AssetPricingJohnH.Cochrane2AcknowledgmentsThisbookowesanenormousintellectualdebttoLarsHansenandGeneFama.Mostoftheideasinthebookdevelopedfromshuttlingbackandforthbetweentheirof¿ces,andtryingtomakesenseofwhateachwassayinginthelanguageoftheother.IamalsogratefultoallmycolleaguesinFinanceandEconomicsattheUniversityofChicago,andtoGeorgeCon-stantinidesespecially,formanylongdiscussionsabouttheideasinthisbook.IthankGeorgeConstantinides,AndreaEisfeldt,GeneFama,WayneFerson,OwenLamont,AnthonyLynch,DanNelson,AlbertoPozzolo,MichaelRoberts,MikeStutzer,andseveralgenerationsofPh.D.studentsattheUniversityofChicagoforcommentsonearlierdrafts.PietroVerson-esikindlysharedhisclassnotesontermstructuremodels.IthanktheNSFandtheGraduateSchoolofBusinessforresearchsupport.Untilpublication,ever-improvingdraftsofthisbookareavailableatJohnH.Cochrane1997,1998,1999,2000JohnH.CochraneGraduateSchoolofBusinessUniversityofChicago1101E.58thSt.ChicagoIL606377737023059john.cochrane@gsb.uchicago.eduMay1,20003ContentsAcknowledgments31Preface5PartI.Assetpricingtheory92Consumption-basedmodelandoverview102.1Basicpricingequation102.2Marginalrateofsubstitution/stochasticdiscountfactor122.3Prices,payoffsandnotation132.4Classicissuesin¿nance152.5Discountfactorsincontinuoustime292.6Problems343Applyingthebasicmodel383.1Assumptionsandapplicability383.2GeneralEquilibrium403.3Consumption-basedmodelinpractice443.4Alternativeassetpricingmodels:Overview474ContingentClaimsMarkets494.1Contingentclaims494.2Riskneutralprobabilities504.3Investorsagain514.4Risksharing534.5Statediagramandpricefunction545Thediscountfactor585.1Lawofonepriceandexistenceofadiscountfactor585.2No-Arbitrageandpositivediscountfactors645.3Analternativeformula,andx incontinuoustime??6846Mean-variancefrontierandbetarepresentations726.1Expectedreturn-Betarepresentations726.2Mean-variancefrontier:IntuitionandLagrangiancharacterization756.3Anorthogonalcharacterizationofthemean-variancefrontier786.4Spanningthemean-variancefrontier846.5AcompilationofpropertiesofU Uh and{ 846.6Problems877Relationbetweendiscountfactors,betas,andmean-variancefrontiers887.1Fromdiscountfactorstobetarepresentations887.2Frommean-variancefrontiertoadiscountfactorandbetarepresentation927.3Factormodelsanddiscountfactors957.4Discountfactorsandbetamodelstomean-variancefrontier997.5Threeriskfreerateanalogues1007.6Mean-variancespecialcaseswithnoriskfreerate1057.7Problems1098Implicationsofexistenceandequivalencetheorems1109Conditioninginformation1189.1Scaledpayoffs1199.2Suf¿ciencyofaddingscaledreturns1219.3Conditionalandunconditionalmodels1239.4Scaledfactors:apartialsolution1309.5Summary13210Factorpricingmodels13310.1CapitalAssetPricingModel(CAPM)13510.2IntertemporalCapitalAssetPricingModel(ICAPM)14610.3CommentsontheCAPMandICAPM14810.4ArbitragePricingTheory(APT)15110.5APTvs.ICAPM16010.6Problems1615PartII.Estimatingandevaluatingassetpricingmodels16211GMMinexplicitdiscountfactormodels16511.1TheRecipe16511.2InterpretingtheGMMprocedure16811.3ApplyingGMM17212GMM:generalformulasandapplications17612.1GeneralGMMformulas17612.2Testingmoments18012.3Standarderrorsofanythingbydeltamethod18112.4UsingGMMforregressions18212.5Prespeci¿edweightingmatricesandmomentconditions18412.6Estimatingononegroupofmoments,testingonanother.19312.7Estimatingthespectraldensitymatrix19312.8Problems20013Regression-basedtestsoflinearfactormodels20213.1Time-seriesregressions20213.2Cross-sectionalregressions20713.3Fama-MacBethProcedure21613.4Problems22214GMMforlinearfactormodelsindiscountfactorform22314.1GMMonthepricingerrorsgivesacross-sectionalregression22314.2Thecaseofexcessreturns22514.3HorseRaces22714.4Testingforcharacteristics22814.5Testingforpricedfactors:lambdasorb’s?22914.6Problems23315Maximumlikelihood23515.1Maximumlikelihood235615.2MLisGMMonthescores23715.3Whenfactorsarereturns,MLprescribesatime-seriesregression.23915.4Whenfactorsarenotexcessreturns,MLprescribesacross-sectionalregression24315.5Problems24416Time-seriesvs.crosssectionMLvs.GMM24616.1Timeseriesvs.cross-section24616.2MLvs.GMM250PartIII.Bondsandoptions26117Optionpricing26317.1Background26317.2Black-Scholesformula27017.3Problems27618Optionpricingwithoutperfectreplication27718.1Ontheedgesofarbitrage27718.2One-periodgooddealbounds27818.3Multipleperiodsandcontinuoustime28518.4Extensions,otherapproaches,andbibliography29419Termstructureofinterestrates29619.1De¿nitionsandnotation29619.2Yieldcurveandexpectationshypothesis30019.3Termstructuremodels–adiscrete-timeintroduction30319.4Continuoustimetermstructuremodels30719.5Threefamouslineartermstructuremodels31219.6Bibliography32319.7Problems325PartIV.Abriefempiricalsurvey326720Equitypremiumpuzzle??32721Hansen-Jagannathanbounds32921.1Results34121.2Beyondmeanandvariance.34121.3Whatdoweknowaboutdiscountfactors:asummary34321.4CommentsontheHansen-Jagannathanbound.34322Bibliography34522.1References345PartV.Generalequilbrium348PartVI.Appendix35