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Cochrane_AP

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简介:本文档为《Cochrane_APpdf》,可适用于经济金融领域

AssetPricingJohnHCochraneJune,AcknowledgmentsThisbookowesanenormousintellectualdebttoLarsHansenandGeneFamaMostoftheideasinthebookdevelopedfromlongdiscussionswitheachofthem,andtryingtomakesenseofwhateachwassayinginthelanguageoftheotherIamalsogratefultoallmycolleaguesinFinanceandEconomicsattheUniversityofChicago,andtoGeorgeConstantinidesespecially,formanydiscussionsabouttheideasinthisbookIthankGeorgeConstantinides,AndreaEisfeldt,GeneFama,WayneFerson,OwenLamont,AnthonyLynch,DanNelson,AlbertoPozzolo,MichaelRoberts,JuhaSeppala,MikeStutzer,PietroVeronesi,ananonymousreviewer,andseveralgenerationsofPhDstudentsattheUniversityofChicagoformanyusefulcommentsIthanktheNSFandtheGraduateSchoolofBusinessforresearchsupportAdditionalmaterialandbothsubstantiveandtypographicalcorrectionswillbemaintainedathttp:wwwgsbuchicagoedufacjohncochraneresearchpapersCommentsandsuggestionsaremostwelcomeThisbookdraftiscopyrightc°JohnHCochrane,,,JohnHCochraneGraduateSchoolofBusinessUniversityofChicagoEthStChicagoILjohncochranegsbuchicagoeduJune,ContentsAcknowledgmentsPrefacePartIAssetpricingtheoryConsumptionbasedmodelandoverviewBasicpricingequationMarginalrateofsubstitutionstochasticdiscountfactorPrices,payoffsandnotationClassicissuesinfinanceDiscountfactorsincontinuoustimeProblemsApplyingthebasicmodelAssumptionsandapplicabilityGeneralEquilibriumConsumptionbasedmodelinpracticeAlternativeassetpricingmodels:OverviewProblemsContingentClaimsMarketsContingentclaimsRiskneutralprobabilitiesInvestorsagainRisksharingStatediagramandpricefunctionThediscountfactorLawofonepriceandexistenceofadiscountfactorNoArbitrageandpositivediscountfactorsAnalternativeformula,andx∗incontinuoustimeProblemsMeanvariancefrontierandbetarepresentationsExpectedreturnBetarepresentationsMeanvariancefrontier:IntuitionandLagrangiancharacterizationAnorthogonalcharacterizationofthemeanvariancefrontierSpanningthemeanvariancefrontierAcompilationofpropertiesofR∗,Re∗andx∗Meanvariancefrontiersform:theHansenJagannathanboundsProblemsRelationbetweendiscountfactors,betas,andmeanvariancefrontiersFromdiscountfactorstobetarepresentationsFrommeanvariancefrontiertoadiscountfactorandbetarepresentationFactormodelsanddiscountfactorsDiscountfactorsandbetamodelstomeanvariancefrontierThreeriskfreerateanaloguesMeanvariancespecialcaseswithnoriskfreerateProblemsImplicationsofexistenceandequivalencetheoremsConditioninginformationScaledpayoffsSufficiencyofaddingscaledreturnsConditionalandunconditionalmodelsScaledfactors:apartialsolutionSummaryProblemsFactorpricingmodelsCapitalAssetPricingModel(CAPM)IntertemporalCapitalAssetPricingModel(ICAPM)CommentsontheCAPMandICAPMArbitragePricingTheory(APT)APTvsICAPMProblemsPartIIEstimatingandevaluatingassetpricingmodelsGMMinexplicitdiscountfactormodelsTheRecipeInterpretingtheGMMprocedureApplyingGMMGMM:generalformulasandapplicationsGeneralGMMformulasTestingmomentsStandarderrorsofanythingbydeltamethodUsingGMMforregressionsPrespecifiedweightingmatricesandmomentconditionsEstimatingononegroupofmoments,testingonanotherEstimatingthespectraldensitymatrixProblemsRegressionbasedtestsoflinearfactormodelsTimeseriesregressionsCrosssectionalregressionsFamaMacBethProcedureProblemsGMMforlinearfactormodelsindiscountfactorformGMMonthepricingerrorsgivesacrosssectionalregressionThecaseofexcessreturnsHorseRacesTestingforcharacteristicsTestingforpricedfactors:lambdasorb’sProblemsMaximumlikelihoodMaximumlikelihoodMLisGMMonthescoresWhenfactorsarereturns,MLprescribesatimeseriesregressionWhenfactorsarenotexcessreturns,MLprescribesacrosssectionalregressionProblemsTimeseries,crosssection,andGMMDFtestsoflinearfactormodelsThreeapproachestotheCAPMinsizeportfoliosMonteCarloandBootstrapWhichmethodPartIIIBondsandoptionsOptionpricingBackgroundBlackScholesformulaProblemsOptionpricingwithoutperfectreplicationOntheedgesofarbitrageOneperiodgooddealboundsMultipleperiodsandcontinuoustimeExtensions,otherapproaches,andbibliographyProblemsTermstructureofinterestratesDefinitionsandnotationYieldcurveandexpectationshypothesisTermstructuremodels–adiscretetimeintroductionContinuoustimetermstructuremodelsThreelineartermstructuremodelsBibliographyandcommentsProblemsPartIVEmpiricalsurveyExpectedreturnsinthetimeseriesandcrosssectionTimeseriespredictabilityTheCrosssection:CAPMandMultifactorModelsSummaryandinterpretationProblemsEquitypremiumpuzzleandconsumptionbasedmodelsEquitypremiumpuzzlesNewmodelsBibliographyProblemsReferencesPartVAppendixContinuoustimeBrownianMotionDiffusionmodelIto’slemmaProblemsPrefaceAssetpricingtheorytriestounderstandthepricesorvaluesofclaimstouncertainpaymentsAlowpriceimpliesahighrateofreturn,soonecanalsothinkofthetheoryasexplainingwhysomeassetspayhigheraveragereturnsthanothersTovalueanasset,wehavetoaccountforthedelayandfortheriskofitspaymentsTheeffectsoftimearenottoodifficulttoworkoutHowever,correctionsforriskaremuchmoreimportantdeterminantsofanmanyassets’valuesForexample,overthelastyearsUSstockshavegivenarealreturnofaboutonaverageOfthis,onlyaboutisduetointerestratestheremainingisapremiumearnedforholdingriskUncertainty,orcorrectionsforriskmakeassetpricinginterestingandchallengingAssetpricingtheorysharesthepositivevsnormativetensionpresentintherestofeconomicsDoesitdescribethewaytheworlddoesworkorthewaytheworldshouldworkWeobservethepricesorreturnsofmanyassetsWecanusethetheorypositively,totrytounderstandwhypricesorreturnsarewhattheyareIftheworlddoesnotobeyamodel’spredictions,wecandecidethatthemodelneedsimprovementHowever,wecanalsodecidethattheworldiswrong,thatsomeassetsare“mispriced”andpresenttradingopportunitiesfortheshrewdinvestorThislatteruseofassetpricingtheoryaccountsformuchofitspopularityandpracticalapplicationAlso,andperhapsmostimportantly,thepricesofmanyassetsorclaimstouncertaincashflowsarenotobserved,suchaspotentialpublicorprivateinvestmentprojects,newfinancialsecurities,buyoutprospects,andcomplexderivativesWecanapplythetheorytoestablishwhatthepricesoftheseclaimsshouldbeaswelltheanswersareimportantguidestopublicandprivatedecisionsAssetpricingtheoryallstemsfromonesimpleconcept,derivedinthefirstpageofthefirstChapterofthisbook:priceequalsexpecteddiscountedpayoffTherestiselaboration,specialcases,andaclosetfulloftricksthatmakethecentralequationusefulforoneoranotherapplicationTherearetwopolarapproachestothiselaborationIwillcallthemabsolutepricingandrelativepricingInabsolutepricing,wepriceeachassetbyreferencetoitsexposuretofundamentalsourcesofmacroeconomicriskTheconsumptionbasedandgeneralequilibriummodelsdescribedbelowarethepurestexamplesofthisapproachTheabsoluteapproachismostcommoninacademicsettings,inwhichweuseassetpricingtheorypositivelytogiveaneconomicexplanationforwhypricesarewhattheyare,orinordertopredicthowpricesmightchangeifpolicyoreconomicstructurechangedInrelativepricing,weaskalessambitiousquestionWeaskwhatwecanlearnaboutanasset’svaluegiventhepricesofsomeotherassetsWedonotaskwherethepriceoftheothersetofassetscamefrom,andweuseaslittleinformationaboutfundamentalriskfactorsaspossibleBlackScholesoptionpricingistheclassicexampleofthisapproachWhilelimitedinscope,thisapproachoffersprecisioninmanyapplicationsAssetpricingproblemsaresolvedbyjudiciouslychoosinghowmuchabsoluteandhowmuchrelativepricingonewilldo,dependingontheassetsinquestionandthepurposeofthecalculationAlmostnoproblemsaresolvedbythepureextremesForexample,theCAPManditssuccessorfactormodelsareparadigmsoftheabsoluteapproachYetinapplications,theypriceassets“relative”tothemarketorotherriskfactors,withoutansweringwhatdeterminesthemarketorfactorriskpremiaandbetasThelatteraretreatedasfreeparametersOntheotherendofthespectrum,mostpracticalfinancialengineeringquestionsinvolveassumptionsbeyondpurelackofarbitrage,assumptionsaboutequilibrium“marketpricesofrisk”ThecentralandunfinishedtaskofabsoluteassetpricingistounderstandandmeasurethesourcesofaggregateormacroeconomicriskthatdriveassetpricesOfcourse,thisisalsothecentralquestionofmacroeconomics,andthisisaparticularlyexcitingtimeforresearcherswhowanttoanswerthesefundamentalquestionsinmacroeconomicsandfinanceAlotofempiricalworkhasdocumentedtantalizingstylizedfactsandlinksbetweenmacroeconomicsandfinanceForexample,expectedreturnsvaryacrosstimeandacrossassetsinwaysthatarelinkedtomacroeconomicvariables,orvariablesthatalsoforecastmacroeconomiceventsawideclassofmodelssuggeststhata“recession”or“financialdistress”factorliesbehindmanyassetpricesYettheorylagsbehindwedonotyethaveawelldescribedmodelthatexplainstheseinterestingcorrelationsInturn,IthinkthatwhatwearelearningaboutfinancemustfeedbackonmacroeconomicsTotakeasimpleexample,wehavelearnedthattheriskpremiumonstocks–theexpectedstockreturnlessinterestrates–ismuchlargerthantheinterestrate,andvariesagooddealmorethaninterestratesThismeansthatattemptstolineinvestmentupwithinterestratesareprettyhopeless–mostvariationinthecostofcapitalcomesfromthevaryingriskpremiumSimilarly,wehavelearnedthatsomemeasureofriskaversionmustbequitehigh,orpeoplewouldallborrowlikecrazytobuystocksMostmacroeconomicspursuessmalldeviationsaboutperfectforesightequilibria,butthelargeequitypremiummeansthatvolatilityisafirstordereffect,notasecondordereffectStandardmacroeconomicmodelspredictthatpeoplereallydon’tcaremuchaboutbusinesscycles(Lucas)Assetpricesarebeginningtorevealthattheydo–thattheyforegosubstantialreturnpremiatoavoidassetsthatfallinrecessionsThisfactoughttotellussomethingaboutrecessions!ThisbookadvocatesadiscountfactorgeneralizedmethodofmomentsviewofassetpricingtheoryandassociatedempiricalproceduresIsummarizeassetpricingbytwoequations:pt=E(mtxt)mt=f(data,parameters)wherept=assetprice,xt=assetpayoff,mt=stochasticdiscountfactorThemajoradvantageofthediscountfactormomentconditionapproachareitssimplicityanduniversalityWhereoncetherewerethreeapparentlydifferenttheoriesforstocks,bonds,andoptions,nowweseeeachasjustspecialcasesofthesametheoryThecommonlanguagealsoallowsustouseinsightsfromeachfieldofapplicationinotherfieldsThisapproachalsoallowsustoconvenientlyseparatethestepofspecifyingeconomicassumptionsofthemodel(secondequation)fromthestepofdecidingwhichkindofempiricalrepresentationtopursueorunderstandForagivenmodel–choiceoff(·)–wewillseehowthefirstequationcanleadtopredictionsstatedintermsofreturns,pricedividendratios,expectedreturnbetarepresentations,momentconditions,continuousvsdiscretetimeimplicationsandsoforthTheabilitytotranslatebetweensuchrepresentationsisalsoveryhelpfulindigestingtheresultsofempiricalwork,whichusesanumberofapparentlydistinctbutfundamentallyconnectedrepresentationsThinkingintermsofdiscountfactorsoftenturnsouttobemuchsimplerthanthinkingintermsofportfoliosForexample,itiseasiertoinsistthatthereisapositivediscountfactorthantocheckthateverypossibleportfoliothatdominateseveryotherportfoliohasalargerprice,andthelongargumentsovertheAPTstatedintermsofportfoliosareeasytodigestwhenstatedintermsofdiscountfactorsThediscountfactorapproachisalsoassociatedwithastatespacegeometryinplaceoftheusualmeanvariancegeometry,andthisbookemphasizesthestatespaceintuitionbehindmanyclassicresultsForthesereasons,thediscountfactorlanguageandtheassociatedstatespacegeometryiscommoninacademicresearchandhightechpracticeItisnotyetcommonintextbooks,andthatisthenichethatthisbooktriestofillIalsodivergefromtheusualorderofpresentationMostbooksarestructuredfollowingthehistoryofthought:portfoliotheory,meanvariancefrontiers,spanningtheorems,CAPM,ICAPM,APT,optionpricing,andfinallyconsumptionbasedmodelContingentclaimsareanesotericextensionofoptionpricingtheoryIgotheotherwayaround:contingentclaimsandtheconsumptionbasedmodelarethebasicandsimplestmodelsaroundtheothersarespecializationsJustbecausetheywerediscoveredintheoppositeorderisnoreasontopresentthemthatwayIalsotrytounifythetreatmentofempiricalmethodsAwidevarietyofmethodsarepopular,includingtimeseriesandcrosssectionalregressions,andmethodsbasedongeneralizedmethodofmoments(GMM)andmaximumlikelihoodHowever,intheendalloftheseapparentlydifferentapproachesdothesamething:theypickfreeparametersofthemodeltomakeitfitbest,whichusuallymeanstominimizepricingerrorsandtheyevaluatethemodelbyexamininghowbigthosepricingerrorsareAswiththetheory,IdonotattemptanencyclopediccompilationofempiricalproceduresTheliteratureoneconometricmethodscontainslotsofmethodsandspecialcases(likelihoodratioanaloguesofcommonWaldtestscaseswithandwithoutriskfreeassetsandwhenfactorsdoanddon’tspanthemeanvariancefrontier,etc)thatareseldomusedinpracticeItrytofocusonthebasicideasandonmethodsthatareactuallyusedinpracticeTheaccentinthisbookisonunderstandingstatementsoftheory,andworkingwiththattheorytoapplications,ratherthanrigorousorgeneralproofsAlso,Iskipverylightlyovermanypartsofassetpricingtheorythathavefadedfromcurrentapplications,althoughtheyoccupiedlargeamountsoftheattentioninthepastSomeexamplesareportfolioseparationtheorems,propertiesofvariousdistributions,orasymptoticAPTWhileportfoliotheoryisstillinterestinganduseful,itisnolongeracornerstoneofpricingRatherthanuseportfoliotheorytofindademandcurveforassets,whichintersectedwithasupplycurvegivesprices,wenowgotopricesdirectlyOnecanthenfindoptimalportfolios,butitisasideissuefortheassetpricingquestionMypresentationisconsciouslyinformalIliketoseeanideainitssimplestformandlearntouseitbeforegoingbackandunderstandingallthefoundationsoftheideasIhaveorganizedthebookforsimilarlymindedreadersIfyouarehungryformoreformaldefinitionsandbackground,keepgoing,theyusuallyshowuplateroninthechapterAgain,myorganizingprincipleisthateverythingcanbetracedbacktospecializationsofthebasicpricingequationp=E(mx)Therefore,afterreadingthefirstchapter,onecanprettymuchskiparoundandreadtopicsinasmuchdepthororderasonelikesEachmajorsubjectalwaysstartsbackatthesamepricingequationThetargetaudienceforthisbookiseconomicsandfinancePhDstudents,advancedMBAstudentsorprofessionalswithsimilarbackgroundIhopethebookwillalsobeusefultofellowresearchersandfinanceprofessionals,byclarifying,relatingandsimplifyingthesetoftoolswehavealllearnedinahodgepodgemannerIpresumesomeexposuretoundergraduateeconomicsandstatisticsAreadershouldhaveseenautilityfunction,arandomvariable,astandarderrorandatimeseries,shouldhavesomebasiclinearalgebraandcalculusandshouldhavesolvedamaximumproblembysettingderivativestozeroThehurdlesinassetpricingarereallyconceptualratherthanmathematicalPARTIAssetpricingtheoryChapterConsumptionbasedmodelandoverviewIstartbythinkingofaninvestorwhothinksabouthowmuchtosaveandconsume,andwhatportfolioofassetstoholdThemostbasicpricingequationcomesfromthefirstorderconditionstothatproblem,andsaythatpriceshouldbetheexpecteddiscountedpayoff,usingtheinvestor’smarginalutilitytodiscountthepayoffThemarginalutilitylossofconsumingalittlelesstodayandinvestingtheresultshouldequalthemarginalutilitygainofsellingtheinvestmentatsomepointinthefutureandeatingtheproceedsIfthepricedoesnotsatisfythisrelation,theinvestorshouldbuymoreoftheassetFromthissimpleidea,IcandiscusstheclassicissuesinfinanceTheinterestrateisrelatedtotheaveragefuturemarginalutility,andhencetotheexpectedpathofconsumptionHighrealinterestratesshouldbeassociatedwithanexpectationofgrowingconsumptionInatimeofhighrealinterestrates,itmakessensetosave,buybonds,andthenconsumemoretomorrowMostimportantly,riskcorrectionstoassetpricesshouldbedrivenbythecovarianceofassetpayoffswithconsumptionormarginalutilityForagivenexpectedpayoffofanasset,anassetthatdoesbadlyinstateslikearecession,inwhichtheinvestorfeelspoorandisconsuminglittle,islessdesirablethananassetthatdoesbadlyinstatesofnaturelikeaboomwhentheinvestorfeelswealthyandisconsumingagreatdealTheformerassetswillsellforlowerpricestheirpriceswillreflectadiscountfortheirriskiness,andthisriskinessdependsonacovarianceThisisthefundamentalpointofthewholebookOfcourse,thefundamentalmeasureofhowyoufeelismarginalutilitygiventhatassetsmustpa

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