《资本定价模型》PPT课件

第9章资本资产定价模型TheCapitalAssetPricingModel,9.1股票的需求与均衡价格9.2资本资产定价模型9.3资本资产定价模型的扩展形式9.4资本资产定价模型与流动性,资本资产定价模型CapitalAssetPricingModel(CAPM),Thesupplyanddemandforsharesdetermineequilibriumpricesandexpectedratesofreturn.Imagineasimpleworldwithonlytwocorporations:BottomUpInc.(BU)andTopDownInc.(TD).StockpricesandmarketvaluesareshowninTable9.1.Investorscanalsoinvestinamoneymarketfund(MMF)whichyieldsarisk-freeinterestrateof5%.,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,SigmaFundisanewactivelymanagedmutualfundthathasraised$220milliontoinvestinthestockmarket.ThesecurityanalysisstaffofSigmabelievesthatneitherBUnorTDwillgrowinthefutureandtherefore,thateachfirmwillpaylevelannualdividendsfortheforeseeablefuture.Thisisausefulsimplifyingassumptionbecause,ifastockisexpectedtopayastreamofleveldividends,theincomederivedfromeachshareisaperpetuity.Therefore,thepresentvalueofeachshareoftencalledtheintrinsicvalueoftheshareequalsthedividenddividedbytheappropriatediscountrate.AsummaryofthereportofthesecurityanalystsappearsinTable9.2.,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,UsingthesedataandassumptionsSigmaeasilygeneratestheefficientfrontiershowninFigure9.1andcomputestheoptimalportfolioproportionscorrespondingtothetangencyportfolio.Theseproportions,combinedwiththetotalinvestmentbudget,yieldthefundsbuyorders.Withabudgetof$220million,SigmawantsapositioninBUof$220,000,000X0.8070=$177,540,000,or$177,540,000/39=4,552,308shares,andapositioninTDof$220,000,000X0.1930=$42,460,000,whichcorrespondsto1,088,718shares.,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,TheexpectedratesofreturnthatSigmausedtoderiveitsdemandforsharesofBUandTDwerecomputedfromtheforecastofyear-endstockpricesandthecurrentprices.If,say,ashareofBUcouldbepurchasedatalowerprice,SigmasforecastoftherateofreturnonBUwouldbehigher.Conversely,ifBUsharesweresellingatahigherprice,expectedreturnswouldbelower.Anewexpectedreturnwouldresultinadifferentoptimalportfolioandadifferentdemandforshares.,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,SigmasdemandcurveforBUstockisgivenbytheDesiredSharescolumninTable9.3andisplottedinFigure9.2.Noticethatthedemandcurveforthestockslopesdownward.WhenBUsstockpricefalls,Sigmawilldesiremoresharesfortworeasons:(1)anincomeeffect-atalowerpriceSigmacanpurchasemoreshareswiththesamebudget,and(2)asubstitutioneffect-theincreasedexpectedreturnatthelowerpricewillmakeBUsharesmoreattractiverelativetoTDshares.Noticethatonecandesireanegativenumberofshares,thatis,ashortposition.Ifthestockpriceishighenough,itsexpectedreturnwillbesolowthatthedesiretosellwilloverwhelmdiversificationmotivesandinvestorswillwanttotakeashortposition.Figure9.2showsthatwhenthepriceexceeds$44,SigmawantsashortpositioninBU.,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,股票的需求与均衡价格DEMANDFORSTOCKSANDEQUILIBRIUMPRICES,ThedemandcurveforBUsharesassumesthatthepriceandthereforeexpectedreturnofTDremainconstant.AsimilardemandcurvecanbeconstructedforTDsharesgivenapriceforBUshares.Asbefore,wewouldgeneratethedemandforTDsharesbyrevisingTable9.2forvariouscurrentpricesofTD,leavingthepriceofBUunchanged.WeusetherevisedexpectedreturnstocalculatetheoptimalportfolioforeachpossiblepriceofTD,ultimatelyobtainingthedemandcurveshowninFigure9.3.,资本资产定价模型是现代金融学的奠基石(风险与期望收益均衡模型)Itistheequilibriummodelthatunderliesallmodernfinancialtheory.由诸多简单假定原理来建立Derivedusingprinciplesofdiversificationwithsimplifiedassumptions.马克维茨,威廉夏普,林特纳和简莫辛研究和发展了资本资产定价模型。Markowitz,Sharpe,LintnerandMossinareresearcherscreditedwithitsdevelopment.,资本资产定价模型CapitalAssetPricingModel(CAPM),个体投资者是价格的接受者Individualinvestorsarepricetakers单周期投资期限Single-periodinvestmenthorizon投资限制在金融资产的交易Investmentsarelimitedtotradedfinancialassets无税负和交易成本Notaxes,andtransactioncosts,假设Assumptions,投资者是理性的均值-方差完善者Investorsarerationalmean-varianceoptimizers同质期望Homogeneousexpectations给定一系列证券的价格和无风险利率，所有投资者的证券收益的期望收益率与协方差矩阵相等，从而产生了有效率边界和一个独一无二的最优风险资产组合。这一假定也被称为同质期望。Givenasetofsecuritypricesandtherisk-freeinterestrate,allinvestorsusethesameexpectedreturnsandcovariancematrixofsecurityreturnstogeneratetheefficientfrontierandtheuniqueoptimalriskyportfolio.Thisassumptionisoftenreferredtoashomogeneousexpectations.对投资者来说信息是无成本的和有效的Informationiscostlessandavailabletoallinvestors,假设Assumptions(contd),全部投资者将持有相同的风险资产-市场组合Allinvestorswillholdthesameportfolioforriskyassetsmarketportfolio.市场组合含有全部股票和每只股票在市场资产组合所占的比例等于它的市值占所有股票的市值Marketportfoliocontainsallsecuritiesandtheproportionofeachsecurityisitsmarketvalueasapercentageoftotalmarketvalue.,均衡条件ResultingEquilibriumConditions,市场的风险溢价取决于全部市场参与者的平均风险厌恶Riskpremiumonthemarketdependsontheaverageriskaversionofallmarketparticipants,均衡条件ResultingEquilibriumConditions(cont.),式中2M为市场资产组合的方差；A为投资者风险厌恶的平均水平。请注意由于市场资产组合是最优资产组合，即风险有效地分散于资产组合中的所有股票，2M也就是这个市场的系统风险。,个体证券的风险溢价是市场协方差的函数Riskpremiumonanindividualsecurityisafunctionofitscovariancewiththemarket贝塔是用来测度股票与一起变动情况下证券收益的变动程度的。贝塔的正式定义如下：Betameasurestheextenttowhichreturnsonthestockandthemarketmovetogether.Formally,betaisdefinedas,均衡条件ResultingEquilibriumConditions(cont.),个体证券的风险溢价是市场协方差的函数Riskpremiumonanindividualsecurityisafunctionofitscovariancewiththemarket单个证券的风险溢价等于：Theriskpremiumonindividualsecuritiesis,均衡条件ResultingEquilibriumConditions(cont.),当我们把所有个人投资者的资产组合加总起来时，借与贷将互相抵消（这是因为每个借入者都有一个相应的贷出者与之对应），加总的风险资产组合价值等于整个经济中全部财富的价值，这就是市场资产组合。每只股票在这个资产组合中的比例等于股票的市值占所有股票市场价值的比例。资本资产定价模型认为每个投资者均有优化其资产组合的倾向，最终所有个人的资产组合会趋于一致，每种资产的权重等于它们在市场资产组合中所占的比例。Theportfoliosofallindividualinvestors,lendingandborrowingwillcancelout(sinceeachlenderhasacorrespondingborrower),andthevalueoftheaggregateriskyportfoliowillequaltheentirewealthoftheeconomy.Thisisthemarketportfolio,M.Theproportionofeachstockinthisportfolioequalsthemarketvalueofthestock(pricepersharetimesnumberofsharesout-standing)dividedbythesumofthemarketvaluesofallstocks.5TheCAPMimpliesthatasindividualsattempttooptimizetheirpersonalportfolios,theyeacharriveatthesameport-folio,withweightsoneachassetequaltothoseofthemarketportfolio.,市场资产组合TheMarketPortfolio,依据前文给定的假定条件，不难看出所有的投资者均倾向于持有同样的风险资产组合。如果所有的投资者都将马克维茨分析(假定5)应用于同样广泛的证券(假定3)，在一个相同的时期内计划他们的投资(假定2)，并且投资顺序内容也相同的话(假定6),那么他们必然会达到相同的最优风险资产组合。正如下图所示.Giventheassumptionsoftheprevioussection,itiseasytoseethatallinvestorswilldesiretoholdidenticalriskyportfolios.IfallinvestorsuseidenticalMarkowitzanalysis(Assumption5)appliedtothesameuniverseofsecurities(Assumption3)forthesametimehorizon(Assumption2)andusethesameinputlist(Assumption6),theyallmustarriveatthesamedeterminationoftheoptimalriskyportfolio,theportfolioontheefficientfrontieridentifiedbythetangencylinefromT-billstothatfrontier,asinfollowingfigure.,市场资产组合TheMarketPortfolio,资本市场线CapitalMarketLine,E(r),E(rM),rf,M,资本市场线CML,m,M=市场组合Marketportfoliorf=无风险率RiskfreerateE(rM)-rf=市场风险溢价MarketriskpremiumE(rM)-rf=风险市场价格Marketpriceofrisk=CAPM斜率SlopeoftheCAPM,M,市场风险溢价和斜率SlopeandMarketRiskPremium,市场资产组合的均衡风险溢价，E(rM)-rf，与投资者群体的平均风险厌恶程度和市场资产组合的风险2M是成比例的。Theequilibriumriskpremiumonthemarketportfolio,E(rM)-rf,willbeproportionaltotheaveragedegreeofriskaversionoftheinvestorpopulationandtheriskofthemarketportfolio.Nowwecanexplainthisresult.,市场资产组合的风险溢价TheRiskPremiumoftheMarketPortfolio,在简化了的CAPM模型经济中，无风险投资包括投资者之间的借入与贷出。任何借入头寸必须同时有债权人的贷出头寸作为抵偿。这意味着投资者之间的净借入与净贷出的总和为零。那么在风险资产组合上的投资比例总的来说是100%，或y=1。设y1，代入9-1式经整理，我们发现市场资产组合的风险溢价与风险厌恶的平均水平有关：InthesimplifiedCAPMeconomy,risk-freeinvestmentsinvolveborrowingandlendingamonginvestors.Anyborrowingpositionmustbeoffsetbythelendingpositionofthecreditor.Thismeansthatnetborrowingandlendingacrossallinvestorsmustbezero,andinconsequencetheaveragepositionintheriskyportfoliois100%,ory=1.Settingy=1inequation9.1andrearranging,wefindthattheriskpremiumonthemarketportfolioisrelatedtoitsvariancebytheaveragedegreeofriskaversion:,市场资产组合的风险溢价TheRiskPremiumoftheMarketPortfolio,单个证券的风险益价是单个证券对市场组合风险的贡献函数Theriskpremiumonindividualsecuritiesisafunctionoftheindividualsecurityscontributiontotheriskofthemarketportfolio.单个证券的风险益价是构成市场组合资产收益协方差的函数Anindividualsecuritysriskpremiumisafunctionofthecovarianceofreturnswiththeassetsthatmakeupthemarketportfolio.,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,假定现在我们要测算通用公司股票的资产组合风险，我们用通用公司股票（GM股）同市场资产组合的协方差来刻画其对资产组合的风险贡献程度。为解释这种测算方法，先要再次阐明市场资产组合的方差是如何计算的。为此，我们按第8章讨论过的方法将n阶协方差矩阵各项按照从行到列的顺序分别乘以各证券在市场资产组合中的权重。Suppose,forexample,thatwewanttogaugetheportfolioriskofGMstock.Wemea-surethecontributiontotheriskoftheoverallportfoliofromholdingGMstockbyitscovariancewiththemarketportfolio.Toseewhythisisso,letuslookagainatthewaythevarianceofthemarketportfolioiscalculated.Tocalculatethevarianceofthemarketport-folio,weusetheborderedcovariancematrixwiththemarketportfolioweights,asdiscussedinChapter8.WehighlightGMinthisdepictionofthenstocksinthemarketportfolio.,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,通用公司股票对市场资产组合方差的贡献为：ThecontributionofGMsstocktothevarianceofthemarketportfoliois:,通用公司股票对市场资产组合方差的贡献度市场资产组合的收益率可以表示如下:Therateofreturnonthemarketportfoliomaybewrittenas,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,通用公司股票与市场资产组合的协方差为:ThecovarianceofthereturnonGMwiththemarketportfoliois:,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,测度了通用公司股票对市场方差的贡献度后，我们就可以来确定通用公司股票的合理风险溢价了。首先，我们注意到市场资产组合的风险溢价为E(rM-rf)，方差为2M，酬报与波动性比率为:HavingmeasuredthecontributionofGMstocktomarketvariance,wemaydeterminetheappropriateriskpremiumforGM.WenotefirstthatthemarketportfoliohasariskpremiumofE(rM-rf)andavarianceof2M,forareward-to-riskratioof,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,假定某位平均的投资者投资于市场资产组合的比例为100%，现在他打算通过借入无风险贷款的方式来增加比例为小量的市场资产组合头寸。新的资产组合由以下三部分组成：收益为rM的原有市场资产组合头寸，收益为-rf的无风险资产空头头寸，以及收益为rM的市场资产组合的多头头寸。总的资产组合收益为rM(rM-rf)，将其期望值与最初期望值E(rM)比较，期望收益的增加额为,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,为了度量新资产组合的风险，我们重新计算资产组合的方差。新资产组合由权重为(1)的市场资产组合与权重为-的无风险资产组成，调整后的资产组合的方差为:Tomeasuretheimpactoftheportfolioshiftonrisk,wecomputethenewvalueoftheportfoliovariance.Thenewportfoliohasaweightof(1+)inthemarketand-intherisk-freeasset.Therefore,thevarianceoftheadjustedportfoliois:,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,由于非常小，所以相比于2而言2可以忽略，因而我们这里对这一项忽略不计However,ifisverysmall,then2willbenegligiblecomparedto2,sowemayignorethisterm,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,综合以上结果，增加的风险溢价与增加的风险之间的平衡，即风险的边际价格为:Summarizingtheseresults,thetrade-offbetweentheincrementalriskpremiumandincrementalrisk,referredtoasthemarginalpriceofrisk,isgivenbytheratio,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,现在，作为一个替代，假定投资者用以无风险利率借入的资金投资于通用公司股票。他的平均超额收益的增加值为:Nowsupposethat,instead,investorsweretoinvesttheincrementinGMstock,alsofinancedbyborrowingattherisk-freerate.Theincreaseinmeanexcessreturnis:,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,这一资产组合中投资于市场资产组合的资金权重为1.0，投资于通用公司股票的资金权重为，投资于无风险资产的资金权重为-。这一资产组合的方差为:Thisportfoliohasaweightof1.0inthemarket,inGM,and-intherisk-freeasset.ItsGMvarianceis:,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,因此，方差增加值包括两部分：通用公司股票新增头寸的方差和两倍通用公司股票与市场资产组合的协方差：TheincreaseinvariancethereforeincludesthevarianceoftheincrementalpositioninGMplustwiceitscovariancewiththemarket:,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,2忽略不计，通用公司股票的风险边际价格为Droppingthenegligibleterminvolving2,themarginalpriceofriskofGMis,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,建立通用公司股票的风险边际价格同市场资产组合的风险边际价格相等的等式如下：EquatingthemarginalpriceofriskofGMsstocktothatofthemarketresultsinarelationshipbetweentheriskpremiumofGMandthatofthemarket:,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,经调整我们得到通用公司股票的正常风险溢价：TodeterminethefairriskpremiumofGMstock,werearrangeslightlytoobtain,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,这里，Cov(rGM，rM)/2M测度的是通用公司股票对市场资产组合方差的贡献程度，这是市场资产组合方差的一个组成部分。这一比率称作贝塔（beta），以表示，这样，9-6式可以写作为：TheratioCov(rGM，rM)/2MmeasuresthecontributionofGMstocktothevarianceofthemarketportfolioasafractionofthetotalvarianceofthemarketportfolio.Theratioiscalledbetaandisdenotedby.Usingthismeasure,wecanrestateequation9.6as,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,上式即是CAPM模型的最普通形式期望收益-贝塔关系,我们对这一关系式还要做更详尽的论述。ThisexpectedreturnbetarelationshipisthemostfamiliarexpressionoftheCAPMtopractitioners.Wewillhavealotmoretosayabouttheexpectedreturnbetarelationshipshortly.,单个证券的收益和风险ExpectedReturnandRiskonIndividualSecurities,Iftheexpectedreturnbetarelationshipholdsforanyindividualasset,itmustholdforanycombinationofassets.SupposethatsomeportfolioPhasweightwkforstockk,wherektakesonvalues1,.,n.WritingouttheCAPMequation9.7foreachstock,andmultiplyingeachequationbytheweightofthestockintheportfolio,weobtaintheseequations,oneforeachstock:,证券市场线SecurityMarketLine,E(r),E(rM),rf,证券市场线SML,b,bM=1.0,=COV(ri,rm)/m2证券市场线斜率SlopeSML=E(rm)-rf=市场风险溢价marketriskpremiumSML=rf+E(rm)-rfBetam=Cov(ri,rm)/sm2=sm2/sm2=1:证券的协方差风险,证券市场线关系SMLRelationships,系数。美国经济学家威廉夏普提出的风险衡量指标。用它反映资产组合波动性与市场波动性关系（在一般情况下，将某个具有一定权威性的股指（市场组合）作为测量股票值的基准）。如果值为1.1，即表明该股票波动性要比市场大盘高10，说明该股票的风险大于市场整体的风险，当然它的收益也应该大于市场收益，因此是进攻型证券。反之则是防守型股票。无风险证券的值等于零，市场组合相对于自身的值为1。,E(ri)=rf+i(E(rm)-rf)资本资产定价模型的最普通形式期望收益贝塔关系E(rm)-rf=.08rf=.03x=1.25E(rx)=.03+1.25(.08)=.13or13%y=.6E(ry)=.03+.6(.08)=.078or7.8%,证券市场线计算实例SampleCalculationsforSML,计算图形GraphofSampleCalculations,E(r),Rx=13%,SML,b,1.0,Rm=11%,Ry=7.8%,3%,1.25bx,.6by,.08,By,布莱克的零贝塔模型BlacksZeroBetaModel,缺少无风险资产Absenceofarisk-freeasset在有效边界上的任何资产组合是有效资产组合。Combinationsofportfoliosontheefficientfrontierareefficient.有效率边界上的任一资产组合有不相关组合相伴Allfrontierportfolioshavecompanionportfoliosthatareuncorrelated.任何单个资产的收益可以准确地由任意两个边界资产组合的期望收益的线性函数表示。任何单个资产的收益可以由有效组合的线性函数表示。Returnsonindividualassetscanbeexpressedaslinearcombinationsofefficientportfolios.,布莱克的零贝塔模型BlacksZeroBetaModel,布莱克的禁止卖空无风险资产的CAPM模型建立在下列三项有效率资产组合的方差均值性质之上：1)任何有效率资产组合组成的资产组合仍然是有效率资产组合。2)有效率边界上的任一资产组合在最小方差边界的下半部分（无效率部分）上均有相应的“伴随”资产组合存在，由于这些“伴随”资产组合是不相关的，因此，这些资产组合可以被视为有效率资产组合中的零贝塔资产组合。BlacksmodeloftheCAPMintheabsenceofarisk-freeassetrestsonthethreefollowingpropertiesofmean-varianceefficientportfolios:1.Anyportfolioconstructedbycombiningefficientportfoliosisitselfontheefficientfrontier.2.Everyportfolioontheefficientfrontierhasa“companion”portfolioonthebottomhalf(theinefficientpart)oftheminimum-variancefrontierwithwhichitisuncorrelated.Becausetheportfoliosareuncorrelated,thecompanionportfolioisreferredtoasthezero-betaportfoliooftheefficientportfolio.,有效组合和零贝塔伴随EfficientPortfoliosandZeroCompanions,Q,P,Z(Q),Z(P),Erz(Q),Erz(P),E(r),s,布莱克的零贝塔模型方程BlacksZeroBetaModelFormulation,任何资产的期望收益可以准确地由任意两个边界资产组合的期望收益的线性函数表示。例如，考虑有两个最小方差边界资产组合P与Q，布莱克给出任意资产i的期望收益的表达如下：Theexpectedreturnofanyassetcanbeexpressedasanexact,linearfunctionoftheexpectedreturnonanytwofrontierportfolios.Consider,forexample,theminimum-variancefrontierportfoliosPandQ.Blackshowedthattheexpectedreturnonanyasseticanbeexpressedas,布莱克的零贝塔模型方程BlacksZeroBetaModelFormulation,假定经济中只有两个投资者，一个相对来说厌恶风险，而另外一个可以忍受风险。厌恶风险的投资者选择资本配置线上的资产组合T，如图9-5所示，也就是说，他的资产组合由资产组合T与按无风险利率贷出的无风险资产组成。T是由无风险借贷利率rf出发的有效率边界的切点。忍受风险的投资者愿意在承担更多风险的前提下取得更高的风险溢价：他选择图中的S。S资产组合与T资产组合相比较，虽同处于有效率边界但其风险与收益均高于T资产组合。总的风险资产组合（也就是市场资产组合，M）由T与S结合而成，各自权重由两个投资者的相对财富与风险厌恶程度决定。由于T与S都在有效率边界上，所以根据性质1，市场资产组合M也在有效率边界上。,布莱克的零贝塔模型方程BlacksZeroBetaModelFormulation,Imagineaneconomywithonlytwoinvestors,onerelativelyriskaverseandonerisktolerant.Therisk-averseinvestorwillchooseaportfolioontheCALsupportedbyportfolioTinFigure9.8,thatis,hewillmixportfolioTwithlendingattherisk-freerate.Tisthetangencyportfolioontheefficientfrontierfromtherisk-freelendingrate,rf.Therisk-tolerantinvestoriswillingtoacceptmorerisktoearnahigher-riskpremium;shewillchooseportfolioS.ThisportfolioliesalongtheefficientfrontierwithhigherriskandreturnthanportfolioT.Theaggregateriskyportfolio(i.e.,themarketportfolio,M)willbeacombinationofTandS,withweightsdeterminedbytherelativewealthanddegreesofriskaversionofthetwoinvestors.SinceTandSareeachontheefficientfrontier,soisM(fromProperty1).,布莱克的零贝塔模型方程BlacksZeroBetaModelFormulation,布莱克的零贝塔模型方程BlacksZeroBetaModelFormulation,根据性质2，市场资产组合M也存在一个在最小方差边界上的零贝塔“伴随”资产组合：Z(M)，见图9-5。根据性质3及9-8式，我们可以用市场资产组合M及Z(M)来表示任何证券的收益。由于Cov(rM，rZ(M)0，所以有FromProperty2,Mhasacompanionzero-betaportfolioontheminimum-variancefrontier,Z(M),showninFigure9.8.Moreover,byProperty3wecanexpressthereturnonanysecurityintermsofMandZ(M)asinequation9.8.But,sincebyconstructionCov(rM，rZ(M)0,theexpressionsimplifiesto,零贝塔市场模型ZeroBetaMarketModel,式中的资产组合P与资产组合Q分别由市场资产组合M及Z(M)代替。上式可视为一个简化了的CAPM模型，在其中，E(rz(m)取代了rf。wherePhasbeenreplacedbyMandQhasbeenreplacedbyZ(M).Equation9.9maybeinterpretedasavariantofthesimpleCAPM,inwhichrfhasbeenreplacedwithE(rz(m),资本资产定价模型和流动性CAPM&Liquidity,流动性流动性是指资产转化为现金时所需的费用与便捷程度。交易者非常注重流动性，一些研究证实缺乏流动性将大大降低资产的市场出售价格水平。LiquidityLiquidityreferstothecostandeasewithwhichanassetcanbeconvertedintocash,thatis,sold.Tradershavelongrecognizedtheimportanceofliquidity,andsomeevidencesuggeststhatilliquiditycanreducemarketpricessubstantially.,资本资产定价模型和流动性CAPM&Liquidity,非流动溢价IlliquidityPremium流动性差的资产低价交易，流动性高的资产期望收益也高，流动性效用的大小同资产的交易费用分布状况以及投资者投资内容的分布有关。illiquidassetstradeatlowerpricesor,equivalently,thattheexpectedreturnonilliquidassetsmustbehigher.研究支持非流动溢价Researchsupportsapremiumforilliquidity.AmihudandMendelson,流动溢价的资本资产定价模型CAPMwithaLiquidityPremium,E(ri)rf=iE(rM)-rf+f(ci)f(ci)=证券i的流动溢价，f(ci)是关于ci的一阶单调递增函数。liquiditypremiumforsecurityi,非流动性与平均收益关系IlliquidityandAverageReturns,平均月收益率Averagemonthlyreturn(%),买卖差价Bid-askspread(%),Summary,CAPM模型假定所有投资者均为单期投资，并且遵循相同的投资构，并力求获得具有最小方差的最优资产组合。TheCAPMassumesthatinvestorsaresingle-periodplannerswhoagreeonacommoninputlistfromsecurityanalysisandseekmean-varianceoptimalportfolios.,Summary,CAPM模型假定理想状态下的股票市场具有以下特征：a.股票市场容量足够大，并且其中所有的投资者为价格接受者。b.不存在税收与交易费用。c.所有风险资产均可公开交易。d.投资者可以以无风险利率借入或贷出任意额度资产。TheCAPMassumesthatsecuritymarketsareidealinthesensethat:a.Theyar