2025年CFA一級(jí)考試投資組合管理試卷（含答案）考試時(shí)間：______分鐘總分：______分姓名：______試卷內(nèi)容1.AccordingtotheMarkowitzmodel,whichofthefollowingstatementsismostaccurateregardingportfoliodiversification?a.Diversificationcaneliminateallrisksassociatedwithinvestinginindividualassets.b.Diversificationcanreducetheoverallriskofaportfolioonlyiftheassetsareperfectlypositivelycorrelated.c.Diversificationcaneffectivelyreducethenon-systematicriskofaportfolio.d.Thebenefitsofdiversificationaregreatestwheninvestinginassetsthathaveidenticalexpectedreturns.2.Aninvestorisconsideringaddinganewassettotheirportfolio.Theexpectedreturnoftheassetis12%,itsstandarddeviationis15%,andthecorrelationcoefficientbetweentheasset'sreturnsandtheportfolio'sreturnsis0.3.Theportfolio'sexpectedreturnis10%anditsstandarddeviationis20%.Iftheinvestoraddsthisassettotheirportfolio,whatistheapproximatenewportfoliostandarddeviation?a.18.0%b.19.3%c.20.5%d.21.7%3.TheCapitalAssetPricingModel(CAPM)isusedtodeterminetheexpectedreturnofanasset.WhichofthefollowingcomponentsisNOTarequiredinputfortheCAPMformula?a.Therisk-freerateofreturn.b.Theasset'sbeta.c.Themarketriskpremium.d.Thestandarddeviationoftheasset'sreturns.4.Aninvestmentmanagerclaimsthattheirportfoliohasgenerateda15%returnoverthepastyear,whilethebenchmarkindexhasreturned10%.Thestandarddeviationofthemanager'sportfoliois12%,andthestandarddeviationofthebenchmarkindexis8%.Ifthebetaoftheportfoliois1.2,whatistheapproximateinformationratiooftheportfolio?a.0.44b.0.50c.0.56d.0.625.WhichofthefollowingstatementsbestdescribestherelationshipbetweentheCapitalMarketLine(CML)andtheEfficientFrontier?a.TheCMLrepresentsasubsetoftheefficientfrontier,specificallythemostefficientportfoliosofriskyassets.b.TheefficientfrontierrepresentsasubsetoftheCML,specificallytheportfoliocombinationsthatofferthehighestSharperatio.c.TheCMLisastraightlinethatrepresentsallpossiblecombinationsoftherisk-freeassetandthemarketportfolio,anditistangenttotheefficientfrontieratthemarketportfolio.d.Theefficientfrontierisacurvedlinethatrepresentsallpossiblecombinationsofriskyassets,andtheCMLisaseparatelinethatshowstheoptimalallocationbetweentherisk-freeassetandthemarketportfolio.6.Aportfoliomanagerisevaluatingtheperformanceoftwoportfolios.PortfolioAhasanactualreturnof12%andabenchmarkreturnof10%.PortfolioBhasanactualreturnof8%andabenchmarkreturnof10%.IfthestandarddeviationofPortfolioA'sexcessreturnsis5%andthestandarddeviationofPortfolioB'sexcessreturnsis3%,whichportfoliohasthehigherTreynorratio,assumingbothportfolioshavethesamerisk-freerate?a.PortfolioAb.PortfolioBc.TheTreynorratiosareequal.d.Insufficientinformationtodetermine.7.WhichofthefollowingstatementsismostaccurateregardingtheEfficientFrontier?a.Itrepresentsallpossiblecombinationsofriskyassetsthatofferthehighestexpectedreturnforagivenlevelofrisk.b.Itincludesallpossiblecombinationsoftherisk-freeassetandthemarketportfolio.c.Itisadownward-slopingcurvethatshowsthetrade-offbetweenriskandreturnforindividualassets.d.Itisindependentoftherisk-freerateofreturn.8.Astockhasabetaof1.5.Ifthemarketriskpremiumis8%andtherisk-freerateis3%,whatistheexpectedreturnofthestockaccordingtotheCAPM?a.9.0%b.12.0%c.15.0%d.18.0%9.WhichofthefollowingisakeyassumptionoftheCapitalAssetPricingModel(CAPM)?a.Investorscanborrowandlendatthesamerisk-freerate.b.Allinvestorshavethesamerisktolerance.c.Investorsonlycareabouttheexpectedreturnandstandarddeviationoftheirportfolio.d.Allassetsareinfinitelydivisible.10.Aportfolioconsistsof60%stocksand40%bonds.Theexpectedreturnofthestocksis12%,theexpectedreturnofthebondsis6%,andthecorrelationcoefficientbetweenthereturnsofstocksandbondsis0.1.Whatistheexpectedreturnoftheportfolio?a.7.2%b.8.4%c.9.6%d.10.8%11.WhichofthefollowingstatementsismostaccurateregardingtheSharperatio?a.Itmeasurestheexcessreturnperunitoftotalrisk.b.Itiscalculatedbysubtractingtherisk-freeratefromtheportfolio'sexpectedreturnanddividingbytheportfolio'sstandarddeviation.c.Itismostusefulforcomparingtheperformanceofportfolioswithdifferentlevelsofrisk.d.Itassumesthatallinvestorshaveariskaversioncoefficientof1.12.Aninvestorisconsideringaddinganassettotheirportfolio.Theassethasanexpectedreturnof10%,astandarddeviationof20%,andacorrelationcoefficientwiththeportfolioof0.2.Theportfolio'sexpectedreturnis12%anditsstandarddeviationis15%.Whatistheapproximateimpactofaddingthisassetontheportfolio'sexpectedreturnandstandarddeviation?a.Expectedreturnincreasesby2%,standarddeviationdecreasesby3%.b.Expectedreturnincreasesby2%,standarddeviationincreasesby3%.c.Expectedreturnincreasesby10%,standarddeviationincreasesby20%.d.Expectedreturnincreasesby2%,standarddeviationisunaffected.13.Whichofthefollowingisaprimaryobjectiveofportfolioconstruction?a.Tomaximizetheexpectedreturnoftheportfoliowithoutconsideringrisk.b.Tominimizetheriskoftheportfoliowithoutconsideringreturn.c.Tobalancetheexpectedreturnandriskoftheportfoliobasedontheinvestor'spreferencesandconstraints.d.Toensurethattheportfolioisdiversifiedacrossallassetclasses.14.Aportfoliomanagerusesatop-downapproachtoassetallocation.Whichofthefollowingstatementsbestdescribesthisapproach?a.Themanagerfirstidentifiesspecificsecuritiesthatareexpectedtooutperformthemarketandthenbuildstheportfolioaroundthesesecurities.b.Themanagerfirstdeterminestheoptimalallocationtodifferentassetclassesbasedonbroadeconomicforecastsandthenselectsspecificsecuritieswithineachassetclass.c.Themanagerfocusesonthedetailedanalysisofindividualsecuritiesbeforemakinganyallocationdecisions.d.Themanagerprimarilyusesquantitativemodelstodeterminetheoptimalportfolioweights.15.WhichofthefollowingstatementsismostaccurateregardingtheFama-Frenchthree-factormodel?a.ItisanextensionoftheCapitalAssetPricingModelthatincludesadditionalfactorstoexplainassetreturns.b.Itsuggeststhatthemarketriskpremiumistheonlyfactorthatsignificantlyexplainsassetreturns.c.Itisprimarilyusedtoevaluatetheperformanceofactivelymanagedportfolios.d.Itassumesthatallinvestorshavethesameexpectedreturnonthemarketportfolio.16.Aportfoliomanagerisconstructingaportfolioforaninvestorwhohasalowrisktolerance.Whichofthefollowingstrategieswouldbemostappropriateforthisinvestor?a.Allocatealargeportionoftheportfoliotosmall-capstocks.b.Allocateasignificantportionoftheportfoliotobondsandotherfixed-incomesecurities.c.Investprimarilyinoptionsandotherderivativesecurities.d.Focusonstockswithhighgrowthpotential,eveniftheyhavehighvolatility.17.Whichofthefollowingisakeyconsiderationwhenevaluatingtheperformanceofaninvestmentportfolio?a.Theabsolutereturnoftheportfoliooveraspecificperiodoftime.b.Therelativereturnoftheportfoliocomparedtoarelevantbenchmark.c.Thelevelofrisktakentoachievetheportfolio'sreturn.d.Themanager'sfeestructureformanagingtheportfolio.18.Aportfolioisconstructedwith50%stocksand50%bonds.Theexpectedreturnofthestocksis10%,theexpectedreturnofthebondsis5%,andthecorrelationcoefficientbetweenthereturnsofstocksandbondsis0.Thestandarddeviationofthestocksis15%andthestandarddeviationofthebondsis8%.Whatistheapproximatestandarddeviationoftheportfolio?a.6.5%b.9.0%c.11.5%d.13.0%19.Whichofthefollowingstatementsismostaccurateregardingtheconceptofrisktolerance?a.Risktoleranceisthesameasthestandarddeviationofaninvestor'sportfolioreturns.b.Risktoleranceisthedegreeofvariabilityinaninvestor'sreturnsthattheyarewillingtoacceptinexchangeforahigherexpectedreturn.c.Risktoleranceisprimarilydeterminedbyaninvestor'sageandinvestmenthorizon.d.Risktoleranceisonlyrelevantforinvestorswhoareactivelymanagingtheirownportfolios.20.WhichofthefollowingisapotentiallimitationoftheSharperatio?a.Itassumesthatallinvestorshavethesameriskaversioncoefficient.b.Itisnotsuitableforcomparingtheperformanceofportfolioswithdifferentlevelsofrisk.c.Itgivesequalweighttoupsideanddownsiderisk.d.Itcanbedistortedbyextremereturnsinthetailsofthedistribution.21.Aninvestorisconsideringaddinganewassettotheirportfolio.Theassethasahighexpectedreturnbutalsoahighstandarddeviation.Whichofthefollowingstatementsismostaccurateregardingtheimpactofaddingthisasset?a.Theexpectedreturnoftheportfoliowilldefinitelyincrease,butthestandarddeviationwillincreaseordecreasedependingonthecorrelationbetweentheassetandtheexistingportfolio.b.Thestandarddeviationoftheportfoliowilldefinitelydecrease,buttheexpectedreturnwillincreaseordecreasedependingonthecorrelationbetweentheassetandtheexistingportfolio.c.Boththeexpectedreturnandstandarddeviationoftheportfoliowilldefinitelyincrease.d.Neithertheexpectedreturnnorthestandarddeviationoftheportfoliowillbeaffected.22.Whichofthefollowingstatementsbestdescribesthedifferencebetweenstrategicassetallocationandtacticalassetallocation?a.Strategicassetallocationfocusesonthelong-termallocationofassets,whiletacticalassetallocationfocusesonshort-termadjustmentsbasedonmarketconditions.b.Strategicassetallocationisprimarilyconcernedwiththeselectionofspecificsecurities,whiletacticalassetallocationisconcernedwiththeoverallassetclassallocation.c.Strategicassetallocationusesquantitativemodels,whiletacticalassetallocationreliesonqualitativeanalysis.d.Strategicassetallocationistypicallyusedbypassiveinvestors,whiletacticalassetallocationistypicallyusedbyactiveinvestors.23.Aportfoliomanagerisevaluatingtherisk-adjustedperformanceoftwoportfoliosusingtheTreynorratioandtheSharperatio.Whichofthefollowingstatementsismostaccurate?a.TheTreynorratioismoreappropriateforevaluatingtheperformanceofactivelymanagedportfolios,whiletheSharperatioismoreappropriateforevaluatingtheperformanceofpassiveportfolios.b.TheTreynorratiomeasurestheexcessreturnperunitoftotalrisk,whiletheSharperatiomeasurestheexcessreturnperunitofbeta.c.TheTreynorratioismoresensitivetothechoiceofbenchmark,whiletheSharperatioisnot.d.TheTreynorratioisprimarilyusedtoevaluatetheperformanceofportfolioswithlowlevelsofrisk,whiletheSharperatioisprimarilyusedtoevaluatetheperformanceofportfolioswithhighlevelsofrisk.24.Whichofthefollowingisakeybenefitofdiversificationinaportfolio?a.Itcaneliminateallrisksassociatedwithinvestinginindividualassets.b.Itcanreducetheoverallriskoftheportfoliobycombiningassetswithlowornegativecorrelations.c.Itincreasestheexpectedreturnoftheportfoliowithoutincreasingrisk.d.Itrequirestheinvestortoholdalargenumberofassetstobeeffective.25.Aninvestorisconsideringaddinganassettotheirportfolio.Theassethasabetaof1.5.Ifthemarketriskpremiumis8%andtherisk-freerateis3%,whatistheexpectedreturnoftheassetaccordingtotheCAPM?Theinvestor'scurrentportfoliohasanexpectedreturnof10%andabetaof1.0.Whatistheexpectedreturnoftheportfolioiftheinvestoradds20%oftheircapitaltothisnewasset?a.15.0%;10.6%b.15.0%;11.2%c.16.5%;10.6%d.16.5%;11.2%試卷答案1.c解析思路：分散化通過組合不同資產(chǎn)可以降低非系統(tǒng)性風(fēng)險(xiǎn)，即資產(chǎn)之間相關(guān)性較低的資產(chǎn)組合在一起，可以減少整體組合的風(fēng)險(xiǎn)。系統(tǒng)性風(fēng)險(xiǎn)無法通過分散化消除。2.b解析思路：根據(jù)投資組合標(biāo)準(zhǔn)差的公式，新組合標(biāo)準(zhǔn)差約為sqrt(0.2^2+0.15^2+2*0.2*0.15*0.3)=sqrt(0.04+0.0225+0.012)=sqrt(0.0745)≈27.3%*0.7=19.3%。注意：此題計(jì)算略復(fù)雜，實(shí)際考試中可能簡(jiǎn)化或提供更易計(jì)算的數(shù)據(jù)。3.d解析思路：CAPM公式為E(Ri)=Rf+βi*[E(Rm)-Rf]。所需輸入為無風(fēng)險(xiǎn)利率(Rf)、資產(chǎn)Beta(βi)和市場(chǎng)風(fēng)險(xiǎn)溢價(jià)[E(Rm)-Rf]。標(biāo)準(zhǔn)差(σi)是單個(gè)資產(chǎn)的波動(dòng)性，不是CAPM模型的必需輸入，市場(chǎng)組合的方差(σm^2)或標(biāo)準(zhǔn)差(σm)也不是必需的，因?yàn)轱L(fēng)險(xiǎn)溢價(jià)是預(yù)期收益差。4.a解析思路：信息比率=(PortfolioReturn-BenchmarkReturn)/TrackingError。TrackingError=StandardDeviationofPortfolioReturns-StandardDeviationofExcessBenchmarkReturns=sqrt(0.12^2-0.08^2)=sqrt(0.0144-0.0064)=sqrt(0.008)=0.0894.信息比率=(0.15-0.10)/0.0894=0.05/0.0894≈0.559≈0.56。5.c解析思路：CML表示連接無風(fēng)險(xiǎn)資產(chǎn)與市場(chǎng)組合的直線，它一定與有效前沿相切于市場(chǎng)組合點(diǎn)。有效前沿是所有風(fēng)險(xiǎn)資產(chǎn)的最優(yōu)組合，CML則包含了無風(fēng)險(xiǎn)資產(chǎn)與不同比例市場(chǎng)組合的組合。SML是CAPM的圖形表示，表示資產(chǎn)或投資組合的預(yù)期回報(bào)與貝塔的關(guān)系。6.a解析思路：TreynorRatio=(PortfolioReturn-Risk-FreeRate)/Beta.由于風(fēng)險(xiǎn)-freerate相同，比較Treynorratio只需比較(PortfolioReturn-BenchmarkReturn)/Beta.對(duì)于PortfolioA，該值為(0.12-0.10)/1.2=0.025.對(duì)于PortfolioB，該值為(0.08-0.10)/1.0=-0.02.因此PortfolioA的Treynorratio更高。7.a解析思路：有效前沿展示了在給定風(fēng)險(xiǎn)水平下預(yù)期收益最高的資產(chǎn)組合，或者在給定預(yù)期收益水平下風(fēng)險(xiǎn)最低的資產(chǎn)組合。它是由所有風(fēng)險(xiǎn)資產(chǎn)的最優(yōu)組合構(gòu)成的集合。8.c解析思路：根據(jù)CAPM，E(R_stock)=Rf+Beta_stock*MarketRiskPremium.E(R_stock)=3%+1.5*8%=3%+12%=15%。9.a解析思路：CAPM的關(guān)鍵假設(shè)之一是投資者可以無風(fēng)險(xiǎn)地借入和貸出資金，以構(gòu)建杠桿或無杠桿的投資組合。10.b解析思路：PortfolioReturn=w_stock*E(R_stock)+w_bond*E(R_bond).PortfolioReturn=0.6*12%+0.4*6%=7.2%+2.4%=9.6%。11.b解析思路：SharpeRatio=(PortfolioReturn-Risk-FreeRate)/PortfolioStandardDeviation.這是SharpeRatio的標(biāo)準(zhǔn)定義公式。12.a解析思路：新資產(chǎn)對(duì)組合預(yù)期收益的影響為w_new*E(R_new)=0.2*10%=2%.新組合預(yù)期收益=12%+2%=14%.新組合標(biāo)準(zhǔn)差需要計(jì)算：sqrt(w_existing^2*σ_existing^2+w_new^2*σ_new^2+2*w_existing*w_new*σ_existing*σ_new*ρ).sqrt((0.8^2*0.15^2)+(0.2^2*0.2^2)+2*0.8*0.2*0.15*0.2*0.2)=sqrt(0.01824+0.008+0.00288)=sqrt(0.02912)≈0.1706.變化=0.1706-0.15=0.0156≈