第五章CAPM的应用(证券投资学-北大,杨云红)

第五章CAPM的应用利用Markowitz模型进行积极证券组合管理市场模型在消极证券组合管理中的应用利用Beta去得到好的协方差估计利用Beta去得到好的期望回报率估计CAPM在消极证券组合管理中的应用Black-Litterman方法例子：GlobalPortfolioOptimization1.利用Markowitz模型进行积极证券组合管理经典Markowitz模型的缺点待估计的期望值、协方差参数数量大利用历史数据得到的最优证券组合权重不合理Wheninvestorsimposenoconstraints,themodelsalmostalwaysordainlargeshortpositionsinmanyassets.Whenconstraintsruleoutshortpositions,themodelsoftenprescribecornersolutionswithzeroweightsinmanyassets,aswellasunreasonablylargeweightsintheassetsofmarketswithsmallcapitalizations.Theseunreasonableresultsstemfromtwowellrecognizedproblems:由历史数据得到的期望值估计对将来回报率预测能力很差最优证券组合权重对于期望回报率假设非常敏感例：100种证券形成的证券组合例：letuslookatthesortofportfolioallocationwegetifweusehistoricalreturnsandvolatilitiesasinputs:Historicalcorrelations:Ifyouuseourproceduresandcalculateandoptimalportfolio,with,youwillgetportfolioweightsof:%7.10PWecanmakeanumberofpointsabouttheseoptimalportfolios.Theyillustratewhatwemeanwhenweclaimthatstandardmean-varianceoptimizationmodelsoftengenerateunreasonableportfolios.Theuseofpastexcessreturnstorepresentaneutralsetofviewsisequivalenttoassumingthattheconstantportfolioweightsthatwouldhaveperformedbesthistoricallyareinsomesenseneutral.Inreality,ofcourse,theyarenotneutralatall,butratherareaveryspecialsetofweightsthatgoshortassetsthathavedonepoorlyandgolongassetsthathavedonewellintheparticularhistoricalperiod.Aremedyforbothoftheseproblemsistouse(1)marketmodeltocalculateassetcovariance,(2)andusetheCAPMtodeterminewhatmarketexpectationmustbe,andthencombineyour“view”withtheCAPMderivedestimatestogetportfolioweights.Thekeyinputwewillneedforbothoftheseisthesetofassetbetas,so,first,wemustconsidertheproblemofestimatingbetas2.Beta值的估计利用市场模型估计Anapproachtoestimatingandistoassumethatamarketmodel(andtheCAPM)describesreturnsThemarketmodelTogetexpectedreturnsuse:Togetcovariances/correlations,use:Forstandarddeviations:fMifirrErrEirEij2MjiijjiMjiij22222iMiiiiitftMtiiftitrrrr待估计的参数数量大大减少（例如，100种证券形成的证券组合）i3.CAPM与积极的证券组合管理为了得到最优证券组合，我们需要估计证券组合前沿，有效集方法一：完全忽略市场的观点，而估计所有证券的期望回报率、协方差例如：利用历史的数据该方法存在问题方法二：接受市场的观点，简单的持有市场证券组合如果你拥有市场价格还没有反映的信息，该方法并不告诉该如何处理Theapproachwewillinsteadtakeisto1.Calculatebeta’sforthesecuritiesweplantohold2.Usingthesebeta’s,calculateand,assumingtheCAPMholdsexactly3.Then,incorporateourinformationby“perturbing”thevaluesawayfromtheCAPM-calculatedvalues4.Finally,usingtheseestimatesandtheMarkowitzportfoliooptimizationtoolsdetermineouroptimalportfolioweights.ijirENotethatifWestartwithalloftheassetsinmarketportfolioWeusetheunmodifiedandwegetfromstep2aboveThentheweightswecalculateinstep4willbeexactlythoseofthemarketportfolioijirEAnexampleUsingmonthlydataforGE,IBM,Exxon(XON),andGMfor94:01-98:12---VWistheValue-WeightedindexofallNYSE,AMEX,andNASDAQcommonstocks.Rfisthe(nominal)1-monthT-Billyield,whichwas4.394%/year(0.359%/month)inJanuary’99.ExcessReturnsMean(%)Std(%)alpha(%)betaStd(%)(%)IBM3.228.441.721.147.1328.5XON1.414.030.630.593.2833.7GM0.647.34-0.691.026.1430.0GE2.265.860.901.044.1549.9VW1.314.02Rf0.390.052adjRTogetthecorrelationstructure,wehave:jiMjiij2IBMXONGMGEIBM10.320.300.39XON0.3210.330.42GM0.300.3310.40GE0.390.420.401Pluggingthe(1)expectedreturn,(2)returnstandarddeviation,and(3)correlationmatrixintotheExcelspreadsheetwegetthefollowingweightsforthetangencyportfolio:Isthisareasonableportfolio?Why?Weight(%)IBM29.6XON49.4GM-21.4GE42.4Itseemsunreasonablethatweshouldholdsuchextremeportfoliopositions.TheequilibriumargumentsweusedindevelopingtheCAPMsuggestthatthemarketknowssomethingwedon’taboutfutureexpectedreturns!UsetheCAPMasawayofgettingaroundthisproblem:UsetheSML:andthepast(average)returnonthemarkettogetequilibriumestimatesoftheexpectedreturns:fMifirrErrE(%)IBM1.91XON0.99GM1.70GE1.73irEWiththisequilibriumsetofexpectedreturns,wenowgettheportfolioweights:Isthisamorereasonableportfolio?Now,whatisdrivingtheportfolioweights?Whyarethesenotthemarketweights?Whenwouldthesebetheactualmarketweights?Isthistheportfolioyouwanttohold,giventhatyouwereconstrainedtoholdthesefourassets?Weight(%)IBM13.6XON33.3GM16.4GE36.6However,theremaybetimeswhenwethinkthatthemarketisalittlewrongalongoneormoredimensions(averydangerousassumption!)1.First,supposethatIthinkthatthemarkethasunderestimatedtheearningsthatIBMwillannounceinthenextmonth,andthatIBM’sexpectedreturnis2%higherthanthemarketexpects.Also,Ihavenoinformationontheotherthreesecuritiesthatwouldleadmetothinkthattheyaremispriced,andIbelievethatthepastbetas,andresidualstddev’saregoodindicationsoftherelativefuturevalues.2.Inthiscase,wewouldusethesamevarianceandcovarianceinputs,butwouldchangetheexpectedreturnsto:andgivesportfolioweightsof:(%)IBM3.91XON0.99GM1.70GE1.73irEWeight(%)IBM54.1XON17.7GM8.7GE19.53.Alternatively,supposethatIthinktherisk()ofExxonisincreasing.4.IguessthatExxon’swillrisefrom0.59to0.8First,Ishouldrecalculatealmosteverythingusingtheequations:fMifirrErrE2MjiijjiMjiij22222iMiiiiThenewcorrelationswe