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1、2020年12月CFA三级写作题ASSETALLOCATIONANDRELATEDDECISIONSINPORTFOLIOMANAGEMENT今年由于疫情的缘故，CFA考试被迫延期。虽然给了大家更多的复习时间，但也不可掉以轻心。近年来，CFA考试的难度在逐步提高，并且在三级中更偏向实务与理论结合的考察。相比2019年考纲，2020年考纲发生了较多的变化。其中关于经济学的部分，更名为资本市场预期，并进行了重大改变；衍生产品与资产配置中的外汇管理合并在一起，并进行了较大的改写；另类投资的内容完全重新改写；交易与业绩评估合并在一起.并重新编写。而一向是考试重点的私人财富管理和机构组合管理也发生了较大
2、变化，其中私人财富管理的第一个RCading重新编写，而机构组合管理也进行了重新编写，这些变化需引起考生重视。为了全面应对考试，我们全面推出了的各种学习平台，如金程网校、手机APP、金程CFA答疑等活动，请各位充分利用。如有学术问题，请登录至金程网校提问。祝大家好运，顺利通过CFA三级考试，加油！AssetAllocationandRelatedDecisionsinPortfolioManagementCaseIzJohnTombJohnTombisaninvestmentadvisoratanassetmanagementfirm.Heisdevelopinganassetallocati
3、onforJamesYoungmall,aclientofthefirm.TombconsiderstwopossibleallocationsforYoungmall.AllocationAconsistsoffourassetclasses:cash,USbonds,USequities,andglobalequities.AllocationBincludesthesesamefourassetclasses,aswellasglobalbonds.Youngmallhasarelativelylowrisktolerancewithariskaversioncoefficient()o
4、f7.Tombrunsmean-varianceoptimization(MVO)tomaximizethefollowingutilityfunctiontodeterminethepreferredallocationforYoungmall:UIH=(/U-Ooo5TheresultingMVOstatisticsforthetwoassetallocationsarepresentedinExhibit1.Exhibit1MVOPortfolioStatisticsAllocationAAllocationBExpectedreturn6.7%5.9%Expectedstandardd
5、eviation11.9%10.7%DeterminewhichallocationinExhibit1TombshouldrecommendtoYoungmall.Justifyyourresponse.DeterminewhichallocationinExhibit1TombshouldrecommendtoYoungmall.(circleone)AllocationAAllocationBJustifyyourresponse.Solution:DeterminewhichallocationinExhibit1TombshouldrecommendtoYoungmaIL(circl
6、eone)AllocationAAllocationBJustifyyourresponse.TombshouldrecommendAllocationB.TheexpectedutilityofAllocationBis1.89%,whichishigherthanAllocationA,sexpectedutilityof1.74%.MVOprovidesaframeworktodeterminehowmuchtoallocatetoeachassetclassortocreatetheoptimalassetmix.Thegivenobjectivefunctionis:U.=(仆)-0
7、.005UsingthegivenobjectivefunctionandtheexpectedreturnsandexpectedstandarddeviationsforAllocationsAandBztheexpectedutilities(certainty-equivalentreturns)forthetwoallocationsarecalculatedas:AllocationA:6.7%-AllocationB:5.9%-0.005(7)(10.7%)2=1.89%Therefore,TombshouldrecommendAllocationBbecauseitresult
8、sinhigherexpectedutilitythanAllocationA.Case2:WalkerPatelWalkerPatelisaportfoliomanagerataninvestmentmanagementfirm.Aftersuccessfullyimplementingmean-varianceoptimization(MVO),hewantstoapplyreverseoptimizationtohisportfolio.Foreachassetclassintheportfolio,Patelobtainsmarketcapitalizationdata,betasco
9、mputedrelativetoaglobalmarketportfolio,andexpectedreturns.Thisinformation,alongwiththeMVOassetallocationresults,arepresentedinExhibit1.Exhibit1AssetClassDataandMVOAssetAllocationResultsAssetClassMarketCap(trillions)BetaExpectedReturnsMVOAssetAllocationCash$4.20.02.0%10%USbonds$26.80.54.5%20%USequiti
10、es$22.21.48.6%35%Globalequities$27.51.710.5%20%Globalbonds$27.10.64.7%15%Total$107.8Therisk-freerateis2.0%,andtheglobalmarketriskpremiumis5.5%.Contrast,usingtheinformationprovidedabove,theresultsofareverseoptimizationapproachwiththatoftheMVOapproachforeachofthefollowing:i.Theassetallocationmixii.The
11、valuesoftheexpectedreturnsforUSequitiesandglobalbondsJustifyyourresponse.Solution:Contrast,usingtheinformationprovidedabove,theresultsofareverseoptimizationapproachwiththatoftheMVOapproachforeachofthefollowing:i.TheassetallocationmixTheassetallocationweightsforthereverseoptimizationmethodareinputsin
12、totheoptimizationandaredeterminedbythemarketcapitalizationweightsoftheglobalmarketportfolio.TheassetallocationweightsfortheMVOmethodareoutputsoftheoptimizationwiththeexpectedreturns,covariances,andariskaversioncoefficientusedasinputs.Thetwomethodsresultinsignificantlydifferentassetallocationmixes.In
13、contrasttoMVOzthereverseoptimizationmethodresultsinahigherpercentagepointallocationtoglobalbonds,USbonds,andglobalequitiesaswellasalowerpercentagepointallocationtocashandUSequities.Thereverseoptimizationmethodtakestheassetallocationweightsasitsinputsthatareassumedtobeoptimal.Theseweightsarecalculate
14、dasthemarketcapitalizationweightsofaglobalmarketportfolio.Incontrast,theoutputsofanMVOaretheassetallocationweights,whicharebasedon(1)expectedreturnsandcovariancesthatareforecastedusinghistoricaldataand(2)ariskaversioncoefficient.Thetwomethodsresultinsignificantlydifferentassetallocationmixes.Incontr
15、asttoMVO,thereverseoptimizationmethodresultsina4.9,5.5,and10.1higherpercentagepointallocationtoUSbonds,globalequities,andglobalbonds,respectively,anda6.1and14.4lowerpercentagepointallocationtocashandUSequities,respectively.Theassetallocationunderthetwomethodsisasfollows:AssetAllocationWeightsAssetCl
16、assMarketCap(trillions)ReverseOptimizationMVOApproachDifferenceCash$4,23.9%10%-6.1%USbonds$26.824.9%20%4.9%USequities$22.220.6%35%-144%Globalequities$27.525.5%20%5.5%Globalbonds$27.125.1%15%10.1%Total$107.8100.0%100.0%ii.ThevaluesoftheexpectedreturnsforUSequitiesandglobalbonds.Forthereverseoptimizat
17、ionapproach,theexpectedreturnsofassetclassesaretheoutputsofoptimizationwiththemarketcapitalizationweights,covariances,andtheriskaversioncoefficientusedasinputs.Incontrast,fortheMVOapproach,theexpectedreturnsofassetclassesareinputstotheoptimization,withtheexpectedreturnsgenerallyestimatedusinghistori
18、caldata.ThecomputedvaluesfortheexpectedreturnsforglobalbondsandUSequitiesusingthereverseoptimizationmethodare5.3%and9.7%zrespectively.Incontrast,theexpectedreturnestimatesusedintheMVOapproachfromExhibit1forglobalbondsandUSequitiesare4.7%and8.6%zrespectively.Theoutputofthereverseoptimizationmethodare
19、optimizedreturnswhichareviewedasunobservedequilibriumorimputedreturns.Theequilibriumreturnsareessentiallylong-runcapitalmarketreturnsprovidedbyeachassetclassandarestronglylinkedtoCAPM.Incontrast,theexpectedreturnsintheMVOapproacharegenerallyforecastedbasedonhistoricaldataandareusedasinputsalongwithc
20、ovariancesandtheriskaversioncoefficientintheoptimization.Thereverse-optimizedreturnsarecalculatedusingaCAPMapproach.ThereturnonanassetclassusingtheCAPMapproachiscalculatedasfollows:ReturnonAssetClass=Risk-FreeRate+(Beta)(MarketRiskPremium)Therefore,theimpliedreturnsforglobalbondsandUSequitiesarecalc
21、ulatedasfollows:ReturnonGlobalBonds=2.0%+(0.6)(5.5%)=5.3%ReturnonUSEquities=2.0%+(1.4)(55%)=9.7%TheimpliedequilibriumreturnsforglobalbondsandUSequitiesare5.3%and9.7%frespectively.Theseimpliedreturnsareabovetheforecastedreturnsbasedonhistoricaldata(fromExhibit1)usedasinputsintheMVOapproachforglobalbo
22、ndsandUSequitiesof4.7%and8.6%,respectively.Case3:ViktoriaJohanssonViktoriaJohanssonisnewlyappointedasmanagerofABCCorporationspensionfund.Thecurrentmarketvalueofthefund,sassetsis$10billion,andthepresentvalueofthefund,sliabilitiesis$8.5billion.Thefundhashistoricallybeenmanagedusinganasset-onlyapproach
23、,butJohanssonrecommendstoABCsboardofdirectorsthattheyadoptaliability-relativeapproach,specificallythehedging/return-seekingportfoliosapproach.Johanssonassumesthatthereturnsofthefundsliabilitiesaredrivenbychangesinthereturnsofindex-linkedgovernmentbonds.Exhibit1presentsthreepotentialassetallocationch
24、oicesforthefund.Exhibit1PotentialAssetAllocationsChoicesforABCCorpsPensionFundAssetClassAllocation1Allocation2Allocation3Cash15%5%0%Index-linkedgovernmentbonds70%15%85%Corporatebonds0%30%5%Equities15%50%10%DeterminewhichassetallocationinExhibit1wouldbemostappropriateforJohanssongivenherrecommendatio
25、n.Justifyyourresponse.DeterminewhichassetallocationinExhibit1wouldbemostappropriateforJohanssongivenherrecommendation,(circleone)Allocation1Allocation2Allocation3Justifyyourresponse.Solution:DeterminewhichassetallocationinExhibit1wouldbemostappropriateforJohanssongivenherrecommendation,(circleone)Al
26、location1Allocation2Allocation3Justifyyourresponse.Allocation3ismostappropriate.Tofullyhedgethefund,sliabilities,85%($8.5billion/$10.0billion)ofthefund,sassetswouldbelinkedtoindex-linkedgovernmentbonds.Residual$1.5billionsurpluswouldbeinvestedintoareturn-seekingportfolio.Thepensionfundcurrentlyhasas
27、urplusof$1.5billion($10.0billion-$8.5billion).Toadoptahedging/return-seekingportfoliosapproach,Johanssonwouldfirsthedgetheliabilitiesbyallocatinganamountequaltothepresentvalueofthefundsliabilities,$8.5billion,toahedgingportfolio.Thehedgingportfoliomustincludeassetswhosereturnsaredrivenbythesamefacto
28、rsthatdrivethereturnsoftheliabilities,whichinthiscasearetheindex-linkedgovernmentbonds.So,Johanssonshouldallocate85%($8.5billion/$10.0billion)ofthefund,sassetstoindex-linkedgovernmentbonds.Theresidual$1.5billionsurpluswouldthenbeinvestedintoareturn-seekingportfolio.Therefore,Allocation3wouldbethemos
29、tappropriateassetallocationforthefundbecauseitallocates85%ofthefundsassetstoindex-linkedgovernmentbondsandtheremaindertoareturn-seekingportfolioconsistingofcorporatebondsandequities.Case4:MikeandKerryArmstrongMikeandKerryArmstrongareamarriedcouplewhorecentlyretiredwithtotalassetsof$8million.TheArmst
30、rongsmeetwiththeirfinancialadvisor,BrentAbbott,todiscussthreeoftheirfinancialgoalsduringtheirretirement.Goal1:An85%chanceofpurchasingavacationhomefor$5millioninfiveyears.Goal2:A99%chanceofbeingabletomaintaintheircurrentannualexpendituresof$100,000forthenext10years,assumingannualinflationof3%fromYear
31、2onward.Goal3:A75%chanceofbeingabletodonate$10milliontocharitablefoundationsin25years.Abbottsuggestsusingagoals-basedapproachtoconstructaportfolio.Hedevelopsasetofsub-portfoliomodules,presentedinExhibit1.AbbottsuggestsinvestinganyexcesscapitalinModuleA.ExhibitlHighestProbability-andHorizon-AdjustedR
32、eturnSub-PortfolioModulesunderDifferentHorizonandProbabilityScenariosPortfolioCharacteristicsABCDExpectedreturn6.5%7.9%8.5%8.8%Expectedvolatility6.0%7.7%8.8%9.7%AnnualizedMinimumExpectationReturnsTimeHorizon5YearsRequiredSuccess99%03%-0.1%-0.7%-13%85%3.7%4.3%4.4%4.3%75%4.7%5.6%S.8%5.9%TimeHorizon10Y
33、earsRequiredSuccess99%2.1%22%2.0%1.7%85%45%5.4%5.6%5.6%75%5.2%6.3%6.6%6.7%TimeHorizon25YearsRequiredSuccess99%3.7%4.3%4.4%43%85%5.3%6.3%67%68%75%5,7%6.9%73%7.5%1.Select,foreachofArmstrongsthreegoals,whichsub-portfoliomodulefromExhibit1Abbottshouldchooseinconstructingaportfolio.Justifyeachselection.S
34、elect,foreachofArmstrongsthreegoals,whichsub-portfoliomodulefromExhibit1Abbottshouldchooseinconstructingaportfolio,(circleonemoduleforeachgoal)GoallGoal2Goal3ModuleAModuleAModuleAModuleBModuleBModuleBModuleCModuleCModuleCModuleDModuleDModuleDSolution:Select,foreachofArmstrongsthreegoals,whichsub-por
35、tfoliomodulefromExhibit1Abbottshouldchooseinconstructingaportfolio,(circleonemoduleforeachgoal)Goal1Goal2Goal3ModuleAModuleAModuleAModuleModuleBModuleBModuleCModuleCModuleCModuleDModuleDModuleDJustifyeachselection.ModuleCshouldbechosenforGoal1,ModuleBshouldbechosenforGoal2,andModuleDshouldbechosenfo
36、rGoal3.Themodulethatshouldbeselectedforeachgoalistheonethatoffersthehighestreturngiventhetimehorizonandrequiredprobabilityofsuccess.Themodulethatshouldbeselectedforeachgoalistheonethatoffersthehighestreturngiventhetimehorizonandrequiredprobabilityofsuccess.ForGoal1,whichhasatimehorizonoffiveyearsand
37、arequiredprobabilityofsuccessof85%,ModuleCshouldbechosenbecauseits4.4%expectedreturnishigherthantheexpectedreturnsofalltheothermodules.Similarly,forGoal2,whichhasatimehorizonof10yearsandarequiredprobabilityofsuccessof99%,ModuleBshouldbechosenbecauseits2.2%expectedreturnishigherthantheexpectedreturns
38、ofalltheothermodules.Finally,forGoal3,whichhasatimehorizonof25yearsandarequiredprobabilityofsuccessof75%,ModuleDshouldbechosenbecauseits7.5%expectedreturnishigherthantheexpectedreturnsofalltheothermodules.2.Constructtheoverallgoals-basedassetallocationfortheArmstrongsgiventheirthreegoalsConstructthe
39、overallgoals-basedassetallocationfortheArmstrongsgiventheirthreegoalsandAbbotfssuggestionforinvestinganyexcesscapital.(insertthepercentageofthetotalassetstobeinvestedineachmodule)ModuleAModuleBModuleCModuleDShowyourcalculations.Solution:GuidelineAnswer:Themodulethatshouldbeselectedforeachgoalistheon
40、ethatoffersthehighestreturngiventhetimehorizonandrequiredprobabilityofsuccess.Approximately16.4%,12.7%,50.4%,and20.5%shouldbeinvestedinModulesA,B,C,andD,respectively.Theappropriategoals-basedallocationfortheArmstrongsisasfollows:Goals123SurplusHorizon(years)51025Probabilityofsuccess85%99%75%Selected
41、moduleCBDADiscountrate4.4%22%7.5%Dollarsinvested(millions)$4.03$1.01$1.64$1.32Asa%oftotal50.4%127%20.5%16.4%Supportingcalculations:ForGoal1,whichhasatimehorizonoffiveyearsandarequiredprobabilityofsuccessof85%,ModuleCshouldbechosenbecauseits4.4%expectedreturnishigherthantheexpectedreturnsofalltheothe
42、rmodules.ThepresentvalueofGoal1iscalculatedasfollows:N=5,PV=-5,000Qoo,l/Y=4.4%;CPTPV=$4,031,508(or$4.03million)So,approximately50.4%ofthetotalassetsof$8million(=$4.03million/$8.00million)shouldbeallocatedtoModuleC.ForGoal2,whichhasatimehorizonof10yearsandarequiredprobabilityofsuccessof99%,ModuleBsho
43、uldbechosenbecauseits2.2%expectedreturnishigherthantheexpectedreturnsofalltheothermodules.ThepresentvalueofGoal2iscalculatedasfollows:PV=$1,013,670(or$1.01million)So,approximately12.7%ofthetotalassetsof$8million(=$1.01million/$8.00million)shouldbeallocatedtoModuleB.ForGoal3,whichhasatimehorizonof25y
44、earsandarequiredprobabilityofsuccessof75%,ModuleDshouldbechosenbecauseits7.5%expectedreturnishigherthantheexpectedreturnsofalltheothermodules.ThepresentvalueofGoal3iscalculatedasfollows:N=25,PV=-10,000,000,l/Y=7.5%;CPTPV=$1,639,791(or$1.64million)So,approximately20.5%ofthetotalassetsof$8million(=$1.64million/$8.00million)shouldbeallocatedtoModuleD.Finally,thesurplusof$1,315,032(=$8,000,000-$4,031,508-$1,013,670-$1,639,791),representing16.4%(=$1.32million/$8.00million),shouldbeinvestedinModuleAfollowingAbbotfssuggestion.
