Essentials-Of-Investments-8th-Ed-Bodie-投资学精要(第八版)课

Chapter07-CapitalAssetPricingandArbitragePricingTheory7-1CHAPTER07CAPITALASSETPRICINGANDARBITRAGEPRICINGTHEORY1.Therequiredrateofreturnonastockisrelatedtotherequiredrateofreturnonthestockmarketviabeta.AssumingthebetaofGoogleremainsconstant,theincreaseintheriskofthemarketwillincreasetherequiredrateofreturnonthemarket,andthusincreasetherequiredrateofreturnonGoogle.2.AnexampleofthisscenariowouldbeaninvestmentintheSMBandHML.Asofyet,therearenovehicles(indexfundsorETFs)todirectlyinvestinSMBandHML.Whiletheymayprovesuperiortothesingleindexmodel,theyarenotyetpractical,evenforprofessionalinvestors.3.TheAPTmayexistwithouttheCAPM,butnottheotherway.Thus,statementaispossible,butnotb.Thereasonbeing,thattheAPTacceptstheprincipleofriskandreturn,whichiscentraltoCAPM,withoutmakinganyassumptionsregardingindividualinvestorsandtheirportfolios.TheseassumptionsarenecessarytoCAPM.4.E(rP)=rf+[E(rM)–rf]20%=5%+(15%–5%)=15/10=1.55.Ifthebetaofthesecuritydoubles,thensowillitsriskpremium.Thecurrentriskpremiumforthestockis:(13%-7%)=6%,sothenewriskpremiumwouldbe12%,andthenewdiscountrateforthesecuritywouldbe:12%+7%=19%Ifthestockpaysaconstantdividendinperpetuity,thenweknowfromtheoriginaldatathatthedividend(D)mustsatisfytheequationforaperpetuity:Price=Dividend/Discountrate40=D/0.13D=400.13=$5.20Atthenewdiscountrateof19%,thestockwouldbeworth:$5.20/0.19=$27.37Theincreaseinstockriskhasloweredthevalueofthestockby31.58%.6.Thecashflowsfortheprojectcomprisea10-yearannuityof$10millionperyearplusanadditionalpaymentinthetenthyearof$10million(sothatthetotalpaymentinthetenthyearis$20million).Theappropriatediscountratefortheprojectis:rf+[E(rM)–rf]=9%+1.7(19%–9%)=26%Usingthisdiscountrate:NPV=–20+101tt26.1101026.110Chapter07-CapitalAssetPricingandArbitragePricingTheory7-2=–20+[10Annuityfactor(26%,10years)]+[10PVfactor(26%,10years)]=15.64Theinternalrateofreturnontheprojectis49.55%.ThehighestvaluethatbetacantakebeforethehurdlerateexceedstheIRRisdeterminedby:49.55%=9%+(19%–9%)=40.55/10=4.0557.a.False.=0impliesE(r)=rf,notzero.b.False.Investorsrequireariskpremiumforbearingsystematic(i.e.,marketorundiversifiable)risk.c.False.Youshouldinvest0.75ofyourportfoliointhemarketportfolio,andtheremainderinT-bills.Then:P=(0.751)+(0.250)=0.758.a.Thebetaisthesensitivityofthestock'sreturntothemarketreturn.CalltheaggressivestockAandthedefensivestockD.Thenbetaisthechangeinthestockreturnperunitchangeinthemarketreturn.Wecomputeeachstock'sbetabycalculatingthedifferenceinitsreturnacrossthetwoscenariosdividedbythedifferenceinmarketreturn.00.2205322A70.0205145.3Db.Withthetwoscenariosequallikely,theexpectedrateofreturnisanaverageofthetwopossibleoutcomes:E(rA)=0.5(2%+32%)=17%E(rB)=0.5(3.5%+14%)=8.75%c.TheSMLisdeterminedbythefollowing:T-billrate=8%withabetaequaltozero,betaforthemarketis1.0,andtheexpectedrateofreturnforthemarketis:0.5(20%+5%)=12.5%Seethefollowinggraph.Chapter07-CapitalAssetPricingandArbitragePricingTheory7-3E(r)8%12.5%1.02.0ASMLM.7DDTheequationforthesecuritymarketlineis:E(r)=8%+(12.5%–8%)d.Theaggressivestockhasafairexpectedrateofreturnof:E(rA)=8%+2.0(12.5%–8%)=17%Thesecurityanalyst’sestimateoftheexpectedrateofreturnisalso17%.Thusthealphafortheaggressivestockiszero.Similarly,therequiredreturnforthedefensivestockis:E(rD)=8%+0.7(12.5%–8%)=11.15%Thesecurityanalyst’sestimateoftheexpectedreturnforDisonly8.75%,andhence:D=actualexpectedreturn–requiredreturnpredictedbyCAPM=8.75%–11.15%=–2.4%Thepointsforeachstockareplottedonthegraphabove.e.Thehurdlerateisdeterminedbytheprojectbeta(i.e.,0.7),notbythefirm’sbeta.Thecorrectdiscountrateistherefore11.15%,thefairrateofreturnonstockD.9.Notpossible.PortfolioAhasahigherbetathanPortfolioB,buttheexpectedreturnforPortfolioAislower.Chapter07-CapitalAssetPricingandArbitragePricingTheory7-410.Possible.IftheCAPMisvalid,theexpectedrateofreturncompensatesonlyforsystematic(market)riskasmeasuredbybeta,ratherthanthestandarddeviation,whichincludesnonsystematicrisk.Thus,PortfolioA'slowerexpectedrateofreturncanbepairedwithahigherstandarddeviation,aslongasPortfolioA'sbetaislowerthanthatofPortfolioB.11.Notpossible.Thereward-to-variabilityratioforPortfolioAisbetterthanthatofthemarket,whichisnotpossibleaccordingtotheCAPM,sincetheCAPMpredictsthatthemarketportfolioisthemostefficientportfolio.Usingthenumberssupplied:SA=5.0121016SM=33.0241018ThesefiguresimplythatPortfolioAprovidesabetterrisk-rewardtradeoffthanthemarketportfolio.12.Notpossible.PortfolioAclearlydominatesthemarketportfolio.Ithasalowerstandarddeviationwithahigherexpectedreturn.13.Notpossible.Giventhesedata,theSMLis:E(r)=10%+(18%–10%)Aportfoliowithbetaof1.5shouldhaveanexpectedreturnof:E(r)=10%+1.5(18%–10%)=22%TheexpectedreturnforPortfolioAis16%sothatPortfolioAplotsbelowtheSML(i.e.,hasanalphaof–6%),andhenceisanoverpricedportfolio.ThisisinconsistentwiththeCAPM.14.Notpossible.TheSMListhesameasinProblem12.Here,therequiredexpectedreturnforPortfolioAis:10%+(0.98%)=17.2%Thisisstillhigherthan16%.PortfolioAisoverpriced,withalphaequalto:–1.2%15.Possible.PortfolioA'srat