empirical likelihood based nonparametric testing for capm lee carter

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1、EmpiricallikelihoodbasednonparametrictestingforCAPMPietroCorettoandMariaLuciaParrellaAbstract.TheCapitalAssetPricingModel(CAPM)predictsalinearrelationbetweenassets’returnandtheirbetas.However,thereisempiricalevidencethatsucharelationshipdoesnotnecessarilyoccur,andinsom

2、ecasesitmightevenbenonlinear.Inthispaperweexploreanonparametricapproachwherethelinearspecificationistestedagainstanonparametricalternative.ThismethodologyisimplementedonS&P500data.Keywords:CAPM,goodness-of-fittest,empiricallikelihood1IntroductionAnassetpricingmodelprovid

3、esamethodforassessingtheriskinessofcashflowsfromaproject.Themodelprovidesanestimateoftherelationshipbetweenthatrisk-inessandthecostofcapital.Accordingtothe“capitalassetpricingmodel”(CAPM),theonlyrelevantmeasureofaproject’sriskisavariableuniquetothismodel,knownastheproje

4、ct’sbeta.IntheCAPM,thecostofcapital,i.e.,thereturn,isalinearfunc-tionofthethebetaoftheprojectbeingevaluated.AmanagerwhohasanestimateofthebetaofapotentialprojectcanusetheCAPMtoestimatethecostofcapitalfortheproject.IftheCAPMcapturesinvestors’behaviouradequately,thenthehi

5、storicaldatashouldrevealapositivelinearrelationbetweenreturnonfinancialassetsandtheirbetas.Also,noothermeasureofriskshouldbeabletoexplainthedifferencesinaveragereturnsacrossfinancialassetsthatarenotexplainedbyCAPMbetas.ThefactthatCAPMtheorypredictstheexistenceofacross-se

6、ctionlinearrelationbetweenreturnsandbetascanbeempiricallytested.Tothisendweproposeanonparametrictestingmethodology(see[10]and[3]amongothers).ThefirsttestoftheCAPMwasrunbyFamaandMacBeth[7]andtheirstudyvalidatedthetheory.Theauthorstestedthelinearityagainstsomeparametricno

7、nlinearalternatives.HoweversubsequentempiricalanalysishighlightedthatthevalidityoftheCAPMcoulddependonthetestingperiod.Thereisahugeamountofliteratureonthistopic(foracomprehensivereviewsee[11]),however,finalconclusionshavenotbeenmade.M.Corazzaetal.(eds.),MathematicalandS

8、tatisticalMethodsforActuarialSciencesandFinance©Springer-VerlagItalia2010104P.CorettoandM.L.ParrellaThefamousFama-Mac