The equity premiummehra.docx
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The equity premiummehra.docx
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Theequitypremiummehra
Theequitypremium:
Whyisitapuzzle?
文本全文 (8021 个单词)
CopyrightAssociationforInvestmentManagementandResearchJan/Feb2003
[眉批]
Thisarticletakesacriticallookattheequitypremiumpuzzle-theinabilityofstandardintertemporaleconomicmodelstorationalizethestatisticsthathavecharacterizedU.S.financialmarketsoverthepastcentury.AsummaryofhistoricalreturnsfortheUnitedStatesandotherindustrializedcountriesandanoverviewoftheeconomicconstructitselfareprovided.Theintuitionbehindthediscrepancybetweenmodelpredictionandempiricaldataisexplained.Afterdetailingtheresearcheffortstoenhancethemodel'sabilitytoreplicatetheempiricaldata,Iarguethattheproposedresolutionsfailalongcrucialdimensions.
Almosttwodecadesago,EdwardPrescottandI(seeMehraandPrescott1985)challengedtheprofessionwithaposer:
ThehistoricalU.S.equitypremium(thereturnearnedbyariskysecurityinexcessofthatearnedbyarelativelyriskfreeU.S.T-bill)isanorderofmagnitudegreaterthancanberationalizedinthecontextofthestandardneoclassicalparadigmoffinancialeconomics.Thisregularity,dubbed"theequitypremiumpuzzle,"hasspawnedaplethoraofresearcheffortstoexplainitaway.Inthisarticle,Itakearetrospectivelookatthepuzzleandcriticallyevaluatethevariousattemptstosolveit.1
EmpiricalFacts
Historicaldataprovideawealthofevidencedocumentingthatformorethanacentury,U.S.stockreturnshavebeenconsiderablyhigherthanreturnsforT-bills.AsTable1shows,theaverageannualrealreturn(thatis,theinflation-adjustedreturn)ontheU.S.stockmarketforthepast110yearshasbeenabout7.9percent.Inthesameperiod,therealreturnonarelativelyrisklesssecuritywasapaltry1.0percent.Thedifferencebetweenthesetworeturns,6.9percentagepoints(pps),istheequitypremium.Thisstatisticaldifferencehasbeenevenmorepronouncedinthepost-WorldWarIIperiod.Siegel's(1998)dataonU.S.stockandbondreturnsgoingbackto1802revealasimilar,althoughsomewhatsmaller,premiumforthepast200years.
Furthermore,thispatternofexcessreturnstoequityholdingsisnotuniquetoU.S.capitalmarkets.Table2confirmsthatequityreturnsinotherdevelopedcountriesalsoexhibitthishistoricalregularitywhencomparedwiththereturntodebtholdings.TheannualreturnontheU.K.stockmarket,forexample,was5.7percentinthepost-WWIIperiod,animpressive4.6pppremiumovertheaveragebondreturnof1.1percent.SimilarstatisticaldifferenceshavebeendocumentedforFrance,Germany,andJapan.Andtogether,theUnitedStates,theUnitedKingdom,Japan,Germany,andFranceaccountformorethan85percentofcapitalizedglobalequityvalue.
ThedramaticinvestmentimplicationsofthedifferentialratesofreturncanbeseeninTable3,whichmapstheenormousdisparityincapitalappreciationof$1investedindifferentassetsfor1802-1997andfor1926-2000.
(2)
Thiskindoflong-termperspectiveunderscorestheremarkablewealth-buildingpotentialoftheequitypremiumandexplainswhytheequitypremiumisofcentralimportanceinportfolioallocationdecisions,inmakingestimatesofthecostofcapital,andinthecurrentdebateabouttheadvantagesofinvestingSocialSecurityfundsinthestockmarket.
APremiumforBearingRisk?
Whyhastherateofreturnonstocksbeensignificantlyhigherthantherateofreturnonrelativelyriskfreeassets?
Oneintuitiveansweristhatstocksare"riskier"thanbondsandinvestorsrequireapremiumforbearingthisadditionalrisk.Indeed,thestandarddeviationofthereturnstostocks(about20percentayearhistorically)islargerthanthatofthereturnstoT-bills(about4percentayear),soobviously,stocksareconsiderablyriskierthanbills.
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Table1.
Table2.
Table3.
Butarethey?
Figure1illustratesthevariabilityintheannualrealrateofreturnontheS&P500Index(PanelA)andarelativelyriskfreesecurity(PanelB)overthe1889-2000period.
Toenhanceanddeepenourunderstandingoftherisk-returntrade-offinthepricingoffinancialassets,wemakeadetourintomodernasset-pricingtheoryandlookatwhydifferentassetsyielddifferentratesofreturn.Thedeusexmachinainasset--pricingtheoryisthatassetsarepricedinsuchawaythat,exante,thelossinmarginalutilityincurredbysacrificingcurrentconsumptionandbuyinganassetatacertainpriceisequaltotheexpectedgaininmarginalutilitycontingentontheanticipatedincreaseinconsumptionwhentheassetpaysoffinthefuture.
Theoperativeconcepthereis"incrementallossorgaininwell-beingbecauseofconsumption,"andtheconceptshouldbedifferentiatedfromincrementalconsumptionitself.Thesameamountofconsumptionmayresultindifferentdegreesofwell-beingatdifferenttimes.(Forexample,afivecoursedinnerafteraheavylunchyieldsconsiderablylesssatisfactionthanasimilardinnerwhenoneishungry!
)
Asaconsequence,assetsthatpayoffwhentimesaregoodandconsumptionlevelsarehigh(i.e.,whentheincrementalvalueofadditionalconsumptionislow)arelessdesirablethanthosethatpayoffanequivalentamountwhentimesarebadandadditionalconsumptionisbothdesirableandmorehighlyvalued.Thus,assetsthatpayoffwhentimesaregoodmustofferapremiumtoinduceinvestorstoholdthem.
Letmeillustratethisprincipleinthecontextofthestandardpopularparadigm,thecapitalassetpricingmodel.TheCAPMpostulatesalinearrelationshipbetweenanasset'sbeta(ameasureofsystematicrisk)andexpectedreturn.Thus,high--betastocksyieldahighexpectedrateofreturn.IntheCAPM,goodtimesandbadtimesarecapturedbythereturnonthemarket.Theperformanceofthemarket,ascapturedbyabroad-basedindex,actsasasurrogateindicatorfortherelevantstateoftheeconomy.Ahigh-betasecuritythustendstopayoffmorewhenthemarketreturnishigh(whentimesaregoodandconsumptionisplentiful),butasjustnoted,suchasecurityprovideslessincrementalutilitythanasecuritythatpaysoffwhenconsumptionislow.Itislessvaluabletoinvestorsand,consequently,sellsforless.Thus,assetsthatpayoffinstatesoflow-marginalutilitywillsellforalowerpricethansimilarassetsthatpayoffinstatesofhighmarginalutility.Sinceratesofreturnareinverselyproportionaltoassetprices,ahigh-betaassetwill,onaverage,haveahigherrateofreturnthanalow--betasecurity.
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Figure1.
Anotherperspectiveonassetpricingemphasizesthateconomicagentsprefertosmoothpatternsofconsumptionovertime.Assetsthatpayoffarelativelylargeramountattimeswhenconsumptionisalreadyhigh"destabilize"thesepatternsofconsumption,whereasassetsthatpayoffwhenconsumptionlevelsarelow"smoothout"consumption.Naturally,theselatterassetsaremorevaluableandthusrequirealowerrateofreturntoinduceinvestorstoholdthem.(Insurancepoliciesareaclassicexampleofassetsthatsmoothconsumption.Individualswillinglypurchaseandholdtheminspiteoftheirverylowratesofreturn.)
Toreturntotheoriginalquestion:
ArestockssomuchriskierthanT-billsthata7ppdifferentialintheirratesofreturnisjustified?
WhatcameasasurprisetomanyeconomistsandresearchersinfinancewastheconclusionofaresearchpaperthatPrescottandIwrotein1979.Stocksandbondspayoffinapproximatelythesamestatesofnatureoreconomicscenarios,andhence,asarguedearlier,theyshouldcommandapproximatelythesamerateofreturn.Infact,usingstandardtheorytoestimaterisk-adjustedreturns,wefoundthatstocks,onaverage,shouldcommand,atmost,a1ppreturnpremiumoverbills.Becauseforaslongaswehadreliabledata(aboutahundredyears),themeanpremiumonstocksoverbillswasconsiderablyandconsistentlyhigher,werealizedthatwehadapuzzleonourhands.Ourpaperdetailingthisresearch,"TheEquityPremium:
APuzzle,"waspublishedin1985.
Toillustratethepuzzle,considerafrictionlesseconomythathasasinglerepresentative,"standin"household.Thishouseholdunitordersitspreferencesoverrandomconsumptionpathsby
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wheretheparameterccmeasuresthecurvatureoftheutilityfunction.Whena=1,theutilityfunctionisdefinedtobelogarithmic,whichisthelimitofEquation2asaapproaches1.
ThefeaturethatmakesEquation2the"preferencefunctionofchoice"inmuchoftheliteratureongrowthandinRealBusinessCycletheoryisthatitisscaleinvariant.Althoughthelevelsofaggregatevariables,suchascapitalstock,haveincreasedovertime,theequilibriumreturnprocessisstationary.Asecondattractivefeatureisthatitisoneofonlytwopreferencefunctionsthatallowforaggregationanda"stand-in"(representative)agentformulationthatisindependentoftheinitialdistributionofendowments.Onedisadvantageofthisrepresentationisthatitlinksriskpreferenceswithtimepreferences.WithCRRApreferences,agentswholiketosmoothconsumptionacrossvariousstatesofnaturealsoprefertosmoothconsumptionovertime;thatis,theydislikegrowth.Specifically,thecoefficientofrelativeriskaversionisthereciprocaloftheelasticityofintertemporalsubstitution.Thereisnofundamentaleconomicreasonwhythismustbeso.Irevisittheimplicationsofthisissuelater,inexaminingpreferencestructuresthatdonotimposethisrestriction.3
Forthisillustrationofthepuzzle,assumeoneproductiveunitthatproducesinperiodtoutputyt,whichis
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