empirical asset pricing hansen-jagannathan bounds

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1、DoctoralSeminarinEmpiricalFinanceTopic8Hansen-JagannathanBoundsLecturer:LarsA.LochstoerLondonBusinessSchoolFebruary20,20081MainConceptsUpuntilnowhaveevaluatedmodels(stochasticdiscountfactors)bylookingatpricingerrorsinexpectedexcessreturns.–Absoluteevaluation:GRS:^T^1^–Relativeevalu

2、ation:Cross-sectionalR2Twoproblems1.Noattemptto…ttheriskfreerate(usually).Inpowerutility,rep.agentcase,that’sexactlytheissue-…ttingboththeriskfreerateandtheslopeofbeta(theSharperatio).ThatwaswhyHansenandSingleton(1983)didnotrejectthemodel.2.Rewardshighvarianceoftheresiduals.Ifthemodelh

3、asapoor…rstpass…t,itishardertoreject.Letmeknowofanyerrors,please.ThesenotesdrawontheexcellentPhDcourseinempirical…nanceItookatBerkeley,taughtbyGregoryR.Du¤ee.Contactinfo:LarsLøchstøer,P222,LondonBusinessSchool,SussexPlace,Regent’sPark,NW14SA,London,UnitedKingdom.E-mail:LLochstoer@londo

4、n.edu0TheHansenandJagannathanDistanceisrobusttothesecriticisms.–However,disadvantageisitemphasizesthemaximallymis-pricedassets,whichisacriteriathatissensitivetonoiseinthedata,small(withintransactioncost)departuresfromno-arbitrage.–Thisproblemisthesameaswithe¢cientGMMtests.–Itdoesprovid

5、euswithaconsistentmetricwithwhichwecancomparedi¤erentmodelsandrunhorseracesofwhichmodelisthebest.TheHansen-JagannathanBoundsgiveminimumvariancefrontierforadmissiblestochasticdiscountfactors.–Visualinterpretationofperformanceofamodel–Notapropertestorevennecessarilyveryinformative.–Can’t

6、beusedtoestimateparametersHodrickandZhang(2003)isarecentexampleoftheuseoftheHansen-Jagannathandistance–ComparesasetofmodelsincludingtheCAPM,CCAPM,FF1.1Hansen-JagannathanBoundsLawofonepriceforNassetsqt=Et[xt+1mt+1]whereqtisNx1vectorofassetprices,xt+1isNx1vectorofpayo¤sandmt+1isthe1x1st

7、ochasticdiscountfactorAssumeoneriskfreeasset,i.e.canobserveEt[mt+1]Findtheminimumvariancestochasticdiscountfactorbyhypotheticallyregressingmt+1onthesetofassetpayo¤sxt+1Tmt+1=xt+10+"t+1Coe¢cientsa0arethenT
10=Ext+1xt+1E[xt+1mt+1]1SubstituteinthelawofonepricefromaboveT