stock market

THEJOURNALOFFINANCE•,NO.3•JULY1987

FurtherEvidenceOnInvestorOverreactionand

StockMarketSeasonality

*

ABSTRACT

Inapreviouspaper,wefoundsystematicpricereversalsforstocksthatexperience

extremelong-termgainsorloss:Pastlorssignificantlyoutperformpastwinners.

Weinterpretedthisfindingasconsistentwiththebehavioralhypothesisofinvestor

follow-uppaper,additionalevidenceisreportedthatsupportsthe

overreactionhypothesisandthatisinconsistentwithtwoalternativehypothesbad

onfirmsizeanddifferencesinrisk,sonalpattern

returnsinJanuaryarerelatedtobothshort-term

andlong-termpastperformance,aswellastothepreviousyearmarketreturn.

INAPREVIOUSPAPER(DeBondtandThaler[11]),weinvestigatedasimple

stockmarketinvestmentstrategymotivatedbyworkincognitivepsychologyon

ategyisbadonthenotionthatmanyinvestorsare

mentalandsurveyevidenceindicatesthat

inprobabilityrevisionproblemspeopleshowatendencyto"overreact,"i.e.,they

ectured

that,asaconquenceofinvestoroverreactiontoearnings,stockpricesmayalso

icesini-

tiallybiadbyeitherexcessiveoptimismorpessimism,prior"lors"wouldbe

moreattractiveinvestmentsthanprior"winners."

Wefoundconsiderableevidenceconsistentwiththissimplehypothesis.^For

example,usingmonthlyreturndatabetween1926and1982forstockslistedon

theNewYorkStockExchange(ascompiledbytheCenterforRearchin

SecurityPrices(CRSP)attheUniversityofChicago),weformedportfoliosof

the50mostextremewinnersand50mostextremelors(asmeasuredby

cumulativeexcessreturnsoversuccessivefiveyearformationperiods).Itwas

reportedthatoverthefollowingfive-yeartestperiodstheportfoliosoflors

outperformedtheportfoliosofwinnersbyanaverageof31.9percent.

However,manyissuesregardingthe"winner-lor"effectwereleftunresolved.

First,thereisapronouncedasonalityinthe"pricecorrection."Almostallofit

occursinthesuccessivemonthsofJanuary,,the

*UniversityofWisconsinatMadisonandCornellUniversity,,

AlanKraus,JofLakonishok,TheoVermaelenandmembersoftheCornellandWisconsinfinance

LemkeandCharlesLeeprovidedexpertcomputational

dliketoacknowledgefinancialsupportfrom

thePeteJohnsonFundforRearchinFinanceattheUniversityofWisconsin-Madison(DeBondt)

oundation(Thaler).

'Otherempiricalworkreportingevidence(onafirm-by-firmbasis)consistentwithoverreaction

includesBrownandHarlow[6]andHowe[17].

557

558TheJournalofFinance

correctionappearstobeasymmetric:afterthedateofportfolioformation,lors

,thecharac-

importantsincestudiesby,e.g.,Keim[19]andReinganum[26]containresults

thatsuggestthatthewinner-loreffectmaysimplybeanotherinstanceofthe

well-knownsizeand/orturn-of-the-yeareffects(forareview,eSchwert[31]).

Finally,theinterpretationofourresultsavidenceofinvestoroverreactionhas

reatleasttwoalternativeexplanations,bothinvolving

ethodologysimilartoourown,

VermaelenandVerstringereplicatethewinner-loranomalyfortheBelgian

gue,however,that"...this'overreaction'effectisa

rationalmarketrespontoriskchanges..."[33,p.13].Their"risk-change

hypothesis,"alsoprentedbyChan[8,9],statesthatadecline(increa)in

stockpricesleadstoanincrea(decline)indebt-equityratiosandriskas

cently,FamaandFrench[13]againreport

significantnegativerialcorrelationinstockreturns,explaining25to45percent

heauthorsagreethattheir

findingsareconsistentwithourown(aswellaswithothermodelsinwhich

pricestakelongswingsawayfromfundamentalvalues,e.g.,Keynes[21]or

Shiller[32]),theysuggestthatmean-revertingfactorriskpremiamaybethe

cau,citing(amongotherstudies)theworkofKeimandStambaugh[20].

Inanefforttore-evaluatetheoverreactionhypothesis,thispaperdiscuss

newempiricalfindingsthatarerelevanttothewinner-lor,size,andJanuary

effects,aswellastothebroaderissuesoftime-varyingriskpremiaandmarket

nI,badonCRSPdata,extendsourearlierresultsandfurther

discusstheasonalityinthereturnbehaviorofextremewinnerandlor

tion,weaddresstheissueofwhetherthewinner-loranomaly

n

IIusaccountingnumbersdrawnfromCOMPUSTATtocharacterizethe

extremeportfoliosandtocompareandcontrastthesmallfirmandwinner-lor

ctionalsomatchearningsmovementstotheobrvedreturn

ricesmaybethoughtofasdiscountedexpectedearnings,

p=E(c)/p,mary

,weexamine

undthat,atleastfortheextremeportfolios,priorstock

t

thatearningsreversalsareaccompaniedbycontemporaneousstockpricerever-

salssuggeststhatthemarketfailstorecognizethetendencytowardsmean

reversioninextremeearningsnumbers.

Whilewestressoverreaction,weconcedethatpartofthemeanreversionin

stockpricesmayalsobeduetotime-varyingequilibriumexpectedreturns,and

,the

andothervalidargumentsarenotmutuallyexclusivewithoverreactionbias.

However,ourprincipalmotivationremainsaconcernwiththemicrofoundations

eltoGeorgeAkerlof'sapproachtoeconomictheory,we

aim"toexploretheconquencesofnewbehavioralassumptions"[1,p.1].

InvestorOverreaction559

ner-LorEffect,StockMarketSeasonality,andRisk

Perhapsthemostcuriousresultinourpreviouspaperisthestrongasonality

portionoftheexcess

RSPmonthlyreturndata,wenowexplore

somequestionsmotivatedbytheearlierfindingsandotherrearchwhich

linkstheunusualJanuaryreturnithertothetaxcode(e.g..Branch[4],Chan

[7],Dyl[12],Reinganum[26],Roll[28]andRozeff[30])ortoasonalityinthe

risk-returnrelationship(e.g.,KeimandStambaugh[20],andRogalskiandTinic

[27]).First,arethereanyasonalpatternsinreturnsduringtheformation

period?Next,withintheextremeportfolios,dosystematicpricereversalsoccur

throughouttheyear,ordotheyoccuronlyinJanuary?Finally,aretheJanuary

correctionsdrivenbyrecentsharepricemovements(say,overthelastfew

months),orbymorelong-termfactors?Usingthesamedatat,wealso

investigatethehypothesisthatthewinner-loreffectcanbeexplainedby

changesinCAPM-betas(eChan[9],andVermaelenandVerstringe[33]).

Beforeturningtotheresults,webriefiydescribetheempiricalmethodsudin

thisction.

calMethods

rystock;ontheCRSPMonthlyReturnTape(1926-1982)withat

least61monthsofreturndata(withoutanymissingvaluesinbetween,and

startinginJanuary,1926),weestimate120monthlymarket-adjustedexcess

returns,uy,=Rjt—Rmt,coveringbothafive-yearportfolio"formation"anda

five-year"test"period.^Anequal-weightedaverageofthemonthlyreturnsonall

stockslistedontheNYSEisudforR^cedureisrepeated48times

foreachoftheten-yearperiodsstartinginJanuary1926,January1927up

eyears,thevarioussamplesgrowfrom381to1245

stocks.

rystockineachsample,wefindthecumulativeexcessreturnCUy

hat,theCUy'sarerankedand

50stockswiththehighestCUj'sareassignedtoa

winnerportfolioW;the50stockswiththelowestCU/

total,thereare48winnerand48lorportfolioachcontaining50curities.

eofthedescriptivestatisticsandregressiontestsbelow,wecombine

the48winnerand48lorportfoliosintotwo"master"samples,oneofwinners

wo"master"sampleachcontain2400obrvations.

Forthecorrelationtestsbelow,newtsofportfoliosareformedasfollows.

Forthefivequencesofallnon-overlappingformationperiodsthatstartin

January1926,January1927January1930,thesinglemostextremewinners

cksthat

^Ifsomeoralloftherawreturndatabeyondmonth#61aremissing,theexcessreturnsare

hich

whichdropoutduringthetestperiod,

weuthelastentryontheCRSPfiletocomputethefinalreturn,whichcanbe-1iftheshares

tnote4ofourpreviouspaper.

560TheJournalofFinance

cameincondintheformationperiodsformgroupW2,have,for

eachoffiveexperiments,50ofwhatwecall"rankportfolios"forwinners,Wi,...,

W50,and50"rankportfolios"l,

ingonthenumberof

periods,eachrankportfoliocontainsamaximumofeithernineortenstocks.

Averageandcumulativeaverageexcessreturnsarefoundforeachrankport-

erareturnismissing,theaverageexcessreturnforthatportfolio

ulationperiodsinclude

theformationperiod,tsinvolve

simple,partialandSpearmanrankcorrelationsbetweenrelevantpairsofaverage

returnperformancescoveringdifferent(sub-)periods.

Returns,SeasonalityandTaxes

Itisimmediatelyapparentfromtheplotsoftestperiodreturnsinourprevious

paper([11],Figures1,2and3)thattheycontainanimportantasonalcompo-

inethisasonalityingreaterdetail,andtoewhetherthe

prentsaverageexcess

returnarnedbyboththewinnerandlor"master"portfoliosforvarious

suhperiods.^Duringthetestperiod,lorarnvirtuallyalloftheirexcessreturns

inJanuary(withthelastthreemonthsoftheyearoffttinganygainsbetween

FebruaryandSeptemher).Winnerexcessreturns,thoughsmaller(inabsolute

terms)thanforlors,ormation

period,theJanuaryexcessreturnsforwinnersareaboutdoublethatofthe

ers,bythelasttwoyearsofthe

formationperiod,theasonalpatternstartstoremblethatofthetestperiod:

positiveJanuaryreturnsandthelargerthanusualnegativereturnstowardsthe

endoftheyear.

Oneimplicationoftheoverreactionhypothesisisatendency(whichBrown

andHarlow[6]callthe"magnitudeeffect")forthemostextremeinitialwinners

lier

paperprovidedsupportingevidencebycomparingthetestperiodperformanceof

gerthe

formationperiod,thegreaterboththeinitialpricemovementsandthesubquent

ndHarlow'sstudyofthemagnitudeeffectusamorestringent

ndthattheeffectholdvenwithinportfoliosofextremewinners

kportfolios,describedintheempiricalmethodsctionabove,

tion,theyallowusto

focusontheasonalityofthemagnitudeeffect.

WestartbycalculatingSpearmanrankcorrelationsbetweencumulativeav-

erageexcessreturns(CAR)fortheentireformationperiodandthefirstone,

two,...,ers,consistentwithoverreaction,

theaveragecorrelationsare-.14,-.28,-.22,-.29and-.ebivariate

regression(usingall250lorrankportfolios)ofCARfortheformationperiod

onCARforthetestperiodyieldsaninterceptof—.205(t-statistic:—2.55)anda

'TheaveragereturnsinTableIarebadon48replicationswiththetestperiodsstartingin

Januaryofallyearsbetween1931-1978,whileourpreviouspaperudtheyears1933-1978.

InvestorOverreaction

561

I

(2eg

tl

S

e

.s

CD(NCO

(N(NCO

III

-^O-H

(NINC<

III

I

--

r-

CNIN

III

COCOCO

INC>iIN

ICCOp

•»)"iriCO

III

I..»

.oa

2g

ll

1

p

CO

o

d

COr

00r

INr

in

-1-

I-H-H

r

to

CO

l>

1—1

COr

COT

COr

CO

+

1-H+

?

1

CO

CO

CO

r

I-Hr

rHr

r

in

+

+

'I'

562TheJournalofFinance

slopeof—.421(—6.67).Thei?-square(adjustedfordegreesoffreedom)is.149.

Ontheotherhand,forwinners,

oftheequivalentSpearmanrankcorrelationsaresignificantlydifferentfrom

zero,andneitheristheslope-coefficientofthehivariateregression.

r

correlationtestsindicatethat,exceptinJanuary,winnerandlorexcessreturns

areunrelatedtoformationperiodCAR.''Thisraisthequestiontowhatextent

theexceptionalJanuaryreturnsoflong-termwinnersandlorsareactually

drivenbyperformanceovertheimmediatelyprecedingmonths,possiblyrefiect-

ingtax-motivatedtrading.

TableIIshowsOLSregressionswiththeexcessreturninthefirstJanuaryof

dictorvariablesmeasurerelative

performanceover,respectively,[1]thepriorDecember,[2]thelastfivemonths

(JulythroughNovember)priortoDecember,and[3]theremaining4^/2yearsof

theformationperiod.^atethattheJanuaryexcess

lors,thereversalsmayrefiecttax-lossllingpressure(ee.g..Branch[4],

Reinganum[26]andRoll[28]).Forwinners,theshort-runreversalsareconsist-

entwithacapitalgainstax"lock-in"earenotawareofanyother

studydocumentingturn-of-the-yearreturnreversalsforwinners,Dyl[12]and

LakonishokandSmidt[22]reportunusuallylowtradingvolumeforthestocks

inDecemberandunusuallyhighvolumeinJanuary,factsalsoconsistentwitha

lock-ineffect.

EquationsA.3andB.3furthershowastatisticallysignificantlinkbetween

ers,thelong-

ere

prence,thelong-termeffectcontradictsrationaltax-lossllingasanexpla-

nationoftheJanuaryasonal(ealsoChan[7]).Forwinners,surprisingly,

rvationisinconfiictwiththeoverreac-

tionhypothesis.^

'*Usingfivetimes100rankportfolios,wecomputeSpearmanrank,simpleandpartialcorrelations

(controllingforexcessreturnsduringthelastDecemberoftheformationperiod)betweenformation

periodCARandsubperiodCAR'sforJanuary,FebruarythroughSeptember,andOctoberthrough

forJanuary,ers,theJanuary

ners,theyarepositiveforthefirstJanuaryofthetest

rregressiontests(badonthetwo

"master"samples)indicatethat,eventhoughtheii-squaresaresmall(varyingbetween.018and

.120),Januarytestperiodexcessreturnsofbothwinnersandlorsarereliablyrelatedtoreturn

movementsinadjacentJanuaries.

*Ishowsonlyresultsbadonthetwo"master"

curitiesineachsamplearenotindependentlylectedsincetheformationperiodsarepartially

r,testsusingfivesubsamplesthatovercomethisproblemdonotaffectour

conclusions.

°OLS-regressionswithlorJanuaryexcessreturnsforlatertestyearsasthedependentvariable

mple,forthe5thJanuary,thecoefficientontheexcessreturn

forthepreviousDecember(i.e.,theDecemberofthe4thtestyear)is-.462(t-statistic:-12.96),while

thecoefficientontheformationperiodcumulativeresidualequals-.066(t-statistic:-6.71)!For

winners,theshort-termreversalspersist(e.g.,forthe5thJanuary,therelevantcoefficientis—.169

(t-statistic:-7.60))butthe(positive)long-termeffectdisappearsbeyondthe2ndJanuaryofthetest

period.

InvestorOverreaction

563

o

1

2

•§

COI

COo

I5^^I22

CO.-^

I-HQ5

00p

CO>a

n

Ti-

ed

pppp

l'COl'COICDI*00

'I'I'I'I

f^^jQT)t^^^GOOOt^

C-;C3;pCNC-;®pC0

I'2T^I'STS

IIII

'"T

•rH•00frH

CN

<:

CO

<

(N

PQ

CO

CQ

PQ.

•Sis

2I

o

o

IN

ar

e

g1

'c

o

m

s

ar

e

tic

S1

N

ot

e:

1

si

tiv

e

in

a

.2

1

z

all

"S

I

ht

ed

1-

w

eig

e

eq

ua

o

"a

1

eq

u

Q

ia

bI

a

>

a

s

>.

Oj

.5

1

I

u

th

e

"^a

IM

Q

ab

le

re

di

ct

c

Oi

otl

ze

ro

.a

io

d(

3

Qa

564TheJournalofFinance

rto

compareitwiththeeconomicweightoftheshort-termeffects,wecomputethe

"componentcontribution"ofeachpredictorvariable,i.e.,theproductofits

ers(equationB.3),theaverage

Januaryexcessreturnof7.9percentcanbedecompodintoanunexplained

intercept(-2.2percent),2.9percentthatisduetoashort-termreversalfrom

thepreviousDecember,1.7percentduetoreversalsfromthepreviousJuly

throughNovember,ners

(equationA.3),theaverageJanuaryexcessreturnequals—1.8percentandthe

long-termcomponentisapositive3.5percent.

Earlierwork(e.g.,Rozeff[30])suggeststhatthesizeoftheJanuaryexcess

returnsdependsontheperformanceofthemarketasawholeovertheprevious

year(orprevioussixmonths).Inordertoewhetherthisappliestoour

portfolios,interceptandslopedummyvariablesareaddedtotheOLS-regressions

erceptdummyequalsoneifR^t,annuallycompounded,is

slopedummyisdefinedastheinterceptdummymultipliedhytheexcessreturn

onsA.2,A.4,B.2andB.4showthat,onaverage,following

downyears,long-termwinnersperformworandlong-termlorsbetterthan

ers,theslope

dummyindicatesthatalsotheDecember-Januaryreversalsaresignificantly

,thefindingsare

consistentwithtaxexplanationsoftheunusualJanuaryreturns.

ReturnsandChangingRisk

Inourpreviouspaper,weinvestigatedwhethertheexcessreturnstowinner

as

lessofthelengthofthe

formationperiod(varyingbetweenonetofiveyears),thebetaforthelor

efore

concludedthat,withintheCAPMframework,thereportedmarket-adjusted

excessreturnswereconrvativeestimatesofthe"true"risk-adjustedexcess

r,Chan[8,9]andVermaelenandVerstringe[33]arguethatthe

usualprocedureofestimatinghetasoverapriorperiodisinappropriateifhetas

nersandlors,anegativecorrelation

betweenriskandmarketvalueisplausiblebecauofchangesinfinancial

li-

cationisthatthewinner-loreffectmaydisappeariftheriskestimatesare

obtainedduringthetestperiod.

Totestthishypothesis,weconstruct"arbitrage"portfoliosthatfinancethe

purchaoflorshyllingwinnersshort,andweregress(usingOLS)the

annualtestperiodreturnsRAt=Ru~Rwt,onthemarketriskpremium,Rmt~

Rft,i.e.,RAI=aA+PA{Rmt—Rft)+tAt-Ashefore,Rmtisthe(annuallycompounded)

akenfrom

IhhotsonandSinquefield[18],anditismeasuredasthe(annuallycompounded)

stantterma^t

InvestorOverreaction565

isthewell-knownJennperformanceindex;0Aisanestimateofthedifference

equationisalsoestimatedparatelyforthewinnersandlorswith,respectively,

Rwt—RftandRu—onalregressionsinclude

y,allthe

previousregressionsarerepeatedwithJanuaryandFebruarythroughDecember

returnsasthedependentvariables.

atesthat,duringthetest

period,theestimatedbetaforthelorportfolioisindeed.220greaterthanthe

r,thisdifferenceinriskisinsufficienttoexplainthereturn

onthearbitrageportfoliosincea^,at5.9percent,,

thissimpletestoftherisk-changehypothesisfailstoexplainthewinner-lor

oofinterestbecau,unlikeourpreviousresults,it

indicatesthat,onaCAPMrisk-adjustedbasis,thewinnerportfoliohassignifi-

fficientsonthedummyvariablesreveal

thefamiliarpatternofdecliningexcessreturnsthroughthetestperiod.

Usingalternativemethodswhichallowfortime-varyingbetas,Chan[9]finds

atestperiodbetaofabout0.1forthearbitrageportfolio,butobtainsanalpha

haandbetaareaveragecoefficients

obtainedfromparateequationstimated(usingmonthlydata)foreachof18

adilyadmitsthatthesmall

differenceinbetas"wouldappeartohavenochancetoexplaintheaverage

monthlyreturnof0.586percent"([9],p.12).Instead,heexplainsthecombined

obrvationsofasmallalpha,asmallbeta,andalargereturnbypositive

argumentisthatboththebetasandtheexpectedmarketriskpremiummaybe

respondingtocommonstatevariables.

Tofurtherinvestigatethisissue,werecalculatetheregressionsinTableIIIin

awaythatpermitstwobetastobeestimated,oneforperiodswhenthestock

marketisrising,adummyvariableD

whichequalsoneifR^t>0andzeroifR^t

arbitrageportfolioisnowR^t=a^+0Au(.Rmt-Rft)D-¥0AdiRm-Rft)(l-D)+

tAi,withsimilarequationsforthewinnerandlorportfolios.

AsshowninTableIV,oncebetasareallowedtovarywiththemarket,the

esults,whichconfirmChan's

findings,,whilethe

averageCAPM-betaofthearbitrageportfoliowaarlierestimatedtobe.220,

theportfolioactuallyhasapositivebetawhenthemarketgoesup,andanegative

rwords,thearbitrageportfoliodoeswellinbothup

winnerportfolio,lor

portfolio,ngmarkets,thelorshavea

tendencytogainmorethanthewinners,whileinfallingmarkets,thewinners

onsA.2,B.2andC.2revealasimilar

rast,duringtherestofthe

year,theresultsaremutedandtheloralphaissignificantlynegative.

Therisk-changehypothesisclaimsthatduringthetestperiodthelorsare

566

TheJournalofFinance

.2

s

rH^^00.-^

COt»l>00

pC-;p

t>

'I'I

CM,-^CO^-v

8pp?2

I

I

a

a

P^-,TO^~-g

CMTOCMTOS

p•<*p

in051

rr

I

^.—^

00^^

(NCO

l-H

P

O•*pTC

HO?CM00^

p

X'T

CM?J

IMC-

CO

»-H

CMi00

CO

in

rH

CM

00

TO-^in^~.

p53pS

CMC^CM

f-;pHt>

m'CO

TO

TO--.

O•<»•»-i

O

^-.

P^^

TOO^TOOS

£iIT

o

O

1

•e

<

<

CM

PQ

TO

CQ

InvestorOverreaction

567

I

s

I

Q

I

XIT

1IT

CO00

05l>

CD

CN

'T

PQ

So

(NIN

r;00

CO

tao

'•?

PQ

00^-.

CN

o

aIo

CNdCOd

d

2fe:^gPU75B

568TheJournalofFinance

TableIV

OLS-RegressionsofAnnual,January,andFebruarythroughDecember

PortfolioRiskPremiaontheMarketRiskPremiuminUpandDownMarkets

Regression

IndependentVariables

Intercept-R,)D(fl™-fl/)(l-D)-sq.

A:ArbitragePortfolio

AnnualReturns

A.I

A.2

A.3

B:WinnerPortfolio

B.I

B.2

B.3

C:LorPortfolio

C.I

C.2

C.3

-.005

(-.24)

.008

(.83)

-.032

(-1.85)

-.015

(-1.43)

.004

(1.04)

-.011

(-1.24)

-.020

(-1.29)

.012

(1.73)

-.043

(-3.73)

.395

(6.43)

.748

(8.08)

-.323

(-2.36)

JanuaryReturns

-.848

(-2.33)

February-DecemberReturns

.376

(6.24)

.993

(33.77)

.854

(20.39)

-.176

(-1.60)

AnnualReturns

1.198

(18.25)

JanuaryReturns

1.439

(8.73)

February-DecemberReturns

1.007

(32.87)

1.388

(31.80)

1.602

(23.15)

1.168

(20.97)

AnnualReturns

.875

(8.98)

JanuaryReturns

.591

(2.17)

February-DecemberReturns

1.384

(34.54)

.992

(13.63)

.142

.215

.138

.908

.763

.906

.868

.746

.892

Note:mmyvariablewhichequalsoneifthereturnonthemarketportfolio

(asmeasuredbyanequally-weightedindexofNYSEstocks)rootherwi.

InvestorOverreaction569

riskierthanthewinners,andthatthisdifferenceinriskisresponsibleforthe

sk

ismeasuredbyCAPM-betas,theriskdisparityisinsufficienttoaccountforthe

enthebetasareallowedtovarywiththelevelofthemarket

rmore,thetime-

varying"split"ary,forexample,

theCAPM-betasarehigherforthelorsthanforthewinners(1.469vs..931).

Yet,itemsoddtosaythataportfoliowithabetaof1.602inupmarketsand

.591indownmarketsisriskierthanonewithupanddownbetasof.854and

1.439.'

ner-LorEffect,theSizeEffect,andOverreactionto

Earnings

estionsremainthat

ortantissueiswhetherthewinner-lor

ingfirmsparticularly

small?Aresmallfirmsforthemostpartlors?Totheextentthatthesmall

firmeffect(wheresizeismeasuredbymarketvalueofequity)isalosingfirm

effect,arethereanyadditionalexcessreturnsgenuinelyattributabletocompany

sizewhensizeismeasuredinawaythatisindependentofshort-termprice

movements?Canweuaccountingdatatodistinguishtheoverreactionhypoth-

esisfromotherexplanationsofthewinner-loreffect?Toanswertheand

,webeginbydescribing

ourempiricalmethods.

calMethods

plesarechonfromthemainanddelisted(rearch)filesofthe

AnnualIndustrialCOMPUSTATtapesfortheperiodbetween1965and1984.

Inordertobelected,acompanyneedscompletefive-yearrecordspriorto(and

including)theportfolioformationyears1969,1971,1973,1975,1977and1979

forthefollowingannualdataitems:#6(TotalAsts;LiabilitiesandSharehold-

ers'Equity),#12(Sales),#18(IncomeBeforeExtraordinaryItemsandDiscon-

tinuedOperations),#24(ClosingPricefortheCalendarYear),#25(Common

SharesOutstanding),#26(DividendsPerSharebyEx-Date),#27(Cumulative

AdjustmentFactor),#58(PrimaryEarningsPerShare,ExcludingExtraordinary

ItemsandDiscountedOperations)and#60(CommonEquity).Also,foreachof

thefiveyearspriortoandincludingtheformationyear,thecompanymusthave

tion,itmustbelistedeitherontheNYSEor

y,firmsthatarepartoftheS&P40FinancialIndexare

sixsampleslistedbyformationdate,thenumberofcompanies

'RogalskiandTinicuargumentssimilartoChan'

showthattheCAPM-betasofsmallfirmsarehigherinJanuarythaninothermonthsandthat,

therefore,"the'abnormal'returnsonthestocksmaynot,afterall,beabnormal"([27],p.63)if

r,giventhatsomanysmallfirmstirelors,wespeculate

thatsmallfirmsalsohavehighJanuarybetasinupmarketsandlowbetasindownmarkets,aresult

whichwouldleavetheabnormalreturnsabnormal.

570TheJournalofFinance

(andthenumberofcompanieslistedontheNYSE)are:1969:1015(789);1971:

1106(842);1973:1262(931);1975:1336(996);1977:1339(975);and1979:1263

(939).

hfirm;,annualrawreturnsRjtandexcessreturnsUjtarecomputed

fromCOMPUSTATdata(withappropriateadjustmentsmadeforstocksplits,

etc.)forallyearsbetweent-3andt+4,withtreprentingthefinalyearof

essreturnsaremarket-adjusted,Ujt=Rjt-Rmt,

wherethemarketreturnRmtistimatedhycompounding(over12months)a

monthlyequal-weightedNYSEindextakenfromCRSP.

ampleisorderedhyeachofthefollowingfourrankingvariables:(a)

cumulativeexcessreturn(CU;)overafour-yearformationperiodbetweenthe

endofyeart-4andtheendofyeart;(h)marketvalueofequity(MV)at(the

endofyear)t;(c)marketvalueofequitydividedhybookvalueofequity(MV/

BV)att;(d)companyastsatt(COMPUSTATitem#6).

hsampleandforeachrankingvariable,withminoradjustments,

quintile,decile,and"ventile"(20)eandcumulative

averageexcessreturns(CAR)arecalculatedforthefouryearsbetweent-3and

t,andforthefouryearsbetweent+1andt+uently,the(cumulative)

averageexcessreturnsareaveragedonceagain,eitheracrossthesixsamples,or

acrosstwotimesthreesamples(formationyears1969,1973and1977,vs.

formationyears1971,1975and1979).WithCUjasrankingvariahle,thetwo

timesthreesamplesreprenttrulyindependentohrvationssincetheformation

periodsarenon-overlapping.

Forthesakeofbrevity,thetahleshelowreportourfindingsprimarilyforthe

r,thestatisticaltestsaredoneonthebasisofventile

ordecileportfolios.

hrankingmethod,portfolioaveragesandmediansarealsocomputed

forothervariablesofinterest,mostimportantly,companyincomeandearnings

pershare(EPS).TheEPS-numbersfordifferentyearsareadjustedforstock

splits,stockdividends,etc.;asaresult,theyremainstrictlycomparablethrough

rtoimprovetheircross-ctionalcomparability,theyarescaledhy

theclosingstockpriceattheendofyeart—4.^

rtomakeportfoliocomparisonsoftime-riesmovementsinany

givenvariahleXeasier,theportfolioaveragesXpareindexedhyttingthem

equalto1.0inahayear(eithertOTt-4).Thus,theohrvationsmayhe

reprentedbyX%=(Xpt/Xpb)whereXpbistheportfolioaverageintheha

emethodtodetrendX*t(or,inotherwords,toremovethemarket-

widecomponentinitsmovementthroughtime)startsbyrepeatingtheabove

,ifX^tstandsfor

thetotalsampleaverageatt,Xft=(Xst/Xsb).Thenextstepistofindthe

detrendedX^tbydividingX'pthyX*VIIandVIIIhelowlistXft

multipliedby100.

*Whenevertherearemissingdata,theportfolioaveragesandmediansarecomputedoverthe

rethreesourcesofmissingdata:[1]fiscalyearchanges;[2]removal

ofthecompanyfromtheCOMPUSTATrearchfiles;[3]missingobrvationsinotherwicomplete

inca[3],thestockisremovedfromallportfolioaveragesatthesamepoint

intime.

InvestorOverreaction571

an's[15]two-wayanalysisofvariancebyranksisudtotest

nonparametricallywhether,foranyrankingmethod,thereisatendencyforthe

annualexcessreturnsofoneportfoliotoexceedortobesmallerthanthesame-

plecomparisonprocedurespecifically

aareaverage

excessreturnsduringtheformation£mdtestperiodsfortwentyportfoliosof

tsareruntwice:oncefortheaverageexcessreturnscomputed

with1969,1973and1977astheformationyears,andagainwith1971,1975and

twotimesfour(yearst—S...t,t+1...

t+4)independentsamplesandtwenty"treatments"(portfolios).Thetest

statisticisdistributedapproximatelychi-squarewithnineteendegreesoffreedom.

's[25]nonparametrictestfororderedalternativesprovides

kswhether,foranyranking

method,thek"treatment"effectsareorderedinthefollowingway:ti<^2^•••

lternativehypothesisischangedtoti>^2>•••>t*,theteststatistic

gesamples,thestatisticisdistributedapproximately

ctcomputationalformulasforboththeFriedman

andPagetestscanbefoundin,e.g.,Daniel[10].

sComparingtheSizeandWinner-LorEffects

areplicationofouroriginalwinner-lorexperimentusing

bothNYSEandAMEXfirmslistedonCOMPUSTATfortheyears1966-1983.

Thetableshowsthatevenforquintileportfolios(whicharelesxtremethan

thedecilesorgroupsof50stocksudinourpreviousstudy)thelorshave

,the

Pagetestdoesnotallowustorejectthehypothesisthattherankingofexcess

returnsinthetestperiodistheinverofthe(forced)rankingduringthe

formationperiod(eTableVI).

howstheaverageandmedianmarketvaluesforeachquintile.

ItisinformativetocomparethefigureswiththoinpanelBwheremarket

valueofequity(theusualmeasureoffirmsize)istherankingmethod,andalso

withpanelD,msinboth

extremeCARquintilesaresmallerthanthointhemiddleportfolios,butthey

,themeanforbothquintilesiscomparabletothe

4thquintileoftheMVandcompanyastsrankings.(Similarresultsobtainfor

theaverageMVoftheextremedecilesandventiles.)Theaveragemarketvalue

forthesmallestquintilerankedbyMVisabout30timessmallerthantheaverage

risonoftherelevantaveragesand

mediansindicatesthat,whilethereissomeskewnessinthedistributions,it

,thewinner-loranomaly

cannotbeaccuratelydescribedasprimarilyasmallfirmphenomenon.'

"FamaandFrench[14]heCRSPmonthlyreturnfileofNYSE

firms,theystudywinnerandlorportfolioscontaining35stocksfor19non-overlappingthree-year

ketvalueofthelorportfolio

isonaverageinthe26thpercentile,whilethemarketvalueofthewinnersisinthe58thpercentile.

Thus,themostextremeNYSElorstendtobesomewhatsmallerthanaverage,butnotextremely

salsoconsiderablevariationfromoneexperimenttoanotherand,onoccasion,the

572TheJournalofFinance

>

CSI

a

O

CO3

en

>

Q

B2

£

o

I

TOrHC^pm

CMO>CM00CM

PPrHrHTO

CO1-HIOt>

COO>

OO1-41-H

00

COCM

t-CO

ceasCO(dd

cecd

c3

P

TO

QiO0)TO

3.l>rHTO

^rHrH

COCSCOCOcd

dsced

COO4-^IOC^

TjtOlOrH,-H

Ol1-HOO»-H'''r

umu

O

C

rit

er

io

n:

ki

ng

.8

07

1

l-H

.3

23

.0

03

,3

21

26

4

1--I

OlCO^Ut

TOrH

t-

o

OCO

TO3

lO•^

(NTH

CQeeCQ

GCG

l-HOiCO•^

I

oI

I

I

B

oI

I

COCOCOCOCO

ddddd

SCOCOOSCOCO

>.dddad

03QCQCQCQ

ddddd

II

rHC<1Pr-t00

r-l0000TOCM

i*ttO

rHCMCO'^

COO5

COCOCO

aac

CdCO

ad

COCOCO

add

COCO

dti

InvestorOverreaction

573

8O)OiQt^

TfCD55-^

»-

COCDC4

COC~O

csa00COCO

Gaaac

dCOCNO»CO

HCO*U5O

2I

qCOCOCOaceded

ICO

pr

COCN

_l>CO

rHCOt-

CNO^CDC^CD

rH00COCOCO

OC-p*l>

COOSO5rHO5

CNCOTjiCOTf

COLOO

OCOt^

rHrHCN

COIO

CDOi

CNCN

COCOCOC^t*

COC^Oi"^

C30

r-tr~.ir^C^r^

aCO

cq'

COaGaa

COCOCOCOCOddddd

OirHCO05

COCOCOCN

•-HrHCOOiCO

CNCOINOrH

COrH

(MCOs§

l>"^CO1-tlO

-HlOTj"COt-l

rH^GO

rHCNCNIN

2

&I

d

oI

O

aCOCO

ccj

COaatiap

II

t>00COOO

rH04«*COrH

IN04rHp

.-I

'''''

aCISaaCO

ddddd

COccjacciCO

aaaaa

rH(NCO""I*lO

2

=e:g

.2

a>>CO^^*^

Er-=•

fc.5

574TheJournalofFinance

TableVI

FriedmanTwo-WayAnalysisOfVarianceByRanksandPage's

TestForOrderedAlternatives

RankingVariable

A:FormationPeriod

CAR(t-3,t)

MV

MV/BV

Asts

B:TestPeriod

CAR(t-3,t)

MV

MV/BV

Asts

Friedman

chi-square

*

*

8.30

29.16

67.60(X)

65.97(X)

8.90

11.91

41.31(X)

15.67

46.76(X)

62.46(X)

34.10(X)

37.86(X)

31.66(X)

46.50(X)

Friedman

multiple

comparison

procedure

*

-8.0

-17.0

-32.0(-I-)

-30.0(-1-)

3.0

-1.0

23.0

10.0

33.0{+)

34.0(-I-)

26.0(+)

29.0(+)

22.0

29.0(-I-)

•

Page

2-stati8tic

-1.08

-2.39(-)

-8.06(-)

-8.01(-)

1.21

.79

5.63(-)

3.41(-)

6.01(-)

7.67(-)

5.04(-)

5.48(-)

4.79(-)

6.25(-)

Notes:[1]Thetest-statisticsinthetop(bottom)rowsarebadonthereplications

withformationyears1969,1973and1977(1971,1975and1979).Entriesthatare

significantbyconstruction(theformationperiodreturnsforportfoliosrankedby

cumulativeaverageresiduals)aremarkedwithanasterisk.[2]Friedman'stest-

statisticisdistributedchi-squarewithk-ldegreesoffreedomwherek,thenumber

ofportfolios,lhypothesiscanberejectedatthe5(10)percent

levelofsignificanceifthetest-statisticisgreaterthanorequalto30.14(27.20).

Entriessignificantatthe5percentlevelaremarkedwithX.[3]Thetestsusing

Friedman'smultiplecomparisonprocedurearebadondecileportfolios,comparing

ticalvaluesforthistestare25.3(p=.05),

23.6(p=.10),22.7(p=.15)and21.9(p=.20).Entriessignificantatthe5percent

levelaremarkedwith+.[4]ThePagez-statisticisdistributedapproximatelyasthe

slargerthan

2.0aremarkedwith—.

Incontrast,itemsmoreapttocharacterizethewinner-loreffectasan

ditionalmeasureofunder-(orover-)

valuation(similartoTohin'sQ)istheratioofmarketvaluetohookvalueof

equity(MV/BV).FromtheMV/BVcolumninTahleV.A,oneesthatthe

rankinghyCARcoincideswiththerankingofMV/ilarityofthetwo

udes

AMEXfirms,coversonlytheperiod1965-84,r

quintileportfolios(ratherthan35stocks).Evenso,

thesubtofperiodsstudiedbyFamaandFrenchwhichoverlapwithourCOMPUSTATsample

(1965-1982),theaveragemarketvalueoftheirlorsis$164millionwhichislargerthanthemedian

bermaybeufullycomparedwiththeaveragemarketvalue,$234

million,ofourmostextremelorventile(containing,onaverage,61stocks).

InvestorOverreaction575

rankingmethodscanalsobejudgedbycomparingpanelsAandCwhereMV/

thattheCAR'sfortheextremeMV/BV

etestinTable

returnsforportfolios

formedona"book/price"strategyhavebeenreportedearlierbyRonberg,Reid,

andLanstein[29].

Whilethelosingfirmeffectcannotbecharacterizedasasmallfirmeffect,one

maystillask:Towhatextentisthesmallfirmeffectalosingfirmeffect?^"Table

VIIprovidesindexed,detrendedmeasuresofMVforportfoliosformedonthe

thatthecompaniesinthesmallestquintile

(rankedbyMV)haverecentlyshrunkinsizerelativetootherfirmsinthe

sample."InfacttheV-shapedpatternissimilartothatenfortheextreme

portfoliosrankedbyCARandbyMV/structivetocomparetheMV

etsthereisnotrendinmarketvalueduring

isamorepermanentmeasureoffirm

sizethanMV.^^

Sincethesizeeffect,asmeasuredbyMV,ispartlyalosingfirmeffect,itis

interestingtoewhethertherearestillexcessreturnstosmallfirmsifanother

measureofsizesuchasAsts(orSales)esV(panelD)andVI,

weshowthat,infact,excessreturnsarestillsignificantlyrelatedtosize.(Similar

results,notreportedhere,areobtainedifSales(COMPUSTATitem#12)isud

astherankingcriterion).

ReturnsandOverreactiontoEarnings

Incontrasttotherisk-changeandtime-varyingdiscountrateexplanationsof

thewinner-loreffect,oneinterpretationoftheoverreactionhypothesisstress

misperceptionsoffuturecashflowsforextremewinnersandlors.^^The

hypothesintailsthatinvestors,onaverage,haveanexcessivelyshort-term

orientation:Theyfocusontherecentpastanddonotlookbeyondtheimmediate

icationofthehypothesisisthatthereshouldbeaclocorre-

spondencebetweenstockreturnsandshort-termchangesintheearningsoutlook.

Ofcour,ifearningsweretofollowarandomwalk(eveninthetailsofthecross

ctionoffirms),thenmyopicforecastscouldcoincidewithrationalexpectations

(intheabnceofotherinformation).However,ifearningsaremean-reverting

inthetails,assuggestedbye.g..BrooksandBuckmaster[5],thenstockprices

'"PreviousrearchbyReinganum[26,Table1]indicatesthatthesmallestMVdecilehasa

disproportionatenumberofpriorshort-termlors,andthatamongthesmallfirms,thelorsdo

oChan[8,Table1].

"Notethat()wearedetrendingrelativetothewholesample

population,whiletheCAR'sshowninTableVwerecalculatedwithrespecttoaNYSEequal-

dexislikelytounderestimatetheannualreturnstoourCOMPUSTAT

samplessincetheyincludeabout26%emoderatefallinreturnseninthe

inconsistentwithTableVII.

*^Inaddition,usingAststomeasurefirmsizeavoids'anyconfoundingeffectintroducedby

changesinthefinancialstructureofafirm(suchasacorporationrepurchasingitssharesandissuing

debt).

'^orsmightbeoverly

nsitivetoperceivedrisks,atively,someinves-

tors'decisionsmightbeinfiuencedbytemporaryfads,aspropodbyShiller[32].

576TheJournalofFinance

I

en

I

I

>

I

ItU3V

B°C

COi-HOO

SQOOl©CO^C^O

1-H00OOiOOlO

88888888

>I

I

I

O'^

CO^^II

*a

0)CQS

Is

InvestorOverreaction577

infiuencedbymyopicforecastswillshowmeanreversionaarningsrealizations

ore,paradoxically,ex-

tremestockpriceincreasanddecreasshouldbepredictiveofsubquent

patternisnotobrved,thenatleastthissimpleform

oftheoverreactionhypothesiscanberejected.

TableVIIIshowsaverageandmedianearningspershare,normalizedbyshare

priceattheendofyeart-4,detrended,andindexedtobeequalto100atthe

ultsfortheportfoliosformedbyCARare

nnersandlorsshowthe

predictedreversalpattern."'^*ThesamepatternisobrvedfortheMV/BV

rankingcriterion,whichisanotherproxyformarketpricedeviationsfrom

riguingaspectoftheresultsisthatthereversalof

fersone

nomalous

pricebehaviorisdrivenbyearningssurpris,thenthereturnspatternshould

besimilartotheearningspattern.^^

Incontrast,bothsizemeasures,MVandAsts,showdistinctlydifferent

irms,byeithermeasure,showfasterearningsgrowththanlarge

ggeststhatone

possibleexplanationforthesizeeffectisafailurebythemarkettorecognizethe

smallfirms'dotherrelatedhypothesare

investigatedbyGivolyandLakonishok[16],butarenotpursuedanyfurther

here.

yandConclusions

Theprincipalfindingsofthisstudyare:

returnsforlorsinthetestperiod(andparticularlyinJanuary)are

"AcomparisonoftheaverageandmedianEPSmakesitclearthattheaveragesaresomewhat

inaryworksuggeststhatthereissimilarcross-ctionalskewnessinthe

binomialtestsfurther

indicatethat,foramajorityoftestperiodsstartingeachyearbetween1970and1980,thepercentage

offirmsinthelordecileportfoliothatexperienceabove-averageearningsgrowthissignificantly

largerthantheequivalentpercentageinthewinnerdecile.

'*Sincethesamplesarelectedfromboththemainanddelisted(rearch)filesofCOMPUSTAT,

theydonotsufferfrom"expostlection"(survivorship)biasasitisnormallyunderstoodinthe

literature(e,e.g.,BanzandBreen[2]).However,forourpurpos,theearningspatternofcompanies

ewereunusualattritionintheextreme

quintileportfolios,theearningstrendsdocumentedinTableVIIwouldbebiadinadirectionthat

tthatthisisactuallyhappeninginanimportant

overthesixsamples,eachquintileportfoliocontains1452companiesintheformation

Rastherankingcriterion,thelorportfoliostillcontains1349(92.9%)companiesat

theendofyeart+otherquintiles,therelevantpercentagesare93.9,94.9,95.2,and93.3

(withtheextremewinnerportfoliolast).Whilethereasonsfordelistingmaydiffer,itisalsoimportant

tonoteatthispointthatthenumberoffirmsremovedfromCOMPUSTATbecauoffinancial

difficultyis"substantiallysmallerthanthenumberdelistedbecauofmergerorlimiteddistribution"

(McElreathandWiggins[23,p.74]).

'*,LambertandMoralsostudytherelationship

ncludethatpricesbehave"asifearningsare

perceivedtobedramaticallydifferentfromasimplerandomwalkprocess"([3],p.3).Inparticular,

themarketexpectventsthatcaupositiveornegativeearningssurpristoinduceadditional

indingsareconsistentwithoverreaction.

578

TheJournalofFinance

I

Q

I

2

CM

I

2

I

w

OH

(2

"^O1-tCO1-HO

t-HOl

•^CO00"^00"^

IOCO1-HCOCOO

COCDCOOlt*IO

§CDrHCOOlp00

J3t^C^COt^LOCD

03^HU5WDOl00CO

S)1-HCD"^COCO»O

.2OCOt^^jOt**

grH,-HO)

^CO001-JpCOCO

^1-H,-HOl

COCOIOCD00^

lOCOCO00-^cd

T-HC^t>OlCO1-H

1-HOl

^oqCOCOoqOl

1-H

pppppp"

8888885

rHrHrHrHrHrH|

rHCMTO00O5P"^

COCO

CM<»

CU5PCM

OOrHS-H

;

rH.*P

rHrHS

op

o

TOm

o>8^

3Oit>inp-^rH0»CMS»^P^PCMCM

OsOPPrHPp

(2

pp

88

OPPOPPPP

88188888888

^rHrr^^rH^rH^rHw^

1-HO43g

O>lO

r-Jr.J

toa>

pTO

o

TOU3PCMTOTOrH

C^TOrHCOTO*^CMO5

O)OOCOCO001^^CO

rHTOrHrH

BB

TO

II

i

TO

I

O

i

I

l

B

o

g

.3

InvestorOverreaction579

negativelyrelatedtobothlong-termandshort-termformationperiodperfor-

ners,Januaryexcessreturnsarenegativelyrelatedtotheexcess

returnsforthepriorDecember,possiblyrefiectingacapitalgainstax"lock-in"

effect.

ner-loreffectcannotbeattributedtochangesinriskasmeasured

he(zero-investment)arbitrageportfoliohasapositive

betaof.220,thisisinsufficienttoexplainitsaverageannual(testperiod)return

ranalysisshowsthatthearbitrageportfoliohasapositive

betainupmarketsandanegativebetaindownmarkets,acombinationthat

wouldnotgenerallybeconsideredparticularlyrisky.

ner-loreffectisnotprimarilyasizeeffect.

llfirmeffectispartlyalosingfirmeffect,butevenifthelosing

firmeffectisremoved(byusingamorepermanentmeasureofsize,suchas

asts)therearestillexcessreturnstosmallfirms.

ningsofwinningandlosingfirmsshowreversalpatternsthatare

consistentwithoverreaction.

Whatconclusionsemwarrantedatthistime?Manypuzzlesremain,espe-

nosatisfactory

explanationfortheJanuaryeffects,rationalorotherwi.

Onthemorepositiveside,thereversalpatterndocumentedbyourearlierpaper

hasnowbeenreplicatedbymanyotherrearchers(BrownandHarlow[6],Chan

[9],FamaandFrench[13,14],Howe[17]),andthereisplentyofevidencethat

stockreturnsvaryovertimeinamannerthatcanbepredictedbyvariablesthat

refiectlevelsofastprices(KeimandStambaugh[20]).

AccordingtoFamaandFrench[14,p.24],"Whetherpredictabilityrefiects

marketinefficiencyortime-varyingexpectedreturnsgeneratedbyrationalinves-

torbehavioris,andwillremain,anopenissue."Infact,theyconcludethatthe

ncanprogressbemade?Inourview,studentsof

financialmarketshavelittlechoicebuttobroadlyexaminetheevidenceonreturn

predictabilityandmakeajudgmentregardingwhichtypeofmodeloffersthe

mostparsimoniouxplanationofthefacts.

Thispaperhasmadecontributionstothistaskintwodifferentdirections.

First,twoplausibleexplanationsofthewinner-loreffect,namelythobad

onthesizeorriskcharacteristicsofthewinningandlosingfirms,havebeen

,the

paperprovidesnewevidenceconsistentwiththesimplebehavioralviewthat

investorsoverreacttoshort-term(i.e.,afewyears)-

tainly,withintheframeworkoftheefficientmarkethypothesis,itisdistinctly

puzzlingthatadramaticfall(ri)instockpricesispredictiveofasubquent

ri(fall)incompany-specificearnings.

Astotime-varyingdiscountrates,wecertainlyagreethattheymayplayarole

r,eveniftime-varyingdiscount

ratescanbeshowntoofferacoherentexplanationofthewinner-loreffectand

otheranomalies,forthe"marketrationalityhypothesis"(Merton[24])tobe

accepted,itwillalsobenecessarytodemonstratethatthefiuctuationsin

discountratescanbecharacterizedasrationalresponstoeconomicconditions

ratherthanemotionalshiftsinthemoodofmarketparticipants.

580TheJournalofFinance

REFERENCES

omicTheorist':CambridgeUniversityPress,

1984.

."Sample-DependentResultsUsingAccountingandMarket

Data:SomeEvidence."JournalofFinance(September1986),pp.779-793.

mBeaver,RichardLambert,andDaleMor."TheInformationContentofSecurity

Prices."JournalofAccountingandEconomics(2:1980),pp.3-28.

nch."ATaxLossTradingRule."JournalofBusiness(April1977),pp.198-207.

ster."FurtherEvidenceoftheTimeSeriesPropertiesof

AccountingIncome."JournalofFinance(December1976),pp.1359-1373.

."AsssingtheMagnitudeandIntensityofStockMarket

Overreaction."JournalofPortfolioManagement(forthcoming).

."CanTax-LossSellingExplaintheJanuarySeasonalinStockReturns?"Journalof

Finance(December1986),pp.1115-1128.

."TheUofInformationinMarketValuesforEstimatingTime-VaryingStock

Betas."WorkingPaper,FacultyofFinance,OhioStateUniversity,June1986.

."OntheReturnoftheContrarianInvestmentStrategy."WorkingPaper,Facultyof

Finance,OhioStateUniversity,January1987.

:HoughtonMifflinCompany,1978.

."DoestheStockMarketOverreact?"Journalof

Finance(July1985),pp.793-805.

."CapitalGainsTaxationandYear-EndStockMarketBehavior."Journalof

Finance(March1977),pp.165-175.

."PermanentandTemporaryComponentsofStock

Prices."WorkingPaperNo.178,GraduateSchoolofBusiness,UniversityofChicago,July

1986.

."CommonFactorsintheSerialCorrelationofStock

Returns."WorkingPaper,GraduateSchoolofBusiness,UniversityofChicago,October1986.

Friedman."TheUofRankstoAvoidtheAssumptionofNormalityImplicitinthe

AnalysisofVariance."JournaloftheAmericanStatisticalAssociation(32:1937),pp.675-701.

olyandJofLakonishok."EarningsGrowthandtheFirm-SizeAnomaly."Working

PaperNo.832/84,TheLeonRecanatiGraduateSchoolofBusinessAdministration,TelAviv

University,November1984.

."EvidenceonStockMarketOverreaction."FinancialAnalystsJournal(July/

August1986),pp.74-77.

,Bonds,Bills,andInflation:ThePastandtheFuture.

Charlottesville:TheFinancialAnalystsRearchFoundation,UniversityofVirginia,1982.

."SizeRelatedAnomaliesandStockReturnSeasonality."JournalofFinancial

Economics(June1983),pp.13-32.

ugh."PredictingReturnsintheStockandBondMarkets."

JournalofFinancialEconomics(1986),pp.357-390.

eralTheoryofEmployment,:

HarcourtBraceJovanovich,1964(reprintof1936edition).

akonishokandSeymourSmidt."VolumeforWinnersandLors:TaxationandOther

MotivesforStockTrading."JournalofFinance(September1986),pp.951-974.

ath,Wiggins."UsingtheCOMPUSTATTapesinFinancial

Rearch:ProblemsandSolutions."FinancialAnalystsJournal(January/February1984),pp.

71-76.

."OntheCurrentStateoftheMarketRationalityHypothesis."WorkingPaper

No.1717-85,MassachuttsInstituteofTechnology,October1985.

."OrderedHypothesisforMultipleTreatments:ASignificanceTestforLinearRanks."

JournaloftheAmericanStatisticalAssociation(58:1963),pp.316-230.

num."TheAnomalousStockMarketBehaviorofSmallFirmsinJanuary:

EmpiricalTestsforTax-LossSellingEffects."JournalofFinancialEconomics(June1983),

pp.89-104.

InvestorOverreaction581

."TheJanuarySizeEffect:AnomalyorRiskMeasure-

ment?"FinancialAnalystsJournal(November/December1986),pp.63-70.

dRoll."VasistDas?TheTurn-of-the-YearEffectandtheReturnPremiaofSmallFirms."

JournalofPortfolioManagement(Winter1983),pp.18-28.

nberg,KennethReidandRonaldLanstein."PersuasiveEvidenceofMarketIneffi-

ciency."JournalofPortfolioManagement(Spring1985),pp.9-16.

."TheDecemberEffectinStockReturnsandtheTax-LossSellingHypothesis."

WorkingPaperNo.85-18,CollegeofBusinessAdministration,UniversityofIowa,May1985.

mSchwert."SizeandStockReturns,andOtherEmpiricalRegularities."Journalof

FinancialEconomics(June1983),pp.3-12.

r."StockPricesandSocialDynamics."BrookingsPapersonEconomicActivity

(2:1984),pp.457-510.

rmaelenandMarcVerstringe."DoBelgiansOverreact?"WorkingPaper,Catholic

UniversityofLouvain,Belgium,November1986.