Small and Large Trades Around Earnings Announcements: Does Trading Behavior Explain Post-Earnings-Announcement Drift?

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1 Small and Large Trades Around Earnings Announcemens: Does Trading Behavior Explain Pos-Earnings-Announcemen Drif? Devin Shanhikumar * Firs Draf: Ocober, 2002 This Version: Augus 19, 2004 Absrac This paper analyzes rade-iniiaion by small and large raders for one year following earnings announcemens and examines he predicive abiliy of even-ime rading for fuure reurns. Wih earnings surprises based on a seasonal random walk expecaions model, small raders reac slighly more weakly han large raders, during he even window, o he firs surprise in a series of similar surprises, bu more srongly han large raders o he laer surprises. Wih earnings surprises based on analys forecass, small raders reac more weakly han large raders regardless of he pas series. Large raders rade in he direcion of he earnings surprise for one monh afer he earnings announcemen, while small raders do no. Saring in monh wo his swiches and small raders rade in he direcion of he surprise, while large raders do no. The srengh of he small rade even-ime reacion is a weak posiive predicor of reurns in he firs monh afer he announcemen and a weak negaive predicor of drif afer he firs monh. Large rade reacion is generally a negaive predicor of fuure drif. The collecion of evidence poins o boh small and large rader underreacion o earnings announcemens, wih small rader underreacion more severe in he firs monh. In monh one, large raders capialize on drif, bu afer ha small raders seem o correc and possibly overreac. * Harvard Business School, dshanhikumar@hbs.edu. This work is par of my disseraion, compleed a he Sanford Graduae School of Business. For an updaed version, check hp:// I would appreciae any commens or suggesions regarding his paper. I would especially like o hank Ming Huang for all of his advice hroughou he process of wriing his paper and Darrell Duffie for his careful reading. I would also like o hank seminar paricipans a Sanford Universiy for many helpful commens.

2 I. Inroducion Pos-earnings-announcemen drif is a well-documened, long-sanding and consisen anomaly. Even in Fama (1998), a paper ha criicizes evidence of many marke anomalies, he auhor describes pos-earnings-announcemen drif as an anomaly above suspicion. There are many heories abou he cause of pos-earnings-announcemen drif, and virually all of he heories involve invesors who underreac or overreac o he announcemen. This paper looks direcly a rading as a measure of invesor reacion in an aemp o es differen explanaions of pos-earnings-announcemen drif. On he dae of an earnings surprise, sock prices move dramaically. If an announcemen is a posiive surprise, he associaed price normally moves up. If i is a negaive surprise, he price normally moves down. Pos-earnings-announcemen drif is an anomaly by which he price coninues o move in he same direcion for he nex few monhs. Trading sraegies based on earnings surprises earn consisenly posiive excess reurns, even afer aking rading coss ino accoun (Bernard (1993)). Bernard and Thomas (1989) se ou o show ha pos-earningsannouncemen drif would disappear once oher facors were accouned for. Insead, hey simply provided more evidence for he phenomenon. Chan, Jagadeesh and Lakonishok (1996) show ha pos-earnings-announcemen drif survives afer conrolling for momenum, marke risk, size and book-o-marke effecs. Because earnings announcemens are imporan quarerly informaional evens, and because hey are immediaely public, he coninued exisence of pos-earningsannouncemen drif is paricularly puzzling. While marke fricions, risk and uncerainy may all conribue o he coninued exisence of pos-earnings-announcemen drif, he underlying cause of he drif is sill uncerain. There are hree main explanaions of pos-earnings-announcemen drif in he lieraure. The radiional view is ha invesors underreac iniially and hen laer correc heir reacions causing drif. Barberis, Shleifer and Vishny (1998) predic iniial invesor underreacion and evenual overreacion. Daniel, Hirshleifer and Subrahmanyam (1998) predic iniial overreacion, which increases over ime. The key moivaing quesion for his paper is: Wha is he acual behavior around earnings announcemens? Few people would believe ha every invesor underreacs o earnings informaion. A more likely explanaion is ha cerain invesors 1

3 underreac, and ohers are unable o ake full advanage of his misake a he ime of he announcemen. A naural quesion is: Who underreacs? Does a paricular class of invesors underreac? Does drif occur as hese invesors correc heir misake, or as oher invesors coninue o ake advanage of he drif? Since almos all explanaions of pos-earningsannouncemen drif have he same predicions for reurns, we need o look beyond reurns o gain a deeper undersanding of wha drives pos-earnings-announcemen drif. This paper focuses on measures of ne invesor rade-iniiaion, based on daa from he NYSE Trades and Quoaions (TAQ) daabase, o deermine reacions o earnings news. If abnormal ne buying is significanly posiive afer an announcemen, hen raders are reacing posiively o ha announcemen. We can measure he degree of reacion by a measure of abnormal ne rading, conrolling for he informaion in he announcemen. The paper examines he rading of boh small and large raders o gain a beer undersanding of heir behavior around and afer earnings announcemens. In addiion, we es wheher he rading behavior of small and large raders predics reurns, direcly esing he relaionship beween rading and pos-earningsannouncemen drif. We find mixed resuls for reacions immediaely surrounding he earnings announcemen. When we use an earnings expecaions model based on a seasonal random walk o calculae earnings surprises, we find ha small raders reac slighly more weakly han large raders o he firs surprise in a series of similar surprises, bu more srongly han large raders o he laer surprises. Wih earnings surprises based on analys forecass, small raders reac more weakly han large raders, wheher he surprise differs from he previous quarers surprise or no. Looking a rading behavior beyond he even period, large raders rade in he direcion of he earnings surprise for one monh afer he earnings announcemen, while small raders do no, which seems o sugges ha large raders are rading o ake advanage of he pos-earningsannouncemen drif. Saring in monh wo his swiches and small raders rade in he direcion of he surprise, while large raders do no. This could be a small rader correcion or, if prices have already correced, an overreacion. The srengh of he small rade even-ime reacion is a weak posiive predicor of reurns in he firs monh afer he announcemen and a weak negaive predicor of drif afer he firs monh. Large rade reacion is generally a negaive predicor of fuure drif, which suggess ha while small raders may be underreacing relaive o large raders, large raders hemselves are underreacing during he even period. 2

4 There are several reasons o suspec ha small raders are more likely o display subopimal behaviors han large raders. In paricular, larger raders are more ofen professional invesors and professional invesmen advisors, who are likely o have greaer financial educaion, more experience and more ime o make invesing decisions. Mos srongly, here is a growing empirical behavioral finance lieraure ha has repeaedly shown ha individuals make basic rading misakes which insiuions do no make. (See Barberis and Thaler (2003) for a summary.) The wo benchmarks used o evaluae small-rade reacions are based on informaion and large-rade behavior. Based on pos-earnings-announcemen drif, we can use he ype of earnings surprise o consruc a simple benchmark. Reacions o negaive informaion should be negaive and reacions o posiive informaion should be posiive. Such reacions would earn posiive abnormal reurns, on average, as shown in prior lieraure (Bernard (1993)). For he second benchmark, based on he exising empirical evidence, we posi ha large raders are likely o inerpre he earnings announcemen more accuraely. The analysis compares rading during he even period o deermine if here is an iniial underreacion, and for several monhs following he announcemen o deermine if here is evenual overreacion. Finally, we es he predicive abiliy for fuure reurns of he even-ime rading of boh groups, o es wheher iniial underreacion is driving pos-earnings-announcemen drif. This secion also allows us o draw conclusions abou wheher large raders underreac o earnings announcemens. The radiional explanaion of pos-earnings-announcemen drif is ha invesors underreac o earnings informaion iniially, and laer correc heir misakes. The correcion mus ake abou six monhs o a year o explain pos-earnings-announcemen drif, as a majoriy of he drif occurs wihin he firs year (Bernard (1993)). This leads o several clear predicions for rading behavior. Firs, invesors should underreac o he earnings announcemen iniially. Second, heir reacions should correc hemselves wihin approximeely one year. Third, he level of underreacion should be a posiive predicor of drif, since underreacion is he only facor in deermining he degree of drif. Secion 4 repors ess of he firs predicion, Secion 5 repors ess of he second predicion and Secion 6 repors ess of he hird predicion. Boh Barberis, Shleifer and Vishny (1998) and Daniel, Hirshleifer and Subrahmanyam (1998) predic evenual overreacion o he earnings surprise. Boh of hese behavioral models predic ha reacions o laer announcemens in a same-sign sequence should be sronger han 3

5 reacions o earlier announcemens. The key difference beween hese wo behavioral models is wih respec o he iniial reacion. Daniel, Hirshleifer and Subrahmanyam (1998) predic iniial overreacion, bu Barberis, Shleifer and Vishny (1998) predic iniial underreacion. Shanhikumar (2004) shows ha small raders display increasing reacions in heir rading behavior, bu ha paper does no examine wheher he iniial reacion is an underreacion or overreacion. This paper does, poenially allowing us o differeniae beween hese wo models. This paper looks a hree elemens of invesor reacions o earnings surprises, he firs wo dealing wih he rading reacions hemselves. The findings poin o iniial underreacion by boh small and large raders, and an evenual overreacion by small raders. Firs, we look a he iniial reacion o he surprise. We find ha small raders buy afer a negaive surprise, bu buy more afer a posiive surprise. They also buy more han large raders around all ypes of earnings surprises. This evidence suggess ha invesor reacions o he acual earnings surprise reflec an aenion effec, such as hose described in Barber and Odean (2002). Alernaively, he higher buying levels could be driven by invesor heerogeneiy combined wih higher shor-sale coss. We do no aemp o separae he possible explanaions. Once we conrol for he paern of higher small rade buying levels, i appears ha small raders overreac o earnings surprises, relaive o large raders, bu he overreacion is driven enirely by laer announcemens in a series of similar earnings surprises. We repea hese ess using analys forecas errors as a proxy for earnings surprises, and find ha large raders consisenly reac more srongly han do small raders o he analys-based measure of surprise. Second, we look a lagged rading behavior o deermine wheher drif is driven by small rader correcion or overreacion, or by large raders coninuing o rade o ake advanage of he drif. We regress abnormal rade imbalances during he monhs following an earnings surprise on he earnings surprise decile values o measure reacion coefficiens. During he firs monh, large rade imbalances depend posiively on he earnings surprise, while small rade imbalances do no, suggesing ha large raders may be aemping o profi from pos-earnings-announcemen drif during ha period. Our resuls sugges ha small raders overreac in he second monh and beyond. Small-rader behavior is significanly dependen on an earnings announcemen for over a year afer he even dae, while large rader behavior does no depend on he earnings surprise more han a monh beyond he announcemen. The differences in he esimaed regression coefficiens, comparing resuls using small rader imbalances and resuls using large rader imbalances, are also significan. Finally, we examine wheher even-ime rading behavior predics pos-even reurns. Conrolling for he correc price reacion, he radiional underreacion-correcion hypohesis 4

6 would predic ha he srengh of even-ime price reacions should be a negaive predicor of drif: The more prices adjus iniially, he weaker will be he drif. In Secion 6, we make addiional assumpions o exend his relaionship o rade imbalance, as does Hirshleifer, Myers, Myers and Teoh (2003). We use rade imbalance as a measure of reacion, and earnings surprise level as a conrol for he correc reacion. For example, we posi ha if here is a posiive surprise, a more posiive iniial rade reacion should be relaed o weaker fuure drif, ha is, a more posiive iniial reacion is relaed o less posiive fuure reurns. We find, however, ha small-rader buying is a posiive predicor of reurns for he firs monh afer he earnings announcemen, and only a weakly negaive predicor in he nex five monhs. We find ha largerader buying is a significanly negaive predicor of reurns over many horizons, suggesing ha large raders are underreacing. Several recen empirical papers address he opic of rading behavior surrounding informaional evens. This lieraure is described in Secion 2. The exising lieraure makes an imporan conribuion in showing ha individuals and small raders rade differenly han do insiuions and large raders. Individuals and small raders seem o rade less raionally, generally buying firms wih predicably negaive reurns. The recen lieraure has esablished ha rading behavior around informaional evens is an imporan opic, bu here is a grea deal for his work o add. Secion 2 reviews relaed lieraure. Secion 3 describes he daa and empirical mehodology used, while Secions 4, 5 and 6 describe he resuls. Secion 4 looks a rading reacions o earnings surprises around he even dae and Secion 5 examines rading behavior furher from he announcemen dae. Secion 6 repors resuls regarding he predicive abiliy of even-ime rading for fuure reurns. Secion 7 concludes. II. Relaed Lieraure Pos-earnings-announcemen drif is a well-documened and long-sanding marke anomaly. Bernard (1993) provides a survey of he founding papers in his area. In paricular, Bernard and Thomas (1990) find ha he reurns response o earnings is consisen wih use by 5

7 invesors of a naïve random-walk earnings-expecaions model. Earnings surprises based on a random-walk model have, on average, posiive correlaions a lags of one o hree quarers and negaive correlaions a four-quarer lags. Bernard and Thomas (1990) find ha he hree-day price reacions, surrounding earnings announcemens, reflec a failure of invesors o accoun for hese auocorrelaions, as if invesors incorrecly relied upon he random-walk model. This leads o wo naural quesions. Firs, which invesors use his simple model? And second, do more sophisicaed invesors rade agains hem? Several papers aemp o answer hese quesions. Bhaacharya (2001) and Baalio and Mendenhall (2003), wrien concurrenly wih his paper, focus on he firs quesion, using daa similar o he daa used in his paper. Bhaacharya (2001) finds ha small raders rading behavior around earnings announcemens is srongly relaed o he seasonal random-walk-based earnings surprise, while he large rader response is no. Baalio and Mendenhall (2003) find ha small raders reac more srongly o random walk surprises, while large raders reac more srongly o analys-based surprises. Barov, Radhakrishnan and Krinsky (2000) and Ke and Gowda (2004), also wrien concurrenly wih his chaper, aemp o answer he second quesion by focusing on quarerly insiuional ownership. Several oher papers examine he relaionship beween oher earnings-announcemen-relaed variables and insiuional ownership (see Ke and Peroni (2004) for a summary.) Barov, Radhakrishnan and Krinsky (2000) find ha pos-earnings-announcemen drif is decreasing in insiuional ownership, suggesing ha non-insiuional, and poenially less sophisicaed, invesors are driving he drif. Ke and Gowda (2004) focus on insiuional invesors who rade acively o maximize shorer-erm profis, and find evidence ha hese insiuions rade o exploi he drif, wih a srong relaionship beween quarerly ownership changes and he conemporaneous random-walk-based earnings surprise. Lee (1992) is he firs paper o look a rade imbalances around earnings announcemens, displaying an inra-day focus and looking a a hree-day window around he earnings announcemen. He finds ha small raders buy afer earnings surprises, wheher he surprise is good or bad, and ha hey reac laer han large raders. In a relaed paper, Hirshleifer, Myers, Myers and Teoh (2002) aemp o relae rading behavior o pos-earnings-announcemen reurns. Hirshleifer, Myers, Myers and Teoh (2002) look only a individual invesor behavior, bu hen relae he rading o fuure reurns. They find ha individual invesors are ne buyers afer boh posiive and negaive earnings surprises, and ha individual rading is a weakly negaive predicor of reurns in he following hree quarers. 6

8 The hree empirical papers mos direcly relaed o our work are Lee (1992), Hirshleifer, Myers, Myers and Teoh (2003), and Baalio and Mendenhall (2003). The curren paper makes several addiional conribuions. Firs, we look a rading beyond he even period, and second, we conrol for he previous earnings informaion by doing addiional analyses for a subsample of earnings surprises, which eliminaes earnings laer in a series of similar (op 30% or boom 30%) earnings surprises. Boh of hese addiions o previous mehods yield new resuls, regarding he ways in which small and large raders reac o differen ypes of earnings announcemens. In addiion, we look a reacions o analys forecas surprises, which reveals specific differences in he reacions o analys forecas surprises and he reacions o random-walk surprises. Perhaps mos significanly, his paper examines wheher boh small and large rade behavior around he earnings even has predicive abiliy for fuure reurns, showing ha boh rader ypes seem o underreac o earnings informaion. III. Daa and Empirical Approach There are hree primary daa elemens required for his paper. To examine rading reacions o earnings surprises we need a measure for earnings surprises, and we need a measure for rading reacions. To deermine wheher rading predics reurns, we need reurns daa as well. Overall, an even-sudy mehodology is used, wih earnings announcemens as he key even. Earnings surprises are calculaed using wo alernae approaches. Trading reacions are based on rade-by-rade daa from he New York Sock Exchange. This secion describes he raw daa and he mehods used for his paper. The basic sample is resriced o ordinary common shares rading on he New York Sock Exchange beween January 1, 1993 and December 31, 2002, excluding foreign companies, Americus rus componens, closed-end fund shares and REITs. 1 We do no require daa on he company for he enire period in order for i o be in he sample, bu cerain minimum daa 1 Because mos exising work on pos-earnings announcemen drif uses earlier samples, a sample of earnings announcemens from is also used o compare he pos-announcemen drif of our sample and o ensure ha our measuremen of earnings surprise is accurae. As wih Johnson and Schwarz (2000), we find ha pos-earnings-announcemen drif has declined beween he earlier and laer periods, bu is sill significan in he laer period, and wih our specific sample. 7

9 requiremens do limi he daa. As described below, he primary limi is ha we require enough of a hisory o esimae earnings expecaions. The final sample includes 2,723 firms. Reurns daa are obained from CRSP. Earnings announcemens and firm characerisics are aken from Compusa, and analys earnings forecass are aken from he Insiuional Brokers Esimaes Sysem (I/B/E/S). Trading measures are calculaed from he New York Sock Exchange Trades and Quoaions daabase (TAQ). This daabase repors every round-lo rade and every quoe from 1993 onwards on he New York Sock Exchange, American Sock Exchange and Nasdaq. In calculaing reurns, we use cumulaive abnormal reurns (CARs), which are he sums of daily abnormal reurns, and are defined as i 0, 1 i ( AR ) CAR, (1) = 1 = 0 where i AR is he CRSP bea-adjused abnormal reurn for securiy i on day. Fama (1998) summarizes heoreical and saisical reasons ha CARs are preferable o buy-and-hold reurns. 3.1 Earnings Models The even of ineres o us in his paper is he quarerly earnings announcemen. Quarerly earnings announcemen daes are aken from Compusa. 2 If an announcemen is made on a holiday or weekend, he firs rading day following he announcemen dae is used as he even dae. Our final sample of earnings surprises, for which we have all he necessary daa, conains 59,658 earnings announcemens for he primary earnings surprise measure. Our primary measure of earnings surprise is based on expecaions buil from prior earnings announcemens. We use he sandardized unexpeced earnings measure commonly used in he pos-earnings-announcemen drif lieraure. Bernard and Thomas (1990) show ha sock reurns paerns around earnings announcemens correspond o his naïve earnings expecaions model. This allows us o use a measure ha is boh consisen wih observed behavior in general, and independen of announcemen-specific behavior. In order o calculae sandardized 2 Shanhikumar (2004) finds ha wih a small sub-sample of 125 earnings announcemens for NYSE lised firms, wih he announcemen falling in he years 1993 hrough 2002, Compusa earnings announcemen daes are accurae o wihin one day in 97% of he cases. 8

10 unexpeced earnings (SUE), we assume ha earnings expecaions are based on a seasonal random-walk model. Our primary measure uses a seasonal random walk wih drif, bu we also repea he sudy using a seasonal random walk wihou drif, and our resuls are robus o his variaion. Expeced earnings are E i i i ( e ) e + δ = 4, (2) i where δ is he expeced change in earnings from he same quarer s earnings of he prior year, and is referred o as he earnings drif for firm i. For each sock, we esimae he drif using up o weny quarers of previous daa. The esimaed drif is ˆ 1 δ, (3) i ( i e j e j ) n i = 4 n j= 1 where n is he number of inervals used o calculae he drif, where one inerval requires earnings informaion for a given quarer and he same quarer in he prior year. n is he maximum of he number of inervals wih available daa and 16, so ha no more han 5 years of earnings daa are used. We use less daa if he full period is no available, alhough we require a leas one year s worh of daa. This does inroduce a sligh survivorship bias ino he sample, bu eliminaes only 5.34% percen of he earnings announcemens, and 2.97% of firms. We hen sandardize he unexpeced earnings measure by dividing each firm s surprise by he sandard deviaion of ha firm s earnings, as measured by he available subse of he preceding 20 announcemens. As a robusness check, we also normalize he unexpeced earnings measure by dividing by he sandard deviaion of earnings changes raher han he sandard deviaion of earnings. Resuls are similar. The primary earnings surprise measure is SUE i e e i i = 4 ˆi δ i Var( e ), (4) where Var e ) is esimaed using he previous 20 announcemens. Earnings announcemens are ( hen ranked by he SUE wihin each year, and placed ino deciles 0-9, where he mos negaive 9

11 surprises are in decile 0 and he mos posiive in decile 9. 3 Earnings announcemens in deciles 4 and 5 are no srong surprises. The second measure of earnings surprises is based on analys forecass. The surprise is he difference beween announced earnings-per-share and he analys forecas as repored by I/B/E/S, normalized by sock price. We use wo measures of he consensus forecas. The firs measure is aken from he I/B/E/S summary file. The consensus forecas is defined as he mos recen monhly median forecas before he earnings announcemen, when here are a leas four earnings forecass for he firm. The consensus forecass occur a mean of 15.8 days and median of 13 days before he earnings announcemen daes, so hey end o be approximaely wo weeks old. The mean and median forecass are similar, wih a correlaion coefficien of The second measure of consensus is consruced from he I/B/E/S deail files, and uses he median forecas occurring a leas one week before he earnings announcemen, bu no more han wo monhs before he announcemen, when here are a leas four earnings forecass during ha period. Wih boh consensus measures, he earnings surprise is aken o be he difference beween announced earnings-per-share and he consensus, divided by he price on he dae of he consensus forecas. Using he monhly consensus measure, our sample of surprises conains 29,649 earnings announcemens. The sample using he daily measure conains 14,505 earnings announcemens. 3.2 Creaing he rading daabase Trading reacion is measured using variables based on ne direcional rading or ne order flow. Following esablished algorihms, firs proposed by Lee and Ready (1991), for each rade on he NYSE for our sample socks, we deermine which side of he rade represens he iniiaing side, ha is, which side demands more immediacy of execuion. An abnormally high level of buyer-iniiaed rades indicaes an overall buying pressure and a posiive reacion, while an abnormally high level of seller-iniiaed rades indicaes a selling pressure and a negaive reacion. 3 This choice is equivalen o alernae decile-labeling mehods, such as deciles 1 hrough 10, or deciles -0.5 hrough 0.5, bu each corresponds o a differen inerpreaion of regression coefficiens. In his case, a simple inercep-slope regression will resul in a slope ha indicaes he expeced difference in corresponding dependan variable value from one decile o he nex. The difference beween he mos negaive and mos posiive surprises will be en imes his slope. The inercep will approximae he expeced dependan variable value for he mos negaive surprises, decile 0. The alernae labeling of deciles 1-10 would resul in he same slope coefficien, bu he inercep would now be one uni of esimaed slope below he approximae dependan variable value for he mos negaive surprise. 10

12 The raw rade iniiaion variables are normalized o deermine abnormal levels and adjus for sandard differences beween small and large rade iniiaion paerns. Prior work has compared our rade-iniiaion daa wih wo oher measures of small (individual) and large (insiuional) rading quarerly insiuional ownership from CDA Specrum (Malmendier and Shanhikumar (2004)) and individual rading in accouns from a large discoun reail brokerage firm (Shanhikumar (2004)). In each case, he correlaions beween rade iniiaion and changes in ownership or rading were significan in he expeced direcions. In order o deermine which side iniiaed a given rade, we use he modified Lee and Ready (1991) algorihm recommended in Odders-Whie (2000). This algorihm is commonly used in he empirical marke microsrucure lieraure (see Odders-Whie (2000) for a lis of papers using he Lee-Ready algorihm). The algorihm involves maching a rade o he mos recen quoe, which precedes he rade by a leas 5 seconds. If a price is nearer he bid price i is classified as seller iniiaed and if i is closer o he ask price i is classified as buyer iniiaed. If a rade is a he midpoin of he bid-ask spread, we classify based on he previous price. In his case, a ick es is used if he rade occurs a a price ha is higher han he price of he previous rade i is classified as buyer iniiaed. Similarly, a rade ha occurs a a price lower han he previous rade is classified as seller iniiaed. To separae small and large rades we use wo cuoffs, wih a buffer in beween small and large rades o reduce noise. The primary cuoffs of $5,000 and $50,000 are chosen based on evidence from Lee and Radhakrishna (2000), and we use alernae cuoffs of $10,000 and $20,000 as well. Lee and Radhakrishna (2000) show ha dollar based cuoffs creae less noise in separaing individuals from insiuions han share-based cuoffs and sugges using wo cuoffs, wih a buffer zone separaing small and large rades. They also analyze which paricular cuoffs work bes for heir hree-monh sample from , and heir resuls indicae ha a very low cuoff such as $5,000 or less does he bes job separaing ou individuals while a high cuoff of $50,000, or even $100,000, does he bes job separaing ou insiuions. While our aim is no specifically o discriminae beween individuals and insiuions, his inerpreaion is useful. Even if rades of $50,000 and above are being made largely by individuals, hese individuals are likely o ake advanage of professional invesmen advice. A difference in he behavior of small and large raders is ineresing in and of iself, regardless of mapping o individuals and insiuions. Once he rades are classified, we hen aggregae he rade-by-rade daa o find daily rading measures for each sock. Our final daabase is based on over 640 million classified rades. 11

13 Throughou he paper, we focus on he $5,000 and $50,000 rade-size cuoffs, bu resuls are similar using $10,000 or $20,000 cuoffs. 3.3 Calculaing abnormal rading measures In order o aggregae across firms, and o be able o make clearer conclusions regarding he comparison of even-ime rading and non-even ime rading, we calculae abnormal rading measures. Our primary variable of ineres is a measure of rade imbalance. Inuiively, if every rade afer an announcemen were being iniiaed by he buy side, hen he rading reacion o ha announcemen is exremely posiive. Similarly, if all rades were being iniiaed by he sell side, hen he reacion is srongly negaive. To capure his concep, he raw rade imbalance measure is calculaed as follows, for firm i, invesor ype x, and dae : IMB i, x, buys i, x, i, x, =. (5) buys i, x, sells + sells i, x, We hen normalize his rade imbalance measure by subracing off he non-even-ime firm-year mean, and dividing by he non-even-ime firm-year sandard deviaion, using he equaion IMB abnormal i, x, ( IMB ) IMBi, x, E i, x, year( ) =. (6) Var IMB ) ( i, x, year( ) This conrols for sysemaic differences in rading behavior. We calculae he sample mean and variance of rade imbalance in each year, for he given firm and invesor ype, excluding days ha are close o an earnings announcemen. The even period ha is excluded in calculaing ( ) E IMB i, x, year( ) and Var ( IMB i, x, year( )) consiss of days 5 hrough 5 in even ime; he eleven rading days cenered on any earnings announcemen dae. This period is chosen o be large enough o allow even-ime rade variaion o remain. This allows us o aggregae across firms wihou concerns for general, no-even-ime, differences in he rading behavior associaed wih hem. Normalizing he measures by he sandard deviaion allows us o make qualiaive comparisons of our final values ha would be impossible o make if he values were no normalized. I conrols for sysemaic differences in he volailiy of large rades and small rades or in he volailiy of he socks large and small raders inves in. 12

14 We also use a reurn adjused abnormal rade imbalance measure as a robusness check. This measure accouns for prior reurns over varying horizons and is paricularly imporan in ensuring ha lagged rading behavior is due o he informaion in he earnings surprise, and no a naïve response o he drif in he inervening period. In order o come up wih our adjused measure, we esimae he equaion IMB abnormal i i i i i, = α 0 + α1ar 1 + α2car 5, 2 + α3car 20, 6 + α4car 60, 21 + εi, (7) for each size-based caegory of rade imbalances. This equaion essenially groups prior reurns ino day, week, monh and quarer. Reurn adjused abnormal rade imbalance is he residual from he above equaion he abnormal rade imbalance ha is no accouned for by he previous day, week, monh and quarer reurns. We run all of our long-erm ess using his measure as well as he unadjused measure. Resuls are similar, and are acually slighly sronger for he reurn-adjused measure, bu only he resuls using our unadjused abnormal rade imbalance are repored. An alernae, more general, normalizaion procedure is used as an addiional robusness check. Based on he evidence in Chordia, Roll and Subrahmanyam (2002), we perform a normalizaion conrolling for calendar-effecs, serial correlaion in he rade imbalance variable, and dependence of rade imbalance on prior reurns, similar o Frieder (2004). The firs sep involves regressing raw rade imbalance on indicaors for monh (January, February, ) and dayof-week (Monday, Tuesday, ). This regression is run for each securiy separaely, using he enire sample period. The residual is used in he second sep, where he calendar-adjused imbalance is regressed on he previous fifeen rading-days calendar-adjused imbalance and securiy reurn. Again, hese regressions are run for each sock separaely. The residuals from hese regressions are used in he final sep. In order o ensure ha he final abnormal rade imbalance values are comparable across rade size groups, he final sep is similar o our primary normalizaion, removing he mean and sandard deviaion effecs for each firm and rade-size group from he residuals from sep 2. In his hird sep, he mean of he imbalance measure resuling from sep 2, for a paricular securiy and rade-size group, is subraced from ha groups sep 2 residual and he resuling mean-adjused imbalance is divided by he sandard deviaion of he sep 2 residual for ha securiy and rade-size group. Sep 1 adjuss for calendar effecs. Sep 2 adjuss for prior reurns and prior imbalance measures. Sep 3 normalizes he 13

15 imbalance measure o have a mean of zero and sandard deviaion of one for each securiy and rade-size group. IV. Trading Around he Even Day One of he key differences beween alernae explanaions of pos-earningsannouncemen drif is wheher invesors underreac or overreac a he ime of he earnings announcemen. In his secion, we focus on rading around he even day, for days 1 hrough 1. Based on he evidence in Shanhikumar (2004), we calculae reacions for boh he whole sample, and for a subsample of surprises which differ from he preceding surprise ype. By doing his, we can see how he differen ypes of invesors reac, boh in general and o he firs surprise of a given ype. Full Sample Figure 1 displays small- and large-rader reacions o each earnings surprise decile. As one can see, he abnormal buying of small raders is sronger around an earnings surprise, regardless of he ype of earnings surprise. Small raders buy even for he mos negaive earnings surprises, while large raders sell. The boom wo deciles alone would sugges ha small raders underreac o earnings announcemens. Bu, when we look a he whole picure, we see ha small raders buy even more a posiive earnings surprises, and ha he gap beween small- and largerader reacions is higher for he mos posiive surprises. This seems o poin o a small rader overreacion. The wo resuls are easily reconciled by considering he possibiliy of aenion buying. Barber and Odean (2002) finds ha individuals buy an abnormally high amoun of a company s sock afer news abou he company wheher he news is good or bad. Thinking of he curve of abnormal rade imbalance reacion on he verical axis and earnings surprise decile on he horizonal axis, aenion buying would shif he enire curve up for he raders who are mos suscepible o he aenion effec, increasing he reacions o each earnings surprise, and causing he inercep o be higher for small rades han for large rades. By fiing his daa o a linear model, we can esimae he difference in he slopes of he small rader reacion and he large rader reacion. Using ordinary leas squares, we esimae he equaion: 14

16 , e, x S L S ( x = S) + α Ι( x = L) + Ι( x S) SurpDece VolMeas = α Ι β = + β Ι( + ε, (8) L x = L) SurpDece, e, x where is he rading day in even ime, ha is, he number of rading days beween even e and he dae of he rading daa observaion, e is he earnings announcemen even, x is he rade size caegory, S for small rade, L for large rade, and SurpDec e is he surprise decile for even e. In equaion (8), α is he inercep for he reacion o he earnings announcemen, which is roughly he reacion o an exremely negaive surprise (decile 0), and helps conrol for he aenion buying effec. The β coefficien reflecs he way in which he given volume measure depends on he surprise decile. Essenially, β measures he srengh of he reacion. Table 1 presens he coefficien esimaes for hese regressions, wih -saisics for ess of α S = α L and of β S = β L. One can see ha α S is significanly higher han α L during he enire even period. The relaionship beween β S and β L is no as consisen hrough he even period as he relaionship beween α S and α L. Before he announcemen dae, β S is less han β L bu on and afer he announcemen dae, β S is much higher han β L. I seems as if large raders are learning more abou he earnings value in he few days before he announcemen is made, bu once he earnings are made public, small raders are reacing more srongly han large raders. Overall, hese regression resuls seem o confirm he inerpreaion of Figure 1, ha small raders exhibi some sor of aenion buying and reac more srongly o he ype of earnings surprise han do large raders. When we use he earnings-surprise measure based on analyss earnings forecass, we find ha small raders acually reac more weakly o he earnings surprise han do large raders, in ha β S is less han β L hroughou he even period. Wih only hese wo ses of resuls i is unclear wheher small raders are underreacing or overreacing o earnings surprises. Subsample eliminaing surprises ha are lae in a series A key predicion of he models of Daniel, Hirshleifer and Subrahmanyam (1998) and Barberis, Shleifer and Vishny (1998) is ha invesors reac differenly o differen surprises in a series. For example, invesors reac differenly o he hird negaive surprise in a row han o he firs negaive surprise. Shanhikumar (2004) provides evidence ha small raders exhibi his behavior in he marke. Because of his, we migh see overreacion when we pool all earnings surprises ogeher, when in fac invesors underreac o he firs surprise in a series and overreac only o he laer ones. Due o he imporance of his predicion o he models, and based on he empirical evidence, in his secion we condiion on pas surprises by looking a he firs surprise 15

17 in any given series. We use he same mehods as in he above secion, bu we resric ourselves o a subse of he earnings surprises. In paricular, we assign an earnings surprise a value of N=0 if i is a mild surprise, ha is, in deciles 3, 4, 5 or 6. We assign i a value of N=1 if i is a very negaive surprise (decile 0, 1 or 2) and if he preceding surprise for ha firm was no srongly negaive. Similarly a surprise ges a value of N=1 if i is very posiive (deciles 7,8 or 9) and he preceding surprise was no posiive. The surprise has a value of N=2 if i is he second surprise of he same ype, srongly negaive or srongly posiive, N=3 if i is he hird, and so on. Since boh he model of Daniel, Hirshleifer and Subrahmanyam (1998), and he model of Barberis, Shleifer and Vishny (1998), predic ha invesor reacions will depend on N values, N is an imporan variable in he analysis of hese models. For his secion, we limi he sample o surprises wih N=0 or N=1. Figure 2 displays average reacions o he differen earnings surprise deciles. The largerade reacion does no change much beween he full sample and he N {0,1} subsample. As expeced, since small raders reac more srongly o each consecuive surprise, in ha heir reacion slope increases wih N, heir reacion is weaker when we limi he sample o he firs surprise in each sequence. The small rade reacion o posiive surprises is lower for his subsample, and heir reacion o negaive surprises is higher. Overall, heir reacion does no seem as exreme as wih he full earnings surprise sample. Regression resuls show ha he significan overreacion observed for he full sample does no occur for he N {0,1} subsample. Table 2 displays resuls from regressions of he form of equaion (8), wih he N {0,1} sample. The resuls regarding β change dramaically when we limi our sample o firm-evens wih N {0,1}. Wih he whole sample, small-rader slope is over wice as high as he largerader slope for four days surrounding he earnings announcemen. Wih he N {0,1} subsample, he slope coefficiens are abou he same for he wo groups, from day 0 hrough day 3. Surrounding his period, small rades acually depend less on he earnings surprise han do large rades, wih β S < β L. These resuls provide weak suppor for a small rader underreacion o he firs surprise in a series, as he slope is significanly negaive during he weeks surrounding he earnings surprise. While he resuls are insignifican on days 0-3, and based on hese four days alone i seems possible ha small raders are reacing correcly wih he added effec of aenion buying, hese resuls do provide srong evidence agains he proposiion ha less sophisicaed invesors will display an even-ime overreacion. 16

18 Analys-Based Earnings Surprise Panels B of Table 1 and Table 2 presen resuls using he earnings-surprise measure based on monhly analys consensus forecas, calculaed as described in Secion 3. Our measure of earnings surprises using analys forecass as a proxy for earnings expecaions yields similar resuls, wih he one key difference poined ou in Secion 4, Full Sample, regarding he difference beween β S and β L. Specifically, for he whole sample, we find ha small raders have a weaker reacion han large raders, ha is β S < β L when we use analys-based earnings surprises, in conras wih he SUE based resuls for which small raders have a sronger reacion han large raders, wih β S > β L. As wih he SUE resuls, he difference beween small and large rade slope, (β S β L ), is more negaive when we limi he sample o evens wih N {0,1}. In paricular, he small rader reacion on days 1 hrough 8 is much lower if we limi he sample o only firms wih N {0,1}, when we measure earnings surprises using analys forecass. Overall, small raders reac more weakly o he analys-based surprises, providing more suppor for heories proposing ha small raders underreac. V. Lagged Trading Behavior One of he key differences beween radiional explanaions of pos-earningsannouncemen drif and behavioral explanaions is he implied reacion in he monhs afer he earnings announcemen. According o radiional explanaions, he reacion correcs iself. According o boh of he wo behavioral models we focus on, he models of Daniel, Hirshleifer and Subrahmanyam (1998) and Barberis, Shleifer and Vishny (1998), invesors overreac. In addiion, we would like o know wheher pos-earnings-announcemen drif occurs as one group s reacion changes or as a second group rades agains hem. For example, if he marke as a whole underreacs and correcs does i correc because he underreacing invesors realize heir misake, or because oher invesors are able o correc prices over ime? In order o answer hese quesions, we look a rading behavior for several monhs afer he earnings announcemen dae. Figure 3 displays he slope coefficiens from esimaion of equaion (8) using a moving five-day window for roughly wo years following he earnings announcemen, and wih he sample limied o earnings surprises wih N {0,1}. Table 3 displays he coefficiens from regressions of he form of equaion (8), where he dependen variable is he sum of daily 17

19 abnormal rade imbalances over he given period in even-ime. The paricular periods shown in he able are each of he firs welve monhs following he earnings announcemen. Firs, if we focus on he large raders, we can see from he figure ha heir rading is srongly posiively relaed o he earnings surprise in he firs monh surrounding he surprise. The slope coefficien is significanly posiive for 18 of he 22 days from day 1 hrough day 20. Alhough he coefficien is posiive again during porions of monhs wo and hree, i is only significan for hree days during hose monhs. The regression resuls displayed in Table 3 confirm ha he large rader reacion is only significanly posiive during he firs monh following he earnings surprise. If hese rading resuls are represenaive of he large rader sraegies, i seems ha he large raders rade in such a way as o ake advanage of he poenial pos-earnings-announcemen drif during he enire firs monh, bu afer ha heir rading ceases o depend srongly on he earnings announcemen. Focusing on he small raders, here is a significanly posiive reacion during four days surrounding he earnings announcemen, bu he reacion is roughly zero, or significanly negaive during he remainder of he firs monh. The small rader slope is significanly posiive wo o hree monhs afer he earnings announcemen and remains significanly posiive for a leas en monhs afer ha. Inerpreing hese resuls in erms of rading sraegies, he small raders do no seem o be rading o ake advanage of he poenial drif in he same way ha he large raders are. If anyhing, hey are rading in he opposie direcion during he second and hird weeks following he earnings surprise. Bu during he second and hird monhs, he small raders seem o reac o he earnings announcemen, poenially aking advanage of any remaining drif, or overreacing if prices have already correced. Figure 4A displays he difference beween he slopes of small and large rade response o earnings surprises, using he SUE measure and a moving five-day window o esimae equaion (8), as for Figure 3. Figure 4B displays he -saisics for his difference. As he figure indicaes, small raders exhibi significanly lower sensiiviy o he earnings announcemen han do large raders, in he weeks surrounding he earnings announcemen. Bu in he monhs following he earnings surprise, heir reacion slowly increases relaive o he large rader reacion, and becomes sronger han ha of large raders. We can inerpre he significanly posiive small-rader slope in monhs 3-12 as oversensiiviy based on wo assumed benchmarks. Firs, he small-rader slope would represen an oversensiiviy if, because he informaion has been publicly available for some ime, here is no need o significanly hinge a rading sraegy on he old informaion. 18

20 Second, he small-rader slope would be oversensiiviy if we use he large rader reacion as a benchmark. There may be oher sock characerisics associaed wih he earnings announcemen, or invesor heerogeneiies, which make he small rader behavior opimal, bu he resuls provide preliminary suppor of he proposiion ha small raders exhibi a lagged overreacion o he earnings announcemen, as prediced by he models of Daniel, Hirshleifer and Subrahmanyam (1998) and Barberis, Shleifer and Vishny (1998). While he apparen oversensiiviy develops during he firs six monhs, i akes longer o decrease, saying generally posiive for a year and a half afer he even dae. The paern is similar using analys-forecas surprises. The lagged rading behavior is also consisen wih aenion buying riggered by earnings announcemens. For small raders, he inercep erm is posiive abou every 60 rading days and is negaive he remainder of he ime, suggesing ha small raders are buying more around he ime of each subsequen earnings announcemen. Again, he resuls are similar using he analysforecas surprises. When looking a a long horizon of rade imbalances such as hese, combined wih he esablished reurns paern of pos-earnings-announcemen drif, we mus be paricularly concerned wih conrolling for prior reurns and prior values of rade-imbalance. Table 4 repors robusness checks of he lagged rading behavior, reporing he esimaed (α S α L ) and (β S β L ), for regressions esimaing equaion (8) wih he dependan variable, rade imbalance, measured in each of he firs welve monhs following he earnings announcemen. The able repors resuls from regressions using abnormal rade imbalance measures which have been adjused for prior reurns using equaion (7), as well as using he alernae normalizaion of rade imbalance, which correcs for calendar-ime effecs and prior 15-day rade-imbalances and reurns as described in Secion 3. The able also repors esimaed coefficiens using he primary abnormal radeimbalance measure wih alernae earnings surprise measures. The able displays resuls for a modified version of Sandardized Unexpeced Earnings which does no include earnings drif and earnings-surprises calculaed from analys forecass. All of hese modificaions confirm ha β S > β L during monhs Alhough he difference is no saisically significan in each monh for each variaion, he difference is posiive for each monh, and significan for a leas half of he monhs in each variaion. In unrepored regressions, we esimae equaion (8) using hree oher measures of earnings-surprises, and he resuls are similar. We use earnings-surprises based on an analys consensus seven days prior o he earnings announcemen, consruced from daily analys forecas daa, and SUE-based surprises where he change in earnings, wih or wihou a drif adjusmen, is normalized by he sandard deviaion of earnings changes. 19

21 Togeher, he rading resuls seem o sugges ha small raders underreac iniially, alhough his evidence is mixed, and subsequenly over-correc, causing an overreacion. Large raders seem o be rading in he same direcion as he earnings announcemen in he firs monh afer he earnings announcemen, suggesing ha heir rading may be increasing he posearnings-announemen drif during his period, bu he lack of a relaionship beween large-rade imbalance and earnings surprises afer he firs monh afer he announcemens suggess ha large raders are no driving drif during he laer period. VI. Relaionship Beween Even-ime Trading and Fuure Reurns In order o es wheher even-ime rading behavior predics reurns, we regress fuure CARs on even-ime (days 1, 0 and 1) rade imbalance, conrolling for he earnings surprise. We conrol for he earnings surprise by looking a posiive surprises (deciles 7,8,9), mild surprises (deciles 3,4,5,6) and negaive surprises (deciles 0,1,2) separaely. Hirshleifer e al (2002) also ask his quesion, bu hey do no look a he ineracion beween surprise and rading behavior. While heir mehod gives ineresing new resuls, i is also imporan o conrol for he ineracion wih he surprise and o look as well a large-rade behavior. If we found a rade imbalance of 0 and an earnings surprise of 0, he underreacion and correcion heories would predic no drif. Wih an iniial rade imbalance of 0 and an exremely posiive surprise, he underreacion and correcion heories would predic posiive drif. Similarly, if here were a rade imbalance of 0 and an exremely negaive earnings surprise, we would expec negaive drif. Hirshleifer e al (2002) essenially combine hese hree cases ino one. Our mehod will look a each case separaely 4. One can see from his simple example ha small-rade buying should be a negaive predicor of reurns for a given sock and surprise. If small raders sell afer a posiive earnings surprise, hey are underreacing severely and we would expec higher fuure reurns. If hey bough, on he oher hand, hey would already have reaced o some of he new informaion, 4 Hirshleifer e al (2002) find ha individual rading is a weak negaive predicor of 6 monh and 9 monh reurns. We also aemp our regressions wihou ineracing he rading variables wih surprise ype, and find ha our small rader imbalance does no significanly predic reurns for any of hose horizons, alhough he coefficiens are negaive for he 4-6 monh and 7-9 monh horizons. We do find significan negaive predicive power for he 2 nd and 3 rd monhs, hough. We use CARs whereas Hirshleifer e al use buy-and-hold reurns. Since buy-and-hold reurns would cause he effec of he 2-3 monh reurn on he 0-9 monh reurn o be higher, his could be a conribuing facor o he higher significance Hirshleifer e al find. 20