All ha Gliers: The Effec of Aenion and News on he Buying Behavior of Individual and Insiuional Invesors Brad M. Barber Terrance Odean * Ocober 003 * Barber is a he Graduae School of Managemen, Universiy of California, Davis. Odean is a he Haas School of Business, Universiy of California, Berkeley. We appreciae he commens of Jonahan Berk, David Blake, Ken French, Simon Gervais, John Griffin, Andrew Karolyi, Sendhil Mullainahan, Mark Rubinsein, Bre Trueman and seminar paricipans a Arizona Sae Universiy, he Universiy of California, Irvine, he Universiy of California, Berkeley, he Copenhagen Business School, Cornell Universiy, Emory, Ohio Sae Universiy, he Sockholm School of Economics, Vanderbil, he Wharon School, he 001 CEPR/JFI symposium a INSEAD, Mellon Capial Managemen, he Naional Bureau of Economic Research, and he Risk Percepions and Capial Markes Conference, Norhwesern Universiy. We are graeful o he Plexus Group, o BARRA, and o he reail broker and discoun brokers who provided us wih he daa for his sudy and o he Insiue for Quaniaive Research and he Naional Science Foundaion (gran #SES-0111470) for financial suppor. Shane Shepherd, Michael Foser, and Michael Bowers provided valuable research assisance. All errors are our own. Brad Barber can be reached a (530) 75-051 or bmbarber@ucdavis.edu; Terrance Odean can be reached a (510) 64-6767 or odean@haas.berkeley.edu.
Absrac We es he hypohesis ha individual invesors are more likely o be ne buyers of aeniongrabbing socks han are insiuional invesors. We speculae ha aenion-based buying is a resul of he difficuly ha individual invesors have searching he housands of socks hey can poenially buy. Individual invesors don face he same search problem when selling, because hey end o sell only a small subse of all socks hose hey already own. We look a hree indicaions of how likely socks are o cach invesors aenion: daily abnormal rading volume, daily reurns, and daily news. We calculae ne order imbalances for more han 66,000 individual invesors wih accouns a a large discoun brokerage, 647,000 individual invesors wih accouns a a large reail brokerage, 14,000 individual invesor accouns a a small discoun brokerage, and 43 professional money managers. Individual invesors end o be ne purchasers of socks on high aenion days days ha hose socks experience high abnormal rading volume, days following exreme price moves, and days on which socks are in he news. Insiuional invesors are more likely o be ne buyers on days wih low abnormal rading volume han on hose wih high abnormal rading volume. Their reacion o exreme price moves depends on heir invesmen syle. We develop a heoreical model of how aenion-based buying affecs asse prices. Consisen wih he predicions of our model, we find ha socks bough by individual invesors on high-aenion days end o subsequenly underperform socks sold by hose invesors.
How do invesors choose he socks hey buy? Are heir choices so randomly idiosyncraic ha, in aggregae, hey cancel ou each oher and hus have no influence on sock prices? Or do he purchase paerns of invesors even hose wih heerogeneous beliefs aggregae in a way ha may move price? Several sudies documen ha invesors are sysemaically relucan o sell socks for a loss (e.g., Saman and Shefrin, 1985, Odean, 1998a). Less is known abou how hey make purchases. In his paper, we es he proposiion ha individual invesors simply buy hose socks ha cach heir aenion. While each invesor does no buy every single sock ha grabs his aenion, individual invesors are more likely o buy aenion-grabbing socks han o sell hem. Sysemaic buying behavior, like sysemaic selling, has he poenial o influence prices, especially for asses heavily raded by individual invesors such as he common sock of small capializaion firms and of firms wih recen iniial public offerings. In conras o our findings, many heoreical models of invesor rading rea buying and selling as wo sides of he same coin. Informed invesors observe he same signal wheher hey are deciding o buy or o sell. They are equally likely o sell securiies wih negaive signals as hey are o buy hose wih posiive signals. Uninformed noise raders are equally likely o make random purchases or random sales. In formal models, he decisions o buy and o sell ofen differ only by a minus sign. For acual invesors, he decisions o buy and o sell are fundamenally differen. When buying a sock, invesors are faced wih a formidable search problem. There are over 7,000 U. S. common socks from which o choose. Human beings have bounded raionaliy. There are cogniive and emporal limis o how much informaion we can process. We are generally no able o rank hundreds, much less housands, of alernaives. Doing so is even more difficul when he alernaives differ on muliple dimensions. One way o make he search for socks o purchase more manageable is o limi he choice se. I is far easier, for example, o choose among 10 alernaives han 100. For example, see he well-cied models of Grossman and Sigliz (1980) and Kyle (1985). 1
Odean (1999) proposes ha invesors manage he problem of choosing among housands of possible sock purchases by limiing heir search o socks ha have recenly caugh heir aenion. Invesors do no buy all socks ha cach heir aenion; however, for he mos par, hey only buy socks ha do so. Which aenion-grabbing socks invesors buy will depend upon heir personal preferences. Conrarian invesors, for example, will end o buy ou of-favor socks ha cach heir eye, while momenum invesors will chase recen performers. In heory, invesors face he same search problem when selling as when buying. In pracice, wo facors miigae he search problem for individual invesors when hey wan o sell. Firs, mos individual invesors hold relaively few common socks in heir porfolio. 3 Second, mos individual invesors only sell socks ha hey already own, ha is, hey don sell shor. 4 Thus, invesors can, one by one, consider he meris boh economic and emoional of selling each sock hey own. Raional invesors are likely o sell heir pas losers, hereby posponing axes; behaviorally moivaed invesors are likely o sell pas winners, hereby posponing he regre associaed wih realizing a loss (see Saman and Shefrin, 1985). Thus, o a large exen, individual invesors are concerned abou he fuure reurns of he socks hey buy bu he pas reurns of he socks hey sell. Our argumen ha aenion is a major facor deermining he socks individual invesors buy, bu no hose hey sell, does no apply wih equal force o insiuional invesors. There are wo reasons for his. Firs, unlike individual invesors, insiuions do ofen face a significan search problem when selling. Second, aenion is no as scarce a resource for insiuional invesors as i is for individuals. 3 On average during our sample period, he mean household in our large discoun brokerage daase held 4.3 socks worh $47,334; he median household held.61 socks worh $16,10. 4 0.9 percen of posiions are shor posiions for he invesors in he large discoun brokerage daase ha we describe in Secion II. When he posiions are weighed by heir value, 0.78 percen are shor.
Like individuals, insiuions also face many choices when purchasing, bu, unlike individuals, hey also face many choices when selling. Insiuional invesors, such as hedge funds, rouinely sell shor. For hese invesors, he search se for purchases and sales is idenical. Even insiuions ha do no sell shor face far more choices when selling han do mos individuals, simply because hey own much larger porfolios han do mos individuals. Insiuional invesors devoe more ime o searching for socks o buy and sell han do mos individuals. Insiuions use compuers o narrow heir search. They may limi heir search o socks in a paricular secor (e.g., bioech) or meeing specific crieria (e.g., low price-o-earnings raio) hus reducing aenion demands. While individuals, oo, can use compuers or pre-selecion crieria, on average, hey are less likely o do so. In his paper, we es he hypoheses ha (1) he buying behavior of individual invesors is more heavily influenced by aenion han is heir selling behavior and ha () he buying behavior of individual invesors is more heavily influenced by aenion han is he buying behavior of professional invesors. We also develop a model based on he assumpion ha aenion influences buying more han selling and we es he asse pricing predicions of our model. These predicions are (1) ha socks heavily purchased by aenion-based invesors will subsequenly underperform socks heavily sold by hose invesors and () ha his underperformance will be greaer following periods of high aenion. One measure of he exen o which a sock grabs invesors aenion is is abnormal rading volume. Imagine sanding on a sree and observing a large crowd gahered a one end of he sree and nobody sopped a he oher end. You don know why he crowd has gahered, maybe o wach sree performers, maybe o help an old man who had a hear aack. You do know ha an aenion-grabbing even is aking place on he end of he sree where he crowd has gahered no he end wihou a crowd. Similarly when, as researchers, we observe abnormal rading volume in a sock, we know ha somehing has happened o grab invesors aenion hough we may no know wha ha somehing is. Abnormal rading volume serves as a proxy for he unobserved aenion-grabbing even. As discussed above, we believe ha aenion is a greaer deerminan of wha individual invesors buy 3
han of wha hey sell. Thus, individual invesors will acively buy socks wih unusually high rading volume. They may also sell highly raded socks, however, selling won be as influenced by aenion and will no increase as much when rading volume is abnormally high. For every buyer here mus be a seller. Therefore, on days when aenion-driven invesors are buying, some invesors, whose purchases are less dependen on aenion, mus be selling. We anicipae herefore ha professional invesors (inclusive of marke-makers) will exhibi a lower endency o buy, raher han sell, on days of high abnormal volume and a reverse endency on days of abnormally low volume. (Excepions will arise when he even driving abnormal volume coincides wih he purchase crieria ha he professional invesor is pursuing.) We examine he buying and selling behavior associaed wih abnormal rading volume for four samples of invesors: invesors wih accouns a a large discoun brokerage, invesors a a smaller discoun brokerage firm ha adverises is rade execuion qualiy, invesors wih accouns a a large reail brokerage, and professional money managers. As prediced, individual invesors end o be ne buyers on high aenion days; for example, invesors a he large discoun brokerage make nearly wice as many purchases as sales of socks experiencing unusually high rading volume (e.g, he highes five percen). 5 The buying behavior of he professionals is leas influenced by aenion. In addiion o abnormal rading volume, anoher phenomenon ha is likely o coincide wih salien evens or be salien iself is an exreme one day price move. A sock ha soars or dives caches peoples aenion. News agencies rouinely repor he prior day s 5 Looking a all common sock ransacions, hese invesors make slighly more purchases (1,08,107) han sales (887,594). 4
big winners and big losers. Furhermore, large price moves are ofen associaed wih salien announcemens or developmens. We sor socks based on one-day reurns and examine invesors buying and selling behavior on he subsequen day. 6 We anicipae and find ha aenion driven invesors end o be ne buyers of boh he previous day s big winners and big losers. For example, invesors a he large discoun brokerage firm are nearly wice as likely o buy as o sell a sock wih an exremely poor performance (lowes 5 percen) he previous day. Finally, news caches invesors aenion. We anicipae and find ha aenion driven invesors end o be ne buyers of companies on days ha hose companies are in he news. The plan of he paper is as follows. We discuss relaed research in secion I. We describe he four daases in secion II, and our soring mehodology in secion III. We develop a model of aenion-based buying in secion IV, presen evidence of aenion-based buying in secion V, and discuss an alernaive hypohesis in secion VI. In VII, we es he asse pricing implicaions of our model and we conclude in secion VIII. I. Relaed Research A number of recen sudies examine invesor rading decisions. Odean (1998a) finds ha, as prediced by Shefrin and Saman (1985), individual invesors exhibi a disposiion effec invesors end o sell heir winning socks and hold on o heir losers. Boh individual and professional invesors have been found o behave similarly wih several ypes of asses including real esae (Genesove and Mayer), company sock opions (Heah, Huddar, and Lang, 1999), and fuures (Heisler, 1994; Locke and Mann, 1999) (also see Shapira and Venezia, 1998). 6 We repor order imbalances for socks sored and pariioned on same day news and same day abnormal rading volume, and previous day s reurn. We do no repor order imbalances for socks sored on same day reurns because of poenial endogeneiy problems. While we argue ha an exreme price move may arac buyers, clearly buyers could also cause price moves. Our resuls are qualiaively similar when when we calculae imbalances he same day ha we sor on reurns. 5
I is well-documened ha volume increases on days wih informaion releases or large price moves (Bamber, Barron, and Sober (1997); Karpoff (1987)). For example, when Maria Bariromo menions a sock during he Midday Call on CNBC, volume in he sock increases nearly fivefold (on average) in he minues following he menion (Busse and Green (00)). Ye, for every buyer here is a seller. In general, hese sudies o no invesigae who is buying and who is selling he focus of our analysis. One excepion is Lee (199). He examines rading aciviy around earnings announcemens for 30 socks over a one-year period. He finds ha individual invesors hose who place marke orders of less han $10,000 are ne buyers subsequen o boh posiive and negaive earnings surprises. Hirshleifer, Myers, Myers, and Teoh (00) also documen ha individual invesors are ne buyers following boh posiive and negaive earnings surprises. Lee (199) conjecures ha news may arac invesors aenion or, alernaively, ha reail brokers who end o make more buy han sell recommendaions may rouinely conac heir cliens around he ime of earnings announcemens. Odean (1999) examines rading records of invesors a a large discoun brokerage firm. He finds ha, on average, he socks hese invesors buy underperform hose hey sell, even before considering ransacions coss. He observes ha hese invesors buy socks ha have experienced greaer absolue price changes over he previous wo years han he socks hey sell. He poins ou he dispariy beween buying and selling decisions for individual invesors and he search problem hey face when choosing from among housands of socks. He suggess ha many invesors limi heir search o socks ha have recenly capured heir aenion, wih conrarians buying previous losers and rend chasers buying previous winners. Of course, fully raional invesors will recognize he limiaions of predominanly buying socks ha cach heir aenion. They will realize ha he informaion associaed wih an aenion-grabbing even may already be impounded ino price (since he even has undoubedly been noiced by ohers), ha he aenion-grabbing even may no be relevan o fuure performance, and ha non-aenion-grabbing socks may presen beer purchase opporuniies. Odean (1998b) argues ha many invesors rade oo much because hey are overconfiden abou he qualiy of heir informaion. Such invesors may overvalue he 6
imporance of evens ha cach heir aenion, hus leading hem o rade sub-opimally. Odean (1999) and Barber and Odean (000, 001a, 001b) find ha, on average, individual invesors do rade sub-opimally, lowering heir expeced reurns hrough excessive rading. Meron (1987) noes ha individual invesors end o hold only a few differen common socks in heir porfolios. He poins ou ha gahering informaion on socks requires resources and suggess ha invesors conserve hese resources by acively following only a few socks. If invesors behave his way, hey will buy and sell only hose socks ha hey acively follow. They will no impulsively buy socks ha hey do no follow simply because hose socks happen o cach heir aenion. Thus heir purchases will no be biased oward aenion-grabbing socks. II. Daa In his sudy, we analyze invesor rading daa drawn from four sources: a large discoun brokerage, a small discoun brokerage, a large full-service brokerage, and he Plexus Group a consuling firm ha racks he rading of professional money managers for insiuional cliens. The firs daase for his research was provided by a large discoun brokerage firm. I includes rading and posiion records for he invesmens of 78,000 households from January 1991 hrough December 1996. 7 The daa include all accouns opened by each household a his discoun brokerage firm. Sampled households were required o have an open accoun wih he discoun brokerage firm during 1991. Roughly half of he accouns in our analysis were opened prior o 1987, while half were opened beween 1987 and 1991. In his research, we focus on invesors common sock purchases and sales. We exclude from he curren analysis invesmens in muual funds (boh open- and closed-end), American deposiory receips (ADRs), warrans, and opions. Of he 78,000 households sampled from he large discoun brokerage, 66,465 had posiions in common socks during a 7 Posiion records are hrough December 1996; rading records are hrough November 1996. See Barber and Odean (000) for a more compee descripion of hese daa. 7
leas one monh; he remaining accouns held eiher cash or invesmens in oher han individual common socks. Roughly 60 percen of he marke value in hese households accouns was held in common socks. There were over 3 million rades in all securiies; common socks accouned for slighly more han 60 percen of all rades. During our sample period, he average household held 4.3 socks worh $47,334, hough each of hese figures is posiively skewed. The median household held.61 socks worh $16,10. In December 1996, hese households held more han $4.5 billion in common sock. There were slighly more purchases (1,08,107) han sales (887,594) during our sample period, hough he average value of socks sold ($13,707) was slighly higher han he value of socks purchased ($11,05). As a resul, he aggregae values of purchases and sales were roughly equal ($1.1 and $1. billion, respecively). The average rade was ransaced a a price of $31 per share. The value of rades and he ransacion price of rades are posiively skewed; he medians for boh purchases and sales are subsanially less han he mean values. Our second daa se conains informaion from a smaller discoun brokerage firm. This firm emphasizes high qualiy rade execuion in is markeing and is likely o appeal o more sophisicaed, more acive, invesors. The daa include daily rading records from January 1996 hrough June 15, 1999. Accouns classified by he brokerage firm as professionals are excluded from our analysis. 8 The daa include 14,667 accouns for individual invesors who make 14,73 purchases wih a mean value of $55,077 and 198,541 sales wih a mean value of $55,999. The hird daa se conains informaion from a large reail brokerage firm on he invesmens of households for he 30 monhs ending in June 1999. These daa include daily rading records. Using clien ownership codes supplied by he brokerage firm, we limi our analysis o he 665,533 invesors wih non-discreionary accouns (i.e., accouns classified as individual, join enans wih righs of survival, or cusodian for minor) wih a leas one common sock rade during our sample period. During his period hese accouns execued 8 We analyze he accouns of professional invesors separaely. There are, however, no enough daa o achieve saisically significan resuls. 8
over 10 million rades. We resric our analysis o heir common sock rades: 3,974,998 purchases wih a mean value of $15,09 and 3,19,99 sales wih a mean value of $1,169. The fourh daa se was compiled by he Plexus Group as par of heir advisory services for heir insiuional cliens. The daa include daily rading records for 43 insiuional money managers and span he period January 1993 hrough March 1996. No all managers are in he sample for he enire period. In addiion o documening compleed purchases and sales, he daa also repor he dae and ime a which he manager decided o make a purchase or sale. In he daase, hese money managers are classified as momenum, value, and diversified. 9 During our sample period, he eigheen momenum managers make 789,779 purchases wih a mean value of $886,346 and 617,915 sales wih a mean value of $896,165; he eleven value managers make 409,53 purchases wih a mean value of $500,949 and 350,00 sales wih a mean value of $564,69; he foureen diversified managers make 31,457 purchases wih a mean value of $450,474 and 0,147 sales wih a mean value of $537,947. III. Sor Mehodology A. Volume Sors On he days when a sock experiences abnormally heavy volume, i is likely ha invesors are paying more aenion o i han usual. We wish o es he exen o which he endency o buy socks increases on days of unusually high rading volume for each of our four invesor groups (large discoun, reail, small discoun, and professional). Firs we mus sor socks on he basis of abnormal rading volume. We do so by calculaing for each sock on each rading day he raio of he sock s rading volume ha day o is average rading volume over he previous one year (i.e., 5 rading days). Thus, we define abnormal rading volume for sock i on day, AVi o be AV V V i i = (1) i 9 Keim and Madhavan (1995, 1997, and 1998) analyze earlier daa from he Plexus Group. They classify managers as echnical, value, and index. Based on conversaions wih he Plexus Group, we believe ha hese classificaion correspond o our momenum, value, and diversified classificaions. 9
where Vi is he dollar volume for sock i raded on day as repored in he Cener for Research in Securiy Prices (CRSP) daily sock reurn files for NYSE, ASE, and NASDAQ socks and 1 Vi Vid =. () d= 5 5 Each day we sor socks ino deciles on he basis of ha day s abnormal rading volume. We furher subdivide he decile of socks wih he greaes abnormal rading volume ino wo vingiles (i.e., five percen pariions). Then, for each of our invesor ypes, we sum he buys (B) and sells of socks (S) in each volume pariion on day and calculae order imbalance for purchases and sales execued ha day as: OI np NB np i i= 1 i= 1 p = np np NB + i i= 1 i= 1 where n p is he number of socks in pariion p on day, NS NS i i (3) NBi he number of purchases of sock i on day, and NSi he number of sales of sock i on day. We calculae he ime series mean of he daily order imbalance (OI p ) for he days ha we have rading daa for each invesor ype. Noe ha hroughou he paper our measure of order imbalance considers only execued rades; limi orders are couned if and when hey execue. If here are fewer han five rades in a pariion on a paricular day, ha day is excluded from he ime series average for ha pariion. We also calculae order imbalances based on he value raher han number of rades by subsiuing in he value of he sock i bough (or sold) on day for NB i (or NS i ) in equaion 3.3. Noe ha while oal buys and sells increase as volume increases, on a value weighed basis, aggregae buys and sells will increase equally. Thus aggregae value weighed (execued) order imbalance remains zero as abnormal volume increases, and how he order imbalance of a paricular invesor group changes wih volume is an empirical quesion. In summary, for each pariion and invesor group combinaion, we consruc a imeseries of daily order imbalance. Our inferences are based on he mean and sandard deviaion 10
of he ime series. We calculae he sandard deviaion of he ime series using a Newey-Wes correcion for serial dependence. B. Reurn Sors Invesors are likely o noice when socks have exreme one day reurns. Such reurns, wheher posiive or negaive, will mos ofen be associaed wih news abou he firm. The news driving exreme performance will cach he aenion of some invesors, while he exreme reurn iself will cach he aenion of ohers. Even in he absence of oher informaion, exreme reurns can become news hemselves. The Wall Sree Journal and oher media rouinely repor he previous day s big gainers and losers (subjec o cerain price crieria). If big price changes cach invesors aenion, hen we expec hose invesors whose buying behavior is mos influenced by aenion will end o purchase in response o price changes boh posiive and negaive. To es he exen o which each of our four invesor groups are ne purchasers of socks in response o large price moves, we sor socks based on one day reurns and hen calculae average order imbalances for he following day. We calculae imbalances for he day following he exreme reurns, raher han he same day as exreme reurns, for wo reasons. Firsly, many invesors may learn of or reac o he exreme reurn only afer he marke closes; heir firs opporuniy o respond will be he nex rading day. Secondly, order imbalances could cause conemporaneous price changes. Thus, examining order imbalances subsequen o reurns, removes a poenial endogeneiy problem. 10 Our resuls are qualiaively similar when we sor on same day reurns. Each day (-1) we sor all socks for which reurns are repored in he CRSP NYSE/AMEX/NASDAQ daily reurns file ino en deciles based on he one day reurn. We furher spli decile one (lowes reurns) and decile en (highes reurns) ino wo vingiles. We hen calculae he ime series mean of he daily order imbalance for each pariion on he day 10 Endogeneiy does no pose he same problem for news and abnormal volume sors. I is unlikely ha he percenage of individual invesors (or insiuional invesors ) rades ha is purchases causes conemporaneous news sories. Nor does he percenage of individual invesors (or insiuional invesors ) rades ha is purchases cause abnormal rading volume. 11
following he reurn sor. This calculaion is analogous o ha for our sors based on abnormal volume. 11 C. News Sors Firms ha are in he news are more likely o cach invesors aenion han hose ha are no. We pariion socks ino hose for which here is a news sory ha day and hose wih no news. Our news daase is he daily news feed from Dow Jones News Service. The daa begin in 1994. Due o how he daa were colleced and sored some days are missing from he daa. The Dow Jones news feed includes he icker symbols for each firm menioned in each aricle. On an average day, our daase records no news for 91% of he firms in he CRSP daabase. We calculae order imbalances for each firm s sock as described in Secion IIIa. IV. A Simple Model of Aenion-based Buying Saring wih he assumpion ha invesors buy socks ha cach heir aenion, we develop a simple four-period model wih wo rounds of rading exending Kyle (1985). Our model illusraes how aenion-based buying will look wih respec o our volume and reurn sors and i explores he implicaions of aenion-based buying for asse prices. In he model aenion-based noise raders and a risk-neural, privaely informed insider submi marke orders o a risk-neural markemaker. There are wo asses in he economy, a riskless asse and one risky asse. The riskless ineres rae is assumed o be 0. The disribuions of all marke parameers are known o he insider and o he marke maker. The erminal value of he risky asse is v = y1+ y for = 1,. y 1 and y are independen and can be, y ~ N( 0, φ ) 11 Typically a significan number of socks have a reurn equal o zero on day -1. These socks may span more han one pariion. Therefore, before calculaing he order imbalance for each pariion, we firs calculae he average number (and value) of purchases and sales of socks wih reurns of zero on day -1; in subsequen calculaions, we subsiue his average in place of he acual number (and value) of purchases and sales for zero reurn socks. The average number of purchases on day of a sock wih a reurn of zero on day -1 is S0 NBs, S s= 1 0 where S o is he number of socks wih zero reurn on day -1. There is an analogous calculaion for sales. 1
hough of as he firm s period 1 and earnings. Prior o rading a imes = 1,, he riskneural insider observes y. Afer observing y, he insider demands (submis a marke order for) x unis of he risky asse; x < 0 is inerpreed o be a sell order. y is publicly revealed o he noise raders and o he markemaker a ime +1, ha is, one period afer i is observed by he insider. Thus a =, y 1 is common knowledge. The revelaion of y proxies for news in he model. We assume ha he level of aenion paid o he risky asse by aenion-based noise raders is proporional o y 1. Wihou regard o price or value, noise raders submi marke orders o buy b ~N ( b, σ b ) unis of he risky asse and o sell ( s ~N, ) s σ s No all noise rader aciviy will depend on aenion. We se b m( A y) unis of he risky asse. = +, where m > 0 is a measure of he inensiy of noise rading and ma > 0 is he expeced level of non-aenion driven noise rader purchases. Our conenion is ha aenion has a greaer effec on buying han on selling, furhermore, we wish o have E( b) E( s) raders are neiher ne buyers nor sellers. We se s = m( A+ κ y + ( 1 κ) ε ) = so ha, on balance, noise, where κ, 0< κ < 1, deermines how much less aenion affecs selling compared o buying and ( ( 1 κ) φ ) m A+ is he expeced level of non-aenion driven noise rader sales. Seing aenion based buying in period as proporional o y 1 capures our assumpion ha aenion based raders will be ne buyers on good news (i.e., y 1 > 0 ) or bad news (i.e., y 1 < 0) and is roughly consisen wih he casual observaion ha news inensiy is highly concenraed on more exreme evens and wih he empirical resuls repored in secion V.b. Mean noise rader buying and selling in period one are se equal o he expeced mean of noise rader buying and selling in period wo, i.e., m( A φ ) +. Finally, he variances of noise rader buying and selling are assumed o be proporional o he means, ha is, where NBs is he number of imes sock s was purchased by invesors in he daase on day and S0 is he number of socks wih a reurn of zero on day -1. Similar calculaions are done o deermine he average number of sales and he average value of purchases and sales for socks wih a reurn of zero on day -1. 13
σ b b = b ψ and σ s = bs ψ, where ψ > 0 is a scaling facor. P 0, he period 0 price of he risky asse, is assumed o equal is uncondiional expeced erminal value, v = 0, and P 3, he period 3 price, is se equal o he realized erminal value of he risky asse which is public knowledge in period 3, ha is, P3 = v = y 1+ y. We are primarily ineresed in rading a =, when he rading aciviy of noise raders is influenced by he aenion associaed wih he public revelaion of he insider s firs period signal, y 1. The insider conjecures ha he markemaker s price-seing funcion is a linear funcion of oal demand d = x + b s, He chooses signal, P = µ + λd (4) x o maximize his expeced rading profis, x ( v P), condiional on his y, and he conjecured price funcion. 1 We assume, as in Kyle (1985), ha, due o perfec compeiion, he markemaker earns zero expeced profis. The markemaker conjecures ha he insider s demand funcion is a linear funcion of x y, = α + β y. (5) She ses price o be he expeced value of v condiional on oal demand, d, given he conjecured demand funcion. Proofs for he equilibrium soluion and for he proposiions appear in he appendix. Clearly, from he consrucion of he model, expeced noise rader buying aciviy is increasing in conemporaneous rading volume and in he square of he previous day s price change. We illusrae his by simulaing 100,000 realizaions of our model under he assumpion ha φ =, A =, m =, ψ =, and κ = 0.5. 13 As in our empirical analysis, we firs sor he resuls ino deciles based on curren (period ) rading volume and previous 1 Because y 1 is publicly revealed a =, he risk-neural insider does no need o consider period wo rading when deermining his period one demand. 13 Because b and s are disribued normally, negaive realizaions are possible. The likelihood of hese depends upon he parameer values. There were no negaive realizaions of b and s in his simulaion. 14
(period 1) price change and subdivide he larges and smalles reurn deciles and he larges volume decile ino vingiles. We hen calculae noise rader order imbalance for each pariion as described above in Secion II.A. In Figure 1a, we see ha order imbalance is increasing in volume. The shape of his graph is robus o differen choices of parameer values and closely resembles our empirical findings for individual invesors which we repor in he following secion and graph in Figure a. In Figure 1b, we see ha he simulaed order imbalance is firs decreasing and hen increasing in he previous day s price change; he plo is convex and U shaped. Again, he shape of he graph is robus o differen choices of parameer values and he simulaed resul resembles our empirical finding for individual invesors repored in he following secion and graphed in Figure 3a. Our wo proposiions examine he model s asse pricing implicaions: Proposiion 1: Price change from period wo o period hree is negaively correlaed wih he period wo difference in noise rader buying and selling. Socks more heavily bough han sold by noise raders end o underperform. This resul is no driven by explicily by aenion bu by he willingness of uninformed invesors for any reason o rade in a marke wih an informed insider and by he marke-maker s inabiliy o disinguish informed and uninformed rades. A similar effec could be achieved wihou insider asymmeric informaion if he marke maker were risk averse and responded o invenory risk. Noe ha while he price change from period wo o period hree is negaively correlaed wih period wo noise rader buying, i is uncorrelaed wih period one o period wo price change, wih he period wo aenion level of noise raders, i.e., y 1, or wih period wo oal demand, d. This is because he raional risk-neural marke-maker observes y 1 and d and ses. P equal o E( v y, d ) 1 Proposiion : Period expeced noise rader losses are greaer when he aenion level, y 1, is greaer. When he level of aenion rading is greaer so oo is he volailiy of noise rader demand. This makes i more difficul for he marke maker o deec 15
insider rading. Insider expeced profis increase and so do noise rader losses. Togeher proposiions 1 and give us he esable predicions ha socks more heavily bough by aenion-based invesors will underperform hose more heavily sold and ha his relaive underperformance will be greaer for socks aracing more aenion. We es hese predicions in Secion VII. V. Resuls A. Volume Sors Trading volume is one indicaor of he aenion a sock is receiving. Table I presens order imbalances for socks sored on he curren day s abnormal rading volume. Order imbalance is repored for invesors a a large discoun brokerage, a large reail brokerage, and a small discoun brokerage and for insiuional money managers following momenum, value, and diversified sraegies. Invesors a he large discoun brokerage display he greaes amoun of aenion-based buying. When imbalance is calculaed by number of rades (column wo), 18.15 percen fewer of heir rades are purchases han sales for socks in he lowes volume decile. For socks in he highes volume vingile, 9.5 percen more of heir rades are purchases han sales. Their order imbalance rises monoonically wih rading volume. When imbalance is calculaed by value of rades (column hree), 16.8 percen fewer of heir rades are purchases han sales for socks in he lowes volume decile. For socks in he highes volume vingile, 17.67 percen more of heir rades are purchases han sales. Order imbalance increases nearly monoonically wih rading volume. Looking a he fourh hrough sevenh columns of Table 1, we see ha he ne buying behavior of invesors a he large reail broker and he small discoun brokerage is similar o ha of invesors a he large discoun brokerage. Our principal objecive is o undersand how aenion affecs he purchase decisions of all invesors. Calculaing order imbalance by he value of rades has he advanage of offering a beer gauge of he economic imporance of our observaions, bu he disadvanage of overweighing he decisions of wealhier invesors. In rying o undersand invesors decision processes, calculaing order imbalance by number of rades may be mos appropriae. Figure a graphs he order imbalance based on number of rades for invesors a 16
he large discoun brokerage, he large reail brokerage, and he small discoun brokerage. Noe ha he plos are upward sloping as hey were in our simple example (Figure 1a). The las six columns of Table 1 and Figure b presen he order imbalances of insiuional money managers for socks sored on he curren day s abnormal rading volume. Overall, hese insiuional invesors exhibi he opposie endency of he individual invesors, heir order imbalance is greaer on low volume days han high volume days. This is paricularly rue for value managers who are aggressive ne buyers on days of low abnormal rading volume. B. Reurns Sors Invesors are likely o ake noice when socks exhibi exreme price moves. Such reurns, wheher posiive or negaive, will ofen be associaed wih new informaion abou he firm. Table II and Figures 3a and 3b presen order imbalances for socks sored on he previous day s reurn. Order imbalance is repored for invesors a a large discoun brokerage, a large reail brokerage, a small discoun brokerage, and for insiuional money managers following momenum, value, and diversified sraegies. Invesors a he large discoun brokerage display he greaes amoun of aenionbased buying for hese reurns sors. When calculaed by number of rades, he order imbalance of invesors a he large discoun brokerage is 9.4 percen for he vingile of socks wih he wors reurn performance on he previous day. drops o 1.8 percen in he eighh reurn decile and rises back o 4 percen for socks wih he bes reurn performance on he previous day. We see in Figure 3a, as was he case in our simple example (Figure 1b), ha he order imbalance of hese invesors is U-shaped when socks are sored on he previous day s reurn. 14 They buy aenion-grabbing socks. When imbalance is calculaed by value of rades, he order imbalance of hese invesors is 9.1 percen for he vingile of socks wih he wors reurn performance on he previous day. drops o 14 Order imbalances are very similar when we pariion socks on same day s reurn raher han on he previous day s reurn. 17
negaive 8.6 percen in he eighh reurn decile and rises back o 11.1 percen for socks wih he bes reurn performance on he previous day. In Figure 3a, we see ha invesors a he large reail brokerage also display a U- shaped imbalance curve when socks are sored on he previous day s reurn. However, heir endency o be ne buyers of yeserday s big winners is more subdued and does no show up when imbalance is calculaed by value. Invesors a he small discoun brokerage are ne buyers of yeserday s big losers bu no he big winners. As seen in he las six columns of Table II and in Figure 3b, he hree caegories of insiuional money managers reac quie differenly o he previous day s reurn performance. Momenum managers dump he previous day s losers and buy winners. managers buy he previous day s losers and dump winners. Diversified managers do his as well hough no o he same exen. While one migh inerpre purchases of yeserday s winners by momenum managers and he purchases of yeserday s losers by he value managers as aenion moivaed, i seems more likely ha he evens leading o exreme posiive and negaive sock reurns coincided wih changes relaive o he selecion crieria ha hese wo groups of money managers follow. Unlike he individual invesors, hese money managers were no ne buyers on high abnormal volume days, nor is any one group of hem ne buyers following boh exreme posiive and negaive reurns. C. News Sors Table III repors average daily order imbalance for socks sored ino hose wih and wihou news. Invesors are much more likely o be ne buyers of socks ha are in he news han hose ha are no. 15 When calculaed by number for he large discoun brokerage, order imbalance is.70 percen for socks ou of he news and 9.35 percen for hose socks in he news. A he large reail brokerage, order imbalance is.40 percen for socks ou of he news and 16.95 percen for hose in he news. 15 Choe, Kho, and Sulz (000) find ha individual invesors in Korea buy in he days preceding large one day price increases and sell preceding large one day losses. Large one day price moves are likely o be accompanied by news. Choe, Kho, and Sulz poin ou ha he savvy rading of Korean individual invesors could resul from insider rading. 18
Table III also repors order imbalances separaely for days on which individual socks had a posiive, negaive, or zero reurn. Condiional on he sign of he reurn, average imbalances for individual invesors are always greaer on news days han no news days. For boh news and no news days, average imbalances are greaer for negaive reurn days han for posiive reurn days. One possible explanaion for his is ha when sock prices drop invesors are less likely o sell due o he disposiion effec, i.e., he preference for selling winners and holding losers. Alernaively, he differences in imbalances on posiive and negaive reurn days may resul from he execuion of limi orders. Many individual invesors will no monior heir limi orders hroughou he day. On a day when he marke rises, more sell limi orders will execue han buy limi orders. On days when he marke falls, more buy limi orders will execue. Unforunaely, our daases do no disinguish beween execued limi and marke orders. While boh he disposiion effec and limi orders may conribue o he greaer order imbalance on negaive reurn days, we suspec ha limi orders are he primary cause. To es he robusness of our news sor resuls, we calculae order imbalances for news and no-news days during four day periods surrounding earnings announcemens (he day prior o he announcemen, he day of he announcemen, and he wo days subsequen o he announcemen) and during non-earnings announcemen periods. For boh earnings and non-earnings periods, invesors a all hree brokerages have a greaer propensiy o buy (raher han sell) socks ha are in he news. 16 D. Size Pariions To es wheher our resuls are driven primarily by small capializaion socks, we calculae order imbalances separaely for small, medium, and large capializaion socks. We firs sor and pariion all socks as described above on he basis of same day abnormal 16 During earnings announcemen periods, order imbalance calculaed by number of rades a he large discoun brokerage is 11.49 percen on days wih news and 5.14 percen on days wihou news; a he small discoun brokerage 8.57 percen and -.67 percen, respecively; and a he large reail brokerage, 7.5 percen and 1.63 percen. During non-earnings announcemen periods, order imbalance a he large discoun brokerage is 9.01 percen on days wih news and.53 percen on days wihou news; a he small discoun brokerage, 6. percen and 0.75 percen; and a he large reail brokerage 17.3 percen and.51 percen. 19
rading volume, he previous day s reurn, and same day news. We hen calculae imbalances separaely for small, medium, and large capializaion socks using he same break poins o form abnormal volume and reurn deciles for all hree size groups. We use monhly New York Sock Exchange marke equiy breakpoins o form our size groups. 17 Each monh we classify all socks (boh NYSE lised and non-lised socks) wih marke capializaion less han or equal o he 30 h percenile break poin as small socks, socks wih marke capializaion greaer han he 30 h percenile and less han or equal o he 70 h percenile as medium socks, and socks wih marke capializaion greaer han he 70 h percenile as large socks. Table IV, repors order imbalances by size group for abnormal volume, reurn, and news sors. To conserve space we repor imbalances for he invesors mos likely o display aenion-based buying: hose a he large discoun brokerage. Resuls for he large reail and small discoun brokerages are qualiaively similar. 18 By and large, invesors are more likely o buy raher han sell aenion-grabbing socks regardless of size. This is rue for all hree of our aenion-grabbing measures: abnormal rading volume, reurns, and news. Many documened reurn anomalies, such as momenum and pos earning announcemen drif, are greaer for small capializaion socks han for large socks. Some researchers have suggesed ha hese phenomena may be caused by he rading behavior of individual invesors. We find, however, ha aenion-based buying by individuals is as srong for large capializaion socks as for small socks. I may be ha he individual invesor s psychology of invesing is similar for large and small socks bu ha, due o rading coss and oher limis of arbirage, he impac he individual invesor s psychology is greaer for small socks. VI. An Alernaive Hypohesis An alernaive poenial explanaion for our findings is ha differen invesors inerpre aenion-grabbing evens such as news differenly and so such evens lead o greaer 17 We hank Ken French for supplying marke equiy breakpoins. These breakpoins are available and furher described a hp://web.mi.edu/kfrench/www/daa_library/de_me_breakpoins.hml. 18 The only significan excepion o his paern is ha order imbalances a he large reail brokerage for large capializaion socks are no greaer for deciles of high previous day reurns han for he middle reurn deciles. For small cap and medium cap socks, hese reail invesors do demonsrae a greaer propensiy o buy yeserday s winners han yeserday s average performers. 0
heerogeneiy of beliefs. Individual invesors who become bullish are able o buy he sock, bu hose who become bearish can sell i only if hey already own i or are willing o sell shor. Insiuional invesors can boh buy and sell. On average, bullish individuals and insiuions buy while bearish insiuions, bu no individuals, sell. Thus aenion-grabbing evens are associaed wih ne buying by individuals, no because individuals are buying wha caches heir aenion, bu because aenion-grabbing evens are increasing heerogeneiy of beliefs while limied porfolios and shor sale consrains resric would be sellers. As aenion-grabbing evens become less recen, hey become less salien hereby reducing heerogeneiy of beliefs during non-even periods. While increased heerogeneiy of beliefs and selling consrains may conribue o ne buying by individuals around aenion-grabbing evens, we don hink ha his is he whole sory. We believe ha aenion plays a major role in deermining wha socks invesors buy. We furher es our aenion hypohesis by examining how individual invesors buy and sell he socks ha hey already own. Under his alernaive hypohesis, aenion-grabbing evens increase he heerogeneiy in invesors beliefs hus leading o rade. Invesors wihou selling consrains are as likely o sell as hey are o buy. Invesors who already own a sock can sell i. Thus, under his alernaive hypohesis, we would expec aenion-grabbing evens o increase boh he sales and he purchases of socks ha invesors already own. The aenion hypohesis makes a differen predicion. The aenion hypohesis saes ha aenion is imporan when invesors face a search problem. As discussed above, mos individual invesors do no face a formidable search problem when choosing a sock o sell, bu hey do when buying. Socks hey already own compee wih housands of oher socks as poenial purchases. Thus aenion affecs he rae a which socks are purchased, even socks ha are already owned. Of course invesors are, overall, more likely o sell han o buy socks hey already own. Under he aenion hypohesis, however, he order imbalance of socks ha invesors already own should be greaer on days ha hose socks are aenion-grabbing. 1
In Table V, we repor order imbalances for individual invesors for abnormal volume, reurn, and news sors for socks. In calculaing imbalances for his able, we consider only purchases and sales by each invesor of socks he or she already owns. Since invesors mosly sell socks ha hey already own, bu ofen buy socks ha hey do no own, a far greaer proporion of hese rades are sales. Therefore nearly all of he imbalances are negaive. The relaive paerns of imbalances are, however, similar o hose repored for individual invesors in Tables I, II, and III. The raio of purchases o sales is higher on high aenion days. This is paricularly rue for he abnormal volume sor (Panel A) and he news sor (Panel C). When socks are sored on he previous day s reurn (Panel B), invesors are relaively more likely o purchase socks hey already own on days following large negaive reurns han on oher days. However, following large posiive reurns, order imbalances do no increase as hey do for all socks, regardless of curren ownership (as repored in Table II). I is likely ha for socks invesors already own, he disposiion effec influences heir purchases as well as heir sales. Odean (1998a) repors ha invesors are more likely o purchase addiional shares of socks hey already own if he share price is below, raher han above, heir original purchase price. As prediced by Prospec Theory (Kahneman and Tversky, 1979), invesors assume more risk when in he domain of losses han when in he domain of gains. The resuls in Table V, Panel C are consisen wih his. Thus shor-selling consrains (and heerogeneiy of beliefs) do no fully explain our findings. For individual invesors who can sell a sock wihou selling shor, a higher percenage of heir rades are purchases raher han sales on high aenion days. VII. Asse Pricing Predicions Our heoreical model has wo esable predicions. The firs is ha socks uninformed invesors buy underperform, on average, hose hey sell. This predicion does no depend on aenion and is rue in general for models, such as Kyle (1985), in which noise raders and informed raders submi orders and marke-makers use orderflow o se price. Our second, and more criical, predicion is ha he underperformance of he socks bough relaive o socks sold by uninformed aenion-based invesors will be greaes following periods of high aenion.
The model does no specify he period of ime over which aenion-based buying affecs reurns. Our evidence ha invesors do buy socks ha cach heir aenion is based upon one day sors. I is likely, hough, ha invesors aenion spans more han a single day. Furhermore, he period over which he socks bough by aenion-based invesors will underperform he socks hey sell depends upon how swifly he signals of informed invesors become public knowledge. In he following analysis, we look for underperformance of socks bough by aenion-based invesors over a one monh horizon. We obain similar resuls a oher horizons. To es he model s firs predicion, we form wo porfolios: a porfolio of socks purchased by individual invesors and a porfolio of socks sold by hem. We hen calculae he difference in he reurns of hese wo porfolios. On each day, we consruc a porfolio comprised of hose socks purchased wihin he las monh (1 rading days). The reurn on he porfolio is calculaed based on he value of he iniial purchase as: R b = n b x i i= 1 n b i= 1 R x i i (6) where R i is he gross daily reurn of sock i on day, n b is he number of differen socks purchased during he pas year, and x i is he compound daily reurn of sock i from he close of rading on he day of he purchase hrough day -1 muliplied by he value of he purchase. A porfolio of socks sold wihin he las monh is similarly consruced. and one for he sales. Our predicion is ha he reurns of he purchase porfolio ( R ) will be lower han he reurns of he sales porfolio ( R ). s b To es he second predicion, we firs sor socks ino deciles on he basis of he curren day s abnormal rading volume and on he basis of previous day s reurn. For each decile, we form purchase and sale porfolios. Our predicion is ha here will be greaer underperformance of purchases relaive o sales for he high-aenion deciles. 3