投资学Chapter7

Chapter7CapitalAssetPricingandArbitragePricingTheoryCopyright©2010byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin7-27.1TheCapitalAssetPricingModel7-3CapitalAssetPricingModel(CAPM)EquilibriummodelthatunderliesallmodernfinancialtheoryDerivedusingprinciplesofdiversification,butwithothersimplifyingassumptionsMarkowitz,Sharpe,LintnerandMossinareresearcherscreditedwithitsdevelopment7-4Assumptions•Individualinvestorsarepricetaker•Single-periodinvestmenthorizon•Investmentsarelimitedtotradedfinancialassets•Notaxesandnotransactioncosts•Informationiscostlessandavailabletoallinvestors•Investorsarerationalmean-varianceoptimizers（所有投资者都是理性的，都按照均值-方差理论寻找最优投资组合）•Homogeneousexpectations(同质期望，所有投资者对证劵分布特征的分析是一样的，即有同样的期望，方差，各个证劵之间的协方差矩阵也相同）7-5ResultingEquilibriumConditions7-6I:Optimalriskyportfolioismarketportfolio•Allinvestorswillholdthesameportfolioforriskyassets;the“marketportfolio•Marketportfoliocontainsallsecuritiesandtheproportionofeachsecurityisitsmarketvalueasapercentageoftotalmarketvalue（市值加权的组合）7-7E(r)rfE(rM)MCMLsmCapitalMarketLinesM:isthevalueweighted“market”portfolioOfallriskyportfolioEfficientFrontier7-8LogicalThinkingIfallinvestorsuseidenticalmean-varianceanalysis(assumption5),applyittothesameuniverseofsecurities(assumption3),withanidenticaltimehorizon(assumption2),usethesamesecurityanalysis(assumption6),andexperienceidenticaltax(assumption4),theyallmustarriveatthesameoptimalriskyportfolio.Inthemarketequilibrium,theoptimalportfoliowillhavetoincludeallthesecuritiesinthemarket,thereforethemarketportfolio.(supposeonestockisnotincluded,thenitspricefall,itsreturnincrease,intheend,itwillreachapriceatwhichitisattractiveenoughtobeincludedintheoptimalportfolio)7-9•CAPMimpliesthatpassivestrategyisefficient•Mutualfundtheorem-onlyonemutualfundofriskyassets-themarketportfolio-issufficienttosatisfytheinvestmentdemandsofallinvestors•Twosteps:(1)technicalpart,anefficientmutualfundisfound(hereismarketportfolio)(2)apersonalside,inwhichaninvestor’sriskaversiondeterminestheallocationofthecompleteportfoliobetweenmutualfundandrisk-freeasset.7-10II:CapitalMarketLine如果M点所代表的有风险资产组合的预期收益率和标准差分别是E（rM）和σM，投资于这一有风险资产组合的资金比例是WM，投资于无风险证券的资金比例是l－WM，则加上无风险证券后的组合P的预期收益率E（rP）和标准差σP就应是cpfpffppcfcpcfpfcrrErrrErrEyrrEyrrEssssss)(])([)())(()(7-11•InequilibriumtherewillbeasimplelinearrelationshipbetweentheexpectedreturnandstandarddeviationofreturnforefficientcombinationofriskyassetswhichimpliedbyCML(在市场均衡时最优完整组合（riskyportfolio+riskfreeasset)的风险和收益将满足一种简单的线性关系，对有效组合而言，风险越大，收益越大)•有效组合的风险补偿与该组合的风险成正比例变化，其比例因子是：7-12它是资本市场线的斜率，也称为酬报波动比，即风险的价格，而且是市场组合的风险的价格。7-13TheRiskPremiumoftheMarketPortfolioEquilibriumriskpremiumofthemarketportfolio,E(rm)-rf,willbeproportionaltoaveragedegreeofriskaversionacrossinvestorandtotheriskofthemarketportfolio,σ.Wheninvestorspurchasestocks,theirdemanddriveupprices,therebyloweringexpectedreturnofriskpremium,iftheriskpremiumfalls,thenrelativelymorerisk-averseinvestorswillpulltheirfundsoutoftheriskyportfolio,placingthemtoriskfreeasset.Inequilibrium,theriskpremiumonthemarketportfoliomustbejusthighenoughtoinduceinvestorstoholdtheavailablesupplyofstocks.2*)(MfMArrEsRecallthatwithariskyportfolioandarisk-freeasset,theoptimalchoiceforinvestoris:7-14M=rf=E(rM)-rf=SlopeandMarketRiskPremium{ExcessreturnonthemarketportfolioMMssE(rM)-rf=OptimalMarketpriceofrisk=SlopeoftheCMLMarketportfolioRiskfreerateE(rE(r))E(rE(rMM))rrffMMCMLCMLssmmCapitalMarketLinessM=ThevalueweightedM=Thevalueweighted““MarketMarket””Portfolioofallriskyassets.Portfolioofallriskyassets.→7-15ExpectedReturnsonIndividualSecurities•Equilibriumconditions:Allinvestorswillholdthe__________________________________________E(rE(r))E(rE(rMM))rrffMMCMLCMLssmmCapitalMarketLinessM=ThevalueweightedM=Thevalueweighted““MarketMarket””Portfolioofallriskyassets.Portfolioofallriskyassets.sameportfolioforriskyassets;the“marketportfolio”Pricingofindividualsecuritiesisthereforerelatedtotheriskthatindividualsecuritieshavewhentheyareincludedinthemarketportfolio.7-16III:ExpectedReturnandRiskonIndividualSecurities•Theriskpremiumonindividualsecuritiesisafunctionoftheindividualsecurity’s________________________________________单个证劵的合理风险溢价取决于单个证券对市场组合风险的贡献程度•Anindividualsecurity’stotalrisk(s2i)canbepartitionedintosystematicandunsystematicrisks2i=bi2sM2+s2(ei)contributiontotheriskofTHEmarketportfolioRi=ai+ßi(Rm)+ei7-17ExpectedReturnandRiskonIndividualSecurities•Whattypeofindividualsecurityriskwillmatter？•Non-systematicriskcanbereducedtozerothroughdiversification,therefore,investorsdonotrequireariskpremiumascompensationforbearingnon-systematicrisk.•Theonlyriskthatneededtobecompensatedissystematicrisk,whichcannotbediversified.7-18ExpectedReturnandRiskonIndividualSecurities•Individualsecurity’scontributiontotheriskofthemarketportfolioisafunctionofthe__________ofthestock’sreturnswiththemarketportfolio’sreturnsandismeasuredbyBETAWithrespecttoanindividualsecurity,systematicriskcanbemeasuredbybi=[COV(ri,rM)]/s2Mcovariance7-19ExpectedReturnandRiskonIndividualSecurities•Inequilibrium,a