2016年6月cfa基礎(chǔ)資產(chǎn)配置單頁

SS8AssetAllocationandRelatedDecisionsinPortfolioSlide

CFA站 Slide

CFA咨 ：400-0988- 站Slide：Slide：400-0988-Frameworkof R17:R17:AssetStrategicAsset Strategicassetallocationcombinescapitalmarketexpectations(formallyrepresentedbytheefficientfrontier)andtheinvestor’srisk,return,andinvestmentconstraints(fromtheIPS).Strategicassetallocationislong-terminnature,andhencetheweightsarecalled“targets”andtheportfoliorepresentedbythestrategicassetallocationiscalledthe“portfolio”.Short-termdeviationfromthestrategicassetallocationmaybebasedontermcapitalmarketexpectationsandwouldbetheresultofactiveStrategicassetallocationreflectstheinvestor’sdesiredsystematicriskSlide：Slide：400-0988-TacticalAsset Tacticalassetallocationistheresultofactivemanagementwhereinmanagersshort-termopportunitiesinthemarket.Tacticalassetallocationintroducesadditionalrisk,whichshouldbejustifiedbyadditionalreturn(i.e.,positivealpha).Sinceportfoliomanagersarethe“experts”atseekingouttheseopportunities,whyshouldstrategicallocationevenbeperformed?Providediscipline,thatis,tomaintainfocusonobjectivesandOverthelongrun,assetclassesseemtorespondsomewhathomogeneouslytosystematic(macroeconomic)factors.Theimportanceoflongrun(strategic)assetallocationhasbeenwellestablishedempirically.Onestudyshowsthat94%ofthevariabilityoftotalportfolioreturnsisex inedbythestrategicassetallocation.Slide：Slide：400-0988-Contrasttheasset-onlyandALMapproachestoassetALMapproach(DBn,insuranceForinvestorswithspecific,assetallocationistailoredtomeetliabilitiesandtoizethesurplusgivenanacceptablelevelofrisk.Usuallyresultsinarelativelyhighallocation efutureobligationscanbemodeledasliabilities,andanALMapproachtostrategicassetallocationcanbeapplied.Asset-onlyThefocusisonearningthehighestlevelofreturnforagiven(acceptable)levelofriskwithoutanyconsiderationforliabilitymodeling.Becausetheasset-onlyapproachdoesnotspecificallymodelliabilities,theriskofnotfundingliabilitiesisnotaccuraycontrolled.SlideSlide：400-0988-DynamicandStaticAsset Dynamicassetallocationtakesamulti-periodviewoftheinvestmenthorizon.Inotherwords,itrecognizesthatasset(andliability)performanceinoneperiodaffectstherequiredrateofreturnandacceptablelevelofriskforsubsequentStaticassetallocationignoresthelinkbetweenoptimalassetallocationsacrossdifferenttimeperiods.BehaviorfinanceandassetIndividualstendtodis ylossaversionratherthanriskaversionandapproachinvestingfromasegmented ratherthanfromaportfolio Becauseofthementalaccounting,theymeetgoalsoneatatime,startingwiththemostimportant.Regretisthefeelingofdisappointmentorshamethatinvestorsfeelfromhavingtoadmitmakingapoorinvestmentdecision.FearofregretcanmakeinvestorsavoidtakingactionsthatcouldleadtoTheresultingoverallallocationislikelydifferentfromtheiroptimalstrategicallocationandcouldevenbeinconsistentwiththeirrisktolerance.Slide：Slide：400-0988-CharacteristicCharacteristicliabilityconcernsofvariousPenaltyforNotAssetAllocationApproachinPracticeTaxes,mortgagepayments(livingexpenses,wealthaccumulationtargets)Pensionns(definedbenefit)PensionHigh,legalandALMPensionns(definedcontribution)(RetirementIntegratedwithindividual'sFoundationsandSpendingcommitments,capitalprojectAOLifeVeryhigh,legalandPropertyandliabilityVeryhigh,legalandVeryhigh,legalandSpecifyingSpecifyingRiskandReturn Slide：Slide：400-0988-Thereturnobjectiveforanindividual’sorinstitution’sBebaseduponthesizeoftheportfolio,long-termspending(liquidity)needs,thetimehorizon,andmaintenanceoftheprincipal.Unlessspecificallystatedotherwise,wealwaysassumetheinvestorwillmaintaintheprincipal,sotheportfoliomustnotonlymeetspendingneeds,itmustalsocoverexpectedinflation.Forexample,assumethebefore-taxrequiredreturnisestimatedat4%andinflationisexpectedtoaverage3%.Thenominalbefore-taxrequiredreturnfortheportfolioisRbefore-tax=(1.04)(1.03)?1=0.0712Theinvestor’sriskobjectiveshouldbespecifiedinlightoftheinvestor’sriskWeclassifiedinvestorsashavingbelowaverage,average,oraboveaverageriskThosewithbelowaveragerisktolerance(highlyriskaverseinvestors)aregivenascoreof7to10,whilethosewhoarehighlytolerantofrisk(lowriskaversion)aregivenascoreof1to3.SpecifyingSpecifyingRiskandReturn Slide：Slide：400-0988-1 izing =E(RP)–0.005TwoWhenchoosingfromasetofassetswiththesameriskandreturnrankings(PortfolioBhasbothahigherexpectedreturnandhigherstandarddeviationthanA),thechoiceisdrivenbytheinvestor’sriskaversion.Asriskaversionincreases(denotedwithahigherriskaversionscore),thedeductionfor(adjustmentfor)riskincreases.3、Upperlimitsonstandarddeviation,(targetsemi-VAR1Nx ,x3、Upperlimitsonstandarddeviation,(targetsemi-VAR1Nx ,x2ii1N ,xt(target2ii Slide：Slide：400-0988-Supposeaninvestorrequiresbefore-taxreturnof8%,hisriskaversionscoreis7,andhecaninvestinoneoftwoportfolioallocations,AorB,whichmeethisrequiredreturnandrisk(standarddeviation)objectives:AllocationAhasanexpectedreturnof8.5%andastandarddeviationAllocationBhasanexpectedreturnof8.8%andastandarddeviationofTheinvestorwouldbebetteroffwithAllocationA.Eventhoughithasasomewhatlowerexpectedreturn,itsrisk-adjustedreturnisactuallyhigher:Supposetheinvestor'sriskaversionscorewasPortfolioBhasbothahigherexpectedreturnandhigherstandarddeviationthanA,theAsriskaversionincreases(denotedwithahigherriskaversionscore),thedeductionfor(adjustmentfor)riskincreases.Slide：Slide：400-0988-SpecifyingAsset AssetclasseshavebeenappropriayspecifiedAssetsintheclassaresimilarfromadescriptiveaswellasastatistical.(homogeneous)TheyarenothighlycorrelatedsotheyprovidethedesiredIndividualassetscannotbeclassifiedintomorethanoneclass.(mutuallyTheycoverthemajorityofallpossibleinvestableTheycontainasufficientlylargepercentageofliquidSomewellacceptedassetclassesincludedomesticequity,domestice,globalequity,globalfixed e,cashandequivalents,andalternativeinvestments,whichmaybefurtherdividedintoclasses,suchasrealestate,privateequity,etc.Slide：Slide：400-0988-InflationInflationAdjustedSecurities,GlobalSecurities,andAlternativeInflation-protectedsecuritiesprovidetheobviouscharacteristicofhelguardagainstthepotentialeffectsofrisingorfallinginflation.AddingglobalsecuritiesisthepotentialtoincreasereturnatalllevelsofSomearguethatduringeconomicdownturns,exactlywhentheinvestorneedsthediversificationeffectsthemost,emerginganddevelopedmarketstendtobehighlycorrelatedAlternativeinvestmentscanbeconsideredfairlyrisky,butinaportfoliotheybringthepotentialofsignificantlyincreasedreturns.Theprimarybenefittoincludingalternativeinvestmentsinanassetallocationisthediversificationbenefit.Thepracticaldrawbackstoinvestinginalternativeinvestmentsincludethetypicallylargeamountofcapitalrequiredandtheneedtocarefullyselectout-Slide：Slide：400-0988- If

addingtheinvestmentwillimprovetheportfolioSharpeSiSharperatioofproposedinvestmentSpcurrentportfolioSharperatio

correlationofthereturnsontheproposedinvestmentwithDeterminingwhetherDeterminingwhethertoaddaninvestmenttotheSlideSlide：400-0988-NewExpectedSharpe(12-3)/18=(12-DeterminetheNewExpectedSharpe(12-3)/18=(12-Answer1:Calculatethecorrelationcoefficientthatmakestheequation

S=S

0.30=0.50

Example1:WilladdingtheassetimprovetheportfolioSharpeIfthecorrelation=0.60,Example1:WilladdingtheassetimprovetheportfolioSharpeIfthecorrelation<0.60,addingthenewinvestmentwillincreaseIfthecorrelation>0.60,addingthenewinvestmentwilldecreaseSlideSlide：400-0988-Aportfoliomanagerisconsideringthreeinvestments,onlyoneofwhichhewilladdtohisportfolio.Basedonthedataprovided,determinewhichinvestmentthemanagershouldselect.SharpeCorrelationwithcurrentportfolio, IfS theinvestmentwillincreasethe S =0.410.770 S =0.410.800 S =0.410.40

S S Example2:SelectinganassetfortheOnlyinvestment3Example2:SelectinganassetfortheRiskRiskininternational Slide：Slide：400-0988-Currencyrisk:investinginaforeign-denominatedsecurityexposestheinvestortochangesinvalueofforeignassetandchangesinvalueoftheforeigncurrency.LMR:localmarketreturn;LCR:localcurrencyCurrencyshouldgenerallybeasmallerThecorrelationofLMRandLCRisgenerallylessthan+1.0.ThemorethecorrelationofLMRandLCRapproach-1.0,thelowerthevolatilityoftheinvestmentfortheinvestor.Inaglobalportfolioexposedtomultiplecurrencies.somewilllikelyhavepositiveLCRmorelikelyshowmeanreversion.Empiricalevidencesuggeststhatthestandarddeviationofcurrencyisonlyabouthalfthestandarddeviationofstockprices.Itisthelessimportantdeterminantofrisk.(Inthebondmarket,thecurrencyvolatilityisgenerallyhigherthanbondvolatility.makingitamoreimportantconsiderationforbondinvestors).Politicalrisk:existswhenacountryIrresponsiblefiscaland/ormonetary,and/LacksreasonablelegalandregulatoryrulestosupportbutnotstiflefinancialHomecountrybias:referstotheobservationthatinvestorstendtooverweighinvestmentsintheirowncountry,creatingasuboptimalportfolioallocation.Itcouldreflectlackoffamiliaritywithforeigninvestments,financialreporting,andlanguage.Itcanalsoreflectlackofliquidityandhigherpoliticalriskinforeignmarketsoraneedtomatchdomesticliabilitieswithdomesticassets.Slide：Slide：400-0988-Costsininternational TransactioncostscanbehigherandliquiditycanbeWithholdingtaxesonforeigninvestorsmaynotbefullyoffsetbytax-floatcanbeanissue.Thestatedmarketcapitalizationmayincludesharesheldbytheernmentorotherinvestorswhowillnotsell.settlement,custody,management,orinformation.OpportunitiesOpportunitiesininternational Slide：Slide：400-0988-ThetheoreticalargumentforinternationalinvestmentispotentiallyhigherreturnandlowerriskwithlowcorrelationresultinginenhancedSharperatios.Empiricalevidencedoesnotalwayssupportthisexpectationbecauseitappearsismostneeded,allmarketsgodowntogether.Theriseincorrelationduringfinancialcrisescanbeexined inglesssegmentedandmoreIndustryfactors ingmoreimportantthancountryfactorsindetermininga Foreignmarketscouldbeundervaluedand,thus,offerbetterexpectedWhiletheinvestor’shomemarketmayhavehadthebestreturnsinthepast,thatisnotareliableindicatoroffuturereturns.Evenifcorrelationsriseintheshortrunduringcrises,thelong-runbenefitsofdiversificationcanremain.Correlationsamongbondmarketstendtobelowerthanamongequitymarkets.Addinginternationalbondstodomestic-onlyportfolioscanbeparticularlybeneficialinreducingriskforriskaverseinvestors.SlideSlide：400-0988-ImportanceofImportanceofConditionalReturnThepreviouslydiscussedapproachtodeterminingwhetheranewassetclassisamean-variancebasedapproachthatassumescorrelationsandstandarddeviationsarestableovertime.Theobservationthatcorrelationsincreaseduringfinancialcrisesisinconsistentwiththisassumptionandindicatesconditionalreturncorrelations(i.e.,correlationsthatdependonmarketvolatilityandconditions).Changingcorrelationsamonginternationaleconomiescanhaveverycorrelationshaveincreasedovercorrelationsamongmarketsincreaseduringperiodsofincreasedvolatility(financialcrises).Slide：Slide：400-0988-Internationaldiversificationshouldnot CorrelationshavebeenincreasingovertimetradeamongnationshasCapitalmarkets ingintegratedintotheworldCorporationshaveincreasedexports,foreignoperations,andforeignmergersandacquisitions.ThemobilityofcapitalhasincreasedwithinstitutionalinvestorsmoreactiveininternationalmarketsCorrelationsbetweenmarketsappeartoincreasewhenvolatilityincreasesininternationalmarketsEmergingEmerging Slide：Slide：400-0988-Thetraditionalthinkingistheyofferhigherreturnandstand-aloneriskbutlowcorrelationwithothermarkets.Astheseeconomiesmature,theirreturncharacteristicsareconvergingwithdevelopedmarkets.SpecialInvestability.Liquidityand -floatcanbelimitedwithadversemarketimpact,whichdrivesupthepricepaidtoexecutepurchaseorders. ernmentsofemergingmarketeconomiesmayimposecapitalandcurrencyrestrictionsorNon-normalreturndistributionsinconsistentwithmean-varianceassumptions.Returnscanbeleptokurtic(fartailswithextremehighandlowreturnsoccurringmoreoftenthanconsistentwithanormaldistribution).Strongeconomicgrowthmaynotbenefitexistingshareholders.Newshareissuanceincreasesequitymarketcapbutdilutesexistingshareholdervalue.Growthopportunitiescouldbeunfairlyallocatedbythe ernmentandnotbeavailableto compensation.Corporate ernancetoprotectshareholderscanbeweak.Contagionhasbeenexhibitedwhenacrisisinoneemergingmarketorindevelopedmarketsspreadstootheremergingmarkets(essentiallyjustanotherexampleorrisingcorrelationduringcrisis).Currencydevaluationsasemergingmarketernmentsdevaluetheircurrency(creatinganegativeLCR)orrestricttheabilityofaninvestortorepatriatethefundsbacktotheirownmarker.Despitethesecrises,theevidencesuggestsdeclinesinemergingmarketcurrencyvaluecanbeoffsetInefficientmarketsmayallowbetterinformedandcapitalizedinstitutionalinvestorsorthosewithlocalpresencetoearnexcessreturns.Slide：Slide：400-0988-Generalprogressionasmarkets Asmarketsintegrateandmovethroughemergingmarketstatustodevelopedmarketstatus,thegeneralprogressionis:Equitysharepricesriseas(1)capitalcannowflowintotheformerlyuninvestablemarket,and(2)toreflectdecliningstand-alonerisk.ExpectedreturnsincreaseascapitalflowsintothemarketbutthendeclinesaftertheinitialinflowtobeconsistentwiththenowhigherstockpricesandlowerriskgoingLong-runreturnvolatilityshoulddeclineaspricesreflectinformationthatismore availableandpoliticalriskdeclines.covariancewithworldmarketsincreases.andpricesaremoreinformationallyefficient.Capitalcostsfallwithhigherstockpricesandlowerrisk.LowercapitalcostsfinanceSlide：Slide：400-0988-StepsinAsset Determiningtheinvestor’sreturnrequirementandrisktolerance,subjecttotheinvestor’scurrentwealthandconstraints.Formulatelong-termcapitalmarketexpectationsandtheirpotentialeffectsonthevariousassetclasses.Determinethemixofassets(allocation)thatbestmeetstheobjectivesdefinedintheIPSOncethestrategicallocationhasbeenimplemented,itshouldbemonitoredregularlyasspecifiedintheIPS.Ifthemarketchangesareonlyshort-terminnature,themanagershouldconsiderimplementingtacticalallocationmeasures,whichhavebeenapprovedintheIPS.SlideSlide：400-0988-Optimization:6Optimization:6ApproachestoAssetMean-ResampledefficientBlack-Asset-LiabilityManagementMean-VarianceMean-Variance Slide：Slide：400-0988-Themean-variancefrontieristhe“outeredge”ofagraphicalplotofallpossiblecombinationofriskyassets.Staticapproach(vs.multi-perioddynamicapproach)unconstrainedminimum-variancefrontier:thesimplestoptimization constraintsonassetclassweightsexceptthattheweightssumto100%.sign-constrainedMVF:Inastrategicassetallocationcontext,anallocationwithanegativeasset-classweightwouldgenerallybeirrelevant.Optimizationprogramsusedtogeneratetheefficientfrontierareinexpensiveandreadilyavailable.Identifiesportfolioswiththehighestexpectedreturnateachlevelofriskandtheassociatedassetallocation.Itistypicallysignconstrainedtopreventnegativeweights(shortCashequivalentsaremodeledasariskyassetclassifWidelyunderstoodandEasilyadaptedtomodelriskasdownsideriskortrackingerror,returnasexcessreturnoversomeminimumthresholdreturn,constrainthedeviationsofassetweightsversussomerelevantben ark,modelthecorrelationtochangeovertimeandconvergeduringperiodsofstress(highvolatility).ThemodelingoftheEFcanbesimplifiedwiththeuseofcornerCommerciallyavailablesoftwareMean-VarianceMean-Variance Slide：Slide：400-0988-covariances)canbeoverwhelmingasthenumberofassetclassesincreasesExpectedreturnsaresubjecttoestimationStatic(1-period)approachandessentiallyassumetheinputswillremainconstantoverForthemultipleandoftenongoingtimeperiodsofatypicalportfoliothereisno assetthatmeetstherequireddefinitionofknownreturnwithzerostandarddeviationandcorrelation.Canyieldunder-diversified(concentrated)portfoliosunlessMVOoutputcanbeverysensitivetotheinputs,makingtheresultingoutputSlide：Slide：400-0988-ResampledEfficient Asimulationapproachutilizinghistoricalmeans,variances,andcovarianceofassetclasses,which,combinedwithcapitalmarketforecasts,assumestheyarefairrepresentationsoftheirexpectations.Michaud’sresamplingtechniqueisbasedonaMonteCarlosimulationthatdrawsfromthedistributionstodevelopasimulatedefficientfrontier.EFismorestablethantraditionalSmallchangesininputsproduceonlyminorchangesinPortfoliostendtobebetterdiversifiedthantraditionalCommerciallyavailableNotheoreticalbasisfortheInputsoftenbasedonhistoricalBlack-LittermanBlack-LittermanMethod SlideSlide：400-0988-UnconstrainedBlack-Litterman(UBL)StartswiththeweightsofassetclassesfromaglobalApplyingaBayesianprocess,themanagerincreasesordecreasestheweightsbaseduponherviewsofexpectedassetclassreturnsandthestrengthsofthoseviewswithnoconstraintagainstshortsales(negativeweightsareallowed).TheUBLisintuitiveinthatthemanagerstartswithmarketweightingsanddirectlyincreasesordecreasesthoseweightsbasedonthemanager'sopinionofwhatwillIfthemanagerhasastrongopiniondomesticequitywillunderperform,themanagercanshiftsignificantassetsoutofdomesticequitytoaspecificassetclassexpectedtooutperformorbroadlyacrossallotherclassesifthemanagerhasnospecificviewsonUBLdoesnotdefinehowtomaketheseadjustmentstoweights,butinpracticemostmanagersselectrelativelydiversifiedportfolioswithoutnegativeweights.ThenrunanewMVOusingthemanager-adjustedreturnstoestablishthenewoptimalBlack-LittermanBlack-LittermanMethod Slide：Slide：400-0988-produceswell-diversifiedportfoliosthatincorporatethemanager'sviewsonassetclassreturns,andisamoredefinedprocess.Selectarelevant,globalmarketindex.Inputthemarketweightsfortheassetclassesinthatindexandacovariancematrixforthoseclasses.Usereverseoptimizationtoback-solvefortheimplied,expectedreturnsofthoseassetclasses.Havingstartedwithamarketindexandthemarket'sweightings,thesewillbeconsensusreturnsexpectations.Themanagerthenreviewstheimpliedreturnsandexpressesanyopinionsregardingthereturnsandthestrengthofthoseopinions.Themanagerthenresetsanyimpliedreturnsupordowntoreflectthemanager'sopinionsandconvictionlevel.opinionandthemarketconsensusreturnwherethemanagerhasnoopinion.ThenewMVOproducesthe Black-LittermanBlack-LittermanMethod Slide：Slide：400-0988-Theoreticallyjustifiedwaytoaddressthesensitivityofinputsproblemandincorporatemanagerviews.TypicallygeneratesmorestableSAAandbetterCanbeconstrainedorunconstrainedBlack-Littermanthoughconstrainedisthemoreusefulandrigorousapproach.BL(constrained) fiesandbeginswithmarketconsensusexpectedreturnsandallowsthemanagertosystematicallydivergefromthisstartingCommerciallyavailableOftentheinputsarebasedonhistoricalMonteMonteCarloSimulation Slide：Slide：400-0988-MCSisastatisticalmodelingtooloftenusedtocomplementMVOorotherassetallocationtools.ForexampleamanagercouldbeginbyselectingseveraloptimalportfoliosusingMVOthathaveacceptableriskandreturnforthe andthenuseMCStogeneratemultiplesimulatedpathsdisyinghowtheseportfoliosTheMCScanconsiderpathdependencyeffectsontheportfolio,suchasaconstantnominalorrealamountoffundswithdrawnperiodicallyortaxespaidontheTheMCSpathscouldberankedinorderofvaluetofacilitateansweringsuchquestionsas:Willtheportfoliobeexhausted?When?Howbadorgoodcoulditbe?yzestheSAAoutputoftheothermodelsforpathdependencyissuesandfurther MonteMonteCarloSimulation Slide：Slide：400-0988- ysistooltofurther ModelspathdependencyGeneratesstatisticalprobabilitiesofmeetingornotmeetingreturnCanalsomodelliabilitiesandUsedtocomplementtheotherCommerciallyavailableCanbecomplextoCangeneratefalseconfidence;theoutputisonlyasaccurateastheAsset-LiabilityAsset-LiabilityManagement Slide：Slide：400-0988-Assetliabilitymanagement(ALM)considerstheallocationofassetswithrespecttoagivenliabilityorsetofliabilities.TheALMapproachizethedifference(thesurplus)betweenassetsandliabilitiesateachlevelofrisk(muchliketheefficientfrontierrepresentstheumreturnateachlevelofAsset-LiabilityAsset-LiabilityManagement SlideSlide：400-0988-Withthelowestriskitwillalsogeneratetheminimumexpectedsurplus.Asyoumovetotherightonthefrontier,boththeexpectedsurplusandtheriskincrease.ThereisnoassurancetheMSVPwillhaveapositivesurplus.InthiscasetheMSVPhasaThechoiceofanyportfolioonthefrontierisa andmanagerdecision;theyacceptTheALMefficientfrontiercouldalsobepresentedintermsofthefundingratio(i.e.,thevalueof nassetsdividedbythevalueof nliabilities).Aswithotheroptimizationprocedures,ALMrequiresestimationsofallassociatedmean-varianceparametersandthussuffersfromthesameestimationbiases.Ofcoursethisnowalsoincludesestimatingtheliabilitiesaswell.TohelpavoidtheseinherentlimitationsofV,themanagercanutilizearesamplingtechniqueortheBlack-LittermanapproachforALM.MonteCarlosimulationcouldthenbeaddedasacomplimenttoexaminepathdependencyandgainstatisticalprobabilityinsighttothebehaviorofthesurplusovertime.Asset-LiabilityAsset-LiabilityManagement Slide：Slide：400-0988-ConsiderstheallocationofassetswithrespecttoCangenerateasurplusfrontierthatshowsthecombinationsofriskandCommerciallyavailablesoftware.SameissuesasThenumberandnatureofestimatesrequired(e.g.,expectedreturns,variances,covariances)canbeoverwhelmingasthenumberofassetclassesExpectedreturnsaresubjecttoestimationCanyieldunder-diversified(concentrated)portfoliosunlessMVOoutputcanbeverysensitivetotheinputs,makingtheresultingoutputExperienced-BasedExperienced-Based Slide：Slide：400-0988-1.InvestorswithlongtimehorizonscantoleratemoreYoungprofessionals,forexample,shouldbeinvestedheavilyinriskier,higherAsindividualsapproachretirement,theycantoleratelessriskandshouldbemovedintohighqualitycorporatebondsandtreasuries2.60/40 A60/40mixofequityandfixed eisagoodstartingpointfortheMoreaggressive(lessaggressive)investorsshouldincrease(decrease)theequityallocationandmakethecorrespondingadjustthefixed Alongertimehorizonisgenerallyconsistentwithmore3."100-age"Subtracttheinvestor'sagefrom100toarriveatthepreferredallocationtoTheallocationtoequitiesautomaticallyfallsastheinvestorIncorporatesdecadesofassetallocationEasytounderstandandconsistentwiththemorecomplexInexpensivetoUsefulontheAllocationrulesmaybetoosimpleforsomeExperiencebasedrulescanbecontradictoryinsomeappliedSlide：Slide：400-0988-TheMinimumVariance onewithcornerportfoliosAcornerportfolioisformedwhentheweightsofanassetgofromzerotoNonegativeWecanapproximatethestandarddeviationforanefficientportfoliogiventhoseofadjacentcornerportfoliosChoosingChoosinganAssetAllocation: SlideSlide：400-0988-Anendowment'sreturnobjectiveis7%,whichincludesaspendingrateofGiventhecornerportfolioreturnsonthenextslideandassumingnoshortsales,determinethestandarddeviationandassetweightsfortheportfoliothatwillmeettheirobjectiveσAssetBAssetC1234ChoosingChoosinganAssetAllocation: Slide：Slide：400-0988-EstimatingtheStandardTheapproximatestandarddeviationoftheportfolioisaweightedaverageofthestandarddeviationsofCornerPortfolios2and3:σP=0.75(0.115)+NotethattheestimateisanupperittothetruestandardDoesnotaccountfordiversificationAssetClassTocalculatehowmuchthestrategicportfolioinvestsinassetsA,B,andC,usePortfolio2hasweights80/20/0inAssetsA,B,andPortfolio3hasweights0/40/60inAssetsA,B,andSlide：Slide：400-0988-IntroducingIntroducinga Ifthereisarisk- assetavailable,combiningitwiththecornerportfoliowiththehighestSharperatiocanincreasetheinvestor'sutilityThisisequivalenttocombiningthe assetwiththetangencyIncapitalmarkettheory,themarketportfolio(i.e.,thetangencyportfolio)hasthehighestavailableSharperatioofanyportfolioontheefficientfrontierIfthereturnonthecornerportfoliowithhighestSharperatioisgreatertherequiredreturn,holdpositiveweightsofthecornerportfolioandtheriskIfitsreturnislessthantherequiredreturn,borrowattherisk- ratetoThisassumesnorestrictionsonInourexample,CornerPortfolio2hasthehighestSharpeIntroducingaIntroducingaAsset:Slide：Slide：400-0988-CalculatingthePortfolioGivenareturnobjectiveof7%,CornerPortfolio2returnof7.5%,andarisk-0.07=0.075w2+0.02(1-Put90.9%ofthevalueoftheportfolioinCornerPortfolio2and9.1%in CalculatingtheStandard+Sincethestandarddeviationoftherisk- assetiszero,theportfoliostandarddeviationisdeterminedbytheallocationtoCornerPortfolio2:+σP= RFσP=IntroducingaIntroducingaAsset:SlideSlide：400-0988-CalculatingthePortfolioIftherequiredreturnis9%,CornerPortfolio2hasareturnof7.5%,andthe0.09=0.075w2+0.02(1-Put127%inCornerPortfolio2and-27%intherisk- asset(i.e.,shorttheriskasset)CalculatingtheStandardLeveringtheportfolio(i.e.,borrowingattherisk- rate)increasesboththeexpectedreturnandthestandarddeviation:Pw22wRFP1.27(0.115)P0.146SlideSlide：400-0988-StrategicAssetStrategicAssetAllocationforIndividualIndividuals’goalsincludemeetinglivingexpenses,fundingchildren’seducationalexpenses,fundingretirement,settinguptrusts,etc.Inotherwords,theindividualtypicallylooksprimarilyatwealthaccumulationtomeetrequiredaswellasdesiredexpenditures.Anotherprimarydifferencebetweenanindividualinvestorandaninstitutionalinvestoristhepatternsof egenerationandwealthaccumulation.Theindividual’shumancapital(thetotalpresentvalueoffutureemploymente),therefore,isgreatestatanearlyage,whilehisfinancialcapital(accumulatedwealth)increasesovertimeandreachesa SlideSlide：400-0988-AssetallocationAssetallocationrelatedtolifecycleandcharacteristicsofeInvestorsshouldinvestfinancialcapitalassetsinsuchawayastodiversifyandbalanceouttheirhumancapital.Ayounginvestorwithrelativelysafehumancapitalassetsand/orgreaterflexibilityoflaborsupplyhasanappropriatestrategicassetallocationwithahigherwei