2019cfa ii原版书课后题reading50-analysis of active portfolio management

......打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此的。违者将被4.Constraints:Ananswerthatinvolvesaccountingforsuchconstraintsaslongonlyorturnoverlimitsusingatransfercoefficientisaweakeranswerbecausetheimpactofconstraintsandthetransfercoefficientisawell-knownrefinementofthefundamentallaw,eventhoughitdoesnotappeartobeusedinthisexample.Thisreadingcoversanumberofkeyconceptsandprinciplesassociatedwithactiveportfoliomanagement.Activemanagementisbasedonthemathematicsandprinciplesofriskandreturnfrombasicmean–varianceportfoliotheory,butwithafocusonvalueaddedcomparedwithabenarkportfolio.Criticalconceptscontainedinthereadingincludethefollowing:Valueaddedisdefinedasthedifferencebetweenthereturnonthemanagedportfolioandthereturnonapassivebenarkportfolio.Thisdifferenceinreturnsmightbepositiveornegativeafterthefactbutwouldbeexpectedtobepositivebeforethefactoractivemanagementwouldgenerallynotbejustified.Valueaddedisrelatedtoactiveweightsintheportfolio,definedasdifferencesbetweenthevariousassetweightsinthemanagedportfolioandtheirweightsinthebenarkportfolio.Individualassetscanbeoverweighted(havepositiveactiveweights)orunderweighted(havenegativeactiveweights),butthecompletesetofactiveweightssumstozero.Positivevalueaddedisgeneratedwhenpositive-active-weightassetshavelargerreturnsthannegative-active-weightassets.Bydefiningindividualassetactivereturnsasthedifferencebetweentheassettotalreturnandthebenarkreturn,valueaddedisshowntobepositiveifandonlyifend-of-periodrealizedactiveassetreturnsarepositivelycorrelatedwiththeactiveassetweightsestablishedatthebeginningoftheperiod.Valueaddedcancomefromavarietyofactiveportfoliomanagementdecisions,includingsecurityselection,assetclassallocation,andevenfurther positionsintoeconomicsectorweightingsandgeographicorcountryweights.TheSharperatiomeasuresrewardperunitofriskinabsolutereturns,whereastheinformationratiomeasuresrewardperunitofriskinbenarkrelativereturns.Eitherratiocanbeappliedexantetoexpectedreturnsorexposttorealizedreturns.Theinformationratioisakeycriteriononwhichtoevaluateactivelymanagedportfolios.打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事 。违者将 HigherinformationratioportfolioscanbeusedtocreatehigherSharperatioportfolios.Theoptimalamountofactivemanagementthatizesaportfolio’sSharperatioispositivelyrelatedtotheassumedforecastingaccuracyorexanteinformationcoefficientoftheactivestrategy.Theactiveriskofanactivelymanagedstrategycanbeadjustedtoitsdesiredlevelbycombiningitwithapositionintheben ark.Furthermore,onceaninvestorhasidentifiedtheumSharperatioportfolio,thetotalvolatilityofaportfoliocanbeadjustedtoitsdesiredlevelbycombiningitwithcash(two-fundseparationconcept).ThefundamentallawofactiveportfoliomanagementbeganasaconceptualframeworkforevaluatingthepotentialvalueaddedofvariousinvestmentstrategiesbuthasemergedasanoperationalsystemformeasuringtheessentialcomponentsofthoseactiveAlthoughthefundamentallawprovidesaframeworkfor yzinginvestmentstrategies,theessentialinputsofforecastedassetreturnsandrisksstillrequirejudgmentinformulatingtheexpectedreturns.Thefundamentallawseparatestheexpectedvalueadded,orportfolioreturnrelativetotheben arkreturn,intothebasicelementsofthestrategy:skillasmeasuredbytheinformationstructuringoftheportfolioasmeasuredbythetransferbreadthofthestrategymeasuredbythenumberofindependentdecisionsperyear,aggressivenessmeasuredbythebenarktrackingThelastthreeofthesefourelementsmaybethecontroloftheinvestoriftheyarespecifiedbyinvestmentorconstrainedbyregulation.Thefundamentallawhasbeenappliedinsettingsthatincludetheselectionofcountryequitymarketsinaglobalequityfundandthetimingofcreditanddurationexposuresin efund.Thefundamentallawofactivemanagementhaslimitations,includinguncertaintyabouttheexanteinformationcoefficientandtheconceptualdefinitionofbreadthasthenumberofindependentdecisionsbytheinvestor.Black,,andRobertLitterman.1992.“GlobalPortfolioOptimization.”FinancialystsJournal,vol.48,no.5(September/October):28–43.Brinson,GaryP.,L.RandolphHood,andGilbertL.Beebower.1986.“DeterminantsofPortfolioPerformance.”FinancialystsJournal,vol.42,no.4(July–August):39–44.打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或 。违者将 Buckle,David.2004.“HowtoCalculateBreadth:AnEvolutionoftheFundamentalLawofActivePortfolioManagement.”JournalofAssetManagement,vol.4,no.6:393–405.Clarke,Roger,HarindradeSilva,andStevenThorley.2002.“PortfolioConstraintsandtheFundamentalLawofActiveManagement.”FinancialystsJournal,vol.58,no.5Clarke,Roger,HarindradeSilva,andStevenThorley.2005.“PerformanceAttributionandtheFundamentalLaw.”FinancialystsJournal,vol.61,no.5(September/October):70–83.Clarke,Roger,HarindradeSilva,andStevenThorley.2006.“TheFundamentalLawofActivePortfolioManagement.”JournalofInvestmentManagement,vol.4,no.3:54–72.Cremers,K.J.Martijn,andAnttiPetajisto.2009.“HowActiveIsYourFundManager?”ReviewofFinancialStudies,vol.22,no.9:3329–3365.Elton,Edward,andMartinGruber.1973.“EstimatingtheDependenceStructureofSharePrices.”JournalofFinance,vol.28,no.5:1203–1232.,Bernd,andRussellWermers.2013.PerformanceEvaluationandAttributionofSecurityPortfolios.Oxford,UK:ElsevierInc.Grinold,RichardC.1989.“TheFundamentalLawofActiveManagement.”JournalofPortfolioManagement,vol.15,no.3(Spring):30–37.Grinold,RichardC.1994.“AlphaisVolatilityTimesICTimesScore,orRealAlphasDon’tGetEaten.”JournalofPortfolioManagement,vol.20,no.4(Summer):9–16.Grinold,RichardC.,andRonaldN.Kahn.1999.ActivePortfolioManagement:AtativeApproachforProvidingSuperiorReturnsandControllingRisk,2nded.NewYork:McGraw-Kan,PaulD.2012/2013.“2013.“What’sWrongwithMultiplyingbytheSquareRootofTwelve.”JournalofPerformanceMeasurement,vol.17,no.2(Winter):16–24.Markowitz,HarryM.1952.“PortfolioSelection.”JournalofFinance,vol.7,no.Qian,Edward,andRonaldHua.2004.“ActiveRiskandInformationRatio.”JournalofInvestmentManagement,vol.2,no.3(ThirdQuarter):20–34.Sharpe,WilliamF.1964.“CapitalAssetPrices:ATheoryofMarketEquilibriumunderConditionsofRisk.”JournalofFinance,vol.19,no.3:425–442.Treynor,J.,andBlack.1973.“HowtoUseSecurity ysistoImprovePortfolioSelection.”JournalofBusiness,vol.46:66–86.PRACTICE©2016CFAInstitute.All 打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此 。违者将 WeiLiumakestwostatementsaboutactiveportfolioStatementStatement

The“activereturn”ofanactivelymanagedportfolioisthedifferencebetweentheportfolio’sreturnandthereturnontheben portfolio,andisequaltothemanagedportfolio’salpha.Theactiveweightsarethedifferencesinthemanagedportfolio’sweightsandthebenark’sweights.AreLiu’sstatementsOnlyStatement1isOnlyStatement2isBothstatementsareTheben arkweightsandreturnsforeachofthefivestocksintheCapitolindexaregivenbelow.TheTukolFundusestheCapitolIndexasitsben ark,andthefund’sportfolioweightsarealsoshowninthetable.WeightReturn123485Whatisthevalueadded(activereturn)fortheTukolConsiderthefollowingassetclassreturnsforcalendaryearAssetWeight(%)Return(%)Domestic8International956Whatisthevalueadded(oractivereturn)forthemanaged打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此 。违者将 GertrudementionstwopropertiesoftheSharperatioandtheinformationratiothatshesaysareveryuseful.PropertyProperty

TheSharperatioisunaffectedbytheadditionofcashorleverageinaTheinformationratioforanunconstrainedportfolioisunaffectedbytheaggressivenessoftheactiveweights.Are’stwopropertiesNo.OnlyProperty1isNo.OnlyProperty2isThefollowinginformationrelatestoQuestions5andS&PIndigoExpectedannualReturnstandardSharpeActiveActiveInformationWhatistheumSharperatiothatamanagercanachievebycombiningtheS&P500benarkportfolioandtheIndigoFund?WhichofthefollowingpairsofweightswouldbeusedtoachievethehighestSharperatioandoptimalamountofactiveriskthroughcombiningtheIndigoFundandbenarkportfolio,respectively?1.014onIndigoand–0.014ontheben1.450onIndigoand–0.450ontheben打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 。违者将 1.500onIndigoand–0.500onthe ThebenarkportfolioistheS&P500.WhichofthefollowingthreeportfolioscanbecombinedwiththebenarkportfoliotoproducethehighestcombinedSharperatio?S&PPortfolioPortfolioPortfolioExpectedannualReturnstandardSharpeActive00Active0PortfolioPortfolioPortfolioBasedonthefundamentallawofactivemanagement,ifaportfoliomanagerhasaninformationratioof0.75,aninformationcoefficientof0.1819,andatransfercoefficientof1.0,howmanysecuritiesareintheportfoliomanager’sfund,makingtheassumptionthattheactivereturnsareuncorrelated.AboutAboutAboutTwoystsmakethefollowingstatementsaboutthetransfercoefficientinthefullfundamentallawofactivemanagement:ystOnesays,“Thetransfercoefficientmeasureshowwelltherealizedreturnscorrelatewiththeanticipatedreturns,adjustedforrisk.”ystTwosays,“Thetransfercoefficientmeasureshowwelltherealizedreturnscorrelatewiththeactiveweights,adjustedforrisk.”Which,ifeither,ystisOnlyystOneisOnlyystTwois ystisThefullfundamentallawofactivemanagementisstatedasE(RA)=(TC)(IC)Whichcomponentontherighthandsiderepresentstheextenttowhichtheportfoliomanager’sexpectationsarerealized?The打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此 。违者将 transfercoefficient,informationcoefficient,breadth, ystisgiventhefollowinginformationaboutaportfolioanditsben ark.Inparticular,the ystisconcernedthattheportfolioisaclosetindexfund.1TheT-billreturnchosentorepresenttherisk- rateis0.50%. ActiveActiveSharpeInformationWhichofthefollowingthreestatementsdoesnotjustifyyourbeliefthattheportfolioisaclosetindex?TheSharperatiooftheportfolioisclosetotheSharperatioofthebenTheinformationratiooftheportfolioisrelativelyTheactiveriskoftheportfolioisveryStatementStatementStatementYouareconsideringthreemanagersforasmallcapgrowthmandate.Aftercarefulysis,youproducethefollowingforwardlookingexpectationsaboutthemanagers’activeriskandactivereturn:ManagerManagerManagerActiveActiveIfyouintendtorelyontheinformationratiotomakeyourdecision,whichmanagershouldyouchoose?ManagerManagerManager打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此的。违者将被Youhaveaportfolio100%allocatedtoamanagerwithanex-postactiveriskat8.0%.Youchoosetoallocatea75%positiontotheactivemanagerand25%tothebenarktobringtheportfoliobacktoyourtargetactiveriskof6.0%.Ifthemanager’sinformationratiois0.50,whathappenstotheinformationratiooftheportfolioafterthereallocation?Theinformationratioincreasesbecausetheloweractiveriskreducesthedenominatoroftheratio.Theinformationratioremainsunchangedbecauseallocationsbetweentheactiveportfolioandtheben arkdon’taffecttheinformationratio.Theinformationratiodecreasesbecauseallocatingsomeoftheportfoliotothebenarkmeansthattheexternalmanagergenerateslessactivereturn.ThefollowinginformationrelatestoQuestions14andYouareyzingthreeinvestmentmanagersforanewmandate.Thetablebelowprovidesthemanagers’ex-anteactivereturnexpectationsandportfolioweights.Thelasttwocolumnsincludetheriskandtheex-post,realizedactivereturnsforthefourstocks.Usethefollowingdataforthefollowingtwoquestions:Manager Manager ManagerRealizedSecuritySecurity0Security0SecuritySupposeallthreemanagersclaimtobegoodatforecastingreturns.Accordingtothefullfundamentallawofactivemanagement,whichmanageristhebestatefficientlybuildingportfoliosbyanticipatingfuturereturns?ManagerManagerManagerSupposeallthreemanagersclaimtobeefficientinportfolioconstruction.Accordingtothefullfundamentallawofactivemanagement,whichmanageristhebestatbuildingportfoliostomakefulluseoftheirabilitytocorrectlyanticipatereturns?ManagerManagerManager......打印者打印者:yanzhaoyang 商的事先 或此的。违者将被Manager1hasaninformationcoefficientof0.15,atransfercoefficientof1.0,andinvestsin50securities.Manager2hasadifferentstrategy,investinginmoresecurities,butissubjecttoinvestmentconstraintsthatreducehistransfercoefficient.Manager2hasaninformationcoefficientof0.10,atransfercoefficientof0.8,andinvestsin100securities.Theinvestmentselectionsofeachmanagerareindependentdecisions.Ifbothmanagerstargetanactiveriskof5.0%,whichmanagerwillhavethegreaterexpectedactivereturn?ManagerManagerBothmanagerswillhavethesameactiveNickYoungisconcernedthatGoudonPartners,oneofhismoneymanagers,overestimatesitsexpectedactivereturnbecauseGoudonoverstatesitsstrategybreadth.Youngmakestwonotesabouthisconcern:NoteNote

AlthoughGoudonclaimsthatthenumberofindependentassetdecisionsishighbecauseituses200stocks,manyofthesestocksclusterinindustrieswherethesamegeneralysisappliestoseveralstocks.Goudonclaimsthateachstockisindependentandevaluatedeachmonth,or12timesperyear.Theseysesarenotindependentbecausesomeoftheirstrategies,suchasfavoringaparticularindustryorfavoringvaluestocks,persistonemonth.Forexample,astrategyoffavoringlow-P/Estockswillpersistforseveralmonthsandtheinvestmentdecisionsarenotindependent.Ifhisjudgmentsarecorrect,areYoung’snotesabouttheoverstatementofbreadthOnlyNote1isOnlyNote2isBothNotes1and2areCaramelAssociatesusesthefundamentallawtoestimateitsexpectedactivereturns.Twothingshavechanged.First,Caramelwillloweritsestimateoftheinformationcoefficientbecausetheyfelttheirpriorestimatesreflectedoverconfidence.Second,theirmajorshaverelaxedseveralconstraintsontheirportfolios,includingsocialscreens,prohibitionsonshortselling,andconstraintsonturnover.Whichofthesechangeswillincreasetheexpectedactivereturn?OnlythelowerinformationOnlytherelaxationofseveralportfolioBoththelowerinformationcoefficientandtherelaxationofportfolio......打印者打印者:yanzhaoyang 个人、私人使用 商的事 。违者将 ThefollowinginformationrelatestoQuestionsJamesFrazeeischiefinvestmentofficeratH&FCapitalInvestors.Frazeehiresathird-partyadvisertodevelopacustombenarkforthreeactivelymanagedbalancedfundsheoversees:FundX,FundY,andFundZ.(Balancedfundsarefundsinvestedinequitiesandbonds.)The arkneedstobecomposedof60%globalequitiesand40%globalbonds.Thethird-partyadvisersubmitstheproposedben arktoFrazee,whorejectsthebenarkbasedonthefollowingconcerns:Concern1:ManysecuritieshewantstopurchasearenotincludedinthebenarkConcern2:Onepositioninthe arkportfoliowillbesomewhatcostlytoConcern3:Thebenarkportfolioisafloat-adjusted,capitalization-weightedAfterthethird-partyadvisermakesadjustmentstothebenarktoalleviateFrazee’sconcerns,Frazeeacceptsthebenarkportfolio.HethenaskshisresearchstafftodevelopriskandexpectedreturnforecastsforFundsX,Y,andZaswellasforthebenark.TheforecastsarepresentedinExhibit1.Exhibit ForecastedPortfolioStatisticsforFundsX,Y,andZand FundFundFundPortfolioGlobalequities Globalbonds Expectedreturn Expectedvolatility Activerisk Sharperatio Note:Dataarebasedona rateofFrazeedecidestoaddaofferingtohisgroupoffunds,FundW,whichwillusethesamebenarkasinExhibit1.FrazeeestimatesFundW’sinformationratiotobe0.35.Heisconsideringaddingthefollowingconstrainttohisportfolioconstructionmodel:FundWwouldnowhave umover-andunderweightconstraintsof7%onsingle-countrypositions.打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此的。违者将被FrazeeconductsasearchtohireamanagerfortheglobalequityportionofFundWandidentifiesthreecandidates.HeasksthecandidatestoprepareriskandreturnforecastsrelativetoFundW’sbenarkbasedontheirinvestmentstrategy,withtheonlyconstraintbeingnoshortselling.Eachcandidatedevelopsindependentannualforecastswithactivereturnprojectionsthatareuncorrelatedandconstructsaportfoliomadeupofstocksthatarediversebothgeographicallyandacrosseconomicsectors.Selecteddataforthethreecandidates’portfoliosarepresentedinExhibit2.Exhibit ForecastedPortfolioDataforEquityPortionofFundCandidateCandidateCandidateNumberofInformationratioTransfercoefficientInformation*InformationcoefficientbasedonpreviouslymanagedFrazeeasksCandidateCtore-evaluateitsportfoliodatagiventhefollowingChange1:FixthenumberofsecuritiestoChange2:RebalanceonasemiannualChange3: umover-orunderweightconstraintsonsectorWhichofFrazee’sconcernsbestjustifieshisdecisiontorejecttheproposedbenConcernConcernConcernBasedonExhibit1,theexpectedactivereturnfromassetallocationforFundXBasedonExhibit1,whichfundisexpectedtoproducethegreatestconsistencyofactiveFund打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此的。违者将被FundFundBasedonExhibit1,combiningFundWwithafundthatreplicatestheben arkwouldproduceaSharperatioclosestto:IfFrazeeaddedtheassumptionheisconsideringinFundW’sportfolioconstruction,itwouldmostlikelyresultin:adecreaseintheoptimalaggressivenessoftheactivetheinformation inginvarianttothelevelofactiveanincreaseinthetransferofactivereturnforecastsintoactiveBasedonthedatapresentedinExhibit2,thecandidatewiththegreatestskillatachievingactivereturnsappearstobe:CandidateCandidateCandidateWhichproposedchangetoFundWwouldmostlikelydecreaseCandidateC’sinformationratio?ChangeChangeChangeThefollowinginformationrelatestoQuestionsJohnMartinezisassessingtheperformanceoftheactivelymanageddiversifiedassetportfolio.Thediversifiedassetportfolioisinvestedinequities,bonds,andrealestate,andallocationstotheseassetclassesandtotheholdingswithinthemareunconstrained.Selectedreturnandfinancialdatafortheportfoliofor2015arepresentedinExhibitExhibit DiversifiedAssetPortfolio2015Portfolio打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此的。违者将被

ReturnReturnRealestate95Martinezusesseveralrisk-adjustedreturnmetricstoassesstheperformanceofthediversifiedassetportfolio,includingtheinformationratioandtheSharperatio.Selectedrisk,return,andstatisticaldatafortheportfolioarepresentedinExhibit2.Exhibit DiversifiedAssetPortfolioData,Coefficient(TC)Coefficient(IC)BondRealestateMartinezhasrecentlyhiredKennethSinghtohelphimevaluateportfolios.MartinezasksSinghaboutthepossibleeffectsontheportfolio’sinformationratioifcashwereaddedtothediversifiedassetportfoliooriftheaggressivenessoftheportfolio’sactiveweightswereincreased.Singhrespondswithtwostatements:StatementStatement

Addingcashtotheportfoliowouldchangetheportfolio’sinformationIncreasingtheaggressivenessofactiveweightswouldnotchangetheportfolio’sinformationratio.BasedonExhibit1,thevalueaddedtothediversifiedassetportfolioattributabletothesecurityselectiondecisionin2015wasclosestto:打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此的。违者将被BasedonExhibit1,thevalueaddedofthediversifiedassetportfolioattributabletotheassetallocationdecisionin2015wasclosestto:BasedondatainExhibit2andusingtheinformationratioasthecriterionforevaluatingperformance,whichsubportfoliohadthebestperformanceintheperiod1996–2015?ThebondTheequitiesTherealestateWhichofSingh’sstatementsregardingtheinformationratioisOnlyStatementOnlyStatementBothStatement1andStatementBiscorrect.AlthoughthefirstpartofStatement1iscorrect(activereturn,orvalueadded,equalsthedifferencebetweenthemanagedportfolioreturnandthebenarkreturn),activereturnisnotthesameasalpha.Inotherwords,RA=RP–RB,whileαP=RP–βP×RB.Statement2correctlydefinesactiveweights.Biscorrect.Theportfolioactivereturnisequaltotheportfolioreturnminusthebenarkreturn:RA=RP–nTheportfolioreturnisRP=∑wPRP=0.30(14%)+0.30(15%)+0.20(12%)+0.10(8%)+0.10(10%)=nThe ......打印者打印者:yanzhaoyang 商的事先 或此的。违者将 RB=0.24(14%)+0.20(15%)+0.20(12%)+0.18(8%)+0.18(10%)=TheactivereturnRA=RP–RB=12.9%–12.0%=Notethatthissamecorrectanswercanbeobtainedintwootherequivalentways.Theactiveweightsarethedifferencesbetweentheportfolioandbenarkweights,orΔwi=wP,i–wB,i.Computingtheactiveweightsfromthetableabove,theactivereturnis:NRA=∑=0.06(14%)+0.10(15%)+0(12%)–0.08(8%)–=Finally,wecouldexpresstheactivesecurityreturnsastheirdifferencesfromthebenarkreturn,orRAi=Ri–RB.Computingtheactivesecurityreturnsfromthetableabove,theportfolioactivereturnisthesumproductoftheactiveweightsandtheactivesecurityreturns:NRA=∑=0.06(2%)+0.10(3%)+0(0%)–0.08(–4%)–=Ciscorrect.Theactivereturnisequaltotheportfolioreturnminusthebenark RA=RP−RB=∑wP,jRP,j−∑wB,jRB nTheportfolioreturnisRP=∑wP,iRi=0.55(10%)+0.20(10%)+0.25(5%)=nThe arkreturnisRB=∑wB,iRi=0.40(8%)+0.30(9%)+0.30(6%)=RA=RP–RB=8.75%–7.70%=Aiscorrect.Bothpropertiesarecorrect.ForProperty1,ifwPistheweightofanactivelymanagedportfolioand(1–wP)istheweightonrisk-cash,changingwPdoesnotchangetheSharperatio,ascanbeseeninthisequation.

RC−

wP(RP−RF=

=C STD(RC

wPSTD(RPPForProperty2,theinformationratioofanunconstrainedportfolioisunaffectedbymultiplyingtheactivesecurityweights,∆wibyaconstant.P打印者打印者:yanzhaoyang 商的事先 或此的。违者将 Biscorrect.ThehighestsquaredSharperatioofanactivelymanagedportfolioPP

=

+IR2=0.3332+0.152=BThehighestSharperatioisSRP=√0.1334=BAiscorrect.TheoptimalamountofactiveriskSTD(RA)=

STD(RB)

18.0%=Theweightontheactiveportfolio(Indigo)wouldbe8.11%/8.0%=1.014andtheweightonthebenarkportfoliowouldbe1–1.014=–0.014.WecandemonstratethattheseweightsachievetheumSharperatio(of0.365).Notethat8.11%istheoptimallevelofactiverisk,andthatIndigohasanexpectedactivereturnof1.014(1.2%)=1.217%overthebenark(andatotalexcessreturnof6.0%+1.217%=7.217%.TheportfoliototalriskisSTD(RP)2=STD(RB)2+STD(RA)2=18.02+8.1112=Takingthesquareroot,STD(RP)=19.743,andtheoptimalSharperatioisindeed7.217/19.743=0.365.Biscorrect.TheactiveportfoliothatisoptimalistheportfoliowiththehighestInformationratio,theratioofactivereturntoactiverisk.TheIRsforthethreeactiveportfoliosare:IRA=1.0/10.0=0.10IRB=0.5/3.0=0.167IRC=0/2.0=0.00PortfolioBhasthehighestIRandisthebestactiveportfolio;itisthereforethebestportfoliotocombinewiththebenark.Ciscorrect.UsingtheequationIR*=IC×√BRandassumingthatbreadthcanbeinterpretedasnumberofsecuritiesintheportfolio,solvingforbreadthintheequationaboveyields(0.75)2=Ciscorrect.Thetransfercoefficientmeasureshowwelltheanticipated(ex-ante),riskadjustedreturnscorrelatewiththerisk-adjustedactiveweights.Thisisalsoexpressedintheequationforthetransfercoefficient:TC=COR(μi/σi,Δwiσi).Biscorrect.TheICmeasuresaninvestmentmanager’sabilitytoforecastBiscorrect.AclosetindexwillhaveaverylowactiveriskandwillalsohaveaSharperatioveryclosetothebenark.Therefore,StatementsIandIIIareconsistentwithaclosetindexportfolio.Aclosetindex’sinformationratiocanbeindeterminate(becausetheactiveriskissolow),andoftennegativeduetomanagementfees.......打印者打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或此的。违者将被Aiscorrect.ManagerAhasthehighestinformationratio.TheinformationratioisdefinedasIR=activereturn.ThemanagersinthisexamplehavethefollowinginformationactiveManager Manager ManagerInformation 0.7/3.2= 0.6/3.1= 1.2/6.3=Biscorrect.Theinformationratioisunaffectedbyrebalancingtheactiveportfolioandthebenarkportfolio.Inthiscase,theactivereturnandactiveriskarebothreducedby25%,andtheinformationratiowillbeunchanged.Ciscorrect.Theproperstatistictocalculateistheinformationcoefficient,anditisdefinedasfollows:IC=COR(RAi,μi Amanagerisagoodforecasterifhisorherex-anteactivereturnexpectations(forecasts)arehighlycorrelatedwiththerealizedactivereturns.Theinformationcoefficientrequiresthattheseforecastsandrealizedreturnsberisk-weighted.Whenthisisdoneforthethreemanagers,therisk-weightedforecastsandrealizedreturnsare:Risk-weightedforecasts, ManagerManagerManagerSecuritySecuritySecuritySecurityTheICsarefoundbycalculatingthecorrelationsbetweeneachmanager’sforecastsandtherealizedrisk-weightedreturns.ThethreemanagershavethefollowingICs:Manager Manager ManagerInformation Manager3hasthehighestBiscorrect.TheproperstatistictocalculateisthetransfercoefficientanditisdefinedasTC=TheTCisthecross-sectionalcorrelationbetweentheforecastedactivesecurityreturnsandtheactualactiveweights,adjustedforrisk.Risk-weightedforecasts, Risk-adjustedweights,

打印者:yanzhaoyang打印者:yanzhaoyang >。打印个人、私人使用 商的事先 或 。违者将 Risk-weightedforecasts, Risk-adjustedweights,123123ThethreemanagershavethefollowingManagerManagerManagerTransferManager2hasthehighestAiscorrect.Manager1’sIR=TC×IC×√BR=1.0×0.15×√50=1.06.Manager2’sIR=0.8×0.10×√100=0.80.Manager1’sactivereturnis1.06(5.0)=5.3%andManager2’sexpectedactivereturnis0.80(5.0)=4.0%.Manager1hasthegreaterexpectedactivereturn.Ciscorrect.Ifthedecisionsabouteachofthe200stocksarenotindependent,andifthedecisionsaboutastockfromonemonthtothenextarenotindependent,thenGoudonPartnersisoverstatingitsestimatesofitsbreadthanditsexpectedactivereturns.Biscorrect.Althoughtherelaxationofportfolioconstraintswillincreasethetransfercoefficient(andexpectedactivereturns),thelowerinformationcoefficientreducestheinformationratioandtheexpectedactivereturn.Aiscorrect.BecausethebenarkdoesnotcontainmanyassetsthatFrazeewantstoinvestin,thebenarkmaynotberepresentativeofhisinvestmentapproach.Concern2,asstated,islessimportantbecauseitdoesnotimplythatthecostofreplicatingthebenarkisaseriousconcern.Finally,Concern3actuallystatesagenerallypositivefeatureofthebenark.Biscorrect.Activereturnfromassetallocationisderivedfromdifferencesbetweenthe arkweightandtheportfolioweightacrossassetclasses.ForFundX,theexpectedactivereturnfromassetallocationiscalculatedas:ActiveReturnfromAssetAllocationM∑ΔwjRB,j=(60−60)RB,e+(40−40)RB,b=0WhereΔwjisthedifferenceintheactiveportfolioandtheben arkassetweights,RB,eistheben ark’sreturnfromglobalequities,andRB,bistheben ark’sreturnfromglobalbonds.......打印者打印者:yanzhaoyang 商的事先 或此的。违者将被BecauseFundXhasthesameassetweightsasthebenarkacrossthetwoassetclasses(60%globalequities,40%globalbonds),theexpectedactivereturnfromassetallocationiszero.Ciscorrect.TheIRmeasurestheconsistencyofactivereturn.TheIRiscalculatedforthethreefundsasfollows:IR= RP− = STD(PP−RB)IRforFundX=(10.0–9.4)/5.2=0.6/5.2=0.12IRforFundY=(11.6–9.4)/9.2=2.2/9.2=IRforFundZ=(13.2–9.4)/15.1=3.8/15.1=

STDFundZhasthelargestIRandthusisexpectedtoproducethegreatestconsistencyofactivereturn.Biscorrect.GiventheIRfor