章节3-私人财富管理ss45任务1讲义04.v4cfa

CFA㧞゗㞁䁖㼏㚠SS4-5PrivateWealth【梦轩考 专业提供CFAFRM全 CFA㧞゗㞁䁖㼏㚠SS4-5PrivateWealthTopicTopicinCFALevelSS1SSSSSSSSSSSSSS SS SSSSSSSSSSSSSSSummaryofReadingsandSS4PrivateWealthRR ManagingIndividualInvestorR TaxesandPrivateWealthManagementinaGlobalR nninginaGlobalSS5PrivateWealthR ConcentratedSingle-AssetR13 LifetimeFinancialAdvice:HumanCapital,AssetAllocation,andInsurance1.ThePortfolioManagementSpecifyinvestor’sobjectivesandCreatetheinvestment statement(IPS)–formal allinvestmentdecisionmaking,withacentralroleinthewholeportfoliomanagementprocessFormalize1.ThePortfolioManagementSpecifyinvestor’sobjectivesandCreatetheinvestment statement(IPS)–formal allinvestmentdecisionmaking,withacentralroleinthewholeportfoliomanagementprocessFormalizecapitalmarketCreatethestrategicasset position(portfolioPortfolioimplementation(tradingEvaluation,monitoring,& 1.ThePortfolioManagementProcess— •Timerequiredvs. •Liquidityrealvs.pre-vs.post-tax Risk •Legal&Regulatoryability& •UniqueR TTLL 2.ProfilingIndividual2.ProfilingIndividualInvestorsSourceofEntrepreneurialactivity(actively,normallyaboveaveragewillingnesstotolerateInheritance,onetimewindfalls,builtupoverlongperiodsofsafeemployment(passively,belowaveragewillingnesstotoleraterisk)MeasureofPositivecorrelationbetweenlevelofrisktolerance& ’sperceptionofwealthStageoflife:(typicallyreducedwillingnesstotakerisk)FoundationAccumulationMaintenanceDistribution【梦轩考 专业提供CFAFRM全 +讲2.ProfilingIndividualInvestors

Canover yse,butonceCanover yse,butoncetohavelowturnover&FollowinvestmentRiskless•NotafraidofmakingDecisionsbasedmainlyDecisionstendtobeconservativeinnature3.1Return RRReturnRequiredAssetMaintaintheinflation-adjustedAssetSpecificCashFlowSupport…DesiredNon-primary 3.23.2RiskRRRiskRiskobjectiveRelatesto Assetturnover&investmentstylebetweenwillingness&ability,followthenarrowerofthemedicalexpensesforlovedones) nnedoutlays(vacation,newmedicalexpensesforlovedones) nnedoutlays(vacation,newHowquicklyanassetcanbeconvertedintocashwithoutalossinvalue.Focusisonneedforcashintheshortterminexcessofcashinflowsfromearningsor 3.3InvestmentConstraints RRNewtimehorizoneachtimeancircumstanceschangesignificantlyLengthofeachtimehorizonisOtherindividualscaninfluencetimeyieldtypesoftax: e,capitalgains,wealthtransfer,wealthIftaxtreatmentuncertain,mendationforlegalcounselTaxIsinvestorataxpayer?WhetherannualportfolioreturnssubjecttotaxationAlwaysstrivetominimizecurrent(e.g.,lossharvesting,longterm 3.33.3InvestmentConstraintsRR PrudentinvestorBalancetheinterestsofthe beneficiaryandremaindermen3.43.4ChoosingtheOptimalAssetcharitablecharitable(medicalexpense,uninsuredlosses,responsibleinvesting)Desiredsafetyfirstruleobjective(calculationsmaybenecessary)Thosethatviolateshortfallstatement S 3.5MonteCarlosimulationisflexibleandtheadvantagesItconsiders3.5MonteCarlosimulationisflexibleandtheadvantagesItconsiderspathconsideraninvestorrequiringaGBP25,000peryearwithdrawalforlivingfromaportfolioofGBP500,000.Butsupposeverypoormarketsleadtoadeclineintheportfolioof50%.Thefixedwithdrawalneednow esamuchlargerportionoftheportfolio.Evenifthemarketsrecover,thediminishedportfolioissmallerifthewithdrawalcomesatalowpoint.Thiscouldpermanentlydiminishthelivingstandardoftheinvestorduetotherandomdeclineinthemarket.Pathdependencycouldalsoconsiderissues,suchastheinctionofchanginginflationontheportfoliovaluesandontheinvestor'swithdrawalneeds.ItcanmoreclearlydisytradeoffsofriskandThe10,000pathscanberankedfrombesttoworsttoassesstheprobabilityofany easwellashowmuchbetterorworseitcoulditget.Properlymodeledtaxysis,whichconsiderstheactualtaxratesoftheinvestoraswellastaxlocationoftheassets(heldintaxableortaxdeferredlocations),canbeassessed.Howthetaxburdenchangeswithmarketreturnsandwithdrawalscouldbe 3.5MonteCarlosimulationisflexibleandtheadvantagesAclearerunderstandingofshorttermandlongtermriskcanbeForexample,reducingtheholdingsofriskystockwouldreducetheshorttermvariabilityoftheportfoliobutincreasethelongtermriskofnothavingsufficientItissuperiorinassessingmultiperiodTraditionalysisprojectsportfolioreturnasasimpleweightedaverageoftheassetreturns,geometricallycompounded.Risk(variance)isthetraditionalformulataughtintheCFAcurriculum.MonteCarlosimulationcanbettermodeltherealstochasticprocesswherereturnovertimedependsnotonlyonthestartingvalueoftheperiodbutalsoontheadditionsorwithdrawalstotheportfolioateachfutureperiod.Pointsalongthetimelinecanbeconsideredtoanswerquestions,suchas,"Dosavingsneedtobeincreased?""CanIretireearlier?""MustIretirelater?" 3.5MonteCarlosimulation–MonteCarlosimulation–Simplisticuseofhistoricaldata,suchasexpectedreturns,fortheinputs.ReturnschangeandhaveamajoreffectonprojectedfuturevaluesoftheModelsthatsimulatethereturnofassetclassesbutnottheactualassetsheld.SimulatingthereturnoftheWilshire5000whenafundwithfeeswillbeheldcouldsignificantlyoverstatethefuturevalueortimeperiodoverwhichdistributionscanbesustained.Realassetshaveexpenses.Taxmodelingthatissimplisticandnottailoredtotheinvestor's 【梦轩考 专业提供CFAFRM全 +讲4stepstoformulateindividual’s66stepsto al & Risks4.1Investor’sIPS-Investorclassify•alSourceofEmployeewithannualSizeofalWithchildreneducationWithmortgageliquidityWith 4.24.2Investor’sIPS-ReturnobjectivesalbysalaryinSupportmortgageliquiditySupportfamilies’healthcareSupportinsurancepremiumAssetCashflow••RrNetCFsatRfNetCFsatf4.2Investor’sRrNetCFsatRfNetCFsatf4.2Investor’sIPS-Returnobjectives—Cashflowysis•alinvestorCashDownpaymentatNetcashNetCFatT0>0,asapartof 4.24.2Investor’sIPS-ReturnCalculationalCurrentportfolio’sNetCFinatRealNominal4.2Investor’sIPS-Returnobjectives—Cash ysis…Open- S* Total S* S* S*(1+f)*Living L*Down Mortgage Charity Total S*t+L+D+C+ S*(1+f)*t+L*(1+f)+Netcash 4.2Investor’sIPS-Returnobjectives—Cashflowysis…Cloze-Mainissue:4.2Investor’sIPS-Returnobjectives—Cashflowysis…Cloze-Mainissue:RenewreturnobjectiveclosetoRecalculatethenetCFneedannually→Recalculatetheassetbasenow→Calculatetherequiredrateofreturn→I/YNewobjectives:SupportlivingexpenseinSupportdonatingmoneytoProvideinheritancefor 4.3Investor’sIPS-RiskalAbility eareAbilityAssetbaseisOtherThenarrowone 4.4Investor’sIPS 2008CFAlevel3morningsessionQUESTION1HASFOURPARTS(A,B,C,D)FORATOTALOF36RobertoandMarianaCarvalholiveinalargecityinBrazilwiththeirtwochildren,agesfourandtwo.Robertois30yearsoldandMarianawillbe30yearsoldlaterthismonth.RobertoisamanagerinamanufacturingfacilityandMarianaisamusicianinthelocalsymphonyorchestra.RobertoandMariana’sannualsalariestotal120,000Brazilianreais(BRL)aftertax.Theirsalariesjustcovertheirlivingexpenses.Theaverageannualinflationrateisfourpercentandtheirsalariesandexpensesareexpectedtoincreaseatthisrate.Theyhealthyandbelievetheirjobsandearningpotentialaresecure.TheCarvalhos’salaries,dividends,andinterestaretaxedat20percent,andcapitalgainsat15percent.Mariana’sparentshavesignificantwealthandfundedanirrevocablealtrustforher.Brazilhasawealthtransfertaxthatappliestotransfersintotrustsandtoinheritances.BrazilhasadoptedthePrudentInvestorRulefortheadministrationoftrusts.ThecurrentvalueofthetrustisBRL1,500,000. 4.4Investor’sIPS 2008CFAlevel3morningsessionTheterms4.4Investor’sIPS 2008CFAlevel3morningsessionThetermsofthetruststatethatwhenMarianareachestheageof30,shewillreceiveataxdistributionofhalfthevalueofthetrust.Thebalanceofthetrustwillremaininvestedandwilldistributeintotaltoherwhenshereachesage40.Sinceshedoesnothaveaccesstotheremainingbalancefortenyears,thisbalanceisnotconsideredapartoftheCarvalhos’investableassets,butispartoftheirtotalnetworth.Inaddition,Marianaexpectstoinheritasubstantialsumofmoneyuponthedeathofbothparents.TheCarvalhoshaveBRL500,000ininvestableassets,currentlyallinshorttermbankdeposits.Itistheirintentiontomaintainatleastthisamountininvestableassets,onaninflationadjustedbasis,inthefuture.TheCarvalhoscurrentlylivewithMariana’sparents,butarenowpurchasingahome.ThepurchasepriceofthehomeisBRL850,000.Thedownpaymentis30percentofthecostofthehomeandwillbefundedfromthetrustdistribution.TheCarvalhoswilltakeoutafixedratemortgageforthebalanceofthepurchaseprice.TheaftertaxmortgagecostwillbefixedatBRL55,000(principalandinterest)annuallyfor30years,withthefirstannualpaymentdueoneyearfromnow. 4.4Investor’sIPS 2008CFAlevel3morningsessionTheCarvalhos’immediateinvestmentgoalistohavetheirinvestmentportfoliocoverthecostofthemortgage,whilemaintainingtheportfolio’sinflationadjustedvalue.Theyntoretireattheageof60andtheirlongtermgoalistohaveaninvestmentportfoliothatwillprovideanannual ecomparabletotheircurrentsalariesadjustedbyinflation.TheirfamilyhealthinsuranceisprovidedbyRoberto’semployer,bothnowandinretirement.Theyarehopefultheirtwochildrenwillattendthelocaluniversityatnocost.Theuniversitydoesnotchargetuitionfeesforqualifiedstudentswhopassitsentranceexam.Thosewhodonotpasstheexamarerequiredtopayfulltuition,whichishighrelativetotheCarvalhos’livingexpenses.Inordertomeettheirinvestmentgoals,theCarvalhosrealizetheyneedtoconsiderinvestmentsotherthanshorttermbankdeposits.TheCarvalhoshireLuizOliveira,CFA,tomanageaninvestmentportfoliothattheywillfundwiththeirBRL500,000inbankdepositsandthenetproceedsofMariana’strustdistributionatage30. 4.4Investor’sIPS 2008CFAlevel3morningsessioni.PreparethereturnobjectivesportionoftheCarvalhos’investmentstatementii.Calculatetheaftertaxnominalrateofreturnthatisrequiredforthenextyear.Showyourcalculations.(12minutes) IdentifytwofactorsintheCarvalhos’situationthatincreasetheirabilitytotakerisk.ii.IdentifytwofactorsintheCarvalhos’situationthatdecreasetheirabilitytotakeiii.DeterminewhethertheCarvalhoshavebelowaverage,average,oraboveabilitytotakePreparethefollowingconstraintsoftheCarvalhos’Timei.PreparethecurrentreturnobjectivesportionoftheCarvalhos’ii.Calculatetheaftertaxnominalrateofreturnthatisrequiredfortheportfolio.Showyourcalculations. 4.4Investor’sIPS 2008CFAlevel3morningsessionThereturnobjective4.4Investor’sIPS 2008CFAlevel3morningsessionThereturnobjectivefortheCarvalhos’portfolioisprovideforthemortgagepaymentsforasupporttheirlivingexpensesinmaintaintheinflation-adjustedvalueofthe 4.4Investor’sIPS 2008CFAlevel3morningsession 3.7Investor’sIPS 2008CFAlevel3morningsession 3.7Investor’sIPS 2008CFAlevel3morningsession 【3.7Investor’sIPS 2008CFAlevel3morningsession 3.7Investor’sIPS 2008CFAlevel3morningsessionTwentyfiveyearshavepassed.TheCarvalhosarenow55yearsoldandtheirtwochildrenaregrownandfinanciallyindependent.Mariana’sparentspassedawayearlierthisyearandleftheraninheritanceofBRL8,000,000aftertax.TheCarvalhoshavefiveyearsremainingontheirmortgageandtheBRL55,000annualmortgagepaymentwillcontinuetobefundedfromtheirinvestmentportfolio.Theyintendtoworkanotherfiveyearsandthenretireatage60.Theirsalariesareexpectedtocontinuetocovertheirlivingexpensesuntilretirement.Theirinvestmentportfolio,includingtheinheritance,nowtotalsBRL10,200,000.TheCarvalhosexintoOliveirathatinretirement,theywouldliketomaintaintheircurrentstandardoflivingandstartaregularprogramofdonatingmoneytotheirfavoritecharities.TheyalsohopetoleaveaninheritanceofBRL5,000,000toeachoftheirtwochildrenattheirdeath.OliveiracalculatestheywillneedaportfoliovalueofBRL15,000,000whentheyretireinordertosupportthesegoals. 3.7Investor’sIPS 2008CFAlevel3morningsession 【梦轩考 专业提供CFAFRM全 +讲SummaryofReadingsandSS4PrivateWealthR ManagingIndividualInvestorRR TaxesandPrivateWealthManagementinaGlobalR nninginaGlobalSS5PrivateWealthR ConcentratedSingle-AssetR LifetimeFinancialAdvice:HumanAssetAllocation,and1.OverviewofGlobalTaxationTherearethreeprimarycategoriesofTaxes Paidbyindividuals,corporations,andotherlegalentitiesonvarioustypesofeincludingwages,interest,dividends,andcapitalWealth-basedPaidonthevalueofassetsheldandonwealthTaxesonSalestaxes:PaidbytheValue-addedtaxes:Paidateachintermediateproductionstepaccordingtotheamountofvalueaddedatthestep;ultimaybornebytheconsumer(addedintothepurchaseprice). 1.1GlobalTaxationRegimes—CommonTaxregimesaregenerallyclassifiedasflatorprogressive.Inaprogressivetaxsystemthetaxrateincreasesasthelevelof eincrease.Inmosttaxjurisdictions,ataxratestructureappliestoordinary e(suchasearningsfromemployment).Othertaxratesmayapplytospecialcategories esuchasinvestment e,andisoftentaxeddifferentlybasedonthenatureofthe e:interest,dividends,orcapitalgainsandlosses.Inadditiontoimposingprogressivetaxratesonordinary e,manycountriestaxinvestmentreturnsdifferentlydependingonwhethertheyareintheformofinterest,dividends,orcapitalgains.Interestanddividendsmightbetaxedatareducedrateortaxedatordinaryratesaftertheyexceedsomeamount.Long-termcapitalgainsareoftentaxedatalowerratethanshort-termcapitalgains,withlong-termdefinitionsvaryingfromonetofiveyearsorso.Inmostcountries,capitalgainstaxesarepaidonlywhencapitalgainsarerealized(i.e.,whentheinvestmentissold). 【梦轩考 专业提供CFAFRM全 +讲1.2SevenGeneralTax for CapitalGains?FlatandFlatandconsiderablevariationinthespecialtreatmentofinvestment e,withsomecountriesprovidingexemptionforonlypartofinvestment e.TheUnitedStates,U.K., 2.1SimpleTaxEnvironment—AccrualAccrualAccrualAccrualtaxesarepaidperiodically(e.g.,annually)[(1+R)–RxT]N=[1+R(1-T)]NFuturevalueAT=PV[1+R(1-Taxesarepaideachperiod,sotheperiodicreturnontheaccountisafter-taxreturn,R(1-Theamountoftaxremovedfromtheaccounteachperioddoesnotearnfuture(compounded)returnsThereductioninreturncausedbythepaymentoftaxesisreferredtoastaxdrag2.1SimpleTaxEnvironment—AccrualTaxation:TaxExample:Accountsubjecttoaccrual(annual)taxes$1,000isinvestedfor20yearsandearnsabeforetaxreturnof10%.Assumingtheaccrualtaxrateis30%,calculatetheaftertaxvalueoftheaccountin20years.Notethatifthetaxratewerezero,theinvestmentwouldhavebeenFVT0=futurevalueassumingnotaxes=$1,000[1+0.10(1−0)]20=gainT0=totalgainwithnotaxes=$6,727.50$1,000=FVAT=aftertaxfuturevalue(accrualtaxespaidannually)=$1,000[1+0.30)]20=gainAT=totalgainafteraccrualtaxes=$3,869.68−$1,000gainlosttoThesecalculationshelpillustratethreefundamentalCompoundingofaccrual(annual)taxesmakestheireffectstatedasa%oftotalgaingreaterthanthetaxrate.Thegainlosttotaxes,statedasacurrencyorasa%,isreferredtoastaxdrag.gainlosttotaxes(%)=$2,857.82/$5,727.50=49.9%=taxdrag 2.1SimpleTaxEnvironment—AccrualTaxation:TaxAccrualTax:TaxdragVSInvestment2.1SimpleTaxEnvironment—AccrualTaxation:TaxAccrualTax:TaxdragVSInvestmenthorizon&Taxdrag%>taxInvestmenthorizon taxdrag$&%Investmentreturn taxdrag$&% 2.2SimpleTaxEnvironment—DeferredCapitalGainUsingTCGasthetaxrateoncapitalgains,theafter-taxfuturevalueinterestfactorfordeferredcapitalgains(FVIFCGT)is:FVIFCGT=(1+R)N–[(1+R)N-1]xTCG=(1+R)N–TCGx(1+R)N+=[(1+R)N(1−TCG)+ 2.2SimpleTaxEnvironment—DeferredCapitalGainSummarizingthesamethreerelationshipsweexaminedforaccrualtaxes,weseethattheyarequitedifferentwhencapitalgainstaxesareappliedonadeferredbasis:Taxdrag%=taxAstheinvestmenthorizonincreases֜taxdrag%isAstheinvestmentreturnincreases֜taxdrag%isInaddition,whentaxesareAsinvestmenthorizonincreases֜thevalueofthetaxdeferralAsinvestmentreturnincreases֜thevalueofthetaxdeferral 2.3SimpleTaxEnvironment—CostWehaveassumedthatthecost2.3SimpleTaxEnvironment—CostWehaveassumedthatthecostbasisforcomputingtaxesisthecurrentvalue($1,000),asifweinvestedafter-taxHowever,thecostbasisisoftendifferentfromtheinvestment’scurrentvalue.Forexample,thecostbasiscouldbetheoriginalpurchasepriceandthecurrentvalueof$1,000representstheoriginalcostplusunrealizedcapitalgains.Allelseequal,reducingthecostbasisincreasestherealizedcapitalgain,increasestheamountofcapitalgainstaxesdue,andreducesthenetsellingprice.Thuswemodifyourdeferredcapitalgainstaxformulatoaccountforthebasis(B):FVIFCGT,MV≠Basis=[(1+R)N(1−TCG)]+=[(1+R)N(1−TCG)]+TCG–(1- 2.4SimpleTaxEnvironment—Wealth-BasedInsomecountries,wealth-basedtaxesareassessedannually(similartoaccrualetaxes)onthevalueofassetsheld.Unlikeaccrualtaxesandcapitalgainstaxes,whicharepaidonjusttheinvestmentreturn,wealth-basedtaxesareappliedtoboththeprincipalandreturn.Theyaremostoftenappliedtorealestate,asintheU.K.Fortunaythewealth-basedtaxrateisusuallylowerinpercentagetermsthanaccrualandcapitalgainstaxrates.ContinuingthenotationfrombeforeexceptthatTWisthewealth-basedtaxrate,thefuturevalueinterestfactorafterthewealth-basedtax(FVIFWT)is:FVIFWT=[(1+R)(1− 2.4SimpleTaxEnvironment—Wealth-BasedTaxes:TaxContinuing,assume$1,000isinvestedfor20yearsandearnsareturnof10%.Assumingtheaccountissubjectonlytoawealth-basedtaxof2%,calculatetheafter-taxvalueoftheaccountin20years.FVT=0=futurevalueassumingnotaxes=$1,000FVWT=futurevalueassumingtaxes=$1,000[(1+0.10)(1-Becausethewealthtaxisappliedtotheentireaccount(bothprincipalandreturns),thisfuturevalueisnotdirectlycomparabletothosewhenaccrualorcapitalgainstaxesareapplied.Notehoweverthattheterminalvalueof$4,491.33isconsiderablylessthanthe$6,727.50before-taxterminalvalue.When2%wealthtaxesarepaidannually:taxdrag$=$6,727.50-$4,491.33=taxdrag%=$2,236.17/($6,727.50-$1,000)= 2.4SimpleTaxEnvironment—Wealth-BasedTaxes:TaxForwealth-basedtaxes,thethreeprimary2.4SimpleTaxEnvironment—Wealth-BasedTaxes:TaxForwealth-basedtaxes,thethreeprimaryrelationshipscanbesummarizedTaxdrag%>taxAsinvestmenthorizonincreases֜taxdrag%andtaxdrag$Asinvestmentreturnincreases֜taxdrag$increases;taxdrag%AssumeN=1,whenRincrease,Taxdrag% 2.5BlendedTaxingTocalculatetheafter-taxreturnontheaccount,wemultiplythebeforetaxreturn(R)times1minusrealizedtaxrate,whichconsiderstheproportionofeachformofgainwithitsspecifictaxrate:realizedtaxTherealizedtaxrateisnothingmorethantheweightedaveragetaxratepaidbytheinvestor.Pistheweight(proportion)ofeachtypeofreturn, dividend,orrealizedcapitalgain,andTisthetaxrateoneachtypeofreturn.Multiplyingeachtaxratebytherelatedproportionyieldstheweightedaveragetaxrate.Usingthesamesubscriptsforthetaxrates,T,asfortheproportions,P,theannualreturnafterrealizedtaxesoninterest e,dividends,andrealizedcapitalgains(RART)is:RART=R(1-realizedtaxrate)=R[1-2.5.1BlendedTaxingEnvironments—Ix Dx CGx UCGx?TECG UCGxTECG[1-(PITI+PDTD+PCGTCG)]=TCG[1- 2.5.1BlendedTaxingEnvironments—TECGandTocalculatetheeffectivecapitalgainstaxrate(TECG)thatadjustsfortheannualtaxesalreadypaidoninterest,dividends,andrealizedcapitalgains,weusetheTECG2.5.1BlendedTaxingEnvironments—TECGandTocalculatetheeffectivecapitalgainstaxrate(TECG)thatadjustsfortheannualtaxesalreadypaidoninterest,dividends,andrealizedcapitalgains,weusetheTECG[1-(PITI+PDTD+PCGTCG)]=TCG[1-Usingreturnafterrealizedtaxes(RART)andtheeffectivedeferredcapitalgainstaxrate(TECG),thefuturevalueinterestfactorconsideringalltaxesaswellasthecostbasisoftheaccount(FVIFT)is:RART=R(1realizedtaxrate)=R[1 .1BlendedTaxingEnvironments–Beginningoftheyear:MVEndoftheyear:MVRealizedcapitalTotaltaxesUnrealizedCGs=10,000-300-4,000-TaxatunrealizedCGs=3,500*20%=700TECG*[10,000-(TI+TD+TCG)]=7002.5.1BlendedTaxingEnvironments–Usereturnafterrealizedtaxes(RART)andtheeffectivedeferredcapitalgainstaxrate(TECG)tocalculatethefuturevaluebyconsideringthecostbasis:FVIFT=[(1+RART)N(1-TECG)+TECG-(1-SeeNoteP240RART=(10,000-Costbasis=TECG=B=75,000/100,000=FV=[(1+8.67%)8(1-8.07%)+8.07%-(1-75%)*20%]x= 2.5.2BlendedTaxingEnvironments–AccrualequivalentAccrualequivalentafter-taxreturn:theannualreturnthatproducesthesameterminalvalueasthetaxableportfolio.YoucanthinkitasEffectiveannualUsetheFVIFT2.5.2BlendedTaxingEnvironments–AccrualequivalentAccrualequivalentafter-taxreturn:theannualreturnthatproducesthesameterminalvalueasthetaxableportfolio.YoucanthinkitasEffectiveannualUsetheFVIFTinthepreviousexample=PV=N=RAE= 2.5.3BlendedTaxingEnvironments–AccrualequivalenttaxUsingtheaccrualequivalentafter-taxreturn,wecancalculateanaccrualequivalenttaxrate.Theaccrualequivalenttaxrate(TAE)isthetaxratethatmakesthepre-taxreturn(R)equaltotheaccrualequivalentafter-taxreturn(RAE).Thinkofitastheoveralleffectivetaxrateontheaccount,consideringbothaccrualanddeferredtaxes:RAE=R(1-TAE)֜TAE=1 Inouraccrualequivalentreturnexample,theaccrualequivalentafter-taxreturnis7.76%andthepre-taxreturnis10%.Calculatetheaccrualequivalenttaxrate.theaccrualequivalenttaxrateTAE=1–0.0776/0.10=0.224=Thelowertheaccrualequivalenttaxrate,themoretax-efficient 3.TypesofInvestmentSometimes,thetypesofinvestmentaccountsoverridethetaxtreatmentofaninvestmentbasedonitsassetclass.taxableaccounts:investmentsaremadeonanafter-taxbasisandreturnsaretaxedinavarietyofways.Tax-deferredaccounts:allowtax-deductiblecontributionsand/ortax-deferredaccumulationofreturns,butfundsaretaxedwhenwithdrawn.FVIFTDA=(1+r)n(1-Tn)Tax-exemptaccounts:donotallowtax-deductiblecontributions,buttax-exemptaccumulationofreturnsevenwhenfundsarewithdrawn.FVIFTEA=(1+r)n 3.1Typesofinvestment$100,000investedineachfourTaxedFVIFAT3.1Typesofinvestment$100,000investedineachfourTaxedFVIFAT=[1+R(1- $100,000[1+0.09(1-0.35)]30Deferredcapitalgain=>$100,000[(1+0.09)30(1-TaxeddeferredFVIFAT=(1+R)N(1- =>$100,000[(1+0.09)30(1-Taxexempt =>$100,000(1+0.09)30 3.2ChoosingAmongAccountFVIFTDA=(1+R)N(1-FVIFTEA=(1-T0)IFT0>TN=>FVTDA>FVTEAIFT0=TN=>FVTDA=FVTEAIFT0<TN=>FVTDA<FVTEA 4.TaxandInvestmentInTaxedAccount-Theernment(taxingauthority)bearspartoftheinvestmentriskInTax-exemptaccount–Theinvestorsbearsalltheinvestment Example:RiskReductionwithAccrualTaxesSupposeaninvestorhashalfherportfolioinstocksandhalfinbonds.Thereturnsonthestockinvestmentaretaxedatanannualrateof20%(dividendsreceivespecialtreatment)andthebondreturnsaretaxedatarateof30% eistaxedasordinary e).Thepre-taxstandarddeviationofstockreturnsis16%andthepretaxstandarddeviationofbondreturnsis6%.Calculatethepre-taxandafter-taxstandarddeviationsofportfolioreturns,assumingthecorrelationbetweenstocksandbondsis1.Answer:Ifthecorrelationbetweenstocksandbondsis1,thepre-taxstandarddeviationofportfolioreturnsisasimpleweightedaverageoftheindividualstandarddeviations:σ3 Example:RiskReductionwithAccrualTaxesSupposeaninvestorhashalfherportfolioinstocksandhalfinbonds.Thereturnsonthestockinvestmentaretaxedatanannualrateof20%(dividendsreceivespecialtreatment)andthebondreturnsaretaxedatarateof30% eistaxedasordinary e).Thepre-taxstandarddeviationofstockreturnsis16%andthepretaxstandarddeviationofbondreturnsis6%.Calculatethepre-taxandafter-taxstandarddeviationsofportfolioreturns,assumingthecorrelationbetweenstocksandbondsis1.Answer:Ifthecorrelationbetweenstocksandbondsis1,thepre-taxstandarddeviationofportfolioreturnsisasimpleweightedaverageoftheindividualstandarddeviations:σ3 0.516%0.56%Becausetaxesarepaidannuallyondividendsandinterest,theafter-taxstandarddeviationofreturnsusesbothafter-taxassetstandarddeviations: 0.516%(10.2)0.56%(10.3) Example:RiskReductionwithAccrualandDeferredNowassumethebondsareheldinatax-exemptaccount.Calculatetheafter-taxstandarddeviationofportfolioreturnsandcompareittothebefore-taxportfoliostandarddeviationandtheportfoliostandarddeviationwithaccrualtaxesonly.Answer:Theafter-taxstandarddeviationofportfolioreturnsσ3 0.516%(10.2)0.56% 5.1ImplicationforWealthManagement–TradingFromataxmanagementstandpoint,aninvestorshouldlocateheavilytaxedassetsintaxadvantagedaccountsandholdlightlytaxedassetsintaxableaccounts.thevaluecreatedbyth