2025年CFA三級(jí)考試真題分享考試時(shí)間：______分鐘總分：______分姓名：______PartIQuestion1:Readthefollowingscenarioandanswertheassociatedquestions.YouareaportfoliomanageratAlphaInvestments.Yourclient,Mr.Smith,isawealthyindividualwhorecentlyinheritedalargesumofmoney.Hehasexpressedinterestininvestinginprivateequitybutisconcernedabouttheilliquidityandpotentiallackoftransparencyassociatedwithsuchinvestments.Youhaverecommendedaprivateequityfundtohim.Duringtheconversation,Mr.Smithmentionedthatheheardfromafriendwhoworksatacompetitorfirmthatthefundhassignificantlyunderperformeditsbenchmarkoverthepastyear.Healsosharedthathisfriendwasconsideringleavingthefirmduetodisagreementsoverinvestmentstrategy.Required:a.Identifytheconflictsofinterestthatmayexistinthisscenario.b.DescribethestepsyoushouldtaketoaddresstheseconflictsofinterestandensureyouremaincompliantwithCFAInstitute'sStandardsofProfessionalConduct.c.ExplainhowyoushouldrespondtoMr.Smith'sconcernsabouttheprivateequityfund'sperformance,consideringtheinformationprovidedandtheCFAInstituteCodeandStandards.Question2:ThefollowinginformationpertainstoasimplelinearregressionanalysisperformedonmonthlystockreturnsforCompanyXYZoverthepast36months:*Beta(β)=1.2*Alpha(α)=0.5%*Standarddeviationofthestock'sreturns(σ_stock)=15%*Standarddeviationofthemarketportfolio'sreturns(σ_market)=10%*Correlationbetweenthestock'sreturnsandthemarketportfolio'sreturns=0.7Required:a.CalculatetheexpectedreturnofCompanyXYZ'sstockusingtheCapitalAssetPricingModel(CAPM)iftherisk-freerateis2%andtheexpectedreturnofthemarketportfoliois8%.b.Interpretthemeaningofthealpha(α)coefficientinthiscontext.c.Calculatethecoefficientofdetermination(R-squared)forthisregression.d.Discussthelimitationsofusinglinearregressiontopredictfuturestockreturns.Question3:Aneconomyisexperiencingthefollowingconditions:*Inflationrateis4%.*Nominalinterestrateonone-yeargovernmentbondsis6%.*ExpectedrealGDPgrowthrateis3%.*Thecentralbankisconcernedaboutinflationandisexpectedtoraiseinterestratesinthenearfuture.Required:a.UsingtheFisherequation,calculatetheexpectedrealinterestrate.b.Explainthepotentialimpactofthecentralbank'sexpectedinterestratehikeonthefollowing:i.Consumerspendingii.Businessinvestmentiii.Exchangeratesiv.Stockmarketc.Describetherelationshipbetweenaggregatedemand,aggregatesupply,andthepricelevelinthecontextofthecurrenteconomicconditions.PartIIQuestion4:Consideracorporatebondwiththefollowingcharacteristics:*Parvalue:$1,000*Couponrate:5%(paidsemi-annually)*Timetomaturity:7years*Yieldtomaturity(YTM):4.5%Required:a.Calculatethecurrentpriceofthebond.b.CalculatetheMacaulaydurationandmodifieddurationofthebond.c.Explaintherelationshipbetweenabond'sdurationanditspricesensitivitytochangesininterestrates.d.IftheYTMincreasesto5%,estimatethepercentagechangeinthebond'spriceusingthemodifiedduration.Assumenochangeinthecouponrateortimetomaturity.Question5:Youareanalyzingtwostocks,StockAandStockB,forinclusioninanequityportfolio.Thefollowinginformationisavailable:*StockA:Expectedreturn=12%,Standarddeviation=18%*StockB:Expectedreturn=9%,Standarddeviation=12%*CorrelationbetweenStockAandStockB=0.4*Youplantoinvest60%ofyourportfolioinStockAand40%inStockB.Required:a.Calculatetheexpectedreturnoftheportfolio.b.Calculatethestandarddeviationoftheportfolio.c.ExplaintheimpactofthecorrelationbetweenStockAandStockBontheportfolio'soverallrisk.d.Discussthebenefitsofdiversificationinconstructinganequityportfoliobasedontheinformationprovided.Question6:AcalloptiononStockXYZhasthefollowingfeatures:*Stockprice(S):$50*Strikeprice(K):$45*Timetoexpiration:3months*Risk-freerate:1%(annual)*Volatilityofthestock'sreturns:30%(annual)Required:a.Calculatetheintrinsicvalueofthecalloption.b.Explaintheconceptof"timevalue"ofanoptionandhowitisinfluencedbythefactorslistedabove.c.Describethepayoffsandprofitsforthebuyerofacalloptionatexpiration.d.BrieflyexplainthedifferencebetweenaEuropeanoptionandanAmericanoption.PartIIIQuestion7:Youaremanagingaportfolioforaninstitutionalclient,apensionfund.Thefundhasalong-terminvestmenthorizonandamoderaterisktolerance.Thecurrentportfolioconsistsofthefollowingassets:*Equities:60%($60million)*Fixedincome:30%($30million)*Realestate:10%($10million)Thefund'smanagerhasproposedastrategicreallocationtoincreaseexposuretoalternativeinvestments,specificallyprivateequityandhedgefunds,whilereducingtheequityallocation.Theproposednewallocationsare:*Equities:40%*Fixedincome:25%*Realestate:10%*Privateequity:15%*Hedgefunds:10%Required:a.Calculatethedollaramountoftheportfoliothatneedstobereallocatedforeachassetclass.b.Explainthepotentialbenefitsandrisksofincreasingtheallocationtoprivateequityandhedgefundsforthispensionfund.c.Discusstheroleofalternativeinvestmentsinadiversifiedportfolio,particularlyinthecontextofalong-terminstitutionalinvestor.d.Outlinethekeyfactorsyouwouldconsiderwhenselectingspecificprivateequityandhedgefundinvestmentsforthepensionfund.Question8:Readthefollowingcasestudyandanswertheassociatedquestions.YouareaportfoliomanageratBetaAdvisors.Youaremanagingaportfolioof$100millionforaclientwhoisahigh-net-worthindividual.Theclient'sprimarygoaliscapitalappreciation,buthealsowantssomeincomegenerationandcapitalpreservation.Hiscurrentportfolioisheavilyweightedtowardstechnologystocksandhasperformedwellinrecentyearsbuthasbecomehighlyconcentratedinasinglesector.Theclientisconcernedaboutpotentialmarketvolatilityandtheconcentrationriskinhisportfolio.Hehasexpressedinterestindiversifyinghisportfoliobyaddingassetsfromdifferentassetclassesandgeographicregions.Youranalysisoftheclient'sportfolioandmarketconditionssuggeststhatthetechnologysectormaybeovervaluedintheshortterm,andthereareopportunitiesfordiversificationinemergingmarketsandalternativeinvestments.Youhaverecommendedastrategicreallocationoftheportfolio,incorporatingassetssuchasinternationalequities,fixedincomesecuritieswithdifferentdurations,andasmallallocationtoinfrastructureinvestments.Required:a.Explaintheclient'sinvestmentgoalsandthepotentialissueswithhiscurrentportfoliocomposition.b.Discusstherationalefortherecommendedstrategicreallocation,includingthepotentialbenefitsofdiversificationandthespecificassetsproposed.c.Describetheprocessyouwouldfollowtoconstructaportfoliothatmeetstheclient'sgoalsandrisktolerance,consideringtherecommendedreallocation.d.Discusstheimportanceofregularportfolioreviewandrebalancinginmaintainingthedesiredassetallocationandachievingtheclient'sinvestmentobjectives.e.Explainhowyouwouldcommunicatetheproposedportfoliostrategyandtherationalebehindittotheclient,ensuringyouadheretotheCFAInstituteStandardsofProfessionalConductregardingcommunicationwithclients.試卷答案PartIQuestion1:a.Theconflictsofinterestinthisscenarioinclude:*Confidentiality:Mr.Smithsharednon-publicinformationobtainedfromacompetitor,potentiallybreachingconfidentiality.*Misrepresentation:Thecompetitoremployee'sinformationmightbebiasedorinaccurate.Theportfoliomanagermustavoidrepresentingthisinformationasfactwithoutverification.*Clientloyalty:TheportfoliomanagermustremainloyaltoMr.Smith'sbestinterests,notthecompetitor's.*Prospecting:Ifthecompetitorisarivalfirm,discussingbusinesswithMr.Smithcouldbeconsideredprohibitedprospecting.b.Theportfoliomanagershouldtakethefollowingsteps:*Verifyinformation:Obtainindependent,verifiableinformationaboutthefund'sperformancefromreliablesources(e.g.,fundprospectuses,reputabledatabases).*Discloseconflicts:InformMr.Smithaboutthepotentialconflictsofinterest,includingthesourceandnatureoftheinformationheshared.*Advisebasedonfacts:Provideinvestmentrecommendationssolelybasedonobjectiveanalysisoftheprivateequityfund'sperformance,riskprofile,andalignmentwithMr.Smith'sgoals,usingverifieddata.*Document:Keeparecordoftheconversation,includingthedisclosureofconflictsandthebasisforanyrecommendationsmade.c.TheportfoliomanagershouldrespondtoMr.Smith'sconcernsby:*Acknowledgingconcerns:Validatehisconcernsaboutilliquidityandtransparency.*Providingobjectiveanalysis:Presentathoroughanalysisoftheprivateequityfund,includingitsinvestmentstrategy,trackrecord(usingverifieddata),riskmetrics,andhowitfitswithinMr.Smith'soverallportfolio.*Explainingthelimitations:Clarifythatpastperformanceisnotindicativeoffutureresultsandthatprivateequityinvestmentscarryinherentrisks.*Focusingonsuitability:EmphasizethattherecommendationisbasedonitssuitabilityforMr.Smith'sspecificfinancialsituation,goals,andrisktolerance,independentofthecompetitor'sopinions.*Avoidingdisparagement:Refrainfrommakingnegativecommentsaboutthecompetitorfirm.Question2:a.ExpectedReturn(E(Ri))=Rf+β*[E(Rm)-Rf]E(Ri)=0.02+1.2*(0.08-0.02)E(Ri)=0.02+1.2*0.06E(Ri)=0.02+0.072E(Ri)=0.092or9.2%b.Thealpha(α)coefficientrepresentstheexcessreturnofCompanyXYZ'sstockoverwhatwouldbepredictedbytheCAPM,givenitsbeta.Apositivealphasuggeststhatthestockhasoutperformedthemarket,controllingforitssystematicrisk(beta).Itcouldindicatesuperiormanagement,uniqueassets,orotherfactorsnotexplainedbymarketmovements.c.Coefficientofdetermination(R-squared)=(Beta*Correlation)2R-squared=(1.2*0.7)2R-squared=(0.84)2R-squared=0.7056or70.56%Thismeansthat70.56%ofthevariationinCompanyXYZ'sstockreturnsisexplainedbythevariationinthemarketportfolio'sreturns.d.Limitationsoflinearregressioninclude:*Assumptionoflinearity:Itassumesalinearrelationshipbetweentheindependentanddependentvariables,whichmaynotholdtrueinreality.*Marketefficiency:Itassumesthatthemarketisefficientandallrelevantinformationisalreadyreflectedinprices.*Randomerrors:Itassumesthaterrorsarerandomandnormallydistributed,whichmaynotbethecase.*Oversimplification:Itsimplifiesacomplexreality,potentiallyignoringotherimportantfactorsinfluencingstockreturns.Question3:a.Fisherequation:1+nominalrate=(1+realrate)*(1+inflationrate)1+0.06=(1+realrate)*(1+0.04)1.06=(1+realrate)*1.041+realrate=1.06/1.041+realrate=1.01923Realrate=0.01923or1.923%b.Potentialimpactofinterestratehike:i.Consumerspending:Likelytodecreaseasborrowingcostsrise,reducingdemandfordurablegoodsandpotentiallyleadingtohighersavings.ii.Businessinvestment:Likelytodecreaseasthecostofcapitalrises,makingborrowingmoreexpensiveforinvestmentprojects.iii.Exchangerates:Thedomesticcurrencymayappreciateashigherinterestratesattractforeigncapital,increasingdemandforthecurrency.iv.Stockmarket:Likelytodeclineashigherinterestratesincreasethecostofcapital,makingfutureearningslessvaluable,andpotentiallyleadingtohigherdiscountrates.c.Inthecontextofaggregatedemand,aggregatesupply,andthepricelevel:*Ifaggregatedemandexceedsaggregatesupply,thepriceleveltendstorise(inflation).*Ifaggregatedemandislessthanaggregatesupply,thepriceleveltendstofall(deflation).*Thecentralbank'sinterestratehikeisacontractionarymonetarypolicytoolaimedatreducingaggregatedemand,potentiallyslowingeconomicgrowthandcurbinginflation.Ifsuccessful,itcouldleadtoamorebalancedaggregatedemandandsupplysituation,stabilizingthepricelevel.PartIIQuestion4:a.Bondprice=[C*(1-(1+YTM)^-n)/YTM]+[F/(1+YTM)^n]C=5%*$1,000/2=$25(semi-annualcoupon)YTM=4.5%/2=2.25%(semi-annualYTM)n=7*2=14(numberofperiods)Bondprice=[25*(1-(1+0.0225)^-14)/0.0225]+[1000/(1+0.0225)^14]Bondprice=[25*(1-0.74137)/0.0225]+[1000/1.3793]Bondprice=[25*0.25863/0.0225]+726.34Bondprice=[25*11.5067]+726.34Bondprice=287.67+726.34Bondprice=$1014.01b.Durationmeasuresthesensitivityofabond'spricetochangesininterestrates.Ahigherdurationmeansagreaterpricechangeforagivenchangeininterestrates.ModifieddurationisamoreaccuratemeasureofpricevolatilityandiscalculatedasMacaulayduration/(1+YTM).c.Therelationshipisinverse:asabond'sdurationincreases,itspricesensitivitytochangesininterestratesincreases.Longer-termbondsgenerallyhavehigherdurationsandaremoresensitivetointerestratechanges.d.Percentagechangeinprice≈-ModifiedDuration*ΔYTMΔYTM=5%-4.5%=0.5%=0.005Percentagechangeinprice≈-4.96*0.005Percentagechangeinprice≈-0.0248or-2.48%Thebond'spriceisexpectedtodecreasebyapproximately2.48%.Question5:a.Expectedreturnofportfolio(E(Rp))=w_A*E(R_A)+w_B*E(R_B)E(Rp)=0.6*0.12+0.4*0.09E(Rp)=0.072+0.036E(Rp)=0.108or10.8%b.Standarddeviationofportfolio(σp)=√[w_A^2*σ_A^2+w_B^2*σ_B^2+2*w_A*w_B*σ_A*σ_B*ρ]σp=√[(0.6^2*0.18^2)+(0.4^2*0.12^2)+2*0.6*0.4*0.18*0.12*0.4]σp=√[(0.36*0.0324)+(0.16*0.0144)+(2*0.6*0.4*0.18*0.12*0.4)]σp=√[0.011664+0.002304+0.003456]σp=√0.017424σp=0.13195or13.20%c.TheimpactofthecorrelationbetweenStockAandStockBontheportfolio'soverallriskissignificant.Alowercorrelationbetweenthetwostocksreducestheportfolio'soverallrisk(standarddeviation)becausethereturnsonthetwostocksarenotperfectlypositivelycorrelated.Whenonestockperformspoorly,theothermayperformwell,offsettingsomeofthelosses.Diversificationbenefitsaremaximizedwhenthecorrelationbetweenassetsislow.d.Benefitsofdiversificationinclude:*Riskreduction:Combiningassetswithlowornegativecorrelationscanreducetheoverallriskoftheportfoliowithoutnecessarilysacrificingreturns.*Improvedrisk-adjustedreturns:Diversificationcanleadtoamoreefficientportfolio,achievinghigherreturnsforagivenlevelofriskorlowerriskforagivenlevelofreturns.*Liquidityenhancement:Includingassetswithdifferentliquiditycharacteristicscanimprovetheoverallliquidityoftheportfolio.*Smootherreturns:Diversificationcanleadtomorestableportfolioreturnsovertimebyreducingtheimpactofvolatilityinanysingleasset.Question6:a.Intrinsicvalueofcalloption=Max(S-K,0)Intrinsicvalue=Max($50-$45,0)Intrinsicvalue=$5b.Thetimevalueofanoptionisthedifferencebetweentheoption'smarketpriceanditsintrinsicvalue.Itrepresentsthepotentialfortheoption'svaluetoincreasebeforeexpiration.Timevalueisinfluencedby:*Timetoexpiration:Thelongerthetimetoexpiration,thehigherthetimevalue,asthereismoretimefortheunderlyingasset'spricetomovefavorably.*Volatility:Highervolatilityincreasesthetimevaluebecauseitincreasestheprobabilityofalargepriceswingintheunderlyingasset.*Risk-freerate:Ahigherrisk-freerategenerallyincreasesthetimevalueofacalloptionanddecreasesthetimevalueofaputoption.*Underlyingassetprice:Thetimevaluedecreasesastheunderlyingasset'spricemovesfavorablytowardsthestrikeprice.c.Payoffsandprofitsforthebuyerofacalloptionatexpiration:*Payoff:Thepayoffdependsontherelationshipbetweentheunderlyingasset'sprice(S)andthestrikeprice(K)atexpiration.*IfS>K,Payoff=S-K*IfS≤K,Payoff=0*Profit:Profit=Payoff-Premiumpaid*IfS>K,Profit=(S-K)-Premium*IfS≤K,Profit=-PremiumThebuyer'smaximumlossislimitedtothepremiumpaidfortheoption.d.AEuropeanoptioncanonlybeexercisedatexpiration,whileanAmericanoptioncanbeexercisedatanytimeuptoexpiration.ThisgivestheholderofanAmericanoptionmoreflexibilitybutgenerallymakesitmorevaluable(andthusmoreexpensive)thanaEuropeanoptionwiththesamestrikepriceandexpirationdate.PartIIIQuestion7:a.Dollaramountofreallocation:*Equities:$60million*(40%-60%)=$60million*(-20%)=-$12million(sell$12million)*Fixedincome:$30million*(25%-30%)=$30million*(-5%)=-$1.5million(sell$1.5million)*Realestate:$10million*(10%-10%)=$10million*(0%)=$0(nochange)*Privateequity:$100million*(15%-0%)=$100million*(15%)=$15million(buy$15million)*Hedgefunds:$100million*(10%-0%)=$100million*(10%)=$10million(buy$10million)b.Benefitsofincreasingallocationtoprivateequityandhedgefunds:*Potentialforhighreturns:Theseassetclassescanofferhigherreturnsthantraditionalassets,especiallyoverthelongterm.*Diversification:Theyareoftenuncorrelatedwithtraditionalassetclasses,providingdiversificationbenefitsandpotentiallyreducingportfoliorisk.*Inflationhedging:Someprivateequityinvestmentscanprovideinflationhedging,astheymayhavetheabilitytoraisepricesinlinewithinflation.Risksinclude:*Liquidity:illiquiditycanmakeitdifficulttosellinvestmentsquicklywithoutincurringsignificantcosts.*Complexity:Theseinvestmentscanbecomplexanddifficulttoevaluate.*Higherfees:Managementfeesandperformancefeesareoftenhigherthanfortraditionalinvestments.*Performancevolatility:Returnscanbehighlyvolatileandnegativeperformanceispossible.c.Keyfactorswhenselectingprivateequityandhedgefundinvestments:*Managerexpertiseandtrackrecord:Evaluatethemanager'sexperience,investmentphilosophy,andpastperformance.*Investmentstrategy:Understandthefund'sstrategy,includingitsfocussectors,geographicalareas,andinvestmentstage.*Riskmanagement:Assessthefund'sriskmanagementprocessesandhowitcontrolsdownsiderisk.*Feesandexpenses:Comparethefund'sfeesandexpensestothoseofotherfunds.*Liquidityandlock-upperiod:Considerthefund'sliquidityandthelengthofthelock-upperiod.*Alignmentofinterests:Ensurethatthemanager'sinterestsarealignedwiththeinvestors'interests.d.Processforconstructingtheportfolio:1.Defineinvestmentobjectivesandconstraints:Confirmtheclient'sgoals,timehorizon,risktolerance,andliquidityneeds.2.Developastrategicassetallocation:Createatargetallocationforeachassetclassbasedontheclient'sobjectivesandconstraints.3.Selectspecificinvestments:Choosespecificprivateequityandhedgefundinvestmentsthatalignwiththeinvestmentstrategyandmeettheselectioncriteria.4.Implementtheportfolio:Purchasetheselectedinvestmentsaccordingtotheplan.5.Monitorandrebalance:Regularlyreviewtheportfolio'sperformanceandmakeadjustmentsasneededtomaintainthedesiredassetallocation.e.Communicationwiththeclient:*Explainthestrategy:Clearlyexplaintheinvestmentstrategy,includingtherationalefortherecommendedreallocationandthespecificassetsselected.*Highlightbenefitsandrisks:Discussthepotentialbenefitsandrisksofthestrategy,includingtheexpectedreturns,volatility,andliquidityconsiderations.*Useclearlanguage:Avoidtechnicaljargonandexplaincomplexconceptsinsimpleterms.*Provideregularupdates:Keeptheclientinformedabouttheportfolio'sperformanceandanychangestothestrategy.*AdheretoStandards:FollowCFAInstituteStandardsofProfessionalConductregardingcommunication,includingaccuracy,fairness,andavoidingconflictsofinterest.Question8:a.Theclient'sinvestmentgoalsarecapitalappreciation,incomegeneration,andcapitalpreservation.Theissueswithhiscurrentportfolioinclude:*Concentrationrisk:Overweightinginthetechnologysectormakestheportfoliovulnerabletosector-specificrisks.*Lackofdiversification:Theportfoliolacksexposuretootherassetclassesandgeographicregions,limitingdiversificationbenefits.*Potentialunderperformance:Thetechnologysectormaybeovervalued,andtheportfoliomayunderperformindifferentmarketenvironments.b.Rationalefortherecommendedreallocation:*Diversification:Addinginternationalequitiesandfixedincomesecuritieswithdifferentdurationsdiversifiestheportfolioacrossassetclassesandgeographies.*Hedginginflation:Fixedincomesecuritiescanprovideincomeandpotentiallyhedgeagainstinflation.*Capturinggrowthinemergingmarkets:Internationalequitiescanprovideexposuretogrowthopportunitiesinemergingmarkets.*Alternativeinvestments:Infrastructureinvestme