestion:CalculateFCFusingOCFandassumingstandardCapExcontext.FCF=OCF-CapEx.WithoutexplicitCapEx,adirectanswerisn'tfullyformedfromthenumbersgiven,butconceptuallyFCF=$650,000-CapEx.IfassumingCapExistheimplicit$100kDepreciation(standardpracticemakingFCF=NetIncome+Depreciation),thenFCF=$500k+$100k=$600k.Givenambiguity,statingrelianceonmissingCapExiskey.Let'sanswerbasedontypicalFCFdefinitionOCF-CapEx,whereCapExisoftennotlisteddirectly:FCF=OCF-CapEx.NeedCapEx.IfassumingCapEx=Depreciation($100k)forFCF=NI+DEP,thenFCF=$500k+$100k=$600k.IfassumingstandardFCF=OCF-CapExwithCapExnotgiven,answerisexpressedintermsofmissingCapEx.Let'sresolvetostandarddefinitionusingNI+DEPforFCFcontexthere:FCF=$600,000(assumingCapEx=Depreciation).NeedclarificationonCapExsource.Let'sprovideanswerbasedoncommoninterpretationFCF=NI+DEP.FCF=$600,000.7.Horizontalanalysiscomparesfinancialstatementlineitemsovermultipleperiods(e.g.,years)toidentifytrends,growthrates,andchanges.Verticalanalysisexpresseseachlineitemonafinancialstatementasapercentageofabasefigure(TotalAssetsforBalanceSheet,TotalRevenueforIncomeStatement)withinthesameperiod,tounderstandtherelativeimportanceofeachitemandanalyzethecompany'sstructure.Practicalapplication:Horizontalanalysiscanidentifyrevenuegrowthtrendsorprofitabilitychangesovertime.Verticalanalysiscanrevealhowacompany'scoststructure(e.g.,costofgoodssoldas%ofrevenue)orassetcomposition(e.g.,currentassetsas%oftotalassets)haschangedovertimeorcomparedtoindustrybenchmarks.8.YieldtoCall(YTC)istheinternalrateofreturn(IRR)aninvestorwouldreceiveifthebondiscalledatthespecifiedcallprice(105%offacevalue)beforematurity.Itrequiressettingthepresentvalueoftheexpectedfuturecashflows(annualcouponpaymentsforthecallperiodplusthecallprice)equaltothecurrentmarketpriceofthebond,andsolvingforthediscountrate(YTC).YTC=[AnnualCouponPayment+(CallPrice-CurrentPrice)/NumberofYearstoCall]/[(CallPrice+CurrentPrice)/2].YTC=[$1,000,000*5%+($1,050,000-CurrentMarketPrice)/1]/[($1,050,000+CurrentMarketPrice)/2].Assumingthecurrentmarketpriceisthecleanprice(quotedprice),let'sdenoteitasP.YTC=[$50,000+($1,050,000-P)]/[($1,050,000+P)/2].YTC=[$1,100,000-P]/[($1,050,000+P)/2].Sincethecurrentmarketinterestratefornon-callablebonds(6%)ishigherthanthecouponrate(5%),thebondislikelytradingbelowpar($1,000,000).Let'sassumeacurrentmarketpriceof$950,000(forillustration).YTC=[$50,000+($1,050,000-$950,000)]/[($1,050,000+$950,000)/2].YTC=[$50,000+$100,000]/[$2,000,000/2].YTC=$150,000/$1,000,000.YTC=0.15or15%.TheexpectedYTCis15%.9.Astocksplitinvolvesdividingeachexistingshareintomultiplenewshares(e.g.,2-for-1,3-for-1).Forexample,ina2-for-1split,eachshareholderreceivestwosharesforeveryonetheyownedpreviously.Thecompany'stotalequity,marketcapitalization,andparvaluepersharedecreaseproportionally,butthetotalmarketvalueoftheshareholder'spositionremainsthesame.Astockdividendinvolvesissuingadditionalsharestoexistingshareholders,usuallyinproportiontotheircurrentholdings(e.g.,a10%stockdividendmeansashareholderreceives0.10newsharesforeach1shareowned).Thecompany'stotalequityremainsthesame,butthenumberofoutstandingsharesincreases,causingthepricepersharetodecreaseproportionally.Inbothcases,ashareholder'spercentageownershipinthecompanyremainsunchanged(thoughitmightappeardifferentbeforestocksplitsarefullyex-dividend).10.Hedgefundstypicallyemployawidearrayofstrategies(long/shortequity,event-driven,macro,managedfutures,currency,commodity)aimingforhighabsolutereturns,oftenwithhighleverageandderivatives.Theycatertoaccredited/qualifiedinvestors,havehighminimuminvestments,limitedliquidity(oftenclosedtoredemptionsforyears),andchargeperformancefees(2-and-20).Theirriskprofilecanbeveryhighandvolatile.Privateequityfundsprimarilyinvestinequitystakesinprivatecompanies(bought-outtargets,growthcompanies,venturecapital).Theyfocusongeneratingreturnsthroughactivemanagement,operationalimprovements,andeventualexit(IPOorsale).Minimuminvestmentsaretypicallyveryhigh($1M-$10M+).Liquidityisverylow(typically10-yearinvestmenthorizonwith3-5yearslockedup).Returnsareoftenlinkedtothefund'sperformancebutfees(2%management,20%performance)arestructureddifferently.Botharealternativeinvestments,lessregulatedthanpublicfunds,andcarryhigherriskandilliquidity,buthedgefundsfocusmoreondiversestrategiesoftenincludingshorting,whileprivateequityfocusesonowningandoperatingprivatecompanies.第三部分11.InaProtectiveCallstrategy,aninvestorbuysacalloptionandsimultaneouslybuystheunderlyingstock.Ifthestockpriceremainsbelowthestrikeprice($50)atexpiration,thecalloptionexpiresworthless,andtheinvestorkeepsthestock,realizinganycapitalappreciation.Themaximumlossoccursifthestockpricefallssignificantlybelowthepurchaseprice.Themaximumlosspershareisthepurchasepriceofthestockminusthestrikepriceoftheoptionminusthepremiumpaidfortheoption.MaximumLoss=(StockPurchasePrice-StrikePrice)-Premium.Iftheinvestorboughtthestockat$48andthecalloptionpremiumwas$2,themaximumlosspersharewouldbe($48-$50)-$2=-$2-$2=-$4.However,sincetheinvestoralsoownedthestock,thelossisrelativetothestockholding.ThelossontheProtectiveCallstrategyitself(ignoringstockpriceappreciation)isthepremiumpaid($2),asthestockprovidesafloor(atthestrikepriceminuspremium).Thepotentialoutcomeislimiteddownsideprotection(cappedatstrike-premium)andparticipationinupsidegainsabovethestrikepriceminuspremium.12.Put-callparityisafundamentalrelationshipbetweenthepriceofaEuropeancalloption,aEuropeanputoption,theunderlyingstockprice,thestrikeprice,therisk-freeinterestrate,andthetimetoexpiration.Itstatesthatthecostofaprotectiveput(buyingastockandaputoption)oracoveredcall(buyingastockandacalloption)shouldequalthecostofbuyingacalloptionandlendingthestrikepriceattherisk-freerate.Theput-callparityequationforEuropeanoptionsis:C+K/e^(rt)=P+S0,whereCisthecallprice,Pistheputprice,S0isthecurrentstockprice,Kisthestrikeprice,ristherisk-freeinterestrate,tisthetimetoexpiration,andeisthebaseofthenaturallogarithm.Thisequationensuresnoarbitrageopportunitiesexistinthemarketundercertainassumptions.13.PaybackPeriodisthetimerequiredforthecashinflowsfromaninvestmenttoequaltheinitialinvestment.ItiscalculatedasInitialInvestment/AnnualCashInflow.PaybackPeriod=$500,000/$150,000=3.33years.NetPresentValue(NPV)isthesumofthepresentvaluesofallexpectedfuturecashflowsminustheinitialinvestment.NPV=Σ[CashInflow_t/(1+r)^t]-InitialInvestment.NPV=($150,000/1.10^1)+($150,000/1.10^2)+($150,000/1.10^3)+($150,000/1.10^4)+($150,000/1.10^5)-$500,000.NPV=$136,363.64+$124,184.26+$112,697.22+$102,452.02+$93,138.20-$500,000.NPV=$568,835.34-$500,000=$168,835.34.ThePaybackPeriodis3.33years,andtheNPVis$168,835.34.14.Marketvalueofequityisbasedonthecurrentsharepricemultipliedbythenumberofoutstandingshares,reflectingwhatinvestorsarewillingtopaybasedonperceivedfutureprospects.Bookvalueofequityisbasedonhistoricalcostminusaccumulateddepreciationandothercontra-accountsfromthecompany'sbalancesheet.Differencesarisedueto:1)Marketperceptionvs.historicalcost(intangibleassetslikebrand,reputation,intellectualpropertyoftenundervaluedonbalancesheetbutvaluedbymarket),2)Accountingrulesanddepreciationmethods(accelerateddepreciationmethodslowerbookvaluefaster),3)Assetimpairmentcharges(written-downvaluesnotalwaysfullyreflectingcurrentmarketvalue),4)Interveningcapitalgains/lossesonassetsnotyetsold,5)Profitabilityexpectations(higherexpectedfutureearningsincreasemarketvalue),6)Financialleverage(higherriskassociatedwithleveragecanlowermarketvaluerelativetobook).Marketvaluecanbesignificantlyhigherifthecompanyisexpectedtobehighlyprofitable,hasvaluableintangibles,orisgrowingrapidly.Marketvaluecanbelowerifthecompanyisunprofitable,facingdecline,oritsassetsareovervaluedonthebalancesheet.15.Marketefficiencylevelsdescribehowquicklyandfullymarketpricesreflectavailableinformation:*Weakformefficiencyassumespricesreflectallpasttradinginformation(price,volume).Technicalanalysiscannotgenerateabnormalreturns.Aninvestorcannotconsistentlyoutperformbyanalyzingchartsortradingvolume.*Semi-strongformefficiencyassumespricesreflectallpubliclyavailableinformation(price,volume,financialstatements,news).Fundamentalanalysisusingpublicdatacannotgenerateconsistentabnormalreturns.Aninvestorcannotconsistentlyoutperformbyanalyzingcompanyreportsornews.*Strongformefficiencyassumespricesreflectallinformation,bothpublicandprivate(includinginsiderinformation).Noinvestorcanconsistentlyoutperform,noteveninsiders.Thisformishighlycontroversialandlargelyconsideredunrealistic.Implications:Underweakform,focusshiftstorisk-adjustedreturnsanddiversification.Undersemi-strongform,generatingabnormalreturnsrequiresaccesstoprivateinformation(insidertrading,whichisillegal)orhavingsuperioranalysis/processingspeed(difficult).Understrongform,activemanagementisimpossible,andmarketindexfundsbecometheoptimalstrategy.第四部分16.Theyieldcurveplotstheyieldsofbondswithdifferentmaturities(typicallyUSTreasurybonds)againsttheirtimetomaturity.Itprovidesinsightsintomarketexpectationsforfutureinterestratesandeconomicconditions.Anormal(upward-sloping)yieldcurveindicatesexpectationsofstableorrisingratesandeconomicgrowth.Aninverted(downward-sloping)yieldcurveoftensignalsexpectationsoffallingratesandpotentialeconomicrecession.Aflatyieldcurvesuggestsuncertaintyaboutfutureratemovements.Theslopeandshapeoftheyieldcurvearekeyindicatorsusedbyinvestorsandeconomiststoanticipateeconomiccyclesandmakeinvestmentdecisions.17.ExpectedReturnofPortfolio=(WeightofStock*ExpectedReturnofStock)+(WeightofBonds*ExpectedReturnofBonds).E(Rp)=(0.60*12%)+(0.40*5%)=7.2%+2.0%=9.2%.StandardDeviationofPortfolio=sqrt[(WeightofStock^2*SDofStock^2)+(WeightofBonds^2*SDofBonds^2)+(2*WeightofStock*WeightofBonds*Correlation*SDofStock*SDofBonds)].SDp=sqrt[(0.60^2*0.20^2)+(0.40^2*0.08^2)+(2*0.60*0.40*0.1*0.20*0.08)].SDp=sqrt[(0.36*0.04)+(0.16*0.0064)+(2*0.60*0.40*0.1*0.016)].SDp=sqrt[0.0144+0.001024+0.000384].SDp=sqrt[0.015808].SDp≈0.126.Theexpectedreturnoftheportfoliois9.2%,andthestandarddeviation(risk)oftheportfolioisapproximately12.6%.18.Operatingleveragereferstotheextenttowhichacompanyusesfixedcostsinitsoperations.Itmeasuresthesensitivityofacompany'soperatingincome(EBIT)tochangesinitssalesrevenue.Companieswithhighoperatingleveragehaveahigherproportionoffixedcostsrelativetovariablecosts.Thiscanleadtohigherprofitmarginswhensalesincrease(sincefixedcostsdon'trise),butalsotolargerlosseswhensalesdecrease(sincefixedcostsmuststillbepaid).Highoperatingleverageincreasesbusinessrisk(theriskrelatedtothecompany'soperatingperformance).Lowoperatingleveragemeanslowerfixedcostsandhighervariablecosts,leadingtomorestablebutpotentiallylowerprofitmargins.Acompany'soperatingleverageaffectsitsprofitability(higherleveragecanamplifybothgainsandlosses)andriskprofile(higherleveragegenerallymeanshigherrisk).19.Multinationalcorporationsfaceseveraltypesofforeigncurrencytranslationriskswhenconsolidatingforeignsubsidiaries'financialstatementsintotheirparentcompany'sreports:*TranslationExposure(orEconomicRisk):Riskthatchangesinexchangeratesbetweenthereportingcurrencyandthefunctionalcurrenciesofforeignoperationswillaffectthereportedconsolidatedfinancialresults(assets,liabilities,income,equity)whentranslated.Thisaffectstheparentcompany'sconsolidatednetincomeandequity.*TransactionExposure:Riskrelatedtofuturecashflowsorcontract