Trading Volume and Belief Revisions That Differ Among Individual Analysts

7/28/2019 Trading Volume and Belief Revisions That Differ Among Individual Analysts

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Trading Volume and Belief Revisions That Differ among Individual Analysts

Author(s): Orie E. BarronSource: The Accounting Review, Vol. 70, No. 4 (Oct., 1995), pp. 581-597Published by: American Accounting AssociationStable URL: http://www.jstor.org/stable/248248 .

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THE ACCOUNTING REVIEWVol. 70, No. 4October 1995pp. 581-597

Trading Vo l ume a n d B e l i e fRevisions T h a t D i f f e r A m o n g

Individual Analys ts

Orie E. BarronIndiana UniversityABSTRACT:This study examines the association between tradingvolume andbelief revisions. Mosttradingvolumetheories suggest that investors'differentialbeliefrevisionscause trading olume.A beliefrevision sdifferentialf itchanges thepositionof an individual'sxpectationrelativeo the distributionfexpectationsheldby others. Thus, I use the correlationbetween the relativepositionsof individualanalysts' currentand priorforecasts of earnings to measure differentialbeliefrevisions.Ina multiple egressionanalysis,thiscorrelationmeasureexplains radingvolumebeyondthatexplainedby priordispersion nforecasts, whichis consistentwithKarpoff's1986) predictionhat radings caused bybothdifferentialriorbeliefsand differential eliefrevisions.KeyWords: Disagreement,Trading olume,Differentialeliefrevisions,Analysts'forecasts.Data Availability:Data analyzedin thisstudy maybe obtainedfrom IIB/EIS ndfromthe CRSP (Center orResearch intoSecurityPrices)database.

This study is from the empirical chapter of my dissertation at the University of Oregon. The careful review andguidance of Dale Morse (Chair), Ray King and George Racette deserve special thanks, as does the additional input ofLinda Bamber, Jerry Salamon and two anonymous referees. I am also thankful for useful input from Walt Blacconiere,Larry Brown, Ken Gaver, Jon Karpoff, Charles Kile, Terry O'Keefe, Jamie Pratt, Larry Richards, Doug Stevens, TomStober and Mark Thoma as well as workshop participants at the Emory Business School, Indiana University, theUniversity of Washington, Washington University in St. Louis, and Western Washington University for their usefulcomments. I am responsible for any errors.

I gratefully acknowledge the contribution of I/B/E/S International Inc. for providing earnings per share forecast data,available through the Institutional Brokers Estimate System. This data has been provided as part of a broad academicprogram to encourage earnings expectations research. Submitted January 1994.

Accepted April 1995.

581

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582 The Accounting Review, October 1995I. INTRODUCTION

T his study examines the empirical association between trading volume and belief revisionsthat differ among individual analysts. Accountants' interest in this association stems inpart from interest in interpreting volume reactions observed in financial accountingstudies (e.g., Beaver 1968, Morse 1981, Bamber 1986). It has been suggested that the tradingvolume around earnings announcements arises because belief revisions differ across investors.Beaver (1968, 69), for example, offers the following intuition: "An important distinction betweenprice and volume tests is that the former reflects changes in the expectations of the market as a

whole while the latter reflects changes in the expectations of individual investors." Moreformally, Karpoff (1986) identifies two distinct theoretical links through which changes in theexpectations of individual investors can stimulate trading volume:

[The] links of volume to information [provide] a rationale for the use of volume inevent studies.... Unusually high volume can result from heterogeneous reactions to theinformation, but it does not necessarily reflect disagreement among traders; it can alsoreflect consensus among traders with diverse priors (Karpoff 1986, 1084).

Several accounting studies investigate the link between trading volume and diversity ininvestors' prior beliefs by using the level of dispersion in analysts' earnings forecasts (i.e., thecross-sectional variation in forecasts) as a measure of diversity in prior beliefs (Comiskey et al.1987; Ajinkya et al. 1991; Stickel 1991; Atiase and Bamber 1994; Kross et al. 1994; Bamber andCheon 1995). Most of these studies document a positive association between forecast dispersionand trading volume. ' For example, Ajinkya et al. (1991) examine the trading volume associatedwith an almost continuous flow of information to financial markets and find a positive associationbetween monthly forecast dispersion and firms' percentage of outstanding shares traded.2 Incontrast, there is little direct empirical evidence concerning Karpoff's prediction that tradingvolume is caused by both diversity in prior beliefs and differential belief revisions. Similar linksbetween trading volume and differential belief revisions are also suggested by most of thetheoretical trading volume research in the accounting literature (e.g., Jang and Ro 1989;Holthausen and Verrecchia 1990; Kim and Verrecchia 1991; Dontoh and Ronen 1993).Some prior research can be interpreted as studying the association between trading volumeand differential belief revisions. Ziebart (1990) and Lang et al. (1992) examine changes inanalysts' forecast dispersion around earnings announcements and find significant positiveassociations between dispersion changes and measures of trading volume. Yet, these studies donot provide evidence that dispersion changes reflect a different influence on trading volume thanprior levels of dispersion, since they do not include prior dispersion levels in regression models.3Further, changes in forecast dispersion may not reflect the differential belief revisions referredto by Karpoff (1986). For example, Lang et al. (1992) use squared changes in forecast dispersion.

I Stickel (1991) finds no significant relation between forecast dispersionandtradingvolume aftercontrollingfor pricechanges (although Atiase and Bamber (1994) and Kross et al. (1994) do find a positive relation between forecastdispersion and trading volume after controllingfor price changes).2 Ajinkya et al. (1991) use contemporaneous forecastdispersionin theirstudy. Karpoff s (1986) model only suggests anassociation between contemporaneous dispersionandtradingvolume to the extent it reflects differences in investors'

prior beliefs or differentialcontemporaneous belief revisions.I Ziebart (1990), forexample, uses an eventstudymethodology in which change infirm-specific trading s thedependentvariable. The level of differential priorexpectations is not included in his regression models because Ziebartdoes notexpect it to impact the change in firm-specific tradingacross a two-week event period.



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Barron-Trading Volume and Belief Revisions That Differ Among IndividualAnalysts 583This measure assigns a decrease in dispersion the same value as an increase in dispersion of thesame magnitude. Thus, it may reflect either disagreement or consensus among analysts withdiverse prior beliefs. Ziebart (1990) avoids this ambiguity by using changes in dispersion per se.Yet, Ziebart' s measure may not reflect changes in the relative position of individual expectationswithin the distribution of all expectations (e.g., two forecasts that swap positions). According toKarpoff (1986), it is this type of differential belief revision, or "jumbling" of expectations, thatstimulates trading volume.

The changes in forecast dispersion used in prior studies are also likely to be biased. Recentempirical analysis of detailed forecast data suggests a spurious association between financialnews and increases in forecast dispersion, which simply results from outdated forecasts that donot move (Brown and Han 1992; Stickel 1995). Further, Abarbanell et al. (1995) argueanalytically that inferences from studies using changes in forecast dispersion are threatened bythe failure to control for the magnitude of price changes. The magnitude of price changes controlsfor the information (or informedness) contained in the average belief revision, information thatis likely to be correlated with both trading volume and changes in forecast dispersion.This study tests the predictions that (a) differential belief revisions stimulate trading volumeand (b) differential belief revisions exert a different influence on trading volume than diversityin prior beliefs. As in Ajinkya et al. (1991), I examine monthly trading volume that is not restrictedto months containing formal accounting events/disclosures. Yet, this study differs from Ajinkyaet al. (1991) in three important respects. First, I use the correlation between the relative positionsof individual analysts' current and prior months earnings forecasts as an empirical proxy for thedegree of differential belief revision. The aim of this correlation measure is to capture Karpoff' snotion of "jumbled" expectations. Second, multiple disagreement measures are included in amultiple regression to provide evidence on whetherjumbled forecasts reflect different influenceson trading volume than the dispersion in prior forecasts. I also use the change in dispersionmeasure introduced by Ziebart (1990) as a supplemental measure of disagreement, since forecastsmay become increasingly dispersed without changing their relative positions (i.e., withoutjumbling). Third, I address a concern that the association between trading volume and disagree-ment proxies may be due to either stale forecasts or price effects by (a) constructing disagreementmeasures using detailed I/B/E/S (Institutional Brokers' Estimate System) data that are purged ofpotentially stale forecasts, and (b) controlling for the magnitude of price changes.

Empirical results are consistent with Karpoff's prediction that trading volume is associatedwith both differential prior beliefs and differential belief revisions. In multiple regressionanalysis, estimated coefficients show that the monthly percentage of equity shares traded isassociated with (1) high levels of dispersion in the prior month's forecasts, (2) increasinglydispersed forecasts and (3) low correlations between analysts' current and prior forecasts (i.e.,heterogeneous forecast revisions). Additional analysis suggests an association between tradingvolume and all three disagreement measures, even after controlling for price changes, market-wide trading and firm size. These findings add to prior empirical evidence suggesting that tradingvolume is associated with dispersion measures, while also demonstrating an additional linkbetween volume and the correlation between current and prior forecasts (a proxy for jumbledbeliefs).

Accountants' interest in differential belief revisions extends beyond understanding tradingvolume. For example, the correlation between current and prior forecasts is potentially useful forinterpreting changes in forecast dispersion. Forecast dispersion reflects analysts' average"informedness" (i.e., uncertainty) as well as information asymmetry across analysts (Barron1993; Abarbanell et al. 1995). Thus, decreases in forecast dispersion may arise from eitherpublicly or privately observed news, because both types of news increase average informedness.



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584 The Accounting Review, October 1995Yet, if the news does not jumble forecasts, then this suggests that it is commonly observed andinterpreted. In other words, similar belief revisions are likely to result from news that is similarlyobserved and interpreted.4 Thus, the correlation between current and prior forecasts may be usefulin future studies that examine specific types of events (e.g., earnings announcements) to assesswhether they are commonly interpreted. Accountants' interest in this type of examination extendsto the broader issue of producing financial reports that communicate clearly.

The next section discusses testable hypotheses suggested by Karpoff (1986). Section IIIdiscusses sample selection and research design issues. Section IV presents and analyzes results.Section V concludes with summary comments.

II. DEVELOPMENT OF HYPOTHESESI base hypotheses on the assumption that disagreement among analysts reflects disagreement

among investors. More specifically, I assume that different positions and changes in individualanalysts' earnings forecasts are reasonable proxies for different positions and changes inindividual investors' bid and ask prices. This assumption is consistent with empirical evidencesuggesting that investors use analysts' earnings forecasts as important inputs when evaluatingfirms (Givoly and Lakonishok 1984) and that earnings forecasts are among the most importantdeterminants of analysts' buy/sell recommendations (Previts et al. 1994).

Before considering the association between trading volume and disagreement, it is importantto recognize that trading volume reflects many types of changes in investors' portfolios.According to Karpoff's model, portfolio changes result from a reordering or "jumbling" ofinvestors' bid and ask prices (or simply demand prices). This jumbling can result from non-informational factors such as changes in investors' consumption preferences. Karpoff's modelsuggests that some of this non-informational, or liquidity, trading will occur at all times becauseinvestors' demand prices constantly change due to idiosyncratic consumption needs and portfoliorebalancing.

This paper focuses on the trading volume that results from information arrival. Karpoff'smodel suggests that information induces trading volume in two distinct ways. First, trading resultswhen contemporaneous news causes investors to react heterogeneously. In other words, onecause of jumbled demand prices is the differential changes in investors' expectations that occurwhen investors have different interpretations of public information. Second, trading is predictedwhen investors with different prior period beliefs observe commonly interpreted news. Inessence, commonly interpreted news serves to resolve disagreement between investors who holdlong and short positions in a stock. Although the resolution of prior disagreement does not jumbleinvestors expectations, it does create an incentive for investors to discontinue holding purelyspeculative positions. Thus, Karpoff's model suggests that commonly interpreted news isassociated with the trading volume that results as investors close out their speculative positions(i.e., consume or invest in other securities).

Figure 1illustrates three different empirical proxies for investor disagreement. The first is thePearson correlation between individual analysts' forecasts made in the prior period and corre-

4 Although the interpretation f similarbelief revisions is relatively clear,the interpretation f differentialbelief revisionsis more ambiguous. Differential belief revisions may reflect the influences of differential(i.e., private) information,differential interpretations,or common interpretationsamong investors/analysts possessing private information ofvarying precision (i.e., varyingreliability). Eachof these potential causes of differentialbelief revisions has been linkedtheoreticallywith tradingvolume.



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Barron-Trading Volume and Belief Revisions That Differ Among IndividualAnalysts 585spending forecasts made in the current period. 5 This is the disagreement measure introduced inthis study. For example, the differential forecast revisions occurring from t=O to t=1 in figure 1can be measured using the correlation between forecasts at t=O and t=1. Although Karpoff'smodel suggests that differential belief revisions stimulate trading volume, his model does notnecessarily imply that increases in dispersion cause more trading volume than decreases indispersion.6 The correlation between current and prior forecasts is useful because it is notdependent on changes in the overall distribution of forecasts and more directly proxies forKarpoff' s concept of jumbled expectations. 7

The second measure of disagreement, forecast dispersion, is measured at a point in time. Forexample, in figure 1forecast dispersion is equal in periods t=O, 1 and 3. Karpoff' s model suggeststhat diversity in investors' prior beliefs can stimulate trading volume around contemporaneousnews. Dispersion in analysts' earnings forecasts is used by Atiase and Bamber (1994), whoconfirm the prediction that volume reactions around earnings announcements are positivelyassociated with dispersion in forecasts prior to announcements.

The third measure of disagreement is the change in forecast dispersion from one period to thenext. In figure 1, the change in dispersion from t=1 to t=2 suggests agreement, whereas the changefrom t=2 to t=3 suggests disagreement. This measure of disagreement is the focus of Ziebart(1990). Although Karpoff's model suggests that trading volume can be associated with eitherdivergence or convergence in beliefs, empirical results reported by Ziebart (1990) suggest thattrading volume around earnings announcements is associated with divergence rather thanconvergence in forecasts. Ziebart argues that changes in forecast dispersion capture contempo-

The Spearmancorrelation of analysts' forecasts was also measured as:rho = 1-[(6Yd i2)/(nf (nf2-1))];

whered,is the differencebetween the illqualifyinganalyst's current nd priormonth's forecastrank,andnf is the numberof qualifying orecasts.The Spearmanmeasureplaces moreemphasison thereordering f forecasts.I do notreport egressionresultsusing his measurebecause 1) it does not reflectasmanyconceptual ormsof differential elief revisionsas the Pearsonmeasure, 2) it is highly correlatedwiththePearsonmeasure nd 3)resultsusingtheSpearmanmeasurearevirtuallydenticalto those using the Pearsonmeasure.6 Dontoh and Ronen (1993) provide anotherexample of a model in which tradingvolume is not necessarily affected bywhether changes in dispersion are increases or decreases.7 Compared to forecast dispersion measures, the correlationmeasure introduced in this paper may be a more directmeasure of Holthausen and Verrecchia's (1990) consensus construct(see note 24).

FIGURE 1Aspects of Agreement/Disagreement Among Analyststime t=O t=1 t=2 t=3

F. F. = forecastof analyst i

F2

F5 ____PI______



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586 The Accounting Review, October 1995raneous disagreement that causes trading volume.8 If so, then changes in forecast dispersion alsomay explain trading volume that is incremental to that associated with the correlation measureintroduced in this study. Notice that the relative positions of current and prior forecasts are highlycorrelated across periods two and three in figure 1, although there is a form of heterogeneity inthese forecast revisions (i.e., divergence). Provided that analysts' forecasts of earnings arereasonable proxies for investors' beliefs about underlying security values, this analysis suggeststhe following interrelated research hypotheses:

HI: The correlation between analysts' current and prior period forecasts is inversely relatedto trading volume after controlling for other volume-related effects.

H2: The level of prior dispersion in analysts' forecasts is positively related to trading volumeafter controlling for other volume-related effects.

H3: Change in analysts' forecast dispersion is positively related to trading volume aftercontrolling for other volume-related effects.

In addition to disagreement variables, I use three other variables in alternative tests to controlfor factors beyond the scope of Karpoff's model. The first control variable is the absolutemagnitude of stock returns. Many empirical studies document a positive association betweentrading volume and the absolute magnitude of price changes (see Karpoff 1987 for a review).Further, Abarbanell et al. (1995) show analytically that the magnitude of price changes representan important control in tests of the effects of disagreement.9 Their model suggests that the averagebelief revision causes trading beyond that caused by disagreement. In essence, price changescontrol for the information contained in the average belief revision made by investors. The secondcontrol variable, market-wide trading volume (NYSE), is used to control the trading effects ofevents such as shifts in consumption preferences, changes in interest rates and speculation in othersecurities. Market-wide volume controls for liquidity trading that results from such events, as wellas the corresponding speculation (i.e., disagreement) about economy-wide factors. The thirdcontrol variable is firm size, measured as the total market value of equity (Ziebart 1990 also usesthis variable). The influence of firm size on the association between disagreement and tradingvolume is examined because of the widely held belief that more news is commonly observedabout large firms than small firms (e.g., Demski and Feltham 1994). If so, then measures ofdisagreement and trading volume are likely to be smaller for large firms than for small firms.

III. RESEARCH METHODDisagreement proxies are based on sell-side analysts' forecasts of one-year-ahead earnings.10

I/B/E/S forecast data are used. To measure differential forecast revisions, I searched for monthly

8 Ziebart 1990) is based on forecastsummarydata.This limitsthe types of disagreementmeasuresthat can be constructed.9 Abarbanell et al. also suggest that the number of analysts following a firm is a potentially important control variablefor empirical studies that use analysts' forecasts to proxy for investors' expectations.When the number of analysts isincluded in tests performed in this study, I find a statistically significant negative association between the number ofanalysts andtradingvolume. I do not reportthis result for two reasons:First,it does not affect qualitativeconclusionsconcerning the measuresof disagreementexamined inthis study. Second, thenumberof analystsis correlatedwith firmsize and statistically insignificant when included with firm size in regression models.10Sell-side analysts are the primaryproducersof earnings forecasts. Sell-side analysts serve individual and institutionalinvestors, whereas buy-side analysts' tend to be employed by institutional nvestors ormoney managementfirms.Buy-side forecasts are notused in this studyfor two reasons.First,I/B/E/S does notprovideindividual identification numbersfor analysts making buy-side forecasts. Second, buy-side andsell-side analysts are likely to face dissimilar forecastingincentives. Thus, disagreement measures containing a disproportionate number of buy-side forecasts may besystematically biased.



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Barron-Trading Volume and Belief Revisions That Differ Among Individual Analysts 587

observations in which six or more forecast revisions arerecorded for each firm. Morse et al. (1991)suggest that for a given month, the probability of a revised forecast of the next year' s earnings isabout 0.2 for the average analyst. Thus, I limited the search for monthly observations to firmsfollowed by at least 30 analysts during the period January 1984 to December 1990. Detailed I/B/E/S tapes contained 203 firms with a following of 30 or more analysts during this period. Tenmonths were missing from the IBES tapes.'1 In addition, I excluded October 1987 (the month ofthe market crash) because of systematically unusual trading volume. The "full" sample then consistsof 6,727 firm-months, representing 73 months and 172 firms. This full sample is constructed from216,155 forecasts (64,558 forecast revisions).

Unfortunately, the potential influence of nonsynchronous forecast updating and heteroge-neous update frequencies suggest alternative explanations for observing associations betweentrading volume and disagreement measures in the full sample. Differences in analysts' updatingpractices likely result in some forecasts being more outdated or "stale" than others. Figure 2depicts how news releases can result in uncorrelated forecast revisions and changes in dispersion.News releases may result in forecast updating by a subset of analysts. This can cause the relativepositions of recorded forecasts to change simply because outdated forecasts do not move. Thus,stale forecasts cause measurement error in disagreement proxies.

To mitigate the influence of stale forecasts, I focused on a "reduced" sample that uses onlyforecasts that are revisions of forecasts made one month prior (i.e., revisions of recent revisions).This ensured that forecast revisions are associated with beliefs actually revised in the currentmonth. The reduced sample contains only those firm-months that had (1) at least four forecaststhat met this selection criterion, and (2) monthly NYSE price and trading volume data availablefrom CRSP (Center for Research into Security Prices). This sample consists of 8,120 prior periodforecasts (with 8,120 paired revisions) and 1,520 sample observations (i.e., firm-months)representing 166 firms (appendix A contains more detail concerning the sample).To assess whether different measures of analysts' disagreement have incremental explana-tory power, I used the reduced sample to estimate the following regression:

ln(% Vol.,)= ao+ al ln(Dispj1 l) + a2 ADispj.+ a3 ln(l-pj1)+ u.t.where:

%Vol. = Percentage of outstanding shares traded for firm j in month t. 12Dispjt = Coefficient of variation (i.e., the standard deviation divided by the absolutemean) of analysts' forecasts for firm j in month t- 1. 13

The missing months in my sample areJanuary1984, November 1984, July 1985, August 1985, November 1985, April1986, May 1986, September 1986, March 1987 and December 1990. I/BIE/S informed me (after this article wasaccepted) that they have been concerned about these missing months andhave now recovered some.121 employed %Vol. for two reasons: First, it is consistentwith prior accountingstudies thatfocus on the general effectsof financial information (e.g., Comiskey et al. 1987; Ajinkya et al. 1991). Second, %Vol. controls for the numberofoutstanding shares. In Karpoffs model, volume increases proportionally with the number of outstanding shares.However, %Vol tends to vary across firms, soit is possible that the association betweenfirms' average tradingvolumeand analysts' disagreement is caused by some omittedfirm-specific variable otherthandisagreement. One method ofaddressing this issue might be to use only disagreement and volume changes, or to use mean-adjustedvolume anddisagreement measures. Unfortunately, there are very few contiguous observations of disagreement in the reducedsample andonly a few (sometimes only one) observations formany firms.Moreover, when disagreementitself variedacross firms, the effect of interest would be partiallyeliminated.13Scaling the standarddeviation of forecasts by the absolute mean forecastremedies heteroscedasticityand maintainsconsistency with prior empirical studies. This scaling raises the possibility of results being influencedby small valuesof the denominator. Regression results arequalitativelysimilar results using the measure unscaled, however. Further,regressions yield qualitatively similar estimates using all variables without scaling or log normalizing. It may be,however, that other methods of measuringor scaling dispersion are more appropriate.For example, measures scaledby stock price are not as subject to small values in the denominator (see note 17).



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588 The Accounting Review, October 1995

ADispj1 = Change in the coefficient of variation of analysts' forecasts for firmj in month t.14Pit = The Pearson correlation between individual analysts' forecasts made for firm jin month t- 1 and the corresponding forecasts made in month t.I also estimated alternative models that control for variables beyond the scope of Karpoff' s

model. These control variables are:Ir.I = the absolute value of firm j's stock return during month t.itSize. = the total market value of firm j's stock at the end of month t.%VOlMkt = monthly percentage of outstanding NYSE shares traded.

14I chose to use ADisp. for comparison to Ziebart(1990). Yet, all coefficient estimates are qualitativelysimilar when thecurrent period leveI of dispersion (i.e., ln(Dispj,)) is used as a substitute for ADISPJ,. This is not surprising sinceDispj,_l is alreadyin the model andDispj,= Dispj,1l + ADisp11.

FIGURE 2Influence of "Stale" Forecasts on Disagreement Measurest t+I t+2

time

F. = forecast of analyst i Dispersionat time t+1

F1F

etc.

Panel A: Movement in forecasts around a news event at t+J when allforecasts are 'fresh."t t+1 t+2tim e Ups__rch __

F.=forecast of analyst 1Dsesoat time t+1I

F1Fetc. Outdatedor "Stale"Forecasts

Panel B: Same news as in Panel A, but with "stale "forecasts.



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Barron-Trading Volume and Belief Revisions That Differ Among IndividualAnalysts 589

Severalof the above variablesare transformed orregressionanalysisbecause of skewness. 15The correlationmeasureis also invertedto reflect the jumblingof forecasts, (1-p ), rather han itsabsence (p).16IV. DESCRIPTIVE STATISTICS AND TEST RESULTS

Table 1 provides descriptive sample statistics. The average trading volume for sampleobservationsis greaterthan the averagemarket-widetradingduringthe sample period. This is tobe expected, since news events are associated with increased tradingvolume and firm-monthscontainingnews events are morelikely to contain the largenumberof forecast revisions required

To lessen departuresof residual errorsfrom normalityin estimated regression models and maintain consistency withpriorstudies, the log of tradingvolume, prior dispersionand correlationmeasures areused. ADisp11s not transformedbecause it is not highly skewed and takeson negativevalues. The returnmeasureis not transformedbecause the sampleof raw returns s normallydistributed no outliers)andfrequencydistributions uggest that ransformingabsolutereturnsmaychange the natureof this variable.Results arequalitativelysimilar using log normalizedabsolutereturns,however.The effects of extreme values are also moderated by using log transformations.Nevertheless, I employed severaldiagnostics to assess the potentialinfluenceof outliers. For example, alternative ests were conducted after eliminatingobservations if either %Volj1.isp1,IADispj1lr (l-pf,) are in theirrespective upper2nd percentile. This procedurereduces the sample size by abouteight percent,but it does not change results qualitatively.In addition, results are notchanged qualitatively when the sample size is reduced another 12 percent by eliminating observationsfor which thecorrelation variable of primaryinterest is negative (i.e., p.,> 0).16To simplify notation, the correlation measure is denoted as the simple additive inverse. It is actually computed asln(1.1- p11),however, so that observations are not lost when pj,=1. Further,there is one observation in which pj, stechnically undefined, because the variance of currentperiod forecasts (which is used to compute its denominator) iszero. For this observationI assignedpj,a value of one. This assignmentis somewhat arbitrary,but also consistent withKarpoff's notionof complete consensusfollowing diversityinpriorbeliefs. Testresultsarevirtuallyidentical when thisobservationis omitted.

TABLE 1Descriptive Statistics for Regression Variables (untransformed)N=1520

%Vol1 Disp1t1 ADispit %VolMk SizesMaximum 0.595 1.000 15.481 10.745 0.414 0.064 102,027Median 0.059 0.647 0.055 -0.004 0.014 0.044 4,562Minimum 0.012 -0.995 0.003 -15.222 -0.338 0.030 111Std. Dev. 0.049 0.466 0.637 0.710 0.080 0.008 13,003Mean 0.071 0.494 0.158 -0.008 0.016 0.046 8,715

%Vol. = %of firmj's shares tradedduringmonth .jr%VOlMkt= %of NYSE sharestradedduringmonth .pit = the correlation between analysts'current and prior months earnings forecasts.Disp-1l = coefficientof variation i.e., standard eviationscaledby Imeanl) f priormonthsearningsforecasts.ADispj, = changein the abovecoefficientof variationduring he currentmonth.rit = return on firm j's stock during month t.Size., = the marketvalueof firmj's equityat the end of montht (in millions of dollars).



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590 The Accounting Review, October 1995for inclusion in the sample. Selection criteria also result in large sample firms, although there issignificant variation in size. Further, the median correlation between current and prior forecastsis .65, although values of this measure range from 1.00 to -.99.

Table 2 provides pairwise correlations on the transformed variables. Pairwise correlationssuggest that firm size is associated with analysts' agreement since both Disp1t and (1-p,) tendto be lower for larger firms. This is consistent with the notions that there is more informationavailable about large firms, and more of this information is commonly observed. Pairwisecorrelations also suggest that firm-specific disagreement (or relatively high levels of bothDispj,1_ and (1-pjt)) tends to be higher when there is more market-wide trading. These relationsare consistent with the notion that market-wide disagreement about economy-wide factorsinfluences both market-wide trading volume and analysts' disagreement about individual firms.Karpoff' s model predicts that trading volume is an increasing function of both differential priorbeliefs and differential contemporaneous belief revisions. This prediction is supported by simple

TABLE 2Pairwise Pearson Correlations for Regression Variables (transformed)(Two-Tailed Probability Values Italicized)

ln(%Vol31)ln(%Vol31) 1.000

0.000In(J-pjt)

ln(J-pjt) 0.056 1.0000.030 0.000 Jn(Dispjt_,)

ln(Dispjti) 0.173 -0.068 1.0000.000 0.008 0.000ADispjt

ADispjt 0.025 -0.026 -0.163 1.0000.324 0.306 0.000 0.000Ir I

1r311 0.310 0.000 0.089 -0.118 1.0000.000 0.986 0.001 0.000 0.000

1n(%Volmkt)ln(%VolMk,) 0.190 0.050 0.049 0.010 0.057 1.000

0.000 0.052 0.054 0.707 0.026 0.000In(SIZE1,)

ln(SIZEj,) -0.345 -0.056 -0.297 0.016 -0.213 0.052 1.0000.000 0.030 0.000 0.524 0.000 0.044 0.000%Vol., = % of firmj's shares tradedduringmonth t.%VolMk, = % of NYSE shares tradedduringmonth t.pit = the correlation between analysts' current and prior months earnings forecasts.Dispj1, = coefficient of variation(i.e., standarddeviation scaled by Imeanl)of priormonths earnings forecasts.ADispj, = change in the above coefficient of variationduringthe currentmonth.rj, = return on firm j's stock during month t.Size;, = the market value of firmj's equity at the end of month t (in millions of dollars).



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Barron-Trading Volume and Belief Revisions ThatDiffer Among IndividualAnalysts 591correlation tests in table 2, which reveal statistically significant positive associations between%Vol.t and both Disp._and (1-pjt).Regression estimates of the incrementalassociations between disagreement measures andtradingvolume arepresentedin table 3.17Standard rrorson the coefficients arecalculatedusinga procedure developed by Froot (1989) that adjusts for dependency in residual errors whengeneralized least squares s infeasible.18 Estimatedcoefficients for thereducedsample have signsconsistent with all three researchhypotheses.'9The correlationbetween analysts' current andpriorperiod forecasts is inversely related to tradingvolume, supportingHi. Results supportH2because the level of priordispersionin analysts' forecastsis positively relatedto tradingvolume.Finally, evidence also supportsH3 becausechangesin analysts'forecast dispersionarepositivelyrelatedto trading volume. Further,all three researchhypotheses are supportedaftercontrollingfor price changes and either firm size or market wide trading.20 n other words, all threedisagreement measures areassociated withtradingvolume that s notexplained by pricechanges,firm size or the effects of market-widetrading.2'The explanatory power (R~dJ) of models intable 3 is comparable to that achieved in typical market-basedevent studies. Nevertheless, theexplanatory power of disagreementmeasures alone is low in an absolute sense. 22Table 3 also reportsestimates from the "full"sample.23 reportthese estimates because ofa potential bias in the reducedsample.I cannotdistinguishunrevisedforecasts thatarestale fromunrevisedforecaststhataccuratelyreflect some investors' expectations,andusing only revisions17I also report the following regression estimates using stock price to scale the standarddeviation of forecasts:

ln(%Volb,)= + b ln(DispJ,_1) +b2ADispj, +b3ln(l-pj,) +b4 Ir.,I ECoeff. -2.513 + 0.083 + 3.095 + 0.053 + 3.123 N=1,520(Std. Err. Froot) (0.142) (0.022) (1.174) (0.019) (0.318) R2adj=12.All estimates using price to scale dispersion measures are qualitatively similar to those found in table 3, with thestatistical significance of the coefficient for the correlationbetween currentandprior forecasts being slightly higherwhen price is used.

18The Frootprocedureadjustsstandard rrorswhen multiple observationsfor the same firms areused. It also adjustsforthe serialcorrelation nmonthlytradingvolume. Yet, thisproceduredoes notadjust ordependency withinobservationsfrom the same month. This type of dependency is not a serious concern, however, because results are not greatlyinfluenced by addingmarket-widetradingas acontrolvariable.Monthly NYSE tradingvolume is highly correlatedwiththe average volume in my sample (i.e., a .95 Pearsoncorrelation for both the full andreduced samples).19Evidence of anassociation between tradingvolume anddifferentaspects of analysts'disagreement s foundin all annualsubperiods.For example, when coefficients from the seven annual subperiodsareestimated(using stock returnsas acontrol), 18 of the resulting21 coefficients on disagreementarepositive. Six of the seven coefficients on ln(J-pj,) arepositive. All negative coefficients are statistically insignificant and from differentyears.20 Multicollinearityis extremely highwhenboth firmsize andmarket-wide radingareadded ascontrolvariables, althoughthe results still supportKarpoff s predictions. When both these variablesareadded to regression models, test statistics

(t value (Froot)) for the correlation measure are + 1.49 or +1.68 dependingon whetherdispersionmeasures are scaledby the mean forecast or stock price (see notes 13 and 17). A high level of multicollinearity in these models isunderstandable f both market-widetradingandfirm size proxy for investor disagreement.21 As note nine suggests, models were also tested for sensitivityto inclusion of othervariables.Themagnitudeof analysts'mean forecast revision, or surprise(denoted SURPRISEj.)was also tested, although it is positively correlatedwith themagnitudeof returnsandlikely to reflect similareconomic influences. Surprisemetrics have been used inotherstudies(e.g., Bamber 1986; Ajinkyaet al. 1991; Ziebart1990). Qualitativeconclusions concerning analysts' disagreement arenot influenced by inclusion of SURPRISEjt(for an example of a model including SURPRISEj., ee footnote 24).22Mydissertation(i.e., Barron 1993) arguedthat low R2scan result from disagreement studies even when market-widedisagreement is the sole cause of trading volume and analysts' earnings forecasts are ideal proxies for investors'expectations of cash flows. The argumenthas two parts.First,noise in financialmarketsproduces measurement errorin disagreement proxies constructedusing only a subset of expectations. Measurement errorpartially obscures theassociation between tradingvolume andmarket-widedisagreement. Second, transactioncosts dampenanddistort the

disagreement-volumerelation.Simulationssuggestthat this "friction-effect"greatlyamplifiesthe adverse influence ofmeasurement erroron R2.This argumentsuggests thatR2s n studies like this one arelikely to understate he economicsignificance of the disagreement/volumeassociation.23 Unfortunately, it was not technologically feasible to calculate "Froot" tandard rrors or the full sample because of itssize.



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TABLE 3Regression Estimates of the Incremental Roles of Differential Prior Beliefs and

Differential Belief Revisions in Explaining Trading Volumeln(%Vo1Q)=a0+a11n(Dispj1i )+a2ADispjt+a3ln(1-pjt)+u.,Reduced Sample (includes only forecasts that arerevisions of the priormonth's revision)

N=1,520Disagreement

Differential Differential Belief Average Belief OtherPrior Beliefs Revisions Revisions Variables

R -= 0 04 Intercept ln(Disp111) ADispfl ln(l-p11)adj jtPredicted Sign (+) (+) (+)Coefficient -2.516 0.091 0.045 0.048Std Error(O.L.S.) 0.041 0.012 0.020 0.017Std Error(Froot) 0.082 0.020 0.021 0.020t value (Froot) -30.697 4.566** 2.169* 2.365**Radj=0.13 Ir1j1Coefficient -2.743 0.080 0.070 0.048 3.191Std Error (O.L.S.) 0.043 0.012 0.019 0.017 0.252Std Error(Froot) 0.073 0.017 0.018 0.019 0.336t value (Froot) -37.560 4.666** 3.835** 2.567** 9.509**

adj 0.15 ln(%Volmk,)Coefficient -1.101 0.076 0.067 0.042 3.097 0.532Std Error(O.L.S.) 0.247 0.012 0.019 0.016 0.249 0.078Std Error(Froot) 0.265 0.018 0.019 0.018 0.337 0.088t value (Froot) -4.151 4.335** 3.463** 2.252* 9.179** 6.059**R2d. =0.19 ln(Size11)Coefficient 0.154 0.042 0.058 0.034 2.662 -0.134Std Error(O.L.S.) 0.277 0.012 0.018 0.016 0.259 0.013Std Error(Froot) 0.749 0.016 0.020 0.018 0.282 0.034t value (Froot) 0.206 2.633** 2.953** 1.923* 9.447** -3.930**Full Sample (includes all forecasts for months with at least six revisions)

N=6,727R2-= 0.19 Intercept In(Disp111) ADispjt ln(1-p31) Irfl ln(%VolMkf)adj -rCoefficient -0.558 0.103 0.003 0.042 2.583 0.693Std Error(O.L.S.) 0.114 0.006 0.004 0.013 0.106 0.035t value (O.L.S.) -5.040 17.571** 0.750 3.297** 24.261** 19.945*** and ** denote statistical significance (one tailed) at the .05 and .01 levels%Vol. = %of firm 's shares raded uringmonth.Jr%VolMk, = %of NYSE haresraded uringmonth.r., = returnon firmj's stockduringmontht.Dispj,_ = coefficientof variation i.e., standard eviationscaledby Imeanl) f priormonthsearningsforecasts.ADispj, = changein the above coefficientof variationduring he currentmonth.pit = correlationbetweenanalysts'currentndpriormonthsearnings orecasts.Sizej, = the marketvalueof firmj's equityat the end of montht (in millions of dollars).



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Barron-Trading Volume and Belief Revisions That Differ Among IndividualAnalysts 593

of the prior month' s forecast revisions may introduce measurement error when unrevisedforecasts accurately reflect current period expectations. Further, disagreement measures in thereduced sample are based on relatively few forecasts (sometimes only four). This is also likelyto contribute to measurement error in the reduced sample. Using the full sample of 6,727 firm-months as a robustness check, test results support HI and H2, but not H3. That is, trading volumeis positively related to the level of prior dispersion in analysts' forecasts and inversely related tothe correlation between current and prior period forecasts, but the positive coefficient on thechange in dispersion measure is statistically insignificant in the full sample. One explanation isthat H3 is not suggested by Karpoff' s model. Another explanation is that stale forecasts obscurethe level of divergence in beliefs, consistent with evidence suggesting stale forecasts are likelyto obscure measures of convergence (or divergence) in beliefs (Brown and Han 1992; Stickel1995).

V. CONCLUDING REMARKSResults from this study are consistent with Karpoff' s (1986) predictions. That is, differential

belief revisions and prior dispersion in beliefs both explain trading volume. If the magnitude ofprice changes controls for the influence of the average belief revision made by investors, then thisstudy also provides evidence consistent with the theoretical prediction that trading volume isinfluenced by both the average and differential components of belief revisions (e.g., Kim andVerrecchia 1991).

The conventional wisdom that investor disagreement causes trading volume is consistentwith theoretical research (e.g., Karpoff 1986; Jang and Ro 1989; Holthausen and Verrecchia1990; Kim and Verrecchia 1991; Dontoh and Ronen 1993). Most prior empirical studies find apositive relation between disagreement measures and trading volume, although the results ofthese studies are somewhat mixed and subject to measurement error (Abarbanell et al. 1995). Thisstudy addresses measurement concerns, while further supporting and extending prior evidencesuggesting that disagreement causes trading volume. First, this study corroborates two disagree-ment/volume relations reported in prior accounting studies after eliminating potentially staleforecasts and controlling for price changes (Ziebart 1990; Ajinkya et al. 199 1).24 Second, it showsthat these two disagreement measures have incremental explanatory power in regression models.Finally, this study shows that a new measure of disagreement (i.e., the correlation betweenanalysts' current and prior forecasts) also has incremental explanatory power for trading volume.

These results add to prior evidence suggesting that disagreement is a cause of the tradingreactions observed around accounting events (e.g., Ziebart 1990). However, this study does notaddress the relative importance of differential prior beliefs and differential contemporaneous

24Barron (1993) focused on contemporaneousforecast dispersion(denotedDispj,)ratherthan priorforecast dispersion.For comparison to Ajinkya et al. (1991), I report the following alternative regression results:ln(%Traded)jt c0 + cl ln(Dispj,) + c2 n(l-p) + n(SURPRISE) + c4 nfl + ECoeff. -2.488 + 0.044 + 0.043 + 0.068 + .980 N=1,520(Std. Err. Froot) (0.120) (0.020) (0.020) (0.025) (.310) R2adJ=.3The theoretical basis for this test is Holthausen and Verrecchia's (1990) informedness/consensus model. Thedissertationargued analytically that the dispersion in expectations is an inverse function of both informedness andconsensus. Further,pj,may be an explicit proxy for "consensus."If pjcontrols for consensus in the above model, thendispersionis left to proxy for informedness.Further, f dispersionproxies for informedness,thenitspositive coefficientis inconsistent with the predictionsof HolthausenandVerrecchia(1990). One explanationfor this inconsistency is thatcontemporaneous dispersion proxies for prior period information asymmetry rather than informedness. Anotherexplanationis the influence of transactionprocessingcosts. Barron 1993) also arguedthattransactionprocessing costsare likely to prevent more trades when the dispersionin expectations is small.



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594 The AccountingReview,October1995belief revisions in explaining trading reactions around specific events. The relative importanceof these two influences is potentially important to accountants interested in evaluating the"content" or "quality" of financial disclosures. According to Karpoff (1986), a trading reactioncaused primarily by the resolution of prior period disagreement suggests news with a differentquality (i.e., news with a common interpretation) more than a trading reaction caused primarilyby differential belief revisions. Thus, future studies of trading volume reactions around specifictypes of accounting events (e.g., earnings releases) may benefit from using the correlationbetween analysts' current and prior forecasts.

Use of the correlation measure introduced in this study may extend beyond the study oftrading volume reactions. A high correlation between the relative positions of analysts' currentand prior forecasts likely reflects the common interpretations referred to by Karpoff (1986),especially when this correlation is measured immediately surrounding an event that reducesforecast dispersion. Evidence that an announcement has been commonly interpreted alsosuggests that its contents have been communicated clearly. Accountants strive to create reportsthat communicate clearly. Thus, the correlation between current and prior forecasts could beuseful in tests for evidence of common interpretations around different types of financial reports.Like traditional dispersion measures, this correlation measure can be constructed wheneversufficient quantities of reliable expectational data are obtainable, whether in the field orlaboratory.



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Barron-Trading Volume and Belief Revisions That Differ Among IndividualAnalysts 595APPENDIX A

EMPIRICAL DATA USED FOR THIS STUDY

For firms having a I/B/E/S forecasts for "Full"Sample: "Reduced" Sample:following of 30 or identifiable sell-side I/B/E/S (SS) fore- I/B/E/S (SS)more analysts during analysts (denoted casts (non-October forecasts revisionsthe period from SS). 1987) made during (non-October 1987)January1984 to firm-months having of the prior month'sDecember 1990. 2 6 forecast forecast revisionrevisions and CRSP made during monthsvolume and price having 2 4 suchdata available. revisions and CRSPvolume and pricedata available.Total number of one 452,457 246,161 8,120year aheadforecastsNumber of one year 386,038 216,155 8,120forcasts in a series oftwo or moreNumber of forecast 116,150 64,558 8,120revisionsNumber of firms 203 172 166representedNumber of firm- 13,083 6,727 1,520months represented



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Trading Volume and Belief Revisions That Differ Among Individual Analysts