资本资产定价模型(CAPM（PPT44页)

FoundationsofFinancialAnalysisandInvestmentsLecture3:CapitalAssetPricingModel(CAPM)DrEkaterinaSvetlovaToday‘slecture1.Briefrevision:Lecture22.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerate3.MPTandCAPM:Preliminaryremarks4.TheCapitalAssetPricingModel(CAPM)5.FirstconsiderationsaboutthelimitationsofCAPMDrEkaterinaSvetlovaTheportfolioconsistsoftworiskyassetsD(debt)andE(equity)TheirweightsintheportfolioareWeconstructriskyportfoliosvaryingtoprovidethelowestpossibleriskforanygivenlevelofexpectedreturnE(rp)=wDE(rD)+wEE(rE)DrEkaterinaSvetlovaxDandxE(xD+xE=1;xD≥0,xE≥0)xDandxE222222Cov,pDDEEDEDECov(rD,rE)=DEDESuccessofdiversificationdependsonthecorrelationcoefficientBodieetal.2014,Ch.71.Briefrevision:Lecture2DrEkaterinaSvetlovaDebtEquityExpectedreturnE(r)8%13%Standarddeviation12%20%Bodieetal.(2014),Table7.1,p.208Bodieetal.(2014),Table7.3,p.211ABBodieetal.(2014),p.2141.Briefrevision:Lecture2DrEkaterinaSvetlovaDebtEquityExpectedreturnE(r)8%13%Standarddeviation12%20%Bodieetal.(2014),Table7.1,p.208Bodieetal.(2014),Table7.3,p.211WhenρDE=-1,DEDDEww1WhenρDE=0,1.Briefrevision:Lecture21.Briefrevision:Lecture2Source:Bodieetal.2014:p.220DrEkaterinaSvetlovaDrEkaterinaSvetlovaDiversifiable(nonsystematic)riskvsundiversifiable(systematic)risk1.Briefrevision:Lecture2Bodieetal.(2014),p.207DrEkaterinaSvetlovaHowdoesdiversificationmatter?DrEkaterinaSvetlovaSponsorsTrusteesTheInvestmentManagementFirmInvestmentconsultantstheTampafirefightersandpoliceofficerspensionfundCityofTampa,FloridaHaroldJ.BowenIIIHowdoesdiversificationmatter?Source:=0Asforbeingdiversified,whichisthemantraofnearlyallinstitutionalmoneymanagersandconsultants,[theTampafund]isn’t.…[T]hefund’sassetsareconcentratedinarelativelysmallnumberofstocksandfixed-incomeinvestments.Inshort,theTampapensionfundprettymuchbreaksalltheconventionalrulesoffundmanagement.2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaUnlimitedborrowingandlendingatarisk-freerate:-Risklessassetisanassetwithacertainreturnforthegiventimehorizon.-Forexample:USTreasurybondsthatautomaticallyadjustforinflation(TIPS:Treasuryinflationprotectedsecurities)orshorttermUSTreasurybills(UST-bills)-Standarddeviationofthereturn:σ=0DrEkaterinaSvetlova2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateIfyouinvestinassetHandrisklessasset:xHandxf=1-xHErp=(1-xH)Rf+xHRH=Rf+xH(ErH-Rf)σp=(1-xH)2σf+xH2σH2+2xH(1-xH)ρfHσfσHAsσf=0,weobtain:σp=xHσH2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004DrEkaterinaSvetlovaCombiningequationsforportfolioreturnandrisk,weobtain:ErH-RfErp=Rf+σpσH2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateSource:Perold2004ErH-RfσHTheslope:Sharperatio(ErH-Rf)Riskpremium2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004SharperatioofassetH:(12%-5%)/40%=0.175Important:allcombinationsofassetHwithrisk-freeborrowingandlendinghavethesameSharperatio:itistheslopeofastraightlineSharperatioofassetM:(10%-5%)/20%=0.252.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004UseofSharperatioinpractice:ShaperatioisusedtomeasuretheperformanceofaportfolioAdvantage:theriskadjustedperformancemeasurement2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSharperatioofHSharperatioofMThecombinationofrisk-freeassetandMdominatesthecombinationofrisk-freeassetandH2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004Howmuchofeachriskyassetshouldoneholdintheportfolio?Sharperatio:0.305(higherthan0.25forMand0.175forH)AllinvestorswillholdassetsMandHinproportions74/26Newefficiencylinewhenrisk-freelending/borrowingisallowed2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004CorrelationbetweenMandHassumedtobezeroIncaseofmanyriskyassets:Tobinseparationtheorem:Portfoliochoiceproblemcanbeseparatedintwotasks:1.Identifytheoptimalriskyportfolio2.IdentifythecapitalallocationbetweenriskyandrisklessinvestmentsRiskaversionRiskseeking3.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004UseofTobinseparationinpractice:Source:(CML)=setofpotentialallocationsbetweenariskyassetandano-riskyasset(oraportfoliothatcontainsonlyriskyassetsandrisk-freeassets)MM–themarketportfolioAllinvestorsholdportfolioM(notdependentoninvestors’toleranceforrisk)Themarketportfolioistheonewherethesupplyequalsdemand(marketclearing)2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlov