2025年CFA三級(jí)模擬試卷解析考試時(shí)間：______分鐘總分：______分姓名：______PartI:EssaysEssayTopic1:Youareanalyzingtwomutualfunds,FundAandFundB,bothofwhichinvestprimarilyinU.S.large-capequities.FundAhasahigherexpenseratiothanFundB.Usingtheconceptsofbehavioralfinance,discussthreepotentialbiasesthatmightcauseinvestorstopreferFundAdespiteitshighercost,andanalyzehowthesebiasescouldimpacttheirinvestmentdecisionsandoverallportfolioperformance.EssayTopic2:Describetheprocessofconstructingamean-varianceefficientportfolio.ExplaintheroleoftheCapitalMarketLine(CML)andtheSharperatiointhisprocess.Discusstheassumptionsunderlyingthemean-varianceoptimizationframeworkandidentifytwokeylimitationsofthisapproachinpracticalportfoliomanagement.EssayTopic3:Aportfoliomanagerisconsideringaddingavolatilityswaptotheirportfolioasahedginginstrument.Explainthebasicmechanicsofavolatilityswap.Describethepotentialbenefitsandrisksofusingvolatilityswapsforhedgingpurposes.Discussthefactorstheportfoliomanagershouldconsiderbeforeimplementingsuchahedge.EssayTopic4:Compareandcontrastthevaluationapproachesforamaturecompanyandastartupcompany.Discussthechallengesassociatedwithvaluingeachtypeofcompanyandthespecificfactorsthatshouldbeconsideredwhenapplyingvaluationmodelstothesedifferentscenarios.EssayTopic5:TheCFAInstituteCodeandStandardsofProfessionalConductrequirememberstoactwithintegrityandmaintainobjectivity.Providetwospecificexamplesofsituationswhereaportfoliomanagermightfaceaconflictbetweentheirpersonalinterestsandtheirprofessionalobligations.AnalyzetheethicalconsiderationsinvolvedandexplainthestepsthemanagershouldtaketoresolvetheconflictinaccordancewiththeCodeandStandards.PartII:ItemSetsItemSet1:AssetAllocationClientName:SarahThompsonDate:October26,2023SarahThompsonisa55-year-oldwidowwithaportfoliocurrentlyvaluedat$1.5million.Shehasnodependentsandexpectstoretirein10years.Herrisktoleranceisconsideredmoderate,butsheisconcernedaboutoutlivinghersavings.Shehasareliablepensionthatprovides70%ofherdesiredretirementincome,butshewantstoensureshehassufficientfundstocoverhealthcareexpensesandpotentiallong-termcareneeds.1.Sarahisconsideringaddingrealassetstoherportfoliotomitigateinflationrisk.DescribethecharacteristicsofrealassetsanddiscusstwospecificexamplesofrealassetsthatcouldbesuitableforSarah'sportfolio.Explainthepotentialbenefitsandrisksofincorporatingrealassetsintoherinvestmentstrategy.2.Calculatetheexpectedreturnandstandarddeviationofaportfolioconsistingof60%large-capU.S.stocks,30%investment-gradecorporatebonds,and10%gold.Theexpectedreturns,standarddeviations,andcorrelationcoefficientsbetweentheassetclassesareasfollows:*Large-capU.S.stocks:Expectedreturn=10%,Standarddeviation=15%*Investment-gradecorporatebonds:Expectedreturn=5%,Standarddeviation=5%*Gold:Expectedreturn=3%,Standarddeviation=8%*Correlation(StocksBonds)=0.20,Correlation(StocksGold)=0.10,Correlation(BondsGold)=0.053.Sarahisinterestedinusingfactormodelstobetterunderstandthesourcesofreturnforherportfolio.DescribetheFama-Frenchthree-factormodelandexplainhowitcanbeusedtoevaluatetheperformanceofherportfolio.Discussthelimitationsoffactormodelsinexplainingportfolioreturns.ItemSet2:DerivativesCompanyName:TechInnovateInc.Date:November2,2023TechInnovateInc.isatechnologycompanyexpectedtoreportitsquarterlyearningsonNovember15th.Thecurrentstockpriceis$80pershare.Analystshaveprovidedthefollowingearningsestimates:*AnalystA:$2.00pershare*AnalystB:$1.80pershare*AnalystC:$2.20pershareThecompany's30-dayhistoricalvolatilityis20%.Thecurrentrisk-freerateis2%.1.Themarketpriceofacalloptionwithastrikepriceof$85anda30-dayexpirationis$4.CalculatetheimpliedvolatilityoftheoptionusingtheBlack-Scholes-Mertonmodel.Comparetheimpliedvolatilitytothehistoricalvolatilityandexplainthepotentialreasonsforanydifferences.2.TechInnovateInc.isconsideringusingacollarstrategytohedgetheriskofitsstockpricemovement.Describethecollarstrategyanditspotentialbenefitsandrisks.Assumethecompanybuysacalloptionwithastrikepriceof$90andsellsaputoptionwithastrikepriceof$75.Calculatethenetcostofthecollarandtherangeofstockpricesatwhichthecompanyisprotected.3.Thecompanyisalsoconsideringusingaswaptomanageitsinterestraterisk.Describethebasicmechanicsofaninterestrateswapandexplainhowitcanbeusedtoconvertafixed-rateloanintoafloating-rateloan.Discussthefactorsthecompanyshouldconsiderbeforeenteringintoaninterestrateswapagreement.ItemSet3:PortfolioManagementClientName:JohnandMaryDavisDate:November10,2023JohnandMaryDavisareamarriedcoupleintheirearly60swithaportfoliovaluedat$2million.Theyare5yearsfromretirementandhavealowrisktolerance.Theirportfolioiscurrentlyallocatedasfollows:*Large-capU.S.stocks:50%*Small-capU.S.stocks:20%*Internationalstocks:10%*Investment-gradecorporatebonds:15%*Treasurybonds:5%JohnandMaryareconcernedaboutthepotentialimpactofinflationontheirportfolioandareconsideringmakingsomeadjustments.Theyhavealsoheardaboutthebenefitsofimpactinvestingandwouldliketoexploreoptionsforincorporatingenvironmental,social,andgovernance(ESG)factorsintotheirinvestmentprocess.1.JohnandMaryareconsideringswitchingsomeoftheirstockholdingstobondstoreducetheoverallvolatilityoftheirportfolio.Describethetrade-offsinvolvedinthisdecision.Discussthepotentialimpactonexpectedreturn,risk,andthediversificationbenefitsoftheirportfolio.2.TheDavis'sportfoliomanagerhasrecommendedusingfactorinvestingtoenhancetheirportfolio'srisk-adjustedreturns.DescribetwopopularfactorinvestingstrategiesandexplainhowtheycanbeusedtoimprovetheperformanceoftheDavis'sportfolio.Discussthepotentialrisksandchallengesassociatedwithfactorinvesting.3.JohnandMaryareinterestedinlearningmoreaboutimpactinvesting.Describetheconceptofimpactinvestinganddiscusshowitdiffersfromtraditionalinvesting.ProvidetwospecificexamplesofimpactinvestmentsthattheDavis'sportfoliomanagercouldconsiderincorporatingintotheirportfolio.---試卷答案PartI:EssaysEssayTopic1:Behavioralfinanceexplainsinvestorbiasesthatcanleadtoirrationaldecision-making.ThreebiasesthatmightcauseinvestorstopreferFundAdespiteitshigherexpenseratioare:1.HerdBehavior:InvestorsmayfollowthecrowdandchooseFundAifitispopularorrecommendedbyothers,regardlessofitshighercost.2.Overconfidence:InvestorsmightoverestimatetheirabilitytooutperformthemarketandbelievethatthehigherreturnsgeneratedbyFundA(evenafteraccountingfortheexpenseratio)justifiestheextracost.3.AnchoringBias:InvestorsmayanchortheirdecisionsontheinitialperceptionofFundA'sperformanceorfeatures,makingitdifficulttoobjectivelyevaluatetheimpactofthehigherexpenseratioontheiroverallreturns.Thesebiasescanleadinvestorstoprioritizeperceivedstatusorconfidenceoverthefundamentalprincipleofminimizingcosts,potentiallyresultinginlowernetportfolioreturnsandsuboptimalwealthaccumulation.解析思路：首先點(diǎn)明行為金融學(xué)及其核心——投資者非理性行為。然后，選擇三個(gè)具體的認(rèn)知偏差：羊群效應(yīng)、過度自信和錨定效應(yīng)。分別解釋每個(gè)偏差如何導(dǎo)致投資者選擇高費(fèi)率基金，并強(qiáng)調(diào)這些偏差如何影響投資決策和最終結(jié)果，特別是與成本最小化原則的沖突。EssayTopic2:Mean-varianceefficientportfolioconstructioninvolvesselectingtheoptimalmixofassetstomaximizeexpectedreturnforagivenlevelofriskorminimizeriskforagivenlevelofexpectedreturn.TheCapitalMarketLine(CML)showstheefficientfrontierofriskyassetscombinedwiththerisk-freeasset,illustratingthetrade-offbetweenriskandreturnforfullyinvestedportfolios.TheSharperatiomeasurestheexcessreturnperunitofdeviationinaninvestment,providingawaytoevaluatetherisk-adjustedperformanceofportfoliosorindividualassets.Themean-varianceoptimizationframeworkassumesthatinvestorsarerational,risk-averse,andhaveaccesstocompleteandunbiasedinformation.Limitationsincludeitsassumptionofnormallydistributedreturns,whichmaynotreflectmarketrealities;itssensitivitytoinputdata(e.g.,expectedreturnsandvariances),makingitvulnerabletoestimationerrors;anditsdifficultyinhandlingfactorsliketransactioncosts,taxes,andinvestorpreferencesbeyondriskandreturn.解析思路：首先定義均值-方差有效投資組合的構(gòu)建核心。然后解釋CML的含義及其在投資組合中的位置。接著定義夏普比率及其作用。之后，闡述均值-方差模型的基礎(chǔ)假設(shè)，并列舉其兩大主要局限性：對(duì)正態(tài)分布的假設(shè)和輸入數(shù)據(jù)的敏感性。EssayTopic3:Avolatilityswapisaderivativecontractwhereonepartypaysafixedorfloatingscheduleofpaymentstotheotherparty,whoinreturnpaysthedifferencebetweenapre-agreedvolatilitylevelandtheactualrealizedvolatilityofanunderlyingassetoveraspecifiedperiod.Thebasicmechanicsinvolvethesettlementofpaymentsbasedonthevarianceswaprateandtherealizedvarianceoftheunderlying.Benefitsofusingvolatilityswapsforhedgingincludetheabilitytogainexposuretovolatilitywithoutneedingtotradetheunderlyingassetdirectly,potentialcostadvantagescomparedtobuyingoptions,andflexibilityincustomizingthehedgetospecificriskprofiles.Risksincludecounterpartycreditrisk,modelrisk(inaccuratevolatilitypredictions),marketrisk(volatilitymovingunfavorably),andcomplexityintermsofstructuringandmanagingthecontract.解析思路：首先清晰定義波動(dòng)率互換的基本概念和運(yùn)作機(jī)制。然后分別闡述其作為對(duì)沖工具的兩個(gè)主要優(yōu)勢(shì)：無需直接交易標(biāo)的資產(chǎn)即可獲得波動(dòng)率敞口和潛在的成本優(yōu)勢(shì)。接著，列舉使用波動(dòng)率互換的風(fēng)險(xiǎn)，包括對(duì)手方信用風(fēng)險(xiǎn)、模型風(fēng)險(xiǎn)、市場(chǎng)風(fēng)險(xiǎn)和結(jié)構(gòu)復(fù)雜性。EssayTopic4:Valuationapproachesformaturecompaniestypicallyincludediscountedcashflow(DCF)analysis,comparablecompanyanalysis(usingmultipleslikeP/E,P/B,EV/EBITDA),andpre-moneyvaluationbasedonpriorfinancingrounds.Keyfactorsincludestableearnings,predictablecashflows,competitiveadvantages,andmaturemarketpositions.Challengesincludeestimatingfuturegrowthrates,determiningappropriatediscountrates,andaccountingforpotentialdeclinephases.Valuationapproachesforstartupcompaniesoftenrelyoncomparablecompanyanalysis(usingmultiplesbasedonearly-stagevaluations),first-principlesanalysis(projectingfuturerevenueandprofitability),andpre-moneyvaluationbasedonindustrybenchmarksandinvestorexpectations.Keyfactorsincludegrowthpotential,marketsize,teamquality,intellectualproperty,andcompetitivelandscape.Challengesincludehighuncertainty,lackofprofitabilityorcashflowhistory,difficultyinfindingcomparablecompanies,andsignificantestimationrisk.解析思路：分別概述成熟公司和初創(chuàng)公司的估值方法。對(duì)成熟公司，重點(diǎn)介紹DCF、可比公司法等，并指出其估值中的關(guān)鍵因素和挑戰(zhàn)（如增長率預(yù)測(cè)、折現(xiàn)率確定）。對(duì)初創(chuàng)公司，重點(diǎn)介紹可比公司法（早期）、第一性原理分析等，并指出其估值中的關(guān)鍵因素和挑戰(zhàn)（如不確定性、缺乏歷史數(shù)據(jù)、可比公司難尋）。最后，對(duì)比兩者估值的核心差異。EssayTopic5:Example1:Aportfoliomanagerisofferedalucrativejoboutsidethefirmafterthemarkethashadasignificantrun-up,butbeforereportingthefirm'sperformance.Personalinterest(careeradvancement,highersalary)conflictswithprofessionalobligations(dutyofloyaltytothefirm,potentialinsidertradingconcernsifinformationisusedprematurely).Themanagershouldrefusetheoffer,discloseanyrelevantinformationtothefirm,andfollowtheCodeandStandards'guidanceonconflictsofinterestandloyalty.Example2:Aportfoliomanagerlearnsthatamajorclientisplanningtoliquidatepartoftheirportfolioduetopersonalfinancialdifficulties.Themanageristemptedtousethisnon-publicinformationtomakeprofitabletradesforthemselvesorselectclients.Thisconflictswithprofessionalobligations(dutyofconfidentiality,fairdealing).Themanagermustmaintainclientconfidentiality,cannotusetheinformationforpersonalgain,andshouldreportthesituationaccordingtofirmpoliciesandtheCodeandStandards,potentiallyreferringthemattertocompliance.解析思路：設(shè)計(jì)兩個(gè)具體的投資經(jīng)理面臨利益沖突的場(chǎng)景。場(chǎng)景一涉及外部工作機(jī)會(huì)與對(duì)公司的忠誠義務(wù)沖突；場(chǎng)景二涉及使用非公開信息與保密義務(wù)沖突。在每個(gè)場(chǎng)景中，明確指出沖突的具體內(nèi)容，然后根據(jù)CFA協(xié)會(huì)道德準(zhǔn)則，提供解決沖突的正確處理方式和應(yīng)遵循的原則。PartII:ItemSetsItemSet1:AssetAllocation1.Realassetsareassetswhosevaluederivesfromtangibleorintangibleresources.ExamplessuitableforSarah'sportfolioincluderealestate(providesrentalincomeandpotentialappreciation)andcommodities(likegold,whichcanhedgeagainstinflation).Benefitsincludepotentialinflationprotectionanddiversificationbenefits.Risksincludeilliquidity,volatility,andpotentialcorrelationswithfinancialmarketsduringcrises.2.ExpectedReturn=(0.60*10%)+(0.30*5%)+(0.10*3%)=6.0%+1.5%+0.3%=7.8%Variance=(0.60^2*15%^2)+(0.30^2*5%^2)+(0.10^2*8%^2)+2*0.60*0.30*0.20*15%*5%+2*0.60*0.10*0.10*15%*8%+2*0.30*0.10*0.05*5%*8%Variance=0.0135+0.00225+0.00064+0.00108+0.00012+0.00003=0.01758StandardDeviation=sqrt(0.01758)=13.27%3.TheFama-Frenchthree-factormodelextendstheCapitalAssetPricingModel(CAPM)byincludingmarketrisk,sizerisk,andvalueriskfactors,inadditiontothemarketfactor.Ithelpsevaluatewhetheraportfolio'sreturnsaredrivenbythemarket,firmsize,orbook-to-marketratio,providingamorenuancedviewofperformance.Limitationsincludedatarequirements(largedatasetsneeded),thechallengeofidentifyingandmeasuringfactorsconsistently,andthepotentialforomittedvariablebiasifotherimportantfactorsarenotincluded.解析思路：問題1要求解釋真實(shí)資產(chǎn)的特點(diǎn)、舉例并分析其優(yōu)缺點(diǎn)。問題2要求計(jì)算一個(gè)三資產(chǎn)投資組合的預(yù)期回報(bào)和標(biāo)準(zhǔn)差，需要運(yùn)用加權(quán)平均公式和投資組合方差公式，注意包含協(xié)方差項(xiàng)。問題3要求解釋Fama-French三因子模型及其作用，并討論其局限性，如數(shù)據(jù)需求、因子測(cè)量一致性和潛在遺漏變量問題。ItemSet2:Derivatives1.UsingtheBlack-Scholes-Mertonmodelformulaforcalloptionprice(C=S0*N(d1)-X*e^(-rT)*N(d2)),whered1=[ln(S0/X)+(r+σ^2/2)T]/(σ*sqrt(T)),d2=d1-σ*sqrt(T),andN()isthecumulativedistributionfunctionofthestandardnormaldistribution:d1=[ln(80/85)+(0.02+0.2^2/2)*30/365]/(0.2*sqrt(30/365))d1=[-0.07696+(0.02+0.02)*0.0822]/(0.2*0.2953)d1=[-0.07696+0.003288]/0.05806=-0.073672/0.05806=-1.268d2=-1.268-0.2*0.2953=-1.268-0.05906=-1.327N(d1)≈0.097,N(d2)≈0.092ImpliedVolatility(σ)isfoundbysolvingC=4=80*0.097-85*e^(-0.02*30/365)*0.092,whichrequiresnumericalmethods(e.g.,Newton-Raphson).Approximatecalculationyieldsanimpliedvolatilitysignificantlyhigherthanthehistorical20%(e.g.,around40-50%),suggestingmarketexpectshighervolatilityaroundtheearningsevent.2.Thecollarstrategyinvolvesbuyingaprotectiveput(strike$75)andsellingacoveredcall(strike$90).Netcost=PutPrice-CallPrice=(PutPrice)-$4.Theprotectiveputprotectstheportfolioifthestockpricefallsbelow$75.Thecoveredcallgeneratesincomebutlimitsgainsabove$90.Theprotectedrangeisfrom$75(putstrike)to$90(callstrike).Thenetcostreducesthebreak-evenpointforthecollarstrategy.3.Aninterestrateswapisacontractwheretwopartiesagreetoexchangecashflowsoveraperiod.Inthiscase,TechInnovateInc.wouldpayafixedinterestrateonaloanandreceiveafloatinginterestrate(e.g.,SOFRorLIBOR).Thisconvertsafixed-rateloanintoafloating-rateloan.Factorstoconsiderincludethedifferencebetweenfixedandfloatingrates(spread),counterpartycreditrisk,potentialchangesininterestrateenvironment,costsofenteringtheswap,andtheimpactonfinancialstatements.解析思路：問題1要求使用Black-Scholes模型計(jì)算隱含波動(dòng)率，這是一個(gè)需要數(shù)值方法的計(jì)算題，需要先列出公式，然后進(jìn)行數(shù)值求解，并解釋隱含波動(dòng)率與歷史波動(dòng)率差異的原因。問題2要求描述collar策略，計(jì)算凈成本，并說明保護(hù)范圍。問題3要求描述利率互換的基本機(jī)制，解釋其將固定利率貸款轉(zhuǎn)換為浮動(dòng)利率貸款的作用，并列出進(jìn)入互換前需要考慮的因素。ItemSet3:PortfolioManagement1.Switchingstockstobondsreducesexpectedreturn(bondstypicallyofferlowerreturnsthanstocks)butincreasesportfolio