American Finance Association
Efficient Capital Markets: A Review of Theory and Empirical Work
Author(s): Eugene F. Fama
Reviewed work(s):
Source: The Journal of Finance, Vol. 25, No. 2, Papers and Proceedings of the Twenty-Eighth
Annual Meeting of the American Finance Association New York, N.Y. December, 28-30, 1969
(May, 1970), pp. 383-417
Published by: Wiley-Blackwell for the American Finance Association
Stable URL: http://www.jstor.org/stable/2325486 .
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SESSION TOPIC: STOCK MARKET PRICE BEHAVIOR
SESSION CHAIRMAN: BURTON G. MALKIEL
EFFICIENT CAPITAL MARKETS: A REVIEW OF
THEORY AND EMPIRICAL WORK*
EUGENE
I.
F. FAMA**
INTRODUCTION
THE PRIMARYROLE of the capital market is allocation of ownership of the
economy'scapitalstock.In generalterms,theideal is a marketin whichprices
provideaccuratesignalsforresourceallocation: that is, a marketin which
decisions,and investorscan choose
firmscan make production-investment
amongthe securitiesthat representownershipof firms'activitiesunderthe
assumptionthat securitypricesat any time "fullyreflect"all available inA marketin whichpricesalways"fullyreflect"availableinformaformation.
tionis called"efficient."
This paper reviewsthe theoreticaland empiricalliteratureon the efficient
marketsmodel.Aftera discussionof the theory,empiricalwork concerned
subsets
withthe adjustmentof securitypricesto threerelevantinformation
set is just
is considered.First,weak formtests,in whichthe information
formtests,in whichtheconhistoricalprices,are discussed.Then semi-strong
thatis obviously
cernis whetherpricesefficiently
adjust to otherinformation
of annual earnings,stocksplits,etc.)
publiclyavailable (e.g., announcements
are considered.Finally,strongformtestsconcernedwithwhethergiveninrelevantfor
access to any information
vestorsor groupshave monopolistic
are reviewed.'We shall concludethat,with but a few exprice formation
marketsmodelstandsup well.
ceptions,theefficient
Though we proceed fromtheoryto empiricalwork,to keep the proper
historicalperspectivewe shouldnoteto a largeextentthe empiricalworkin
of thetheory.The theoryis presentedfirst
thisarea precededthedevelopment
here in orderto moreeasily judge whichof the empiricalresultsare most
relevantfromtheviewpointof thetheory.The empiricalworkitself,however,
willthenbe reviewedin moreor less historicalsequence.
Finally,the perceptivereaderwill surelyrecognizeinstancesin thispaper
whererelevantstudiesare not specifically
discussed.In such cases my apolfor
The
is so bountifulthat some such
be
taken
area
granted.
ogies should
the
unavoidable.
But
primarygoal here will have been acinjusticesare
of
main lines of the work on efficient
the
complishedif a coherentpicture
an
marketsis presented,along with accuratepictureof the currentstate of
thearts.
* Researchon thisprojectwas supported
by a grantfromtheNationalScienceFoundation.I
am indebtedto ArthurLaffer,RobertAliber,Ray Ball, MichaelJensen,JamesLorie, Merton
Miller,CharlesNelson,RichardRoll,WilliamTaylor,and Ross Wattsfortheirhelpfulcomments.
** University
Society.
of Chicago-JointSessionwiththe Econometric
betweenweak and strongformtestswas firstsuggested
1. The distinction
by HarryRoberts.
383
The Journalof Finance
384
II.
THE THEORY OF EFFICIENT MARKETS
A. ExpectedReturnor "Fair Game" Models
marketprices"fullyreflect"
thatin an efficient
The definitional
statement
testableimplicais so generalthatit has no empirically
availableinformation
mustbe
tions.To make the modeltestable,the processof price formation
specifiedin moredetail. In essencewe mustdefinesomewhatmore exactly
whatis meantby the term"fullyreflect."
One possibilitywouldbe to posit that equilibriumprices (or expectedreturns) on securitiesare generatedas in the "two parameter"Sharpe [40]Lintner[24, 25] world.In general,however,the theoreticalmodelsand eshave not been this
peciallythe empiricaltests of capital marketefficiency
specific.Most of the availableworkis based onlyon the assumptionthatthe
conditionsof marketequilibriumcan (somehow)be statedin termsof expectedreturns.In generalterms,like the two parametermodelsuch theories
set,the equilibrium
wouldpositthatconditionalon somerelevantinformation
theories
of its "risk."And different
expectedreturnon a securityis a function
in how "risk"is defined.
primarily
woulddiffer
All membersof the class of such "expectedreturntheories"can, however,
be describednotationally
as follows:
E(gj,t+,I|@t)
=[I
+ E(r-,t+1|0t)
]pjtl
1
whereE is theexpectedvalue operator;pit is thepriceof securityj at timet;
cash income
of any intermediate
pj,t+iis its priceat t + 1 (withreinvestment
fromthe security); ri,t+iis the one-periodpercentagereturn(pi,t+l- pjt)/
is assumedto be
pjt; (Dtis a generalsymbolforwhateverset of information
"fully reflected"in the price at t; and the tildes indicate that pj,t+i and r,t+i
are randomvariablesat t.
The value of theequilibriumexpectedreturnE(rj,t+llijt) projectedon the
fromtheparticularexpected
basis of theinformation
iJtwouldbe determined
returntheoryat hand. The conditionalexpectationnotationof (1) is meant
to imply,however,thatwhateverexpectedreturnmodelis assumedto apply,
equilibriumexpected
the information
in 1t is fullyutilizedin determining
in theformation
And thisis the sensein which1t is "fullyreflected"
returns.
of the price pjt.
But we shouldnoterightoffthat,simpleas it is, the assumptionthat the
conditionsof marketequilibriumcan be statedin termsof expectedreturns
elevatesthe purelymathematicalconceptof expectedvalue to a status not
necessarily implied by the general notion of market efficiency.The expected
of
value is just one of manypossible summarymeasuresof a distribution
per se (i.e., thegeneralnotionthatprices"fully
and marketefficiency
returns,
does notimbueit withany specialimportance.
reflect"availableinformation)
Thus, theresultsof testsbased on thisassumptiondependto some extenton
of themarket.But somesuch assumpits validityas wellas on theefficiency
tion is the unavoidableprice one mustpay to give the theoryof efficient
marketsempiricalcontent.
The assumptionsthat the conditionsof marketequilibriumcan be stated
Capital Markets
Efficient
385
in termsof expectedreturnsand thatequilibrium
expectedreturnsare formed
on thebasis of (and thus"fullyreflect")the information
set (Dthave a major
empiricalimplication-theyrule out the possibilityof tradingsystemsbased
in (Dtthathave expectedprofitsor returnsin excess of
onlyon information
equilibriumexpectedprofitsor returns.Thus let
(2)
Xj,t+l - Pj,t+l- E(pj,t+1I4Dt).
Then
E (:j',t+lJ4t) =?0
(3)
which,by definition,
says thatthesequence{xjt} is a "fairgame"withrespect
to theinformation
let
sequence{@t}. Or, equivalently,
zjt+l =rj,t+l
then
-
(4)
E(rj t+lt),
(5)
E(Zjt+i141t) y,
so thatthesequence{zjt} is also a "fairgame"withrespectto theinformation
sequence {41}.
In economic terms,xJ,t+i is the excess market value of security j at time
t + 1: it is the difference
betweenthe observedpriceand the expectedvalue
of the pricethatwas projectedat t on the basis of the information
(Dt.And
similarly,zj,t+l is the returnat t + 1 in excess of the equilibriumexpected
returnprojectedat t. Let
[al(QDt),
a(1(t)
a2(2Dt),
. . .,
a1((Dt)]
be any tradingsystembased on 1?t whichtellstheinvestortheamountsaj ((It)
of fundsavailableat t thatare to be investedin each of then availablesecurities.The totalexcessmarketvalue at t + 1 thatwillbe generatedby such a
systemis
n
Vt+
Ejja((Dt)
j=1
[rj,t+l-E(rj,t+llt)],
which,fromthe "fairgame"propertyof (5) has expectation,
Z
n
E (Vt+lIDt)
j=l
cj((<Dt)E(!j,t+1[(Dt)
=
0.
The expectedreturnor "fair game" efficient
marketsmodel2has other
importanttestableimplications,
but theseare bettersaved forthe later discussionof theempiricalwork.Now we turnto twospecialcases of themodel,
thesubmartingale
and the randomwalk,that (as we shall see later) play an
rolein the empiricalliterature.
important
2. Though we shall sometimesreferto the model summarizedby (1) as the "fair game" model,
keep in mind that the "fair game" propertiesof the model are implicationsof the assumptionsthat
(i) the conditionsof marketequilibriumcan be stated in termsof expected returns,and (ii) the
information(Pt is fullyutilized by the market in formingequilibriumexpected returnsand thus
currentprices.
The role of "fair game" models in the theory of efficientmarkets was first recognized and
studied rigorouslyby Mandelbrot r27] and Samuelson [38]. Their work will be discussedin more
detail later.
386
The Journalof Finance
Model
B. Tke Submartingale
Supposewe assumein (1) thatforall t and (Dt
(6)
E(i,t+1iDt) > 0.
E("',t+1Ilt) > Pit, orequivalently,
thatthepricesequence{pit} forsecurityj followsa subThis is a statement
sequence Ol?t},whichis to say
martingalewith respectto the information
nextperiod'sprice,as projected
of
value
the
expected
nothingmorethanthat
price.
(Dt,is equal to or greaterthanthecurrent
on thebasis oftheinformation
are
changes
and
price
If (6) holds as an equality(so thatexpectedreturns
zero), thenthepricesequencefollowsa martingale.
Consider
empiricalimplication.
in priceshas one important
A submartingale
theset of "one securityand cash" mechanicaltradingrulesby whichwe mean
on individualsecuritiesand thatdefinetheconditions
systemsthatconcentrate
underwhichthe investorwouldhold a givensecurity,sell it short,or simply
hold cash at any timet. Then the assumptionof (6) that expectedreturns
directlyimpliesthat such tradingrules
conditionalon (Dt are non-negative
in Ct cannothave greaterexpectedprofitsthan
based onlyon theinformation
the securityduringthe futureperiodin
a policyof alwaysbuylng-and-holding
question.Tests of such rules will be an importantpart of the empirical
marketsmodel.8
evidenceon theefficient
C. The Random Walk Model
marketsmodel,the statementthat
of the efficient
In the earlytreatments
was
the currentprice of a security"fully reflects"available information
assumedto implythatsuccessivepricechanges (or moreusually,successive
In addition,it was usuallyassumedthat
one-periodreturns)are independent.
Togetherthe two
successivechanges(or returns)are identicallydistributed.
the randomwalk model.Formally,themodelsays
constitute
hypotheses
= f(rj,t+?),
(7)
f(rj,t+?ItDt)
whichis the usual statementthat the conditionaland marginalprobability
variable are identical.In addition,
of an independentrandomn
distributions
f mustbe thesame forall t.4
thedensityfunction
buyvis-'a-vis
and cash" tradingsystems
of "one security
3. Note thattheexpectedprofitability
marketsmodel.
and-holdis not ruledout by the generalexpectedreturnor "fairgame"efficient
but
in excessof equilibrium
expectedreturns,
The latterrulesout systemswithexpectedprofits
to be negative,
holdingcash (whichalways
expectedreturns
it allowsequilibriunm
sincein principle
hag zero actual and thusexpectedreturn)may have higherexpectedreturnthan holdingsome
security.
are quite possible.For example,
expectedreturnsforsomesecurities
And negativeequilibriumn
of the portfolio
in theSharpe[40]-Lintner[24, 25] model(whichis in turna naturalextension
depends
expectedreturnon a security
modelsof Markowitz[30] and Tobin [43]) theequilibrium
in thesecurity's
returndistribution
ig relatedto dispersion
on theextentto whichthe dispersion
on averagemove oppositeto the
whosereturns
A security
on all othersecurities.
in the returns
valuable in reducingdispersionof portfolioreturns,and so its
generalmarketis particularly
maywellbe negative.
expectedreturn
equilibrium
is loose.Priceswill onlyfollowa randomwalk if pricechangesare inde4. The terminology
and even thenwe shouldsay "randomwalk with drift"since
distributed;
pendent,identically
dis.
identically
expectedpricechangescan be non-zero.If one-periodreturnsare independent,
of pricechangeswill depend
priceswillnot followa randomwalk sincethe distribution
tributed,
CapitalMarkets
Efficient
387
Expression(7) of coursesays muchmorethanthegeneralexpectedreturn
modelsummarizedby (1). For example,if we restrict(1) by assumingthat
theexpectedreturnon securityj is constantovertime,thenwe have
(8)
E(,j,t+1|f't)= E(rj,t+?).
This says thatthe meanof the distribution
of rj,t+lis independent
of theinformation
available at t, t, whereasthe randomwalk modelof (7) in additionsays thatthe entiredistribution
of CF.5
is independent
We argue later that it is best to regardthe randomwalk model as an
extensionof the generalexpectedreturnor "fair game" efficient
markets
modelin the sense of makinga moredetailedstatementabout the economic
environment.
The "fairgame" modeljust says thatthe conditionsof market
can be statedin termsof expectedreturns,
equilibrium
and thusit says little
about thedetailsof thestochasticprocessgenerating
returns.A randomwalk
arises withinthe contextof such a modelwhen the environment
is (fortuitously)such thattheevolutionof investortastesand the processgenerating
new information
combineto produceequilibriain whichreturndistributions
repeatthemselves
throughtime.
thatempiricaltestsof the "randomwalk" model
Thus it is not surprising
in support
thatare in facttestsof "fairgame" propertiesare morestrongly
of themodelthantestsof theadditional(and, fromtheviewpointof expected
returnmarketefficiency,
superfluous)pure independence
assumption.(But it
is perhapsequally surprising
that,as we shall soon see, the evidenceagainst
of returnsovertimeis as weak as it is.)
theindependence
D. MarketConditionsConsistentwithEfficiency
Before turningto the empiricalwork,however,a few words about the
marketconditionsthatmighthelp or hinderefficient
adjustmentof pricesto
are in order.First,it is easy to determine
information
conditionsfor
sufficient
capitalmarketefficiency.
For example,considera marketin which (i) there
costsin tradingsecurities,(ii) all availableinformation
are no transactions
is
costlesslyavailable to all marketparticipants,
and (iii) all agree on the imfor the currentprice and distributions
plicationsof currentinformation
of
futurepricesof each security.In sucha market,thecurrentpriceof a security
obviously"fullyreflects"all availableinformation.
marketin whichall information
But a frictionless
is freelyavailable and
investorsagreeon its implications
of marketsmet
is, of course,notdescriptive
in practice.Fortunately,
theseconditionsare sufficient
formarketefficiency,
but not necessary.For example,as long as transactorstake account of all
is usuallydesirable,our loose use of terms
on the pricelevel.But thoughrigorousterminology
shouldnot cause confusion;and our usage followsthat of the efficient
marketsliterature.
Note also thatin the randomwalk literature,
theinformation
set (t in (7) is usuallyassumed
to include only the past returnhistory,rj,t,rj t-1
. . .
5. The randomwalk modeldoes not say, however,that past information
is of no value in
of futurereturns.Indeed since returndistributions
assessingdistributions
are assumedto be
stationary
throughtime,past returnsare the bestsourceof suchinformation.
The randomwalk
thatthesequence(or theorder)of thepast returns
modeldoessay,however,
is of no consequence
of futurereturns.
in assessingdistributions
388
The Journal
of Finance
available information,
even large transactionscosts that inhibitthe flowof
transactions
do notin themselves
implythatwhentransactions
do take place,
priceswillnot "fullyreflect"available information.
Similarly(and speaking,
as above, somewhatloosely),the marketmay be efficient
if "sufficient
numbers" of investorshave readyaccess to available information.
And disagreementamonginvestorsabouttheimplications
of giveninformation
does notin
itselfimplymarketinefficiency
unlessthereare investorswho can consistently
make betterevaluationsof available information
thanare implicitin market
prices.
But thoughtransactions
costs,information
thatis not freelyavailableto all
investors,and disagreement
amonginvestorsabout the implicationsof given
information
are notnecessarilysourcesof marketinefficiency,
theyare potential sources.And all threeexistto someextentin real worldmarkets.Measuring theireffects
on theprocessof priceformation
is, of course,themajorgoal
of empiricalworkin thisarea.
III. THE EVIDENCE
All the empiricalresearchon the theoryof efficient
marketshas been concerned with whetherprices "fully reflect"particularsubsets of available
information.
Historically,
the empiricalworkevolvedmoreor less as follows.
The initialstudieswereconcernedwithwhatwe call weak formtestsin which
theinformation
subsetof interestis just past price (or return)histories.Most
of theresultsherecomefromtherandomwalkliterature.
Whenextensivetests
at thislevel,attentionwas turned
seemedto supportthe efficiency
hypothesis
to semi-strong
formtestsin whichtheconcernis thespeed of priceadjustment
of
to otherobviouslypubliclyavailable information(e.g., announcements
stock splits,annual reports,new securityissues,etc.). Finally,strongform
testsin whichthe concernis whetherany investoror groups (e.g., manageaccess to any information
mentsof mutualfunds)have monopolistic
relevant
of priceshave recentlyappeared.We reviewthe empirical
forthe formation
researchin moreor less thishistoricalsequence.
First, however,we should note that what we have called the efficient
marketsmodel in the discussionsof earliersectionsis the hypothesisthat
securitypricesat any pointin time"fullyreflect"all available information.
Thoughwe shall arguethatthemodelstandsup ratherwell to the data, it is
obviouslyan extremenull hypothesis.And, like any otherextremenull hyof the
posthesis,we do not expectit to be literallytrue.The categorization
and strongformwill servetheusefulpurposeof
testsintoweak,semi-strong,
at whichthehypothesis
breaks
allowingus to pinpointthelevelofinformation
evidenceagainstthe
down.And we shall contendthatthereis no important
formtests (i.e., prices seem to effihypothesisin the weak and semi-strong
to
available
and onlylimited
cientlyadjust obviouslypublicly
information),
evidenceagainst the hypothesisin the strongformtests (i.e., monopolistic
aboutpricesdoes notseemto be a prevalentphenomenon
access to information
in the investment
community).
Efficient
CapitalMarkets
389
MarketsModel
A. Weak Form Tests of theEfficient
1. RandomWalks and Fair Games: A Little HistoricalBackground
marketscan be conAs notedearlier,all of the empiricalworkon efficient
sideredwithinthe contextof the generalexpectedreturnor "fair game"
model,and muchof the evidencebears directlyon the special submartingale
discussionsof
expectedreturnmodelof (6). Indeed,in the early literature,
of
the
even
morespecial
the efficient
marketsmodelwerephrasedin terms
randomwalkmodel,thoughwe shallarguethatmostof theearlyauthorswere
in factconcernedwithmoregeneralversionsof the "fairgame" model.
is understandable.
Someof theconfusionin theearlyrandomwalkwritings
of a theory
Researchon securitypricesdid not beginwiththe development
of price formation
whichwas thensubjectedto empiricaltests.Rather,the
of a theorycame fromthe accumulationof evimpetusforthe development
idencein the middle 1950's and early 1960's that the behaviorof common
stockand otherspeculativepricescould be well approximated
by a random
walk. Faced withthe evidence,economistsfeltcompelledto offersome ratiomarketsstatedin termsof
nalization.What resultedwas a theoryof efficient
randomwalks,but usuallyimplyingsomemoregeneral"fairgame" model.
It was notuntiltheworkof Samuelson[38] and Mandelbrot[27] in 1965
and 1966 thatthe role of "fair game" expectedreturnmodelsin the theory
marketsand the relationships
betweenthesemodelsand thetheory
of efficient
studied.6And thesepapers came somewhat
of randomwalks wererigorously
afterthemajorempiricalworkon randomwalks. In the earlierwork,"theoappealing,werealwayslacking
retical"discussions,thoughusuallyintuitively
in rigorand ofteneithervague or ad hoc. In short,until the MandelbrotSamuelsonmodelsappeared,thereexisteda large body of empiricalresults
in searchof a rigoroustheory.
wereignoredforsixtyyears,the firststateThus, thoughhis contributions
mentand testof the randomwalk modelwas thatof Bachelier[3] in 1900.
But his "fundamental
principle"forthe behaviorof priceswas thatspeculationshouldbe a "fairgame"; in particular,the expectedprofitsto thespeculator should be zero. With the benefitof the moderntheoryof stochastic
principle
processes,we knownowthattheprocessimpliedby thisfundamental
is a martingale.
AfterBachelier,researchon thebehaviorof securitypriceslaggeduntilthe
6. Basing theiranalyses on futurescontractsin commoditymarkets,Mandelbrot and Samuelson
show that if the price of such a contractat time t is the expected value at t (given information
t) of the spot price at the terminationof the contract,then the futuresprice will follow a
martingalewith respectto the informationsequence {jt); that is, the expected price change from
period to period will be zero, and the price changes will be a "fair game." If the equilibriumexpected returnis not assumed to be zero, our more general "fair game" model, summarizedby (1),
is obtained.
But though the Mandelbrot-Samuelsonapproach certainly illuminates the process of price
formationin commoditymarkets,we have seen that "fair game" expected returnmodels can be
derived in much simplerfashion.In particular,(1) is just a formalizationof the assumptionsthat
the conditions of market equilibriumcan be stated in terms of expected returns and that the
informationt is used in formingmarketprices at t.
390
The Journalof Finance
comingof the computer.In 1953 Kendall [21] examinedthe behaviorof
weeklychangesin nineteenindicesof Britishindustrialshare pricesand in
spot prices for cotton (New York) and wheat (Chicago). Afterextensive
he suggests,in quite graphicterms:
analysisof serial correlations,
one,almostas ifoncea weektheDemonofChance
Theserieslookslikea wandering
andaddedit
of fixeddispersion
population
from
a symetrical
number
drewa random
thenextweek'sprice[21,p. 13].
priceto determine
to thecurrent
Kendall's conclusionhad in fact been suggestedearlierby Working[47],
lackedtheforceprovidedby Kendall'sempiricalresults.
thoughhis suggestion
of theconclusionforstockmarketresearchand financial
And theimplications
analysiswere laterunderlinedby Roberts[36].
by Kendall,Working,and Robertsthatseriesof speculaBut thesuggestion
tivepricesmaybe well describedby randomwalkswas based on observation.
None of theseauthorsattemptedto providemucheconomicrationaleforthe
wouldgenerallyrejectit.
and,indeed,Kendall feltthateconomists
hypothesis,
Osborne [33] suggestedmarketconditions,similar to those assumed by
Bachelier,thatwouldlead to a randomwalk. But in his model,independence
of successivepricechangesderivesfromthe assumptionthatthe decisionsof
investorsin an individualsecurityare independentfrom transactionto
is littlein theway of an economicmodel.
transaction-which
Whenevereconomists(priorto Mandelbrotand Samuelson) triedto provide economicjustificationfor the randomwalk, their argumentsusually
implieda "fairgame." For example,Alexander[8, p. 200] states:
is
thata stockor commodity
speculation
If onewereto startoutwiththeassumption
withan
of gainor loss or, moreaccurately,
a "fairgame"withequal expectation
of
thebehavior
of zerogain,onewouldbe wellon thewayto picturing
expectation
walk.
pricesas a random
speculative
There is an awarenessherethatthe "fairgame" assumptionis not sufficient
to lead to a randomwalk, but Alexandernever expands on the comment.
Cootner[8, p. 232] states:
Similarly,
If anysubstantial
pricesweretoo low,theirbuyingwould
groupof buyersthought
due
Exceptforappreciation
wouldbe trueforsellers.
forceup theprices.The reverse
of tomorrow's
theconditional
price,giventoday's
to earnings
expectation
retention,
price,is today'sprice.
thatwouldoccurarethosethatresultfrom
theonlypricechanges
In sucha world,
to be non-ranSincethereis no reasonto expectthatinformation
newinformation.
theperiod-to-period
pricechangesof a stockshouldbe random
domin appearance,
ofoneanother.
statistically
independent
movements,
thelast sentenceof thefirstparagraphseemsto
Thoughsomewhatimprecise,
pointto a "fairgame" modelratherthana randomwalk.' In thislight,the
consecondparagraphcan be viewedas an attemptto describeenvironmental
ditionsthatwouldreducea "fairgame" to a randomwalk. But the specificaforthispurtionimposedon theinformation
processis insufficient
generating
pose; one would, for example,also have to say somethingabout investor
would be "Giventhe sequenceof historicalprices."
statement
conditioning
7. The appropriate
CapitalMarkets
Efficient
391
tastes. Finally,lest I be accused of criticizingotherstoo severelyfor ambiguity,lack of rigorand incorrectconclusions,
By contrast,the stock markettraderhas a much more practicalcriterionfor
judgingwhat constitutesimportantdependencein successiveprice changes.For his
purposesthe randomwalk modelis valid as long as knowledgeof the past behavior
of theseriesof pricechangescannotbe used to increaseexpectedgains.More specifically,the independence
assumptionis an adequate descriptionof realityas long as
to allow
theactual degreeof dependencein theseriesof pricechangesis not sufficient
the past historyof the seriesto be used to predictthe futurein a way whichmakes
expectedprofitsgreaterthan they would be under a naive buy-andhold model
[10, p 35].
We knownow, of course,that this last conditionhardlyrequiresa random
walk. It willin factbe metby thesubmartingale
modelof (6).
But one shouldnot be too hard on the theoreticalefforts
of the earlyempiricalrandomwalk literature.
The arguments
wereusuallyappealing;where
in the theoryof stochastic
theyfellshortwas in awarenessof developments
processes.Moreover,we shall now see thatmostof the empiricalevidencein
the randomwalk literaturecan easilybe interpreted
as testsof moregeneral
expectedreturnor "fairgame" models.8
2. Tests of MarketEfficiency
in theRandomWalk Literature
As discussed earlier,"fair game" models imply the "impossibility"of
varioussortsof tradingsystems.Someof therandomwalk literature
has been
concernedwithtestingtheprofitability
of suchsystems.More of theliterature
has, however,been concernedwithtestsof serial covariancesof returns.We
shall now show that,like a randomwalk, the serial covariancesof a "fair
game" are zero, so thatthesetestsare also relevantforthe expectedreturn
models.
If Xt is a "fair game,"its unconditional
expectationis zero and its serial
covariancecan be written
in generalformas:
E (it+r iit)
xt
xtE (it+rIxt) f(xt)dxt,
wheref indicatesa densityfunction.
But if Xt is a "fairgame,"
E (5Et+ lxt) = 0.
8. Our briefhistoricalreviewis meant only to provide perspective,and it is, of course,somewhat
incomplete.For example, we have ignored the importantcontributionsto the early random walk
literaturein studies of warrants and other options by Sprenkle, Kruizenga, Boness, and others.
Much of this early work on options is summarizedin [8].
9. More generally,if the sequence {xj is a fair game with respectto the informationsequence
{(Dt}, (i.e., E(Xt+1?It) = 0 for aH Pt); then xt is a fair game with respect to any Vt that is a
subset of (t (i.e., E(xt+? I t) = 0 for all 't). To show this,let (P = (Vt, V"t). Then, using
Stieltjes integralsand the symbol F to denote cumulative distinctionfunctions,the conditional
expectation
=
E(xt+ll,t)
% ]
f xt+dF(xt+i t1e, = f[f xt+dF(xt+1I4t)
,
bt Xtt+
(Pt
Xt.+1
dF(O)-
The Journalof Finance
392
From this it followsthat forall lags, the serial covariancesbetweenlagged
valuesofa "fairgame"variableare zero.Thus, observations
of a "fairgame"
variableare linearlyindependent.10
But the "fair game" model does not necessarilyimply that the serial
covariancesof one-periodreturnsare zero. In the weak formtests of this
modelthe "fairgame" variableis
rj,t-2,
E(r-j,tIrj,t_j,
zj,t -rj,t-
. . .).
(Cf. fn.9)
(9)
But thecovariancebetween,forexample,ritand rj,t+iis
E( rFj,t+j-E(r'j,t+j)] [r-jt-E(r'jt)])
[rjt-E(rjt)]
-
[E(rj,t+lIrjt)-E(rj,t?i)]f(rjt)drjt,
rjt
and (9) does not implythat E(rj,t+?irjt) E(ij,t+1): In the "fair game"
marketsmodel,the deviationof the returnfort + 1 fromits condiefficient
tionalexpectationis a "fair game" variable,but the conditionalexpectation
itselfcan dependon thereturnobservedfort.1'
this problemis not recognized,since it is
In the randomwalk literature,
of
assumed that the expected return(and indeed the entiredistribution
returns)is stationarythroughtime.In practice,thisimpliesestimating
serial
covariancesby takingcross productsof deviationsof observedreturnsfrom
theoverallsamplemeanreturn.It is somewhatfortuitous,
then,thatthisproa rathergrossapproximation
fromthe viewpointof
cedure,whichrepresents
marketsmodel,does not seemto greatly
the generalexpectedreturnefficient
affecttheresultsof the covariancetests,at least forcommonstocks.'2
But the integralin bracketsis just E(xt?iI |t)
which by the "fair game" assumptionis 0, so that
E(xt?+l 't) = 0 forall Vt C t.
10. But thoughzero serial covariancesare consistentwith a "fair game," they do not implysuch
a process. A "fair game" also rules out many types of non linear dependence. Lhus using argumentssimilarto those above, it can be shown that if x is a "fair game," E(xtxt+l . . . xt+r) = 0
for all -r,which is not implied by E(Xtxt+T) = 0 for all T. For example, considera three-period
case where x must be either? 1. Suppose the process is xt+2 = sign (xtxt+?), i.e.,
xt
Xt+l i
?
+
-
Xt+2
+
e
?
If probabilitiesare uniformlydistributedacross events,
E(xt?21xt+l) = E(xt+2Ixt) .= E(xt+llxt) = E(xt+2) = E(xt+?) = E(xt) = 0,
so that all pairwise serial covariances are zero. But 'the process is not a "fair game," since
E(Xt?2lXt+?, xt) & 0, and knowledgeof (xt+i, Xt) can be used as the basis of a simple "system"
with positive expected profit.
11. For example,suppose the level of one-periodreturnsfollows a martingaleso that
E(fijt+1?rjt, rj,t_1
... ) = rjt.
Then covariances between successive returnswill be nonzero (though in this special case first
differences
of returnswill be uncorrelated).
12. The reason is probably that for stocks, changes in equilibrium expected returns for the
EfficientCapital Markets
393
TABLE 1 (from [10])
forOne-, Four-, Nine-,and Sixteen-Day
First-orderSerial CorrelationCoefficients
Changesin Loge Price
Stock
One
Differencing
Interval(Days)
Four
Nine
.029
Allied Chemical
.017
.118*
.095
Alcoa
-.124*
AmericanCan
-.087*
-.010
-.039
A. T. & T.
.111*
-.175*
AmericanTobacco
.067*
-.068
Anaconda
.013
-.122
BethlehemSteel
.012
.060
Chrysler
.013
.069
Du Pont
.025
-o.006
Eastman Kodak
.020
.011
GeneralElectric
.061*
-.005
GeneralFoods
-.004
-.128*
General Motors
-.123*
.001
Goodyear
-.017
-.068
InternationalHarvester
.038
InternationalNickel
.096*
.046
.060
InternationalPaper
.006
-.068
JohnsManville
-.021
-.006
Owens Illinois
-.006
Procter& Gamble
.099*
-.070
.097*
Sears
.025
-.143*
StandardOil (Calif.)
.008
StandardOil (N.J.)
-.109
-.004
-.072
Swift& Co.
-.o53
Texaco
.094*
.107*
Union Carbide
.049
.014
United Aircraft
-.190*
.040
-.006
U.S. Steel
-.02 7
-.097
Westinghouse
.028
-.033
Woolworth
* Coefficient
is twiceits computedstandarderror.
Sixteen
-.091
-.112
-.118
-.044
-.009
.033
-.003
.007
-.148
.112
.040
-.055
-.060
-.125
-.026
-.043
-.053
-.004
-.140
.009
-.037
-.244*
.124
-.004
-.002
.003
.098
-.113
-.046
-.082
.118
-.047
-.101
-.192*
-.056
-.137
-.112
.031
.202
-.023
.000
-.098
-.028
.033
.116
.041
-.010
.002
-.022
.076
.041
.040
-.121
-.197
-.178
.124
-.040
.236*
.067
.040
beFor example,Table 1 (taken from[10]) showsthe serialcorrelations
tweensuccessivechangesin the naturallog of price for each of the thirty
stocksof theDow JonesIndustrialAverage,fortimeperiodsthatvaryslightly
fromstockto stock,but usuallyrunfromabout theend of 1957 to September
26, 1962.The serialcorrelations
of successivechangesin loge priceare shown
fordifferencing
intervalsof one,four,nine,and sixteendays.13
commondifferencing
intervalsof a day, a week, or a month,are trivial relativeto other sources of
variation in returns.Later, when we consider Roll's work [37], we shall see that this is not true
for one week returnson U.S. GovernmentTreasury Bills.
13. The use of changesin loge price as the measure of returnis common in the random walk
literature.It can be justifiedin several ways. But for currentpurposes,it is sufficient
to note that
for price changesless than fifteenper cent,the changein loge price is approximatelythe percentage
price change or one-periodreturn.And for differencing
intervalsshorterthan one month,returns
in excess of fifteenper cent are unusual. Thus [10] reportsthat for the data of Table 1, tests
carried out on percentage or one-period returnsyielded results essentiallyidentical to the tests
based on changesin loge price.
394
The Journalof Finance
The resultsin Table 1 are typicalof thosereportedby othersfortestsbased
on serial covariances.(Cf. Kendall [21], Moore [31], Alexander[1], and
the resultsof Grangerand Morgenstern[17] and Godfrey,Grangerand
Morgenstern
[16] obtainedby meansof spectralanalysis.) Specifically,
there
is no evidenceof substantiallineardependencebetweenlaggedprice changes
or returns.
In absolutetermsthemeasuredserialcorrelations
are alwaysclose
to zero.
Lookinghard,though,one can probablyfindevidenceof statistically
"significant"lineardependencein Table 1 (and again thisis trueof resultsreportedby others).For the daily returnselevenof the serial correlations
are
morethantwicetheircomputedstandarderrors,and twenty-two
out of thirty
of thecoefficients
are positive.On theotherhand,twenty-one
and twenty-four
forthefourand nineday differences
are negative.But withsamplesof thesize
underlying
Table 1 (N- 1200-1700observations
per stockon a dailybasis)
statistically
"significant"
deviationsfromzero covarianceare not necessarily
a basis forrejectingthe efficient
marketsmodel.For the resultsin Table 1,
the standarderrorsof the serial correlationswere approximatedas (1/
(N-i) )'/2,whichforthe daily data impliesthat a correlationas small as .06
is morethantwiceits standarderror.But a coefficient
thissize impliesthata
linearrelationship
withthe laggedpricechangecan be used to explainabout
.36% of the variationin the currentprice change,whichis probablyinsignificant
froman economicviewpoint.
In particular,
it is unlikelythatthesmall
absolutelevels of serialcorrelation
thatare alwaysobservedcan be used as
thebasis of substantially
profitabletradingsystems.'4
It is, of course,difficult
to judge what degreeof serial correlationwould
implythe existenceof tradingrules withsubstantialexpectedprofits.(And
indeedwe shall soonhave to be a littlemorepreciseaboutwhatis impliedby
"substantial"profits.)Moreover,zero serialcovariancesare consistent
witha
"fairgame" model,but as notedearlier(fn. 10), thereare typesof nonlinear
dependencethatimplythe existenceof profitable
tradingsystems,and yet do
not implynonzeroserial covariances.Thus, formanyreasonsit is desirable
of varioustradingrules.
to directlytesttheprofitability
The firstmajorevidenceon tradingruleswas Alexander's[1, 2]. He testsa
examinedcan be decribedas
varietyof systems,but the most thoroughly
follows:If the price of a securitymovesup at least y%7,buy and hold the
securityuntilits price movesdownat least y%' froma subsequenthigh,at
sell and go short.The shortpositionis maintained
whichtimesimultaneously
untilthe price rises at least y%oabove a subsequentlow, at whichtimeone
coverstheshortpositionand buys.Moves less thany% in eitherdirection
are
14. Giventhe evidenceof Kendall [21], Mandelbrot[28], Fama [10] and othersthat large
pricechangesoccurmuchmorefrequently
thanwouldbe expectedif the generating
processwere
Gaussian,the expression
(1/(N-1))'/2 understates
the samplingdispersion
of the serialcorrelation
coefficient,
and thusleads to an overstatement
of significance
levels.In addition,the fact that
sampleserialcorrelations
are predominantly
of one signor the otheris not in itselfevidenceof
lineardependence.
If, as theworkof King [23] and Blume[7] indicates,
thereis a marketfactor
whosebehavioraffects
the returnson all securities,
the samplebehaviorof this marketfactor
maylead to a predominance
of signsof one typein theserialcorrelations
forindividual
securities,
even thoughthe populationserial correlations
forboth the marketfactorand the returnson
individual
securities
are zero.For a moreextensive
analysisof theseissuessee [10].
Capital Markets
Efficient
395
ignored.Such a systemis calleda y% filter.It is obviouslya "one securityand
cash" tradingrule,so that the resultsit producesare relevantforthe submartingale
expectedreturnmodelof (6).
Afterextensivetestsusingdaily data on price indicesfrom1897 to 1959
and filtersfromone to fiftyper cent, and aftercorrectingsome incorrect
presumptions
in theinitialresultsof [1] (see fn.25), in his finalpaperon the
subject,Alexanderconcludes:
In fact,at thispointI shouldadviseanyreaderwhois interested
onlyin practical
results,
and whois nota floortraderand so mustpaycommissions,
to turnto other
sources
onhowtobeatbuyandhold.The restofthisarticleis devotedprincipally
to
a theoretical
consideration
of whether
the observedresultsare consistent
witha
random
walkhypothesis
[8], p. 351).
Later in the paper Alexanderconcludesthat thereis some evidencein his
resultsagainstthe independence
assumptionof the randomwalk model.But
marketefficiency
does not requirea randomwalk,and fromthe viewpointof
thesubmartingale
modelof (6), theconclusionthatthefilters
cannotbeat buyand-holdis supportforthe efficient
marketshypothesis.Furthersupportis
providedby Fama and Blume [13] who comparetheprofitability
of various
filtersto buy-and-hold
forthe individualstocksof the Dow-JonesIndustrial
Average.(The data are thoseunderlying
Table 1.)
But again, lookinghard one can findevidencein the filtertests of both
Alexanderand Fama-Blumethat is inconsistent
withthe submartingale
efficientmarketsmodel,if thatmodelis interpreted
in a strictsense.In particular,the resultsforverysmallfilters(1 per centin Alexander'stestsand .5,
1.0, and 1.5 per centin the testsof Fama-Blume)indicatethatit is possible
to devisetradingschemesbased on veryshort-term
(preferablyintra-daybut
at most daily) price swingsthat will on average outperform
buy-and-hold.
The averageprofitson individualtransactions
fromsuch schemesare miniscule, but theygeneratetransactionsso frequently
that over longerperiods
and ignoringcommissionsthey outperform
buy-and-holdby a substantial
margin.These resultsare evidenceof persistenceor positivedependencein
veryshort-term
price movements.
this is consistentwith
And, interestingly,
the evidencefor slightpositivelinear dependencein successivedaily price
changesproducedby theserialcorrelations.15
15. Though strictlyspeaking, such tests of pure independence are not directly relevant for
expected returnmodels, it is interestingthat the conclusionthat very short-termswings in prices
persistslightlylonger than would be expected under the martingalehypothesisis also supported
by the resultsof non-parametricruns testsapplied to the daily data of Table 1. (See [10], Tables
12-15.) For the daily price changes,the actual numberof runs of price changes of the same sign
is less than the expectednumberfor 26 out of 30 stocks.Moreover,of the eightstocksfor which the
actual numberof runs is more than two standarderrorsless than the expectednumber,five of the
same stocks have positive daily, firstorder serial correlationsin Table 1 that are more than
twice theirstandard errors.But in both cases the statistical"significance"of the resultsis largely
a reflectionof the large sample sizes. Just as the serial correlationsare small in absolute terms
(the average is .026), the differences
between the expected and actual number of runs on average
are only three per cent of the total expected number.
On the other hand, it is also interestingthat the runs tests do not support the suggestionof
slight negative dependencein four and nine day changes that appeared in the serial correlations.
In the runs tests such negative dependencewould appear as a tendencyfor the actual number of
runs to exceed the expectednumber.In fact, for the four and nine day price changes,for 17 and
396
The Journalof Finance
But whenone takesaccountof even theminimum
tradingcoststhatwould
be generatedby small filters,theiradvantageover buy-and-hold
disappears.
For example,evena floortrader(i.e., a personwho ownsa seat) on theNew
feeson his tradesthatamount
York StockExchangemustpay clearinghouse
transaction(i.e., sales plus purchase).
to about .1 per cent per turnaround
Fama-Blumeshow that because small filtersproducesuch frequenttrades,
to wipe out theiradvantageover
theseminimumtradingcosts are sufficient
buy-and-hold.
Thus thefiltertests,like theserialcorrelations,
noticeproduceempirically
able departuresfromthe strictimplicationsof the efficient
marketsmodel.
But,in spiteof any statisticalsignificance
theymighthave,froman economic
viewpointthe departuresare so small that it seems hardlyjustifiedto use
themto declarethe marketinefficient.
3. OtherTests of Independencein the Random Walk Literature
It is probablybest to regardthe randomwalk modelas a special case of
themoregeneralexpectedreturnmodelin thesenseof makinga moredetailed
of theeconomicenvironment.
specification
That is, thebasic modelof market
equilibriumis the "fair game" expectedreturnmodel,with a randomwalk
conditionsare such that distributions
arisingwhenadditionalenvironmental
of one-periodreturnsrepeat themselvesthroughtime.From this viewpoint
violationsof thepureindependence
assumption
of therandomwalk modelare
to be expected.But whenjudged relativeto the benchmarkprovidedby the
randomwalk model,theseviolationscan provideinsightsinto the natureof
the marketenvironment.
For example,one departurefromthepure independence
assumptionof the
randomwalk modelhas been notedby Osborne[34], Fama ([10], Table 17
and Figure8), and others.In particular,largedailypricechangestendto be
followedby large daily changes.The signsof the successorchangesare apparentlyrandom,however,whichindicatesthat the phenomenonrepresents
a denialoftherandomwalkmodelbut notof themarketefficiency
hypothesis.
it is interesting
Nevertheless,
to speculatewhythe phenomenon
mightarise.
It may be that whenimportantnew information
comes into the marketit
cannot always be immediatelyevaluated precisely.Thus, sometimesthe
initialpricewill overadjustto the information,
and othertimesit will underadjust.But sincetheevidenceindicatesthatthepricechangeson days followingtheinitiallargechangeare randomin sign,theinitiallargechangeat least
represents
an unbiasedadjustment
to theultimatepriceeffects
of theinformaforthe expectedreturnefficient
tion,and tlhisis sufficient
marketsmodel.
and Osborne [32] documenttwo departuresfromcomplete
Niederhoffer
randomnessin commonstockprice changesfromtransactionto transaction.
First,theirdata indicatethat reversals(pairs of consecutiveprice changes
of oppositesign) are fromtwoto threetimesas likelyas continuations
(pairs
of consecutiveprice changesof the same sign). Second, a continuationis
18 of the 30 stocksin Table 1 the actual numberof runs is less than the expected number.Indeed,
runs testsin generalshow no consistentevidence of dependencefor alnydifferencing
intervallonger
than a day, whichseems especiallypertinentin light of the commentsin footnote14.
Capital Markets
Efficient
397
morefrequentaftera precedingcontinuation
slightly
than aftera reversal.
Thatis,let (+I++)
indicatetheoccurrence
of a positivepricechange,given
twopreceding
and (-I---)
positivechanges.Then the events(+?++)
areslightly
morefrequent
than(+1+-)
or ( _|+).1B
Niederhoffer
and Osborneofferexplanations
forthesephenomenabased on
themarketstructure
of theNew York Stock Exchange (N.Y.S.E.). In parthereare threemajortypesof ordersthatan investormightplace in
ticular,
a givenstock: (a) buy limit (buy at a specifiedprice or lower), (b) sell
limit(sell at a specifiedpriceor higher),and (c) buy or sell at market(at
thelowestsellingor highestbuyingprice of anotherinvestor).A book of
unexecuted
limitordersin a givenstockis keptby thespecialistin thatstock
onthefloorof the exchange.Unexecutedsell limitordersare, of course,at
higher
prices than unexecutedbuy limit orders.On both exchanges,the
smallest
non-zeropricechangeallowedis Y8 point.
Supposenowthatthereis morethanone unexecutedsell limitorderat the
lowest
priceof any such order.A transactionat thisprice (initiatedby an
order
to buy at market'7)can onlybe followedeitherby a transaction
at the
sameprice(if thenextmarketorderis to buy) or by a transaction
at a lower
price(if the nextmarketorderis to sell). Consecutiveprice increasescan
usuallyonly occurwhenconsecutivemarketordersto buy exhaustthe sell
limitordersat a givenprice.'8In short,the excessivetendencytowardreversalforconsecutivenon-zeropricechangescould resultfrombunchingof
unexecuted
buy and sell limitorders.
-) to occurslightly
The tendency
fortheevents(+ ++) and (more
frequently
than(+?+-)
and (-I-+)
requiresa moreinvolvedexplanation
we shall not attemptto reproducein fullhere.In brief,Niederhoffer
which
and Osbornecontendthat the higherfrequencyof (+|++)
relativeto
at in(+I+-) arises froma tendencyforlimitorders"to be concentrated
tegers(26, 43), halves (26X2, 43'2),
quarters and odd eighthsin descending
orderof preference."'9
The frequencyof the event (+I++),
whichusually
requires
thatsell limitordersbe exhaustedat at least twoconsecutively
higher
at an odd eighth),
prices(the last of whichis relativelymore frequently
moreheavilyreflects
the absenceof sell limitordersat odd eighthsthanthe
event(+?+-), whichusuallyimpliesthatsell limitordersat onlyone price
havebeen exhaustedand so moreor less reflectsthe averagebunchingof
limit
ordersat all eighths.
But thoughNiederhoffer
and Osbornepresentconvincing
evidenceof sta16.On a transaction
to transaction
basis,positiveand negativepricechangesare aboutequally
likely.
Thus,underthe assumption
thatpricechangesare random,any pair of non-zerochanges
of consecutive
non-zerochanges.
should
be as likelyas any other,and likewisefortriplets
17.A buy limitorderfora priceequal to or greaterthanthe lowestavailablesell limitprice
an orderto buyat market,
and is treatedas suchby thebroker.
iseffectively
18.The exception
is whenthereis a gap of morethan IX betweenthe highestunexecuted
buy
sell limitorder,so that marketorders(and new limitorders)
limitand the lowestunexecuted
canbe crossedat intermediate
prices.
for this claim is a few samplesof specialists'books for
19.Theirempiricaldocumentation
selected
days,plusthe observation
[34] thatactualtradingprices,at leastforvolatilehighpriced
at integers,
seemto be concentrated
halves,quartersand odd eighths
in descending
order.
stocks,
398
The Journalof Finance
tisticallysignificantdeparturesfromindependencein price changes from
transaction
to transaction,
and thoughtheiranalysisof theirfindings
presents
interesting
insightsintotheprocessof marketmakingon themajorexchanges,
the types of dependenceuncovereddo not implymarketinefficiency.
The
best documented
sourceof dependence,the tendencytowardexcessivereversals in pairs of non-zeroprice changes,seems to be a directresultof the
abilityof investorsto place limitordersas well as ordersat market,and this
negativedependencein itselfdoes notimplytheexistenceof profitable
trading
rules. Similarly,the apparenttendencyfor observedtransactions(and, by
limitorders)to be concentrated
implication,
at integers,
halves,even eighths
and odd eighthsin descendingorder is an interesting
fact about investor
behavior,but in itselfis not a basis on whichto concludethatthe marketis
inefficient.20
The Niederhoffer-Osborne
analysisof marketmakingdoes, however,point
clearlyto theexistenceof marketinefficiency,
but withrespectto strongform
testsof the efficient
marketsmodel.In particular,the list of unexecutedbuy
and sell limitordersin the specialist'sbook is important
information
about
the likelyfuturebehaviorof prices,and thisinformation
is onlyavailable to
the specialist.When the specialistis asked fora quote, he gives the prices
and can give the quantitiesof the highestbuy limit and lowest sell limit
orderson his book,but he is preventedby law fromdivulgingthebook's full
contents.The interested
readercan easilyimaginesituationswherethe structureof limitordersin the book could be used as the basis of a profitable
tradingrule.2'But therecordseemsto speak foritself:
It shouldnotbe assumedthatthesetransactions
undertaken
by thespecialist,
andin
whichhe is involvedas buyeror sellerin 24 per centof all marketvolume,are
necessarily
a burdento him.Typically,
thespecialist
sellsabovehislastpurchase
on
83 per centof all his sales,and buysbelowhis last sale on 81 per centof all his
purchases
( [32], p. 908).
Thus it seemsthatthespecialisthas monopolypoweroveran important
block
of information,
uses his monopolyto turna profit.
and, not unexpectedly,
Andthis,ofcourse,is evidenceof marketinefficiency
in thestrongformsense.
The importanteconomicquestion,of course,is whetherthe marketmaking
and Osborneoffer
20. Niederhoffer
littleto refutethisconclusion.
For example([32], p. 914):
thespecificproperties
in thisstudyhave a significance
Although
reported
froma statistical
point
of view,the readermay well ask whetheror not theyare helpfulin a practicalsense.Certain
tradingrulesemergeas a resultof ouranalysis.One is thatlimitand stop ordersshouldbe placed
at odd eights,
at Y8 forsell ordersand at /8 forbuy orders.Another
preferably
is to buywhena
stockadvancesthrough
a barrierand to sell whenit sinksthrough
a barrier.
The first"tradingrule"tellstheinvestor
to resisthis innateinclination
to place ordersat integers,
but ratherto placesell ordersI/8below an integerand buy ordersI/8above.Successful
execution
of the ordersis thenmorelikely,sincethe congestion
of ordersthatoccurat integers
is avoided.
But the costof thissuccessis apparent.The second"tradingrule"seemsno morepromising,
if
indeedit can evenbe translated
intoa concrete
foraction.
prescription
21. See, forexample,([32], p. 908). But it is unlikely
thatanyonebut thespecialistcouldearn
substantial
of the structure
profitsfromknowledge
of unexecuted
limitorderson the book. The
specialistmakestradingprofitsby engagingin manytransactions,
each of whichhas a small
averageprofit;but forany othertrader,including
thosewithseatson theexchange,
theseprofits
to thespecialist.
wouldbe eatenup by commissions
Efficient
Capital Markets
399
moreeconomicallyby some nonfunctionof the specialistcould be fulfilled
mechanism.22
monopolistic
4. DistributionalEvidence
At this date the weightof the empiricalevidenceis such that economists
wouldgenerallyagree thatwhateverdependenceexistsin seriesof historical
predictionsof the future.Indeed,
returnscannotbe used to make profitable
forreturnsthatcoverperiodsof a day or longer,thereis littlein the evidence
thatwould cause rejectionof the strongerrandomwalk model,at least as a
goodfirstapproximation.
Rather,the last burningissue of the randomwalk literaturehas centered
of price changes (which,we should note
on the natureof the distribution
marketshypothesissince
is an important
issue forthe efficient
immediately,
affects
boththetypesof statisticaltoolsrelevant
thenatureof thedistribution
of any resultsobtained).A
fortestingthe hypothesisand the interpretation
model implyingnormallydistributedprice changes was firstproposedby
Bachelier[3], who assumedthatprice changesfromtransactionto transaction are independent,identicallydistributedrandomvariables with finite
spread across time,and if the
variances.If transactions
are fairlyuniformly
per day,week,or monthis verylarge,thentheCentral
numberof transactions
LimitTheoremleads us to expectthat theseprice changeswill have normal
or Gaussian distributions.
Osborne [33], Moore [31], and Kendall [21] all thoughttheirempirical
but all observedhightails (i.e.,
hypothesis,
evidencesupportedthenormality
vis-a-vis
of largeobservations)in theirdata distributions
higherproportions
on
were normal.Drawing these
whatwouldbe expectedif the distributions
own,
Mandelbrot[28] thensuggested
findings
and someempiricalworkofhis
thatthese departuresfromnormalitycould be explainedby a moregeneral
formof the Bacheliermodel.In particular,if one does not assume that disof price changesfromtransactionto transactionnecessarilyhave
tributions
forprice changesover longer
finitevariances,thenthe limitingdistributions
intervalscouldbe any memberof thestable class, whichincludes
differencing
have higher
the normalas a special case. Non-normalstable distributions
observedfeature
tailsthanthenormal,and so can accountforthisempirically
of price changes.Afterextensivetesting(involvingthe data
of distributions
fromthe stocksin Table 1), Fama [10] concludesthat non-normalstable
of dailyreturnson comdistributions
are a betterdescription
of distributions
mon stocksthan the normal.This conclusionis also supportedby the empiricalworkof Blume [7] on commonstocks,and it has been extendedto
U.S. Government
TreasuryBills by Roll [37].
primarEconomistshave,however,been reluctantto accepttheseresults,2"
22. With moderncomputers,
it is hard to believethat a more competitive
and economical
to replacethe entire
systemwould not be feasible.It does not seemtechnologically
impossible
floorof theN.Y.S.E. witha computer,
fedby manyremoteconsoles,
thatkeptall thebooksnow
keptby thespecialists,
thatcouldeasilymaketheentirebook on any stockavailableto anybody
(so that interested
individualscould then competeto "make a market"in a stock) and that
carriedout transactions
automatically.
23. Somehave suggested
thatthelong-tailed
empirical
distributions
mightresultfromprocesses
400
The Journalof Finance
ily because of the wealthof statisticaltechniquesavailable for dealingwith
normalvariablesand the relativepaucityof such techniquesfornon-normal
stable variables.But perhapsthe biggestcontribution
of Mandelbrot'swork
has been to stimulateresearchon stable distributions
and estimationproceduresto be appliedto stablevariables.(See, forexample,Wise [46], Fama
and Roll [15], and Blattbergand Sargent[6], amongothers.)The advance
of statisticalsophistication(and the importanceof examiningdistributional
assumptionsin testingthe efficient
marketsmodel) is well illustratedin Roll
[37], as compared,forexample,withtheearlyempiricalworkof Mandelbrot
[28] and Fama [10].
5. "Fair Game" Models in the TreasuryBill Market
Roll's workis novel in otherrespectsas well. Comingafterthe efficient
marketsmodelsof Mandelbrot[27] and Samuelson[38], it is the firstweak
formempiricalworkthat is consciouslyin the "fair game" ratherthan the
randomwalk tradition.
Moreimportant,
as we saw earlier,the"fairgame"properties
of thegeneral
expectedreturnmodelsapplyto
zjt= rjt- E(fjtjDt_j).
(10)
For data on commonstocks,testsof "fair game" (and randomwalk) propertiesseem to go well whenthe conditionalexpectedreturnis estimatedas
theaveragereturnforthesampleof data at hand.Apparently
thevariationin
commonstockreturnsabout theirexpectedvalues is so large relativeto any
changesin the expectedvalues thatthe lattercan safelybe ignored.But, as
Roll demonstrates,
thisresultdoes not hold forTreasuryBills. Thus, to test
the "fair game" model on TreasuryBills requiresexpliciteconomictheory
fortheevolutionof expectedreturnsthroughtime.
Roll uses threeexistingtheoriesof thetermstructure(thepureexpectations
hypothesisof Lutz [26] and two marketsegmentation
hypotheses,one of
whichis the familiar"liquiditypreference"hypothesisof Hicks-[18] and
In his modelsrnt
is therateobservedfromthe
Kessel [22]) forthispurpose.24
termstructure
at periodt forone week loans to commenceat t + j - 1, and
can be thoughtof as a "futures"rate. Thus rj+i,t-i is likewisethe rate on
thatare mixtures
of normaldistributions
withdifferent
variances.
Press[35], forexample,
suggests
a Poissonmixture
of normalsin whichtheresulting
of pricechangeshave longtails
distributions
but finitevariances.On the otherhand,Mandelbrot
and Taylor[29] showthatothermixtures
of
normalscan stilllead to non-normal
stabledistributions
of pricechangesforfinitedifferencing
intervals.
of pricechangesare long-tailed
If, as Press'modelwouldimply,distributions
but have finite
thendistributions
of pricechangesover longerand longerdifferencing
variances,
should
intervals
be progressively
to normality
was observedin [101
closerto the normal.No such convergence
the techniquesused weresomewhatrough). Rather,exceptfor originand
(thoughadmittedly
for longerdifferencing
intervalsseem to have the same "high-tailed"
scale, the distributions
forshorter
as distributins
whichis as wouldbe expectedif the
characteristics
differencing
intervals,
are non-normal
stable.
distributions
all availabletestsof marketefficiency
24. As notedearlyin our discussions,
are implicitly
also
modelsof marketequilibrium.
testsof expectedreturn
But Roll formulates
the economic
explicitly
his estimatesof expectedreturns,
and emphasizesthat he is simultaneously
modelsunderlying
as well as marketefficiency.
testingeconomicmodelsof the termstructure
Capital Markets
Efficient
401
one week loans to commenceat t + j -1, but observedin thiscase at t - 1.
Similarly,
Litis theso-called"liquiditypremium"in rjt;thatis
rjt
E((ro,t+j_iIIt) + Ljt.
In words,the one-week"futures"rateforperiodt + j - 1 observedfromthe
at t of the "spot" ratefort + j -1 plus
termstructure
at t is theexpectation
a "liquiditypremium"(whichcould,however,be positiveor negative).
In all threetheoriesof the termstructureconsideredby Roll, the conditionalexpectationrequiredin (10) is of the form
E(r"j,tPt_1)
- rj+?,tl +
E(LjtJI~t-L)- Lj+L,t-..
The threetheoriesdifferonly in the values assignedto the "liquidityprehypothesis,
investorsmust
miums."For example,in the"liquiditypreference"
so
alwaysbe paid a positivepremiumforbearinginterestrate uncertainty,
thatthe Lit are alwayspositive.By contrast,in the "pure expectations"hypothesis,all liquiditypremiumsare assumedto be zero,so that
i( tJOt-:tL)-
rj+L,t -L.
Roll concludes(i) thatthetwomarketsegmentation
Afterextensivetesting,
with
hypothesesfitthe data betterthan the pure expectationshypothesis,
and (ii)
hypothesis,
perhapsa slightadvantageforthe "liquiditypreference"
themarketforTreasuryBills is effcient.
thatas faras his testsare concerned,
that when the best fittingtermstructuremodel is
Indeed, it is interesting
used to estimatetheconditionalexpected"futures"ratein (10), the resulting
thatif he
variablezjt seemsto be seriallyindependent!It is also interesting
were normal,Roll's resultswould
simplyassumedthathis data distributions
marketsmodel.In thiscase taking
in supportof theefficient
notbe so strongly
afsubstantially
accountof the observedhightails of the data distributions
of the results.25
fectedthe interpretation
6. Tests of a MultipleSecurityExpected ReturnModel
markets
Though the weak formtests supportthe "fair game" efficient
model,all of the evidenceexaminedso far consistsof what we mightcall
"single securitytests." That is, the price or returnhistoriesof individual
securitiesare examinedforevidenceof dependencethatmightbe used as the
basis of a tradingsystemforthat security.We have not discussedtestsof
whethersecuritiesare "appropriately
priced"vis-a-visone another.
betweenaveragereturnsare "appropriate"
But to judgewhetherdifferences
an economictheoryof equilibriumexpectedreturnsis required.At the moment,theonlyfullydevelopedtheoryis thatof Sharpe [40] and Lintner[24,
25. The importanceof distributionalassumptionsis also illustratedin Alexander'swork on trading rules. In his initial tests of filtersystems[1], Alexanderassumed that purchases could always
be executed exactly (rather than at least) y% above lows and sales exactly y% below highs.
Mandelbrot [281 pointed out, however, that though this assumptionwould do little harm with
normallydistributedprice changes (since price series are then essentiallycontinuous), with nonnormal stable distributionsit would introducesubstantialpositive bias into the filterprofits(since
with such distributionsprice series will show many discontinuities). In his later tests [2],
Alexanderdoes indeed find that taking account of the discontinuities(i.e., the presence of large
of the filters.
price changes) in his data substantiallylowers the profitability
402
The Journal
of Finance
25] referredto earlier.In this model (which is a directoutgrowth
of the
mean-standard
deviationportfoliomodels of investorequilibriumof Markowitz[30] and Tobin [43]), theexpectedreturnon securityj fromtimet to
t+ 1 is
E(f,t+1j1t)
=
rf,t+l
+
[
E(Fm,t+lfDt) -rf,t+l
co]
C(j,to,y
rm,t+4lDt)
(11)
whererf,t+1is thereturnfromt to t + 1 on an asset thatis risklessin money
terms; rm,t+1is the returnon the "marketportfolio"m (a portfolioof all
investment
assetswitheach weightedin proportion
to the totalmarketvalue
of all its outstanding
units); 02(rm,t+110t) is thevarianceof the returnon m;
cov
(rij,t+i,
rm,t+:Lit)is the covariance between the returnson j and m; and
the appearanceof lIt indicatesthat the various expectedreturns,variance
and covariance,could in principledependon 'Dt. ThoughSharpeand Lintner
derive(11) as a one-periodmodel,the resultis givena multiperiod
justification and interpretation
in [11]. The modelhas also been extendedin (12)
to thecase wherethe one-periodreturnscould have stable distributions
with
infinitevariances.
In words,(11) says thattheexpectedone-periodreturnon a securityis the
risklessrateof interestrf,t+1plus a "riskpremium"thatis proporone-period
tional to cov(rij,t+i,
rm,t+ilDt)/6(rm
t+11100.In the Sharpe-Lintnermodel
each investorholds some combinationof the risklessasset and the market
so that,givena mean-standard
deviationframework,
portfolio,
the riskof an
individualasset can be measuredby its contribution
to the standarddeviation
of the returnon the marketportfolio.This contributionis in fact cov
*26 The factor
(rj,t+i, rm,t+l r(t)/I(imst+it)
[E(r-m,t+,ifDt)- rf,t+1]/0(rm,t+1j@I t),
whichis the same forall securities,is thenregardedas the marketprice of
risk.
Publishedempiricaltestsof theSharpe-Lintner
modelare notyetavailable,
thoughmuchworkis in progress.There is some publishedwork,however,
which,thoughnot directedat the Sharpe-Lintner
model,is at least consistent
withsomeof its implications.
The statedgoal of thisworkhas been to determinethe extentto whichthe returnson a givensecurityare relatedto the
returnson othersecurities.It started (again) with Kendall's [21] finding
thatthoughcommonstockpricechangesdo notseemto be seriallycorrelated,
thereis a high degreeof cross-correlation
betweenthe simultaneousreturns
of different
securities.This line of attackwas continuedby King [23] who
(usingfactoranalysisof a sampleof monthly
returnson sixtyN.Y.S.E. stocks
fortheperiod1926-60) foundthaton averageabout 50% of thevarianceof
an individualstock's returnscould be accountedfor by a "marketfactor"
thereturnson all stocks,with"industryfactors"accountingfor
whichaffects
at mostan additional10%'oof the variance.
26. That is,
coy (rjt+i
=
rm
Crm
,t+ilt)/o
,t+iI1,t) (Yrm,t+iI,Dd.
CapitalMarkets
Efficient
403
For our purposes,however,the workof Fama, Fisher,Jensen,and Roll
[14] (henceforthFFJR) and the more extensivework of Blume [7] on
monthly
returndata is morerelevant.Theytestthefollowing
"marketmodel,"
originally
suggestedby Markowitz[30]:
r,t+i = aj + ijrM,t+1+ ij,t+
(12)
wherera,t+1
is the rateof returnon securityj formontht, rm,t+i
is the correspondingreturnon a marketindexM, aj and ij are parametersthat can
vary fromsecurityto security,and uj,t+l is a randomdisturbance.
The tests
of FFJR and subsequently
thoseof Blumeindicatethat (12) is well specified
as a linearregressionmodel in that (i) the estimatedparametersaj and ij
remainfairlyconstantover longperiodsof time (e.g., the entirepost-World
War II periodin thecase of Blume), (ii) rM,t+1and theestimatedufj,t+,, are
close to seriallyindependent,
and (iii) the uj,t+i seem to be independent
of
rM,t+1.
Thus theobservedpropertiesof the"marketmodel"are consistent
withthe
expectedreturnefficient
marketsmodel,and, in addition,the "marketmodel"
tellsus something
about theprocessgenerating
expectedreturnsfromsecurity
to security.In particular,
E(r- t+c) = aj + PjE(riM,t+1).
(13)
The questionnow is to what extent(13) is consistentwith the SharpeLintnerexpectedreturnmodel summarizedby (11). Rearranging(11) we
obtain
E(r-j,t+1J|t) aj((Dt)+ (3j((Dt)E(rim,t+i1|Dt),
(14)
where,notingthatthe risklessrate rf,t+1is itselfpart of the information
set
t, we have
and
aj(@Dt)
rf,t+l[ P-j
(Dt)],
Pj( D) =cov (r'jja,~rmt+11(Dt)
(15)
( 16)
Withsome simplifying
assumptions,(14) can be reducedto (13). In particular, if the covarianceand variancethat determineWj(Ct) in (16) are the
same forall t and Dt,thenPjf(Dt)in (16) corresponds
to Pj in (12) and (13),
and the least squares estimateof Pj in (12) is in fact just the ratio of the
samplevalues of the covarianceand variancein (16). If we also assumethat
rf,t+1is thesame forall t, and thatthebehaviorof thereturnson themarket
portfoliom are closelyapproximated
by the returnson some representative
indexM, we willhave comea longway towardequating(13) and (11). Indeed,theonlymissinglinkis whetherin the estimatedparametersof (12)
S)
ajrf(I
(17)
Neither FFJR nor Blume attack this question directly,thoughsome of
Blume's evidenceis at least promising.In particular,the magnitudesof the
The Journalof Finance
404
with (17) in the sense thatthe estimates
estimated`j are roughlyconsistent
are alwaysclose to zero (as theyshouldbe withmonthlyreturndata).27
In a sense, though,in establishingthe apparentempiricalvalidityof the
"marketmodel"of (12), both too muchand too littlehave been shownvisa-vis theSharpe-Lintner
expectedreturnmodelof (11). We knowthatduring
thepost-World
interestrateson risklessassets (e.g.,
War II periodone-month
government
bills withone monthto maturity)have not been constant.Thus,
if expectedsecurityreturnswere generatedby a versionof the "market
model"thatis fullyconsistent
withthe Sharpe-Lintner
model,we would,accordingto (15), expectto observesome non-stationarity
in the estimatesof
basis, however,variationthroughtimein one-periodriskless
aj. On a monthly
interestratesis probablytrivialrelativeto variationin otherfactorsaffecting
monthlycommonstock returns,so that more powerfulstatisticalmethods
wouldbe necessaryto studythe effects
of changesin therisklessrate.
In any case, since the workof FFJR and Blume on the "marketmodel"
was not concernedwithrelatingthismodelto the Sharpe-Lintner
model,we
can onlysay thattheresultsforthe formerare somewhatconsistent
withthe
of the latter.But the resultsforthe "marketmodel" are, after
implications
of thereturngenerating
all, just a statisticaldescription
process,and theyare
probablysomewhatconsistentwith other models of equilibriumexpected
returns.Thus theonlyway to generatestrongempiricalconclusionsabout the
Sharpe-Lintner
modelis to testit directly.On theotherhand,any alternative
modelof equilibrium
expectedreturnsmustbe somewhatconsistent
withthe
"marketmodel,' giventhe evidencein its support.
B. Tests of MartingaleModels of the Semi-strong
Form
In general,semi-strong
formtestsof efficient
marketsmodelsare concerned
with whethercurrentprices "fullyreflect"all obviouslypubliclyavailable
Each individualtest,however,is concernedwiththe adjustment
information.
of securityprices to one kind of information
generatingevent (e.g., stock
of financialreportsby firms,
splits,announcements
new securityissues,etc.).
Thus each testonlybringssupporting
evidenceforthe model,withthe idea
thatby accumulating
such evidencethe validityof the modelwillbe "established."
In fact,however,thoughthe availableevidenceis in supportof theefficient
marketsmodel,it is limitedto a few major typesof information
generating
thestudyof stocksplitsby Fama,
events.The initialmajorworkis apparently
27. With least squares applied to monthlyreturndata, the estimateof (X in (12) is
aj = rj,t -
jrm,t,
where the bars indicate sample mean returns.But, in fact, Blume applies the marketmodel to the
wealth relativesRjt = 1 + rjt and RMt = 1 + rmt.This yields preciselythe same estimateof ,1 as
least squares applied to (12), but the interceptis now
a'J=Rjt-
3jRMt = 1 + rJt-3j(1 + rMt) = 1- pj + aj
Thus what Blume in fact finds is that for almost all securities, j'j + 3j
ctj is close to 0.
1, which implies that
Capital Markets
Efficient
405
Fisher,Jensen,and Roll (FFJR) [14], and all the subsequentstudiessummarizedhere are adaptationsand extensionsof the techniquesdevelopedin
FFJR. Thus, thispaper will firstbe reviewedin some detail,and thenthe
otherstudieswill be considered.
1. Splits and the Adjustmentof Stock Prices to New Information
Since theonlyapparentresultof a stocksplitis to multiplythenumberof
sharesper shareholder
withoutincreasing
claimsto real assets,splitsin themselves are not necessarilysourcesof new information.
The presumption
of
FFJR is that splitsmay oftenbe associatedwith the appearanceof more
fundamentally
important
information.
The idea is to examinesecurityreturns
aroundsplitdates to see firstif thereis any "unusual"behavior,and, if so,
to what extentit can be accountedforby relationships
betweensplitsand
othermorefundamental
variables.
The approachof FFJR to theproblemreliesheavilyon the"marketmodel"
of (12). In thismodelif a stocksplitis associatedwithabnormalbehavior,
thiswouldbe reflected
in the estimatedregressionresidualsforthe months
surrounding
thesplit.For a givensplit,definemonth0 as themonthin which
theeffective
date of a splitoccurs,month1 as themonthimmediately
followingthe splitmonth,month-1 as the monthpreceding,etc. Now definethe
averageresidualoverall splitsecuritiesformonthm (whereforeach security
mis measuredrelativeto thesplitmonth)as
N
N'1
u
wherefUjmis thesampleregression
residualforsecurityj in monthm and N is
thenumberof splits.Next,definethecumulativeaverageresidualUm as
m
Um
i
k=-29
Uk.
as the average deviation(in
The averageresidualum can be interpreted
monthm relativeto splitmonths)of the returnsof split stocksfromtheir
withthemarket.Similarly,
normal
relationships
Um can be interpreted
as the
deviation(frommonth-29 tomonthm). Finally,defineu+, u;, U+
cumulative
and Um as the averageand cumulativeaverageresidualsforsplitsfollowed
by"increased"(+) and "decreased"(-) dividends.An "increase"is a case
wherethe percentagechangein dividendson the splitsharein theyearafter
thesplitis greaterthanthe percentagechangeforthe N.Y.S.E. as a whole,
whilea "decrease"is a case ofrelativedividenddecline.
The essenceof theresultsof FFJR are thensummarized
in Figure1, which
showsthe cumulativeaverage residualsUr U+ and U- for -29 ` m
30. The sampleincludesall 940 stocksplitson the N.Y.S.E. from1927-59,
wherethe exchangewas at least fivenew sharesforfourold, and wherethe
was listedforat least twelvemonthsbeforeand afterthe split.
security
For all threedividendcategoriesthe cumulativeaverageresidualsrise in
406
The Journalof Finance
the29 monthspriorto thesplit,and in factthe averageresiduals(not shown
here) are uniformly
positive.This cannotbe attributed
to thesplitting
process,
sincein onlyabouttenper centof thecases is thetimebetweentheannouncementand effective
dates of a splitgreaterthan fourmonths.Rather,it seems
thatfirmstendto splittheirsharesduring"abnormally"good times-thatis,
duringperiodswhenthepricesof theirshareshave increasedmorethanwould
U
m
o.44
, , , , ,
' ' ' ' '
0.33 -
0.22
0.11
o
t
5 10 15 20 25 30
-29 25-20_15-10_50
Monthrelative to split--m
FIGURE
la
Cumulative average residuals-all splits.
u
m
u-
+
m
10.44
o.~~~~~~~~~
44
0.33
,
,
,
,
,T
~0.33
0.22
.
0.22
0.11
-
.
.
0.11 _.
o:i
0
-29 25-2
15-10 _50
5 10 15 20 25 30
Monthrelative to split--m
FIGURE lb
Cumulative average residuals for dividend
"increases."
~-29 --20
-25
-loO0
-15
5
5
1
0
3
1015 20523
Monthrelative to Split--m
FiGuRE lc
Cumulativeaverage residualsfor dividend
"decreases."
CapitalMarkets
Efficient
407
be impliedby theirnormalrelationships
with generalmarketprices,which
itselfprobablyreflectsa sharp improvement,
relativeto the market,in the
earningsprospectsof thesefirmssometimeduringtheyearsimmediately
precedinga split.28
Afterthesplitmonththereis almostno further
movement
in Un, thecumulativeaverageresidualforall splits.This is striking,
since 71.5 per cent (672
out of 940) of all splitsexperienced
greaterpercentagedividendincreasesin
theyear afterthe splitthanthe averageforall securitieson the N.Y.S.E. In
lightof this,FFJR suggestthatwhena splitis announcedthe marketinterprets this (and correctlyso) as a signal thatthe company'sdirectors are
probablyconfident
thatfutureearningswillbe sufficient
to maintaindividend
paymentsat a higherlevel. Thus the largepriceincreasesin the monthsimmediatelyprecedinga splitmay be due to an alterationin expectations
concerningthe futureearningpotentialof thefirm,ratherthan to any intrinsic
effects
of thesplititself.
If thishypothesis
is correct,returnbehaviorsubsequentto splitsshouldbe
substantially
different
forthe cases wherethe dividendincreasematerializes
thanforthe cases whereit does not. FFJR arguethatin factthe differences
are in the directionsthat would be predicted.The fact that the cumulative
averageresidualsforthe "increased"dividends(Figure lb) driftupwardbut
onlyslightlyin the year afterthesplitis consistentwiththe hypothesisthat
whenthesplitis declared,thereis a priceadjustment
in anticipation
of future
dividendincreases.But thebehaviorof theresidualsforstocksplitsassociated
with "decreased" dividendsofferseven strongerevidencefor the splithypothesis.The cumulativeaverageresidualsforthesestocks(Figure lc) risein
the fewmonthsbeforethe split,but thenfall dramatically
in the fewmonths
afterthe split when the anticipateddividendincrease is not forthcoming.
When a year has passed afterthe split,the cumulativeaverageresidualhas
fallento aboutwhereit was fivemonthspriorto thesplit,whichis about the
earliesttimereliableinformation
about a splitis likelyto reachthe market.
Thus by the timeit becomesclear that the anticipateddividendincreaseis
not forthcoming,
the apparenteffectsof the split seem to have been wiped
away,and the stock'sreturnshave revertedto theirnormalrelationship
with
marketreturns.
Finally,and mostimportant,
althoughthebehaviorof post-splitreturnswill
be verydifferent
dependingon whetheror notdividend"increases"occur,and
in spite of the fact that a large majorityof split securitiesdo experience
dividend"increases,"when all splits are examinedtogether(Figure la),
subsequentto thesplitthereis no netmovement
up or downin thecumulative
28. It is importantto note, however,that as FFJR indicate,the persistentupward driftof the
cumulativeaverage residualsin the monthsprecedingthe split is not a phenomenonthat could be
used to increaseexpectedtradingprofits.The reason is that the behavior of the average residuals
is not representativeof the behavior of the residuals for individual securities.In months prior to
the split, successivesample residualsfor individual securitiesseem to be independent.But in most
cases, there are a few months in which the residuals are abnormally large and positive. The
monthsof large residualsdifferfromsecurityto security,however,and these differences
in timing
explain why the signs of the average residualsare uniformlypositive for many months preceding
the split.
408
The Journalof Finance
of
averageresiduals.Thus, apparentlythe marketmakesunbiasedforecasts
of a split forfuturedividends,and theseforecastsare fully
the implications
in thepricesof thesecurityby theend of thesplitmonth.Afterconreflected
here,FFJR conclude
siderablymoredata analysisthancan be summarized
thattheirresultslend considerablesupportto the conclusionthatthestock
at leastwithrespectto its abiliyto adjust to theinformamarketis efficient,
tionimplicitin a split.
2. OtherStudiesof PublicAnnouncements
Variantsof the methodof residualanalysisdevelopedin [14] have been
kindsof publicannouncements,
of different
used by othersto studytheeffects
marketshypothesis.
and all of thesealso supportthe efficient
Thus usingdata on 261 majorfirmsfortheperiod1946-66,Ball and Brown
of annualearningsannouncements.
[4] applythemethodto studytheeffects
of
of theannualearnings
They use theresidualsfroma timeseriesregression
earnings
firm's
the
classify
to
firms
all
their
of
a firmon theaverageearnings
fora givenyearas having"increased"or "decreased"relativeto themarket.
of monthlycommonstockreturnson an indexof
Residualsfromregressions
of (12)) are thenused to computecumulative
model
market
returns(i.e., the
average returnresidualsseparatelyfor the earningsthat "increased,"and
thosethat"decreased."The cumulativeaveragereturnresidualsrisethroughfor the earnings"increased"
out the year in advance of the announcement
Ball and Brown
category,and fall forthe earnings"decreased"category.29
of
percent
[4, p. 175] concludethatin factno morethanabout tento fifteen
has notbeenanticipated
in theannualearningsannouncement
theinformation
by themonthof the announcement.
On themacrolevel,Waud [45] has used themethodof residualanalysisto
of discountrate changesby Federal
examinethe effectsof announcements
ReserveBanks. In thiscase the residualsare essentiallyjust the deviations
of the dailyreturnson the Standardand Poor's 500 Index fromthe average
"announcement
significant
daily return.He findsevidenceof a statistically
an announcement,
effect"on stockreturnsforthe firsttradingday following
but the magnitudeof the adjustmentis small,neverexceeding.5%. More
is his conmarketshypothesis
fromthe viewpointof the efficient
interesting
(or inthe marketanticipatesthe announcements
clusionthat,if anything,
formation
is somehowleaked in advance). This conclusionis based on the
patternsof the signs of average returnresidualson the days
non-random
precedingthe announcement.
immediately
marketshypothesisis proFurtherevidencein supportof the efficient
of common
vided in the workof Scholes [39] on large secondaryofferings
sales of existingcommonstocksby individuals
stock (ie., largeunderwritten
and on newissuesof stock.He findsthaton averageseconand institutions)
daryissuesare associatedwitha declineof betweenone and twoper centin
commonstocks.
thecumulativeaverageresidualreturnsforthecorresponding
Since the magnitudeof the price adjustmentis unrelatedto the size ofthe
28 is againrelevanthere.
of footnote
29. But thecomment
CapitalMarkets
Efficient
409
issue,Scholesconcludesthatthe adjustmentis not due to "sellingpressure"
im(as is commonly
believed),but ratherresultsfromnegativeinformation
block
firm's
sell
a
of
a
in
is
to
stock.
plicit thefactthatsomebody trying
large
in a seconMoreover,he presentsevidencethatthe value of the information
as
would
be
darydependsto someextenton the vendor;somewhat
expected,
by far the largestnegativecumulativeaverage residualsoccur where the
vendoris the corporationitselfor one of its officers,
withinvestment
comof the vendoris notgenerallyknown
paniesa distantsecond.But theidentity
at the timeof the secondary,and corporateinsidersneed only reporttheir
transactions
in theirowncompany'sstockto theS.E.C. withinsix days aftera
sale. By thistimethemarketon averagehas fullyadjustedto theinformation
in the secondary,as indicatedby the fact thatthe averageresidualsbehave
randomlythereafter.
to
Note, however,thatthoughthisis evidencethatpricesadjust efficiently
public information,
it is also evidencethatcorporateinsidersat least sometimeshave importantinformation
about theirfirmthat is not yet publicly
known.Thus Scholes' evidenceforsecondarydistributions
providessupport
forthe efficient
marketsmodelin the semi-strong
formsense,but also some
strong-form
evidenceagainstthe model.
Thoughhis resultshere are onlypreliminary,
Scholes also reportson an
applicationof the methodof residualanalysisto a sampleof 696 new issues
of commonstockduringtheperiod1926-66.As in the FFJR studyof splits,
thecumulativeaverageresidualsrisein themonthsprecedingthenewsecurity
offering(suggestingthat new issues tend to come after favorablerecent
events)30but behaverandomlyin the monthsfollowing
the offering
(indicatingthatwhateverinformation
is containedin thenewissueis on averagefully
reflected
in thepriceof themonthof the offering).
In short,the available semi-strong
formevidenceon the effectof various
sortsof publicannouncements
on commonstockreturnsis all consistent
with
marketsmodel.The strongpointof the evidence,however,is its
the efficient
consistencyratherthan its quantity;in fact, few different
typesof public
have been examined,thoughthose treatedare among the obinformation
viouslymostimportant.
Moreover,as we shall now see, the amountof semiform
is
evidence
voluminouscomparedto the strongformtests that
strong
are available.
C. StrongForm Tests of the Efficient
MarketsModels
The strongformtests of the efficient
marketsmodel are concernedwith
whetherall available information
is fullyreflected
in pricesin the sense that
no individualhas higherexpectedtradingprofitsthanothersbecause he has
access to someinformation.
monopolistic
We wouldnot,of course,expectthis
modelto be an exact description
of reality,and indeed,theprecedingdiscussions have alreadyindicatedthe existenceof contradictory
evidence.In parand Osborne [32] have pointedout thatspecialistson
ticular,Niederhoffer
theN.Y.S.E. apparentlyuse theirmonopolistic
access to information
concern30. Footnote 28 is again relevanthere.
The Journalof Finance
410
ing unfilledlimitordersto generatemonopolyprofits,and Scholes' evidence
of corporations
sometimes
have monopolistic
access
[39] indicatesthatofficers
abouttheirfirms.
to information
Sincewe alreadyhave enoughevidenceto determine
thatthe modelis not
how
strictly
valid,we can nowturnto otherinteresting
questions.Specifically,
do deviationsfromthe model
far down throughthe investment
community
permeate?Does it pay forthe averageinvestor(or the averageeconomist)
Are such acto expendresourcessearchingout littleknowninformation?
forvariousgroupsof market"professionals"?
tivitiesevengenerally
profitable
More generally,who are the people in the investment
community
that have
access to "special information"?
Thoughthis is a fascinating
problem,only one grouphas been studiedin
of open end mutualfunds.Severalstudiesare
any depth-the managements
available (e.g., Sharpe [41, 42] and Treynor[44]), but the most thorough
willbe limitedto his work.We shall
are Jensen's[19, 20], and our comments
modelunderlying
his tests,and thengo on to his
firstpresentthe theoretical
empiricalresults.
1. TheoreticalFramework
of mutualfundsthe majorgoals are to deterIn studyingtheperformance
mine (a) whetherin generalfundmanagersseem to have access to special
and
information
whichallowsthemto generate"abnormal"expectedreturns,
(b) whethersome fundsare betterat uncoveringsuch special information
will simplybe the abilityof fundsto produce
thanothers.Since thecriterion
higherreturnsthan some normwith no attemptto determinewhat is rethat leads to high
sponsibleforthe high returns,the "special information"
could be eitherkeenerinsightinto the implications
of publicly
performance
thanis implicitin marketpricesor monopolistic
available information
access
of themutualfund
Thus the testsof theperformance
to specificinformation.
marketsmodel.
industryare not strictlystrongformtestsof the efficient
The major theoretical(and practical) problemin usingthe mutualfund
marketsmodel is developinga "norm"against
industryto test the efficient
can be judged.The normmustrepresent
whichperformance
the resultsof an
investment
policybased on the assumptionthatpricesfullyreflectall availAnd if one believesthatinvestorsare generallyriskaverse
able information.
and so on averagemustbe compensatedforany risksundertaken,
thenone
of riskand evaluatingeach
has theproblemof finding
appropriatedefinitions
fundrelativeto a normwithits chosenlevelof risk.
Jensenuses the Sharpe [40]-Lintner[24, 25] model of equilibriumexpectedreturnsdiscussedabove to derivea normconsistentwiththesegoals.
From (14)-(16), in thismodeltheexpectedreturnon an asset or portfolioj
fromt to t + 1 is
E(r'j,t?l 10t)
rf,t+l [1
-
(Dt))] + E (rm,t+1ikt)Pj(3t),
(18)
wherethevarioussymbolsare as definedin SectionIII. A. 6. But (18) is an
and to evaluateperformance
an ex post normis needed.
ex ante relationship,
411
Efficient
CapitalMarkets
One way the lattercan be obtainedis to substitutethe realizedreturnon the
marketportfolioforthe expectedreturnin (18) withthe result3'
rf,t+l [1 -
E(rij,t+,(Dt, rm,t+,)
3j((Dt)] + rm,t+,(j(QDt).
(9)
Geometrically,(19) says that withinthe contextof the Sharpe-Lintner
(Dtand thereturnrm,t?lon
model,theexpectedreturnon j (giveninformation
of its risk
themarketportfolio)is a linearfunction
rm
p(34Q>) - COV (irj,t+1,
as indicatedin Figure2. Assumingthatthevalue of (3j(Dt) is somehowknown,
or can be reliablyestimated,if j is a mutualfund,its ex post performance
of realized
fromt to t + 1 mightnowbe evaluatedby plottingits combination
falls
returnrj,t+land riskin Figure2. If (as forthepointa) thecombination
called,the "market
above theexpectedreturnline (or, as it is morecommonly
line"), it has donebetterthanwouldbe expectedgivenits level of risk,while
if (as forthepointb) it fallsbelowtheline it has doneworse.
r
E(ib,t?1lit,rn ,t+1)-
------------------------------------
b,t+- - -------------m,t+IL
a,tR
%+1 t rm,t+1-
o- ?
-
.
Paia( t)
PM(1t
PO t)
04t)
FIGURE 2
Performance
EvaluationGraph
the marketline shows the combinations
of returnand risk
Alternatively,
providedby portfoliosthat are simplemixturesof the risklessasset and the
marketportfoliom. The returnsand risksforsuch portfolios(call themc)
are
(z1))
0
(D)=coy
(3~QD~)
cv
r =,t+l
(" ,t+1, rm,
"m,t+1!
(rcst
t
O2(irm,t+ 11t)
arf,t+l +
t)
co
l|a
cov
(1 -0rM,t+1
( ?(
)mtat
)t
(1a
) r'm, + l, rm,
mt+1IlIPt+l|
-adrm,t+ij(Dt)1-
hereis thatthe returnr; t--l is generated
accordingto
31. The assumption
and
rj,t+l = ri,t+,[l - j(Dt)]
+ rm,t+j0j((Dt) + Uj,t+ls
t+IIrm,t+,)= 0 forall rm,t+.
E(UJ,
a
412
The Journalof Finance
wherea is the proportionof portfoliofundsinvestedin the risklessasset.
of returnand riskalongthe
Thus,when1 > a > 0 we obtainthecombinations
marketline fromrf,t+?to m in Figure 2, whilewhena < 0 (and underthe
assumptionthat investorscan borrowat the same rate that theylend) we
obtainthe combinationsof returnand risk along the extensionof the line
the marketline representsthe resultsof
throughm. In this interpretation,
a naive investment
whichthe investorwho thinkspricesreflectall
strategy,
availableinformation
of a mutualfundis then
mightfollow.The performance
measuredrelativeto thisnaive strategy.
2. EmpiricalResults
framework
to evaluatetheperformance
Jensenuses thisrisk-return
of 115
mutual fundsover the ten year period 1955-64. He argues at lengthfor
measuringreturnas the nominalten year rate withcontinuouscompounding
(i.e., the naturallog of the ratioof terminalwealthafterten yearsto initial
wealth) and for using historicaldata on nominalone-yearrates with continuouscompounding
to estimaterisk.The Standardand Poor Index of 500
majorcommonstocksis used as theproxyforthemarketportfolio.
The generalquestionto be answeredis whethermutualfundmanagements
have any special insightsor information
whichallows themto earn returns
above thenorm.But Jensenattacksthequestionon severallevels.First,can
the fundsin generaldo well enough to compensateinvestorsfor loading
charges,management
fees,and othercosts thatmightbe avoided by simply
of the risklessasset f and the marketportfoliom
choosingthe combination
withrisklevel comparableto thatof the fund'sactual portfolio?The answer
seemsto be an emphaticno. As faras net returnsto investorsare concerned,
in 89 out of 115 cases, the fund'srisk-return
combinationfor the ten year
periodis belowthemarketline fortheperiod,and theaverageoverall funds
of the deviationsof tenyear returnsfromthemarkettimeis -14.6%o. That
is, on averagethe consumer'swealthafterten yearsof holdingmutualfunds
is aboutfifteen
per centless thanifhe held thecorresponding
portfolios
along
the marketline.
But theloadingchargethatan investor
pays in buyingintoa fundis usually
a pure salesman'scommissionthatthe funditselfnevergets to invest.Thus
one mightask whether,ignoringloading charges (i.e., assumingno such
chargeswere paid by the investor),in generalfundmanagements
can earn
returnssufficiently
above the normto coverall otherexpensesthatare presumablymore directlyrelated to the managementof the fund portfolios.
Again,the answerseemsto be no. Even whenloadingchargesare ignoredin
computingreturns,the risk-return
combinations
for 72 out of 115 fundsare
belowthemarketline,and theaveragedeviationof tenyear returnsfromthe
marketline is -8.9%.
Finally,as a somewhatstrongertest of the efficient
marketsmodel,one
would like to knowif, ignoringall expenses,fundmanagements
in general
showedany abilityto pick securitiesthat outperformed
the norm.Unfortunately,this questioncannotbe answeredwithprecisionforindividualfunds
are not publishedregularly.
since,curiously,data on brokeragecommissions
Efficient
Capital Markets
413
But Jensensuggeststhe available evidenceindicatesthat the answerto the
addingback all otherpubquestionis again probablynegative.Specifically,
for58
combinations
lishedexpensesof fundsto theirreturns,the risk-return
out of 115 fundswerebelowthemarketline,and the averagedeviationof ten
year returnfromthe line was -2.5%o. But part of thisresultis due to the
absence of a correctionfor brokeragecommissions.Estimatingthese commissionsfromaverageportfolioturnoverrates forall fundsfor the period
1953-58,and addingthemback to returnsforall fundsincreasesthe average
deviationfromthe marketline from-2.5%o to .09%o,whichstill is not indicativeof the existenceof specialinformation
amongmutualfundmanagers.
But thoughmutualfundmanagersin generaldo notseemto have access to
in prices,perhapsthereare individual
information
not alreadyfullyreflected
do betterthanthenorm,and so provideat least some
fundsthatconsistently
marketsmodel.If thereare such
strongformevidenceagainstthe efficient
funds,however,they escape Jensen'ssearch. For example,for individual
funds,returnsabove thenormin one subperioddo not seem to be associated
above thenormin othersubperiods.And regardlessof how
withperformance
returnsare measured(i.e., netor grossofloadingchargesand otherexpenses),
thenumberof fundswithlargepositivedeviationsof returnsfromthemarket
line of Figure 2 is less than the numberthatwould be expectedby chance
have no special
with115 fundsundertheassumptionthatfundmanagements
talentsin predicting
returtis.32
Jensenargues that thoughhis resultsapply to only one segmentof the
striking
evidencein favorof the
theyare nevertheless
investment
community,
efficient
marketsmodel:
formofthemartingale
do notimplythatthestrong
Although
theseresultscertainly
and forall time,theyprovidestrongevidencein
hypothesis
holdsforall investors
of thathypothesis.
well
One mustrealizethattheseanalystsare extremely
support
markets
everydayandhavewideMoreover,
theyoperatein thesecurities
endowed.
communities.
in boththe businessand financial
ranging
contactsand associations
returns
unableto forecast
enough
accurately
Thus,thefactthattheyareapparently
in favor
andtransactions
costsis a striking
to recover
theirresearch
pieceofevidence
leastas faras the extensive
of the strongformof themartingale
hypothesis-at
is concerned
availableto theseanalysts
subsetofinformation
[20, p. 170].
IV.
SUMMARY AND CONCLUSIONS
The preceding(ratherlengthy)analysiscan be summarizedas follows.In
marketsis concernedwithwhetherprices
generalterms,thetheoryof efficient
The theoryonlyhas
at anypointin time"fullyreflect"availableinformation.
empiricalcontent,however,withinthe contextof a more specificmodel of
32. On the other hand, thereis some suggestionin Scholes' [39] work on secondaryissues that
mutual fundsmay occassionallyhave access to "special information."Aftercorporateinsiders,the
next largest negative price changes occur when the secondary seller is an investmentcompany
(includingmutual funds), though on average the price changes are much smaller (i.e., closer to 0)
than when the seller is a corporateinsider.
Moreover, Jensen'sevidence itself,though not indicative of the existenceof special information
precise to conclude that such informationnever
among mutual fund managers,is not sufficiently
exists. This strongerconclusion would require exact data on unavoidable expenses (including
brokeragecommissions) of portfoliomanagementincurredby funds.
414
of Ftnance
The Journal
marketequilibrium,that is, a model that specifiesthe nature of market
We have seen
equilibriumwhenprices "fullyreflect"available information.
based on
or explicitly
is implicitly
thatall of theavailableempiricalliterature
the assumptionthat the conditionsof marketequilibriumcan be stated in
termsof expectedreturns.This assumptionis thebasis of theexpectedreturn
marketsmodels.
or "fairgame" efficient
The empiricalwork itselfcan be dividedinto threecategoriesdepending
testsare consubsetof interest.Strong-form
on thenatureof theinformation
access
cernedwithwhetherindividualinvestorsor groupshave monopolistic
One would not expectsuch
relevantforprice formation.
to any information
of the world,and it is probably
an extrememodelto be an exact description
of deviationsfrom
againstwhichthe importance
best viewedas a benchmark
tests
semi-strong-form
can be judged.In the less restrictive
marketefficiency
subset of interestincludesall obviouslypubliclyavailable
the information
subset is just
while in the weak formtests the information
information,
historicalpriceor returnsequences.
marketmodel are the most voluminous,
Weak formtestsof the efficient
and it seems fair to say that the resultsare stronglyin support.Though
evidencefor dependencein successiveprice changes
statisticallysignificant
or returnshas been found,some of this is consistentwiththe "fair game"
to declarethe marketinmodeland the restdoes not appear to be sufficient
efficient.
Indeed,at leastforpricechangesor returnscoveringa day or longer,
thereisn'tmuchevidenceagainstthe"fairgame" model'smoreambitiousoffspring,the randomwalk.
Thus, thereis consistentevidenceof positive dependencein day-to-day
price changesand returnson commonstocks,and the dependenceis of a
profitabletradingrules. In
formthatcan be used as the basis of marginally
Fama's data [10] the dependenceshows up as serial correlationsthat are
closeto zero,and as a slighttendency
consistently
positivebutalso consistently
forobservednumbersof runsofpositiveand negativepricechangesto be less
thanthenumbersthatwouldbe expectedfroma purelyrandomprocess.More
thedependencealso showsup in thefiltertestsof Alexander[1, 2]
important,
and thoseof Fama and Blume [13] as a tendencyforvery small filtersto
But any systems(like the filters)
produceprofitsin excessof buy-and-hold.
dependenceinto tradingprofitsof necessity
that attemptto turnshort-term
thattheirexpectedprofitswould be absorbed
generateso manytransactions
commissions
(securityhandlingfees) thatfloortraders
by even theminimum
strictinteron majorexchangesmustpay. Thus, usinga less thancompletely
this positive dependencedoes not seem of
pretationof marketefficiency,
marketsmodel.
to warrantrejectionof the efficient
sufficient
importance
of the "fair game" efficient
marketsmodel for
Evidence in contradiction
price changesor returnscoveringperiodslongerthan a single day is more
negative
to find.Cootner[9], and Moore [31] reportpreponderantly
difficult
in weeklycommonstockreturns,
and this
(but againsmall) serialcorrelations
resultappears also in the fourday returnsanalyzedby Fama [10]. But it
thereis some slight
does notappear in runstestsof [10], where,if anything,
indicationof positivedependence,but actually not much evidenceof any
Capital Markets
Efficient
415
dependenceat all. In any case, thereis no indicationthatwhateverdependence
existsin weeklyreturnscan be used as thebasis of profitable
tradingrules.
Otherexistingevidenceof dependencein returnsprovidesinteresting
insightsinto the processof price formation
in the stockmarket,but it is not
relevantfor testingthe efficient
marketsmodel. For example,Fama [10]
showsthatlargedailypricechangestendto be folowedby largechanges,but
of unpredictablesign. This suggeststhat importantinformation
cannotbe
completelyevaluatedimmediately,
but that the initialfirstday's adjustment
of pricesto theinformation
is unbiased,whichis sufficient
forthe martingale
model.More interesting
and important,
however,is the Niederhoffer-Osborne
[32] findingof a tendencytowardexcessivereversalsin commonstockprice
changesfromtransaction
to transaction.
They explainthisas a logical result
of the mechanismwherebyordersto buy and sell at marketare matched
against existinglimitorderson the books of the specialist.Given the way
this tendencytowardexcessivereversalsarises,however,thereseems to be
no way it can be used as thebasis of a profitable
tradingrule.As theyrightly
claim,theirresultsare a strongrefutation
of the theoryof randomwalks,at
least as appliedto pricechangesfromtransaction
to transaction,
but theydo
not constituterefutation
of the economically
morerelevant"fair game" efficientmarketsmodel.
formtests,in whichprices are assumed to fullyreflectall
Semi-strong
obviouslypubliclyavailable information,
have also supportedthe efficient
marketshypothesis.
Thus Fama, Fisher,Jensen,and Roll [14] findthatthe
information
in stocksplitsconcerning
the firm'sfuturedividendpaymentsis
on averagefullyreflected
in thepriceof a splitshareat the timeof the split.
Ball and Brown[4] and Scholes[39] cometo similarconclusions
withrespect
to the information
containedin (i) annual earningannouncements
by firms
and (ii) newissuesand largeblocksecondaryissuesof commonstock.Though
onlya few different
typesof information
generatingeventsare represented
here,theyare amongthe moreimportant,
and the resultsare probablyindicativeof whatcan be expectedin futurestudies.
efficient
marketsmodel,in whichpricesare
As notedearlier,thestrong-form
is probablybest viewedas
assumedto fullyreflectall availableinformation,
in
a benchmarkagainstwhichdeviationsfrommarketefficiency
(interpreted
its strictest
sense) can be judged.Two such deviationshave in factbeen oband Osborne [32] point out that specialistson
served.First,Niederhoffer
on unexaccess to information
major securityexchangeshave monopolistic
to generatetradingprofits.
ecutedlimitordersand theyuse thisinformation
This raises the questionof whetherthe "marketmaking"functionof the
specialist (if indeed this is a meaningfuleconomicfunction)could not as
be carriedout by some other-mechanism
that did not implymoneffectively
opolisticaccess to information.
Second, Scholes [39] findsthat,not unexpectedly,corporateinsidersoftenhave monopolisticaccess to information
about theirfirms.
At themoment,
however,corporateinsidersand specialistsare theonlytwo
whose
access to information
has been documented.
groups
monopolistic
There
from
deviations
form
of the efficient
no
evidence
that
the
is
markets
strong
416
The Journal
of Finance
modelpermeatedownany further
theinvestment
For the
through
community.
purposesof mostinvestorstheefficient
marketsmodelseemsa good first(and
second) approximation
to reality.
In short,theevidencein supportof theefficient
marketsmodelis extensive,
and (somewhatuniquely in economics) contradictory
evidence is sparse.
we certainlydo notwantto leave the impression
thatall issues
Nevertheless,
are closed.The old saw, "muchremainsto be done,"is relevanthereas elsewhere.Indeed,as is oftenthe case in successfulscientific
research,now that
we knowwe'vebeenin thepast,we are able to pose and (hopefully)to answer
an evenmoreinteresting
set of questionsforthe future.In thiscase themost
pressingfieldof futureendeavoris the development
and testingof modelsof
marketequilibriumunderuncertainty.
When the processgenerating
equilibriumexpectedreturnsis betterunderstood(and assumingthatsomeexpected
returnmodelturnsout to be relevant),we willhave a moresubstantialframeworkformoresophisticated
intersecurity
testsof marketefficiency.
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