Accounting Research Center, Booth School of Business, University of Chicago
An Empirical Evaluation of Accounting Income Numbers Author(s): Ray Ball and Philip Brown Source: Journal of Accounting Research, Vol. 6, No. 2 (Autumn, 1968), pp. 159-178 Published by: Blackwell Publishing on behalf of Accounting Research Center, Booth School of Business, University of Chicago Stable URL: http://www.jstor.org/stable/2490232 .
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of Accounting EmpiricalEvaluationof An EmpiricalEvaluation IncomeNumbers Income Numbers RAY
BALL*
and
PHILIP
BROWNt
the usefulness f accountAccounting heorists ave generally valuatedtheusefulness theiragreementwith a particular nalytic ing practicesby practicesby the extentof extentof theiragreement model. The model may consist of only a few assertions r it may be evaluationhas the method fevaluationhas rgument.n each case, themethod rigorously eveloped rgument.n the morepreferable morepreferable ractices mracticeswiththe been to compareexisting compareexisting racticeswith the model implies all sta ndardwhich whichthe plied by the model or with some standard thismethod s that t ignores houldpossess.The The shortcomingf shortcomingf thismethod practices houldpossess. ofknowledge namely, he extent o which world,namely, knowledge fthe ftheworld, significantource significantourceof thepredictions thepredictions themodelconformo conform o observed ehavior. It is not not enoughto nquiryon the basis that its enough to defend an analytical nquiryon assumptions re empirically upportable, orhow is one to know that a nd howdoes does oftherelevant relevant upportable ssumptions? ndhow theory mbraces ll ofthe which are based on unone explainthe of propositionswhichare explainthe predictive owersofpropositions maximizationof utilityfunctions? utility functions? verifiable ssumptionssuch ssumptions such as the maximizationof etweenpropositions propositionswhich rise resolvedifferencesetween Further, ow one to resolvedifferences from onsideringifferentspectsofthe oftheworld? The limitations f a completely nalytical pproachto pproachto usefulness re ilincome numbers annot be defined ublustratedby lustratedby the argument hat incomenumbers thereforefdoubtful tility.' "meaning"and are thereforef stantively,hat stantively, hatthey they ack "meaning"and he patchwork evelopment accountThe argument tems partfrom part from hepatchwork University of Western Australia. The authors are University of Chicago. indebted to the participants in the Workshop in Accounting Research at the UniverProfessor Myron Scholes, and Messrs. Owen Hewett and Ian Watts. sity of Chicago, ProfessorMyron Versions of this particular argument appear in Canning (1929); Gilman (1939); Paton and Littleton (1940); Vatter (1947), Ch. 2; Edwards and Bell (1961), Ch. 1; Chambers (1964),pp. (1964), pp. 267-68; Chambers (1966), pp. 4 and 102; Lim (1966), esp. pp. 645 and 649; Chambers (1967), pp. 745-55; Ijiri (1967), Ch. 6, esp. pp. 120-31; and Sterling (1967), p. 65.
159
160
JOURNAL OF ACCOUNTING
RESEARCH,
AUTUMN,
1968
ingpractices meetnewsituations s they rise.Accountants ave had to deal withconsolidations,eases, mergers, esearch nd development, ricelevel changes,and taxation charges,to name just a few problemareas. Because accountingacks an all-embracingheoretical ramework,issimilarities practiceshave evolved. As a consequence,net income s an aggregate componentswhich re nothomogeneous.t is thus allegedto be "meaningless"figure, ot unlike the differenceetweentwenty-seven tables and eight hairs.Underthisview,net ncome an be defined nlyas theresult theapplication f setofprocedures X1, X2, ... to set of events Y1, Y2, -.. withno otherdefinitiveubstantivemeaning t all. Canningobserves: What is set out as a measure of net income can never be supposed to be a fact in any sense at all except that it is the figure hat results when the accountant has finishedapplying the procedures which he adopts.2
The value of analyticalattempts o develop measurements apable of definitiventerpretation not at issue.What is at issue thefactthat an analyticalmodeldoes not tself ssessthe significance departures romts impliedmeasurements. ence it is dangerousto conclude, n the absence of further mpirica esting, ha~t lack of substantivemeaning mplies lack ofutility. An empirical valuationof accounting ncome numbers equires greementas to whatreal-worldutcome onstitutes n appropriate est ofusenumber particular nterest investors, fulness. ecause net ncome theoutcomewe use as a predictive riterions the nvestment ecision s it is reflected security rices.3 oth thecontent nd thetiming existing annualnet ncomenumberswillbe evaluated sinceusefulness ouldbe impairedby deficiencies either.
An Empirical Test Recentdevelopments capitaltheory rovide ustificationor electing the behaviorof security ricesas an operational estofusefulness. impressivebody of theory upports heproposition hat capital markets re bothefficientndunbiased that nformations useful formingapital asset prices, henthe marketwill adjust asset pricesto that information quickly and without eavingany opportunityorfurther bnormalgain.4 If, as theevidence ndicates, ecurity ricesdo infact adjustrapidly o new information it becomesavailable,thenchanges security riceswillreCanning (1929), p. 98. Another approach pursued by Beaver (1968) is to use the investment decision, as it is reflected n transactions volume, for predictive criterion. For example, Samuelson (1965) demonstrated that market without bias in its evaluation of informationwill give rise to randomly fluctuatingtime series of prices. See also Cootner (ed.) (1964); Fama (1965); Fama and Blume (1966); Fama, et al. (1967); and Jensen (1968).
EMPIRICAL
EVALUATION
OF ACCOUNTING
INCOME
NUMBERS
161
fleet he flowof nformationo the market.'An observed evision f stock prices ssociatedwiththe release of the ncomereportwould thus provide evidence hat the nformationeflectedn incomenumbers s useful. Our methodofrelating ccounting ncome o stockpricesbuilds on this theory nd evidenceby focusing n the information hich s unique to particular irm.6pecifically, e construct wo alternativemodels of what the market xpects ncometo be and then nvestigate he market'sreactions when its expectations rove false. EXPECTED
AND UNEXPECTED
INCOME
CHANGES
Historically, he incomes of firms ave tendedto move together.One studyfoundthat about half of the variability n the level of an average firm's arningsper share (EPS) could be associated with economy-wide effects.7 lightofthisevidence, t least part ofthechange a firm'sncomefrom neyearto the next to be expected. f, prioryears,the ncome of firm as been related the ncomes other irms particular way,thenknowledge thatpast relation, ogether ith knowledge the incomesof those otherfirms orthe presentyear,yieldsa conditional xpectation or hepresentncomeofthefirm. hus, apartfrom onfirmation effects, he amountof new informationonveyedby the present ncome number an be approximated ythe difference etween he actual change in income and its conditional xpectation. But not all ofthisdifference necessarily ew nformation.ome changes in ncome esult rom inancingnd other olicydecisionsmadebythefirm. We assumethat,to first pproximation,uch changes re reflectedn the average change income hrough ime. Since the impacts of these two components change-economy-wide and policyeffects-arefeltsimultaneously,he relationshipmustbe estimated ointly.The statistical pecification adopt is first o estimate, y Ordinary east Squares (OLS), the coefficientsaijt, a2pt) rom he linear regression thechange firm's income AIlj,t) on the change in the average incomeof all firms other than firm in the market AMj,tT)8 usingdata up to the end ofthepreviousyear (r 1, 2, ... 1): ljt-
dljt
42itAMj,t-r
U3,t-T
1, 2,
...
1,
(1)
One well documented characteristic of the security market is that useful sources of informationare acted upon and useless sources are ignored. This is hardly surprising since the market consists of large number of competing actors who can gain from acting upon better interpretations of the future than those of their rivals. See, for example, Scholes (1967); and footnote above. This evaluation of the security market differs harply fromthat of Chambers (1966, pp. 272-73). More precisely, we focus on informationnot common to all firms, ince some industry effects re not considered in this paper. 7Alternatively, 35 to 40 per cent could be associated with effectscommon to all firmswhen income was defined tax-adjusted Return on Capital Employed. [Source: Ball and Brown (1967), Table 4.] We call M a "market index" of income because it is constructed only fromfirms traded on the New York Stock Exchange.
162
RAY BALL AND PHILIP
BROWN
he expected ncomechangeforfirm in where hats the regression rediction sing the change in the, year for he market yeart: average AIit
dlit
42jtAMjt
The unexpectedncome hange,orforecast rror pjt), is the actual income changeminus xpected: to be the new informationon-
It is this forecast rror veyedby thepresent ncomenumber. THE MARKET'S
(2)
At
Uit =Ijt
REACTION
It has also been demonstratedhat stock prices,and thereforeates of end to move together. one study,' was return holding estimated hatabout30 to40 percentofthevariability a stock'smonthly rate ofreturn vertheperiodMarch, 1944throughDecember,1960 be associated with market-wide ffects.Market-wide ariations stock of nformation hich oncerns ll firms. returns retriggered y report it relatesto the individual Since we are evaluatingthe timing houldbe assessedrelative o changes the firm, ofreturn n thefirm's tocksnet ofmarket-wideffects. the ate of return The impactof firm may be estimatedby its from nvesting ne dollarin the predicted alue from he inearregression themonthly ricerelatives firm's common tock'0 a marketndexofreturns:"1 10The monthly relative of security for month is defined (dim) closing price (pjmpi), divided by opening price (pjm): (pi,m+i
djm)/pim.
rate of return plus relative is thus equal to the discrete unity; its natural logarithm is the monthly rate of returncompounded In this paper, we assume discrete compounding since the results are easier to interpret in that form. 11Fama, et (1967) conclude that "regressions ofsecurity on market returns for abstracting from the effectsof general time are satisfactory individual securities." In arriving at conditions on the monthly rates individual conclusion, they found that "scatter diagrams return]support very well the regression securities [vis-A-vis Fama, et al. studied of linearity, homoscedasticity, price relatives, as did King (1966). However, natural logarithmic transforms with (3). We also performed Blume (1968) (PRim)
b2In6 L.)
vim
where Ine denotes the natural logarithmic function.The results with those reported below.
(3a) closely
EMPIRICAL
EVALUATION
[PRim
11
OF ACCOUNTING
bij
INCOME
b2j[Lm I]
NUMBERS
VjmX
163
(3)
wherePRjm s the monthly ricerelative orfirm and monthm, is the link relativeof Fisher's "Combination nvestmentPerformancendex" [Fisher 1966)], and vjm the stockreturn esidualforfirm in monthm. The value of Lm 1] s an estimate the market'smonthly ate ofreturn. The m-subscriptn our sampleassumesvaluesfor ll months inceJanuary, 1946forwhichdata are available. The residualfrom he OLS regression epresented equation (3) measurestheextent o which herealizedreturn iffersrom he expected eturn conditionalupon the estimatedregression arameters bj, b2J)and the market ndex [Lm 1]. Thus, since the markethas been found o adjust quicklyand efficientlyo new nformation,heresidualmust representhe alone, on thereturn rom olding impact of new information,bout common tock n firm SOME
ECONOMETRIC
ISSUES
One assumption theOLS incomeregressionmodel'2 s that Mi and ui are uncorrelated. orrelation etweenthem can take at least two forms, namely he nclusion ffirm in the market ndexof ncome Mj), and the presence f ndustry ffects. he first as been eliminated y construction (denotedby the -subscript n M), but no adjustmenthas been made for thepresence f ndustry ffects.t has been estimated hat ndustry ffects probablyaccountforonly about 10 percent of thevariabilityn the level of firm'sncome.'3 or thisreasonequation (1) has been adopted as the appropriate pecification thebelief hatanybias intheestimates ljt and a2jtwillnot be significant. owever, s a check on the statistical fficiency of the model,we also present esults or alternative, aive modelwhich predicts hat ncomewill be the same for hisyear as for ast. Its forecast error simply he change income incethepreviousyear. As is thecase with he ncome egression odel, hestockreturnmodel, presented,ontains everal bviousviolations theassumptions theOLS regressionmodel.First,the market ndexof returnss correlatedwiththe the return firm and beresidualbecause cause of ndustryffects. either iolation serious, ecause Fisher's ndex is calculatedoverall stocks istedon theNew York StockExchange hence the return security is onlya smallpart ofthe index),and because industry ffectsccountfor t most10 percent ofthevariability therate inear, That is, an assumption ecessary orOLS to be theminimum-variance, unbiasedestimator. 13 The magnitude ssigned o industryffectsepends ponhowbroadly industry s defined, hich n turndependsupontheparticular mpirical pplication eing considered. he estimate 10 per cent s based on two-digitlassificationcheme. There s someevidence hat ndustry ffctsmight ccount ormore han10percent whenthe association estimated first ifferencesBrealey 1968)]. 12
164
RAY BALL AND PHILIP
BROWN
ofreturn theaverage tock.'4 secondviolationresults rom urprediction that, for ertainmonths roundthe report ates, the expectedvalues ofthe v/s are nonzero.Again, a~ny ias shouldhave little ffect n the results, nasmuch s there s low, observed utocorrelationn the Vj's,'5and in no case was the stockreturn egression itted ver ess than 100observa-
tions.16
SUMMARY
We assume that in the unlikely bsence of useful nformationbout particular irm ver a period, ts rate ofreturn ver that periodwould reflectonly the presenceof market-widenformation hichpertainsto all firms. y abstracting rommarketeffects equation (3)] we identify he effect f informationertaining o individualfirms. hen, to determine partofthis ffect an be associatedwith nformationontained thefirm's. accounting ncome number,we segregatethe expected and unexpected elements f ncome hange. the ncome orecast rror negative that s, ifthe actual change n income s less than ts conditional xpectation),we define as bad news and predict hat there s some associationbetween accounting ncomenumbers nd stock prices,thenrelease of the income numberwould result the return thatfirm's ecurities eing ess than The estimate of 10 per cent is due to King (1966). Blume (1968) has recently questioned the magnitude of ndustry effects, uggesting that they could be somewhat less than 10 per cent. His contention is based on the observation that the significance attached to industry effectsdepends on the assumptions made about the parameters of the distributions underlying stock rates of return. 14
15 See Table 4, below. 16 Fama, et al. (1967) faced a similar situation. The expected values of the stock
return residuals were nonzero for some of the months in their study. Stock return regressions were calculated separately for both exclusion and inclusion of the months for which the stock return residuals were thought to be nonzero. They report that both sets of results support the same conclusions. An alternative to constrainingthe mean v; to be zero is to employ the Sharpe Capital Asset Pricing Model [Sharpe (1964)] to estimate (3b):
(3b) PRjm-RFmb'i b;j [Lm-RFm1] + vm where RF is the risk-free x ante rate of return for holding period m. Results from estimating (3b) (using U.S. GovernmentBills to measure RF and defining he abnormal return forfirm in month m now as b'1 + v'm) are essentially the same as the results from (3). Equation (3b) is still not entirely satisfactory, however, since the mean impact of new information s estimated over the whole history of the stock, which covers at least 100 months. If (3b) were fittedusing monthly data, vector of dummy variables could be introduced to identify the fiscal year covered by the annual report, thus permitting the mean residual to vary between fiscal years. The impact of unusual information eceived in monthm of year would then be estimated by the sum of the constant, the dummy for year t, and the calculated residual formonth m and year t. Unfortunately, the efficiency estimating the stock return equation in this particular formhas not been investigated satisfactorily,hence our report will be confined to the results from estimating (3).
EMPIRICAL
EVALUATION
INCOME
OF ACCOUNTING
NUMBERS
TABLE Deciles of theDistributions f SquaredCoefficients Correlation,hanges andMarket ncome* Variable
(1) Net income (2) EP
02
165 Firm
Decile .1
.2
.3
.4
.5
.6
.7
.8
.9
.03
.07
.10
.1-5
.23
.30
.35
.43
.52
.05
.11
.16
.23
.28
.35
.42
.52
Estimatedoverthe 21 years,1946-1966.
wouldotherwise ave been expected.17uch result a2 0) wouldbe evi0) around dencedby negativebehavioi in the stockreturn esiduals the annual reportannouncement ate. The converseshould hold for positiveforecast rror. Two basic incomeexpectationsmodelshave been defined, regression modeland naive model.We report detail on twomeasuresof ncome EPS, variables 1) and (2)] forthe regressionmodel,and [net ncome one measure EPS, variable (3)] for he naive model.
Data Threeclasses ofdata are of nterest: he contents ncomereports; he dates ofthe report nnouncements;nd the movements f security rices aroundthe announcement ates. INCOME NUMBERS
Income numbers or 1946 through1966 were obtainedfromStandard and Poor's Compustatapes.18 he distributionsf the squared coefficients ofcorrelation'between he changes n the incomesof theindividualfirms and thechanges n the market's ncome ndex20re summarizedn Table 1. For the present ample,about one-fourth thevariabilityn thechanges We laterdividethetotalreturn ntotwoparts: "normalreturn,"defined thereturnwhichwouldhave been expectedgiven he normal elationshipetween stock and themarket ndex; and an "abnormalreturn," hedifferenceetween he actual return nd the normalreturn. ormally, he two parts are givenby: b2s Lm 1]; and vim. 18 Tapes used are dated 9/28/1965nd 7/07/1967. 19All correlation oefficients thispaper are product-momentorrelation oefficients. 20 The marketnet ncome ndexwas computed s thesamplemeanfor ach year. Themarket PS indexwascomputed weighted verage ver he amplemembers, the number stocksoutstandingadjusted forstock splits and stock dividends) providingheweights. ote thatwhen stimatingheassociation etween he ncome of particular irm nd themarket, he ncomeof thatfirmwas excludedfrom he market ndex. 17
166
RAY BALL AND PHILIP
BROWN
TABLE
Deciles of the Distributions of the Coefficients f First-Order Autocorrelation Income RegressionResiduals* Variable
(1) Net income... (2)EPS..........
the
Decile .1
.2
.3
.4
.5
-.35
-.28
-.20
-.12
-.05
-.39
-.29
-.21
-.15
-.08
.6
.02
-.03
.7
.8
.9
.12
.20
.33
.07
.17
.35
Estimatedoverthe 21 years,1946-1966.
in the media firm'sncomecan be associatedwithchanges n the market index. The association etween he evelsofthe earnings ffirms as examined in the forerunnerrticle Ball and Brown 1967)]. At thattime,we referred to the existence f autocorrelation the disturbanceswhenthe levels of net incomeand EPS were regressed n the appropriate ndexes. this paper, the specification as been changedfrom evels to first ifferences because our method of analyzingthe stock market'sreactionto income numbers resupposes he incomeforecast rrors o be unpredictable minimum 12 months rior o the announcement ates.This supposition is inappropriate hentheerrors re autocorrelated. We tested he extent f autocorrelationn the residuals rom he ncome regressionmodelafter he variableshad been changedfrom evelsto first differences.he results re presented n Table 2. They indicatethat the supposition not nowunwarranted. ANNUAL REPORT
ANNOUNCEMENT
DATES
The Wall Street ournal ublishes hreekindsofannualreport nnouncements:forecasts theyear's ncome, s made,for xample, corporation executives hortly fter he year end; preliminaryeports; nd the complete annual report.Whileforecasts re often mprecise, he preliminary report typically condensedpreviewof the annual report.Because the preliminaryeport suallycontains he same numbers ornet incomeand EPS as are given aterwiththe finalreport, he announcement ate (or, effectively,he date on which he annual ncomenumber ecame generally available) was assumed to be the date on whichthe preliminary eport appeared in the Wall StreetJournal.Table reveals that the time ag between heend ofthefiscalyear and the release o the annual report as been declining teadily hroughouthe sampleperiod. STOCK
PRICES
Stock price relativeswere obtainedfrom he tapes constructed the CenterforResearch SecurityPrices (CRSP) at the University f Chi-
EMPIRICAL
OF ACCOUNTING
EVALUATION
TABLE Time Distribution
167
NUMBERS
INCOME
Dates Fiscalyear
Per centof firm
1957
1958
2/07a 2/04 2/25 2/20 3/10 3/06
25 50 75
1959
2/04 2/18 3/04
_
_
1960
- _
_
_
1961
_
_
1962
2/03 2/02 2/05 2/17 2/15 2/15 3/03 3/05 3/04
- _
_
1963
_
_
1964
_
_
1965
2/03 2/01 1/31 2/13 2/09 2/08 2/28 2/25 2/21
Indicatesthat 25 per centofthe ncome eports or he fiscalyearended 12/31/ 1957had been announced y 2/07/1958. TABLE
of the quared Coefficientf Correlation or the Deciles of the f First-Order Return Regression, and of the Autocorrelation n theStock ReturnResiduals* Decile
Coefficient name
.1
.2
.3
.4
.5
.6
.7
.8
Returnre.40 .37 .34 .31 .22 .25 .28 gression 2... .18 Residual autocorrelation.. -.17 -.14 -.11 -.10 -.08 -.05 -.03 -.01
.9
.46 .03
Estimatedover the 246months,January, 946 hroughJune, 966.
cago.2'The data used are monthly losingpriceson the New York Stock Exchange, djustedfordividends nd capital changes, or heperiodJanuary,1946throughJune,1966. Table presents he decilesof thedistributionsofthesquaredcoefficient correlationor he stockreturn egression [equation(3)], and of the coefficient first-orderutocorrelation the stockresiduals. INCLUSION
CRITERIA
Firms ncluded the studymet thefollowingriteria: 1. earnings ata available on the Compustatapes for ach oftheyears 1946-1966; 2. fiscalyearendingDecember31; 3. pricedata available on the CRSP tapes for t least 100 months; nd 4. Wall StreetJournal nnouncement ates available.22 Ouranalysiswas limited o theninefiscalyears1957-1965.By beginning the analysiswith 1957, we were assuredof at least 10 observationswhen The Center orResearch Security ricesat theUniversity Chicago s sponsoredby MerrillLynch,Pierce,Fennerand Smith ncorporated. 22 Announcementates weretaken nitiallyfrom he Wall StreetJournal ndex, 21
then verifiedagainst
StreetJournal.
168
RAY BALL AND PHILIP
BROWN
estimating he income regression quations. The upper limit (the fiscal year 1965, the results f whichare announced n 1966) is imposedbecause the CRSP file erminatedn June,1966. Our selection riteriamay reducethe generality f the results.The subpopulationdoes not include youngfirms, hose whichhave failed,those whichdo not report n December31, and thosewhich re not represented on Compustat,he CRSP tapes, and the Wall StreetJournal.As a result, it may not be representativef all firms.However,note that (1) the 261 remaining irms23re significantn theirown right, nd (2) a replication f our study on differentample producedresultswhichconform losely to thosereported elow.24 Results Definemonth0 as the monthof the annual report nnouncement, nd APIM the Abnormal erformancendex at monthM, as: APIM
1N
-ZNnm=-11 II (1 Vnm).
Then API tracesoutthevalue of onedollar nvested in equal amounts) all securities (n 1, 2, *, N) at the end of month -12 (that is, 12 monthspriorto the monthof the annual report)and held to the end of somearbitrary olding eriod M -11, -10, * * , T) after bstracting frommarketaffects.An equivalent nterpretation as follows.Suppose two individualsA and agree on the following roposition. is to construct portfolio onsisting f one dollar nvested equal amounts securities. he securities re to be purchasedat the end of month -12 and held untilthe end ofmonthT. For some price,B contractswithA to take (ormakeup), at the end ofeach monthM, onlythe normalgains or losses) and to return o A, at the end ofmonthT, one dollarplus or minus any abnormalgainsorlosses.Then APIM is thevalue ofA's equity the mutualportfoliot the end of each monthM.25 Numericalresultsare presented n two forms.Figure plots APIm first or hreeportfolios onstructed rom ll firms nd years which he income orecast rrors,ccording each of hethree ariables,werepositive (the top half); second,for hreeportfolios firms nd years which he incomeforecast rrorswerenegative the bottomhalf); and third,for singleportfolio onsisting all firms nd years in the sample (the line whichwanders ust below the line dividing he two halves). Table includesthe numbers n whichFigure 1 is based. Due to known errors the data, not all firms ould be included in all years. The fiscal year most affectedwas 1964, when three firmswere excluded. 24 The replication investigated 75 firmswith fiscal years ending on dates other than December 31, using the naive income-forecastingmodel, over the longer period 1947-65. 25 That is, the value expected at the end of month T in the absence of further bnormal gains and losses. 23
EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS
169
1.12 1.10
Variable
1.08
1.08 \'tVariable
1.06 1.04 -S1.02 1.00
To~ai sampie ?j<
.....".............
.......".........-
Total a
0.98 0.9
0.92 0.90 0.88 -12
Variable
ssVariable
Variable. -10 -6 -2 -8 -4 2 4 MonthRelative AnnualReportAnnouncementate
FIG. 1 Abnormal Performance Indexes for Various Portfolios
Since thefirst et of resultsmay be sensitive o the distributions fthe stockreturn isturbances,26secondset ofresults presented.The third column nder ach variableheading Table gives he chi-square tatistic for two-by-twolassification firms the signof the incomeforecast error, nd the signofthe stockreturn esidual or hatmonth. OVERVIEW
As one would expect from largesample,both sets of resultsconvey essentially he same picture.They demonstrate hat the informationontained the annual ncomenumber s useful that actual incomediffers The empirical istributions thestockreturn esiduals ppear to be described wellby symmetric,table distributionshat are characterized y tails longer han thoseof thenormaldistributionFama (1965);Fama, et al. (1967)]. 26
170
RAY BALL AND PHILIP
BROWN
TABLE
SummaryStatistics by Month Relative to Annual Report AnnouncementDate Month elative annuali report nnouncement date
2
1.006 1.014 1.017 1.021 1.026 1.033 1.038 1.050 1.059 1.057 1.060 1.071 1.075 1.076 1.078 1.078 1.075 1.072
Total sample
EPS
EPS
Net income
d()a
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Naive model
Regressionmodel
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
.992 .983 .977 .971 .960 .949 .941 .930 .924 .921 .914 .907 .901 .899 .896 .893 .893 .892
16.5 17.3 7.9 9.5 21.8 42.9 17.9 40.0 35.3 1.4 8.2 28.0 6.4 2.7 0.6 0.1 0.7 0.0
1.007 1.015 1.017 1.022 1.027 1.034 1.039 1.050 1.060 1.058 1.062 1.073 1.076 1.078 1.079 1.079 1.077 1.074
.992 .982 .977 .971 .960 .948 .941 .930 .922 .919 .912 .905 .899 .897 .895 .892 .891 .889
20.4 20.2 3.7 12.0 27.1 37.6 21.3 39.5 33.9 1.8 8.2 28.9 5.5 1.9 1.2 0.1 0.1 0.2
1.006 1.015 1.018 1.022 1.024 1.027 1.032 1.041 1.049 1.045 1.046 1.056 1.057 1.059 1.059 1.057 1.055 1.051
.989 .972 .965 .956 .946 .937 .925 .912 .903 .903 .896 .887 .882 .878 .876 .876 .876 .877
24.1 73.4 20.4 9.1 9.0 19.4 21.0 41.5 37.2 0.1 5.7 35.8 9.4 8.1 0.1 1.2 0.6 0.1
1.000 .999 .998 .998 .995 .993 .992 .993 .995 .992 .991 .993 .992 .992 .991 .990 .989 .987
Column headings:
(1) Abnormal erformancendex-firms nd years whichthe incomeforecast errorwas positive. (2) Abnormal erformancendex-firms nd years which he incomeforecast errorwas negative. (3) Chi-square tatisticfor wo-by-twolassification signof ncomeforecast error for hefiscalyear)andsignof tockreturn esidual for he ndicatedmonth). Note: Probability chi-square 3.84 2= 0) .05,for degree freedom. Probability chi-square 6.64 x2 0) .01,for degree freedom.
from xpected ncome, hemarket ypically as reacted thesame direction.This contention supported othby Figure which eveals marked, positive ssociation etween hesignoftheerror forecastingncome nd ndex,and by thechi-square tatisticTable 5). theAbnormal The latter hows t is mostunlikely hat there s no relationship etween thesignofthe incomeforecast rror nd the signof therate of return esidual mostofthemonths to thatoftheannualreport nnouncement. However,most of the informationontained reported ncome s anticipatedby the marketbefore he annual report released. fact,anticipation so accurate hat the actual incomenumber oes not appear to cause any unusual jumps in the Abnorma Performancendex in the announcementmonth.To illustrate, he drifts pward and downward egin at least 12 months efore he report s released when heportfoliosrefirst
EMPIRICAL
OF ACCOUNTING
EVALUATION
INCOME
171
NUMBERS
TABLE
Contingencyableofthe ignsof the ncome orecast rrors-byVariable Signof ncome orecastrror forecastrror
Variable (1) Variable (2) Variable (3)
Variable 3)
Variable 2)
Variable 1)
157
83
83
1026
1074 399
710
83
83
1026
1231
_
1074
157
1074
399
1074
399
1473
1231 1148
157
1109
710
1148
157
1109 710
399
710 867
constructed) nd continuefor approximately ne monthafter.The persistence fthedrifts,s indicatedby theconstant ignsof the ndexes nd by their lmostmonotonicncreases absolutevalue (Figure1), suggests not only hat themarket egins o anticipate orecast rrors arly the 12 monthspreceding he report, ut also that it continues o do so with ncreasing uccessthroughoutheyear.27 SPECIFIC
RESULTS
1. There appearsto be littledifferenceetween he results orthe two regression odelvariables.Table 6, which lassifieshesignofonevariable's forecast rror ontingent pon thesignsofthe errors the other wovariables,reveals he reason.For example,on the 1231 occasionson which he incomeforecast rrorwas positiveforvariable (1), it was also positiveon 1148 occasions out of possible1231) forvariable (2). Similarly, the 1109occasions nwhich he ncome orecast rrorwas negative orvariable fact (1), it was also negativeon 1026 occasionsforvariable (2). the results orvariable 2) strictly ominate hoseforvariable 1) suggests, however, hatwhenthe two variablesdisagreedon the signof an income forecast rror, ariable (2) was moreoften orrect. Whilethere s little o choosebetweenvariables 1) and (2), variable 3) (the naive model) is clearlybest forthe portfoliomade up offirmswith negativeforecast rrors. contributingactor s the following. he naive model gives the same forecast rror s the regressionmodel would give if Note thatFigure contains veragesovermanyfirms nd yearsand is not ndicativeofthebehavior the ecurities anyparticular irm anyoneyear.While theremay be, on average, persistent nd gradualanticipation f the contents the report hroughouthe year,evidence on the extentof autocorrelation the stockreturn esidualswould uggest hatthemarket's eaction o informationbout particular irmendsto occurrapidly. 27
172
RAY BALL AND PHILIP
BROWN
(a) the change n market ncomewere zero,and (b) therewereno drift n the incomeof the firm. ut historically herehas been an increase the market's ncome,particularly uring he latterpart of the sample period, due to general ncrease prices nd thestrong nfluence theprotracted expansion ince 1961. Thus, thenaive model variable 3)] typicallydentifies s firmswithnegativeforecast rrors hose relatively ewfirmswhich showed a decreasein EPS when most firms howed an increase.Of the three ariables, newouldbe most onfidenthatthe ncomes f hosewhich showednegativeforecast rrors orvariable (3) have in fact lost ground relative o the market. This observation as interestingmplications. or example, t points o a relationship etween hemagnitudes f the incomeforecast rrors nd the magnitudes f the abnormal tock price adjustments.This conclusion reinforced y Figure whichshows that the resultsforpositiveforecast errors reweakerforvariable 3) thanfor he other wo. 2. The drift ownward n the AbnormalPerformancendex computed over all firms nd years the samplereflects computational ias.28 he bias arisesbecause
E[fI (1
vm)]
II [1
E(vm)],
where denotesthe expectedvalue. It can readilybe seen that the bias over months at least of order 1) timesthe covariancebetween vm nd Vm._ .29 Since thiscovariance s typicallynegative, the bias is also negative. While the bias does not affect he tenorof our results any way, it shouldbe kept mindwhen nterpretinghevalues ofthevariousAPI's. It helps explain,forexample,whythe absolutechanges the indexes thebottompanel of Figure tendto be greater han those n thetoppanel; whythe ndexes the top panel tendto turndown shortly ftermonth and finally, hythedrifts the ndexes thebottom aneltendtopersist beyondthe month f thereport nnouncement. 3. We also computed esults or he regression odelusing headditional definitionsf ncome: (a) cash flow, approximated y operating ncome,3"nd (b) netincomebeforenonrecurringtems. Neither ariablewas as successful predictinghesignsofthestockreturn The expected value of the bias is of order minus one-half to minus one-quarter of one per cent per annum. The difference etween the observed value of the API computed over the total sample and its expectation is a property of the particular sample (see footnote 26). 29 In particular, the approximation neglects all permutations of the product v.*v, s 1,2, K-2, t s+2,. ,K, as being of second order of smallness. 30 See Table 4. 31 All variable definitionsare specified in Standard and Poor's CompustatManual [see also Ball and Brown (1967), Appendix A]. 28
EMPIRICAL
EVALUATION
OF ACCOUNTING
INCOME
NUMBERS
residuals s net ncome nd EPS. For by month , theAbnormal Performancendexes for whichwere positive were 1.068 income, ncludingnonrecurringtems) (operating ncome). These numbers omparewith income Table 5, variable The respectivenumbers orfirms nd negativeforecast rrors were0.911, 0.917,and 4. Both the API's and chi-square est in Table 5 suggest hat, least forvariable 3), therelationship hesignofthe ncomeforecast error nd that of the stockreturn esidualmay have persisted as long-as womonths eyond month the announcement f the annual report.One explanationmightbe the market's ndexof incomewas not knownforsureuntil after everal announcedtheir ncome numbers. he uncertaintyboutthemarket's ncome quent to some nnouncementsmight end,when firms thesample, o persistence thedrifts the beyondthe month.This explanation an out,however, ince those firmswhichmade their January anyoneyearwereexcluded rom hesamplefor hatyear, no changes thepatterns f overallAPI's as presented n Figure 1, although enerally herewerereductions statistics.32 second xplanation ouldbe random theannouncementates. Drifts API's wouldpersist eyond announcement onth errors ourtreating omefirms s if announced heir ncome numbers arlier han in factwas But this explanation an also probablybe ruledout, sinceall announcement ates takenfrom he Wall Street verified gainstthe Wall StreetJournal. third xplanation ould be preliminaryeports re not perceived by the market beingfinal.Unfortunatelyhis ssue independently f an alternative ypothesis, amelythat the marketdoes take more imeto adjust to information thevalue of nformation lessthanthe transactions oststhatwouldbe incurred an who wished advantage of the opportunity orabnormalgain. That is, relationshipended o persist eyond announcementmonth, it is unlesstransactions osts were one per cent,33 32
The general reduction
x2 tatistic is due largely to the reduction in
This is obtained as follows. The ratio APIm/APImi_ ginal return in month plus unity: 33
equal to the mar-
AP1m
Similarly, APIm_2 APIml APIm-2 -APIm.i
APImi AP1.m2
(1+
rm)(
rm-i),
174
RAY BALL AND PHILIP
BROWN
therewas no opportunityor bnormal rofit nce the ncome nformation had becomegenerally vailable. Our results re thus consistentwithother evidencethat the market ends to react to data withoutbias, at least to within ransactionsosts. TO OTHER SOURCES
THE VALUE OF ANNUAL NET INCOME RELATIVE
OF
INFORMATION34
The resultsdemonstrate hat the informationontained n the annual incomenumber s useful n that it is relatedto stockprices.But annual accounting eports re onlyone of themanysourcesof nformationvailable to investors. he aim ofthissection to assess the relative mportance of informationontained n net income, nd at the same timeto provide some nsightnto hetimeliness f he ncome eport. It was suggested arlier hat the impactof new informationbout an individual stock could be measured by the stock's returnresidual.For example, negativeresidualwould indicatethat the actual return s less than what would have been expectedhad therebeen no bad information. Equivalently, an investor s able to take advantage of the information eitherby sellingor by taking a shortposition n advance of the market adjustment, hen the residualwill represent,gnoring ransactions osts, the extent o whichhisreturn s greater hanwould normally expected. If thedifferenceetween he realized nd expected eturn accepted as also indicating hevalue ofnew nformation,hen t is clear thatthevalue of new, monthly nformation, ood or bad, about an individual tock is given by the absolute value of that stock'sreturn esidualforthe given month. t follows hatthe value of all monthlynformationoncerninghe averagefirm,eceived the12months receding he report,s givenby:
Tloand, in general,
(1 API API8
(1
r.l)
Vjm~) ...
(1
1.00, rm).
Thus, the marginal return for the two months after the announcement date on the portfolio consisting of firmsfor which EPS decrease would have been 0.878/0.887 -.010; similarly, the marginal return on the portfolio of firmsfor which EPS .003. After allowing for the computaincreased would have been 1.059/1.056 tional bias, it would appear that transactions costs must have been within one per cent foropportunities to have existed forabnormal profit rom pplying some mechanical trading rule. 34 This analysis does not consider the marginal contribution of information contained in the annual income number. It would be interestingto analyze dividends in way similar to that we have used for ncome announcements. We expect there would be some overlap. To the extent that there overlap, we attribute the information to the income number and consider the dividend announcement to be the medium by which the market learns about income. This assumption is highly artificial in that historical income numbers and dividend payments might both simply be reflections of the same, more fundamental informational determinants of stock prices.
EMPIRICAL
EVALUATION
OF ACCOUNTING
INCOME
NUMBERS
175
where TI denotes total information.5or our sample, averaged over all firmsnd years, his umwas 0.731. For any one particular tock, ome of the informationetweenmonths willbe offsetting.36 he value ofnet nformationreceived n the 12 months preceding he report) bout the average tock s givenby:
NIo
1+Vjm) -1.00
whereNI denotesnet nformation.his sumwas 0.165. The impact of the annual incomenumber s also a net number n that net income s the resultof both income-increasingnd income-decreasing events. f one acceptsthe forecast rrormodel,37hen he value of nformation contained n the annual income numbermay be estimatedby the averageof the value increments rommonth-11 to month0, wherethe incrementsre averagedover the twoportfoliosonstructed rom buying or selling hort)all firms nd years as classified y the signsofthe ncome forecast rrors. hat is,
II
=
Nl(APIo'
1.00) N2(API2(N1 + N2)
1.00)
where denotes ncome nformation,nd Ni and N2 the numberof occasions on whichthe incomeforecast rrorwas positiveand negativerespectively. his numberwas 0.081 forvariable (1), 0.083 forvariable (2), and 0.077 forvariable (3). From the above numberswe conclude: (1) about75 percent (.731 .165)/.731] fthevalue of all information appearsto be offsetting,hich turn mplies hat about 25 per centpersists;and (2) ofthe25 percentwhichpersists, bout half 49%, 50 %, and 47 %calculated as .081/.165, 083/.165,and .077/.165-for variables (1)-(3)] can be associatedwith the informationontained reportedncome. Two furtheronclusions, ot directly vident, re: (3) of the value of informationontained reported ncome,no more thanabout 10 to 15percent 12 %, 11 %, and 13%) has notbeenanticipated by themonth fthe report;38nd 35Note that the information s reflected
a value increment; thus, the original
$1.00 is deducted from the terminal value. 36 This assertion is supported by the observed low autocorrelation in the stock return residuals. 37 Note that since we are interested in the "average firm,"an investmentstrategy must be adopted on every sample member. Because there are only two relevant strategies involved, it is sufficient o know whetherone is better off o buy or to sell short. Note also that the analysis assumes the strategy is first dopted 12 months prior to the announcement date. 38 The average monthly yield from policy of buying portfolio consisting of all firmswith positive forecast errors and adopting short position on the rest would have resulted in an average monthly abnormal rate of return, from -11 to -1, of
176
RAY BALL AND PHILIP
BROWN
(4) thevalue of nformationonveyed y the ncomenumber t the time of tsrelease onstitutes,n average, nly20 percent 19 %, 18 %, and 19%) ofthevalue of all informationoming o themarket n thatmonth.39 The second conclusion ndicatesthat accounting ncomenumbers aptureabout halfof thenet effect f all informationvailablethroughouthe 12 months receding heirrelease;yet the fourth onclusion uggests hat net income ontributes nlyabout 20 per cent of the value of all information the monthof ts release.The apparentparadox is presumably ue to thefactthat: (a) many otherbits of nformationre usually released the same month s reported ncome for xample,via dividend nnouncements,or perhaps other tems n the financial eports); b) 85 to 90 per cent of the net effect f informationbout annual income s already reflected security ricesby the monthof its announcement; nd (c) the periodofthe annualreports already ne-and-one-half onthsntohistory. Ours is perhaps the first ttempt o assess empirically he relative mportanceof the annual incomenumber, ut it does have limitations. or example,our results re systematically iased againstfindingsn favorof accounting eports ue to: 1. the assumption hat stock prices are from ransactionswhich have takenplacesimultaneouslyt theendofthemonth; 2. theassumption hat there re no errorsn the data; 3. the discretenatureof stockpricequotations; 4. the presumed alidityof the "errors n forecast"model; and 5. the regression stimatesof the incomeforecast rrors eing random variables,which impliesthat some misclassificationsf the "true" earnings orecast rrors re inevitable.
ConcludingRemarks The initialobjectivewas to assess theusefulness existing ccounting heir nformationontent nd timeliness. income The mode of analysispermitted omedefinite onclusionswhichwe shall briefly estate.Of all the informationbout an individualfirmwhichbecomesavailable during year,one-half r more captured that year's incomenumber. ts content thereforeonsiderable.However, he annual incomereport oes not rate highly s a timelymedium, incemost of its content about 85 to 90 per cent) capturedby morepromptmediawhich perhaps nclude nterim eports. ince the efficiency the capital market 0.63%, 0.66%, and 0.60% for variables (1), (2), and (3) respectively. The marginal rate of return n month 0 for that same strategy would have been 0.92%, 0.89%, and 0.94% respectively. However, relatively much more information s conveyed in the month of the report announcement than in either of the two months immediately preceding the announcement month or in the two months immediately following t. This result is consistent with those obtained by Beaver (1968). 39 An optimum policy (that is, one which takes advantage of all information) would have yielded an abnormal rate of return of 4.9% in month 0.
EMPIRICAL
EVALUATION
OF ACCOUNTING
INCOME
NUMBERS
177
is largely etermined y the adequacy of ts data sources,we do not find disconcertinghat the markethas turnedto othersourceswhich can be acteduponmorepromptlyhan annualnet ncome. This studyraisesseveral ssuesforfurthernvestigation. or example, there emains he taskof dentifyinghe media by which hemarket able to anticipatenet income: of what help are interim eports nd dividend announcements?or accountants, here s the problem f assessing hecost of preparing nnual income reportsrelativeto that o the more timely interim eports. The relationship etweenthe magnitude and not merely he sign) of the unexpected ncomechangeand the associatedstockpriceadjustment could also be investigated.40his would offer different ay ofmeasuring the value of informationbout income changes,and might, addition, furnishnsight nto the statisticalnature ofthe incomeprocess, process littleunderstood ut ofconsiderablenterest o accounting esearchers. Finally,a mechanism as been providedforan empirical pproachto restrictedlass ofthe controversialhoices external eporting. REFERENCES
BALL, RAY ANDPHILIP BROWN 1967). "Some PreliminaryFindings on the Association between the Earnings of Firm, Its Industry and the Economy," Empirical Research Accounting:Selected Studies, 1967, Supplement to Volume 5 of the Journal of Accounting Research, pp. 55-77. BEAVER, WILLIAM H. (1968). "The Information Content of Annual Earnings Announcements," forthcoming Empirical Research n Accounting:Selected Studies 1968, Supplement to Volume 6 of the Journal of AccountingResearch. BLUME, MARSHALL E. (1968). "The Assessment of Portfolio Performance" (unpublished Ph.D. dissertation, University of Chicago). BREALEY, RICHARD A. (1968). "The Influence of the Economy on the Earnings of the Firm" (unpublished paper presented at the Sloane School of Finance Seminar, Massachusetts Institute of Technology, May, 1968). BROWN, PHILIP AND VICTOR NIEDERHOFFER (1968). "The Predictive Content of Quarterly Earnings," Journal of Business. CANNING, JOHN B. (1929). The Economics of Accountancy (New York: The Ronald Press Co.). CHAMBERS, RAYMOND J. (1964). "Measurement and Objectivity in Accounting," The AccountingReview, XXXIX (April, 1964), 264-74. (1966). Accounting,Evaluation, and Economic Behavior (Englewood Cliffs,N.J.: Prentice-Hall). (1967). "Continuously Contemporary Accounting-Additivity and Action," The AccountingReview, XLII (October, 1967), 751-57. COOTNER, PAUL H., ed. (1964). The Random Character of Stock Market Prices (Cambridge, Mass.: The M.I.T. Press). 40 There
are some difficult conometric problems associated with this relationship, including specifyingthe appropriate functional form, he expected statistical distributions ofthe underlyingparameters, the expected behavior of the regression residuals, and the extent and effects of measurement errors in both dependent and independent variables. (The functional form need not necessarily be linear, if only because income numbers convey information about the covariability of the income process.)
178
RAY BALL AND PHILIP
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W. BELL (1961). The Theory nd Measurement
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