a two state capital asset pricing model

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1、ATwoStateCapitalAssetPricingModelMosheFridmanInstituteforMathematicsanditsApplicationsUniversityofMinnesota514VincentHallMinneapolis,Minnesota55455March16,1994AbstractAfamousmodelinnancialtheoryistheCapitalAssetPricingModel(CAPM).InthispaperweproposeatwostateCAPMinwhichweassumethatexcessreturnsfo

2、rthemarketandforaparticularsecurityarebivariatenormallydistributed.TheparametersofthedistributionaredeterminedbythestateofanunobservedstationaryMarkovchain.Twostatesrepresenttwobusinessregimesthatarecharacterizedbylowandhighvolatility.Maximumlikelihoodestimatesfortheparametersofthemodelareobtainedv

3、iatheBaum-WelchalgorithmforlocalmaximizationofthelikelihoodfunctionforMarkovRegimeModels(MRM),alsoknownasHiddenMarkovModels(HMM).Weapplythemodeltomonthlyreturndataforthreeoilindustrycorporationsecurities.Acomparisonoftheresultswithtwosimplermodels,theindependentswitchingregressionmodelandthestandar

4、dCAPMwithoneregime,showsasignicantimprovementingoodnessoftobtainedbytheproposedtwostateMRM.Estimatesofthepe-riodsofhighvolatilityforeachcorporationdepictageneraleectofthebusinesscyclesonallthreeprocessescombinedwithuniqueeectssteamingfromcorporationrelatedevents.Keywords:CapitalAssetPricingMode

5、l,MarkovRegimeModel,HiddenMarkovModel,Baum-Welchalgorithm.AMS1991subjectclassications.Primary60J10;Secondary90A12.ResearchpartiallysupportedbyAROGrantDAAL03-91-G-01101IntroductionAfamousandwidelyusedmodelinnancialtheoryistheCapitalAssetPricingModel(CAPM)introducedinSharpe(1964)andLintner(1965).T

6、hemodelrelatesexpectedreturnsoncapitalassetsinvestmentswithex-pectedmarketreturns.Underthemodel,thereturnperperiodtofanassetRishypothesizedtobelinearlyrelatedtothemarketreturnRforthattmtperiodinthefollowingway:(R?R)=(R?R)+;tfmftttt2whereareindependentandidenticallydistributedasN(0;)andRistftther

7、eturnforperiodtonarisk-freeasset.Thequantities(R?R)andtft(R?R)arereferredtoastheexcessreturns.Theparameterofinterestmfttforinvestorsisthesystematicriskassociatedwiththeasset,measuredbytheregressionslope.The