Chap010套利定价定理

INVESTMENTS|BODIE,KANE,MARCUSCopyright©2011byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCHAPTER10ArbitragePricingTheoryandMultifactorModelsofRiskandReturn套利定价定理与风险收益多因子模型INVESTMENTS|BODIE,KANE,MARCUS10-2SingleFactorModel单因子模型•Returnsonasecuritycomefromtwosources:证券的收益来自两个方面–Commonmacro-economicfactor共有的宏观经济因素–Firmspecificevents公司特有因素•Possiblecommonmacro-economicfactors可能的共有宏观经济因素–GrossDomesticProductGrowth国民GDP的增长–InterestRates利率INVESTMENTS|BODIE,KANE,MARCUS10-3SingleFactorModelEquation单因子模型ri=Returnonsecurity证券收益βi=Factorsensitivityorfactorloadingorfactorbeta因子敏感性或因子载荷或者因子贝塔F=Surpriseinmacro-economicfactor宏观经济因子中的不确定性(Fcouldbepositiveornegativebuthasexpectedvalueofzero)F可正可负也有可能为零，期望值为零ei=Firmspecificevents(zeroexpectedvalue)公司特有的隐私，和F一样期望值为零()iiiirErFeINVESTMENTS|BODIE,KANE,MARCUS10-4MultifactorModels多因子模型•Usemorethanonefactorinadditiontomarketreturn在以上基础上使用多个因子–Examplesincludegrossdomesticproduct,expectedinflation,interestrates,etc.比如GDP、预期通胀、利率–Estimateabetaorfactorloadingforeachfactorusingmultipleregression.用多元回归技术为每一个因子估计一个载荷或者贝塔INVESTMENTS|BODIE,KANE,MARCUS10-5MultifactorModelEquation模型方程ri=Returnforsecurityi证券收益βGDP=FactorsensitivityforGDP国民收入增长因子的敏感性βIR=FactorsensitivityforInterestRate利率因子的敏感性ei=Firmspecificevents公司特有iiIRiGDPiieIRGDPrErINVESTMENTS|BODIE,KANE,MARCUS10-6MultifactorSMLModels多因子证券市场线GDP=FactorsensitivityforGDP敏感性RPGDP=RiskpremiumforGDP风险溢价IR=FactorsensitivityforInterestRateRPIR=RiskpremiumforInterestRateiiIRiIRGDPiGDPfiRPRPrrEINVESTMENTS|BODIE,KANE,MARCUS10-7Interpretation理解Theexpectedreturnonasecurityisthesumof:一种证券的预期收益是以下因素之和：1.无风险利率2.GDP敏感性乘以GDP风险溢价3.利率敏感性乘以利率的风险溢价1.Therisk-freerate2.ThesensitivitytoGDPtimestheriskpremiumforbearingGDPrisk3.ThesensitivitytointerestraterisktimestheriskpremiumforbearinginterestrateriskINVESTMENTS|BODIE,KANE,MARCUS10-8ArbitragePricingTheory套利定价定理•Arbitrageoccursifthereisazeroinvestmentportfoliowithasureprofit.如何零投资的组合有正收益就会发生套利Sincenoinvestmentisrequired,investorscancreatelargepositionstoobtainlargeprofits.这样投资就无效，投资者只需要建立大头寸获得高收益就好INVESTMENTS|BODIE,KANE,MARCUS10-9ArbitragePricingTheory套利定价定理•Regardlessofwealthorriskaversion,investorswillwantaninfinitepositionintherisk-freearbitrageportfolio.•无关财富或者风险偏好，投资者会尽可能多的在无风险套利组合中持有头寸•Inefficientmarkets,profitablearbitrageopportunitieswillquicklydisappear.•因此在有效市场中，能够产生盈利的套利机会都已经消失了INVESTMENTS|BODIE,KANE,MARCUS10-10APT&Well-DiversifiedPortfoliosAPT与充分分散的组合rP=E(rP)+PF+ePF=somefactor一些影响因子•Forawell-diversifiedportfolio,eP–approacheszeroasthenumberofsecuritiesintheportfolioincreases当组合中的证券数量增加时其方差趋于零，期望也为零，因此值也就是零–andtheirassociatedweightsdecrease每种证券的权重也趋于很小INVESTMENTS|BODIE,KANE,MARCUS10-11Figure10.1ReturnsasaFunctionoftheSystematicFactor系统性风险函数的收益INVESTMENTS|BODIE,KANE,MARCUS10-12Figure10.2ReturnsasaFunctionoftheSystematicFactor:AnArbitrageOpportunity系统性风险函数的收益：套利机会A、B两组合不可能并存于市场否则将存在套利机会INVESTMENTS|BODIE,KANE,MARCUS10-13Figure10.3AnArbitrageOpportunityC点表示一个套利机会INVESTMENTS|BODIE,KANE,MARCUS10-14Figure10.4TheSecurityMarketLineAPT模型所预示的证券市场线INVESTMENTS|BODIE,KANE,MARCUS10-15APTModel套利定价模型•APTappliestowelldiversifiedportfoliosandnotnecessarilytoindividualstocks.套利定价模型应该应用在充分分散的组合上而不是单个证券商•WithAPTitispossibleforsomeindividualstockstobemispriced-notlieontheSML.•对于套利定价模型有些证券可能会被错误定价，没有位于证券市场线之上•APTcanbeextendedtomultifactormodels.•套利定价模型可以被扩展为多因素模型INVESTMENTS|BODIE,KANE,MARCUS10-16APTandCAPM套利定价与资本资产定价APT•Equilibriummeansnoarbitrageopportunities.均衡意味着没有套利机会•APTequilibriumisquicklyrestoredevenifonlyafewinvestorsrecognizeanarbitrageopportunity.只有有小部分的投资者意识到了套利机会就会很快的重建APT均衡•Theexpectedreturn–betarelationshipcanbederivedwithoutusingthetruemarketportfolio.能够在不使用市场组合的情况下建立期望收益贝塔关系CAPM•Modelisbasedonaninherentlyunobservable“market”portfolio.模型建立在本质上不可观测的市场组合上•Restsonmean-varianceefficiency.TheactionsofmanysmallinvestorsrestoreCAPMequilibrium.建立在均值方差有效边界上，需要很多分散的小投资者建立CAPM均衡•CAPMdescribesequilibriumforallassets.描述了所有资产都达到均衡的情况INVESTMENTS|BODIE,KANE,MARCUS10-17MultifactorAPT多因子的套利模型•Useofmorethanasinglesystematicfactor使用不止一个系统性因子•Requiresformationoffactorportfolios需要因子组合的信息就足够•Whatfactors?模型的因子是什么？–Factorsthatareimportanttoperformanceofthegeneraleconomy能够影响宏观经济的变量–Whataboutfirmcharacteristics?或者是公司特征的变量INVESTMENTS|BODIE,KANE,MARCUS10-18Two-FactorModel两因子的套利模型•ThemultifactorAPTissimilartotheone-factorcase.多因子套利模型类似于单因子的情况1122()iiiiirErFFeINVESTMENTS|BODIE,KANE,MARCUS10-19Two-FactorModel两因子模型•Trackwithdiversifiedfactorportfolios:构建某个完全分散的因子组合具有如下特征：–beta=1foroneofthefactorsand0forallotherfactors.其中一个因子的贝塔是1，其余因子的贝塔都是零•Thefactorportfoliostrackaparticularsourceofmacroeconomicrisk,butareuncorrelatedwithothersourcesofrisk.这意味着这样的因子组合能够复制一种特有的、独立于其他风险来源的宏观经济风险INVESTMENTS|BODIE,KANE,MARCUS10-20WhereShouldWeLookforFactors?我们应该到哪里寻找这样的因子？•Needimportantsystematicriskfactors需要重要的系统性风险因子–Chen,Roll,andRossusedindustrialproduction,expectedinflation,unanticipatedinflation,excessreturnoncorporatebonds,andexcessreturnongovernmentbonds.–CRR使用工业产量、预期通胀、非预期通胀、公司债超额收益、国债超额收益；–FamaandFrenchusedfirmc