指数模型和套利定价理论

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1、CHAPTERFOUR:IndexModelsandAPT1ProblemsofMarkowitzPortfolioSelectionTherearesomeproblemsforMarkowitzportfolioselection:HugenumberofestimatesofcovariancebetweenallpairsofavailablesecuritiesVastcomputingcapacityrequiredtoresolveanoptimizationquadraticprogrammingforlargep

2、ortfolioCAPMisasingle,staticfactormodel25.7%1.1%14.3%6.44.419.27.94.423.47.04.615.65.16.19.22.93.113.0Single-IndexModels123456YearGrowthofGDP（）Inflation（）DifferenceoftherealizedreturnofStockiandtherisk-freerate（）AMiniCase3RegressionModelMacroorsystematicfactorFirm’sor

3、unsystematicfactorExogenous4CovarianceSystematicriskUnsystematicrisk5—MarketModelCAPMisaspecialcaseofSingle-IndexModelstakingasthefactor.CAPM:Themarketisatequilibrium6Canyoubeatthemarket?Ifyoucanfindaportfoliomanagerwithapositiveyoucanbeatthemarket!CML0Thehyperbolathr

4、oughAandMcannotbetangenttotheefficientfrontierThepointAcannotbelocatedontheefficientfrontier7Multi-IndexModelsTheMiniCaseGrowthofGDPInflationFirm’sorunsystematicfactor8Covariance9—MoreAboutArbitrageArisklessarbitrageopportunityexistsifandonlyifeither:Twoportfolioscanb

5、ecreatedthathaveidenticalpayoffsineverystatebuthavedifferentcosts;orTwoportfolioscanbecreatedwithequalcosts,butwherethefirstportfoliohasatleastthesamepayoffasthesecondinallstates,buthasahigherpayoffinatleastonestate;orAportfoliocanbecreatedwithzerocost,butwhichhasanon

6、-negativepayoffinallstatesandapositivepayoffinatleastonestate.10AMiniCaseABCD-2020406007030-2090-20-10701523153625%25%25%25%HighrealratesLowrealratesProbabilityofthestatesHighinflationLowinflationHighinflationLowinflationStockReturn（%）11ABCD$10$10$10$10252032.522.2529

7、.5833.9148.158.58DABC0.68-0.380.221.00-0.15-0.290.68-0.151.00-0.87-0.38-0.29-0.871.000.221.00CorrelationMatrixPriceExpectedReturn（%）StockStandardDeviation(%)12ThePortfolioComparinganequallyweightedportfolioofthestocksA,BandCwiththestockDDHighrealratesLowrealratesHighi

8、nflationLowinflationHighinflationLowinflationStockorPortfolioReturn（%）23.3323.3320.0036.6715.0023.0015.0036.0013Expectedretu