Market Maker Inventories and Stock Prices

Marke Maker Invenories and Sock Prices Terrence Hendersho U.C. Berkeley Mark S. Seasholes U.C. Berkeley This Version March 3, 2006 Absrac This paper examines daily invenory/asse price dynamics using 11 years of NYSE specialis daa. The unique lengh and breadh of our sample enables he firs longer horizon esing of marke making invenory models e.g., Grossman and Miller (1988). We confirm such models predicions ha specialiss posiions are negaively correlaed wih pas price changes and posiively correlaed wih subsequen changes. A porfolio ha is long socks wih he highes invenory posiions and shor socks wih he lowes invenory posiions has reurns of 0.10% and 0.33% over he following 1 and 5 days, respecively. These findings empirically validae he causal mechanism liquidiy supplier invenory ha underlies models linking liquidiy provision and asse prices. Invenories complemen pas reurns when predicing reurn reversals. A porfolio long high-invenory/low-reurn socks and shor low-invenory/high-reurn socks yields 1.05% over he following 5 days. Order imbalances calculaed from signing rades relaive o quoes also predic reversals and are complemenary o invenories and pas reurns. Finally, specialis invenories can be used o predic reurn coninuaions over a one-day horizon. Keywords: Marke Maker, Invenory, Liquidiy Provision JEL number: G12 G14 We hank he New York Sock Exchange for providing daa especially Kaharine Ross and Jennifer Chan. We hank Larry Glosen, Charles Jones, Rich Lyons, and Chrisine Parlour for helpful commens. Hendersho graefully acknowledges suppor from he Naional Science Foundaion. Par of his research was conduced while Hendersho was he visiing economis a he New York Sock Exchange. Conac informaion: Mark S. Seasholes, U.C. Berkeley Haas School, 545 Suden Services Bldg., Berkeley CA 94720-1900; Tel: 510-642-3421; Fax: 510-642- 4700; email: mss@haas.berkeley.edu. 1

1 Inroducion Empirical sudies linking liquidiy provision o asse prices follow naurally from invenory models. Liquidiy suppliers and marke markers profi from providing immediacy o less paien invesors bu have limied invenory carrying and risk bearing capaciy. Similarly, limis o arbirage argumens rely on he idea ha cerain marke paricipans accommodae buying or selling pressure. These liquidiy suppliers/arbirageurs only bear he risk of holding undiversified posiions if hey are compensaed by favorable subsequen price movemens. Thus, when invenories are large, liquidiy suppliers have aken on risk and prices should subsequenly reverse. 1 By idenifying and sudying he invenories of raders who are cenral o he rading process and whose primary roll is o provide liquidiy NYSE specialiss over an 11-year period his paper conribues o a deeper undersanding of invenory/asse price dynamics. To focus on he longer horizons impacs of invenory we use daily invenory measures and eliminae bid-ask bounce by calculaing reurns using quoe midpoins. The lengh of our sample enables us o confirm he underlying causal mechanism liquidiy supplier invenory behind aemps o link liquidiy and sock reurns hrough reurn reversals. Prior daa on invenories ypically cover relaively shor periods of ime and/or a limied number of securiies. While hese limiaions prevened esing for he invenory/price relaionships a inerday horizons, he microsrucure lieraure has been quie successful in showing ha order flow and invenories play an imporan role in inraday rading and price formaion. 2 This paper examines he relaionship beween closing marke maker (specialis) invenories and fuure sock prices a daily and weekly horizons. We find ha specialis invenories are negaively correlaed wih conemporaneous reurns a boh he aggregae marke and individual sock levels. This is consisen wih specialiss acing as dealers and emporarily accommodaing buying and selling pressure. For he specialis o be compensaed for aking 1 Reversals can occur over inraday horizons due o marke makers buying a he bid and selling a he ask, e.g., Amihud and Mendelson (1980), Ho and Soll (1981), and Roll (1984). Over longer horizons, liquidiy provider akes posiions and risk, e.g., Grossman and Miller (1988) and Spiegel and Subrahmanyam (1995), ha lead o reversals. These longer-erm invenory-induced reversals are empirically similar o, bu on a larger and marke-wide scale han reversals following block rades Kraus and Soll (1978). 2 For examples using NYSE specialis daa see Hasbrouck and Sofianos (1993), Madhavan and Smid (1993), and Madhavan and Sofianos (1998). For examples using London Sock Exchange marke maker daa see Hansch, Naik, and Viswanahan (1998), Reiss and Werner (1998), and Naik and Yadav (2003). For fuures markes daa see Mann and Manaser (1996). For opions marke daa see Garleanu, Pedersen, and Poeshman (2005). For foreign exchange daa see Lyons (2001) and Cao, Evans, and Lyons (2006). 2

on invenory, he mus unwind posiions a beer prices han hose prices a which he posiion was accumulaed. Using reurns calculaed wih quoes (o avoid bid-ask bounce), we find ha a value-weighed porfolio of socks where he specialis is long ouperforms a porfolio of socks where he specialis is shor by 10.25 basis poins he nex day (9.96 basis poins risk-adjused). 3 The second day following porfolio formaion, he reurn is 10.15 basis poins. Reurns decline seadily o 3.43 basis poins a day five. All hese reurns are saisically significan. A day en, he long-shor porfolio reurn is down o wo basis poins and is no longer saisically significan. porfolio is 41.12 basis poins over 10 days. The cumulaive reurn of he long-shor While hese reurns seem large, specialiss do no disclose heir invenory posiions. Predicabiliy based on invenories comes from non-public informaion. Because invenory daa have previously been unavailable o sudy longer-horizon reurns, researchers have consruced clever proxies for marke-maker invenories and limied risk bearing capaciy. Proxies such as order imbalances and liquidiy shocks capure he demand for liquidiy, which he suppliers of liquidiy presumably accommodae. Campbell, Grossman, and Wang (1993) examine how rading volume ineracs wih pas reurns in deermining fuure reurn reversals. Pasor and Sambaugh (2003) use a relaed measure o show ha liquidiy is a priced risk facor. Chordia, Roll, and Subrahmanyam (2002) sudy how marke-wide order imbalances buy orders less sell orders predic reversals of marke reurns. 4 Simple reurn reversals in individual socks Lehmann (1990) and ohers may also be relaed o invenory effecs. Our approach of direcly measuring a supply of available liquidiy (i.e., invenories) is complemenary o hese sudies. This paper broadens our undersanding of he complex and dynamic process of demanding and supplying liquidiy by sudying i from he liquidiy-supplier side. 3 The price reversals are also consisen wih invenory models where a marke maker uses his quoes o arac order flow on one side of he marke o reduce his invenory posiion. For example, if oher invesors have been buying from he specialis, prices have been rising and he specialis has a shor posiion; he specialis hen raises his quoes o he poin where invesors begin o sell and his selling leads o prices subsequenly falling. 4 Order imbalances are easily inerpreable if all rades occur wih a marke maker. The NYSE up-ick rule for shor-sales effecively requires all shor sellers o use limi orders. This can resul in misclassificaion of hese rades. Dieher, Lee, and Warner (2005) provide evidence showing how he upick rule causes order imbalances o be posiive on average. The auhors also show how Regulaion SHO s 2005 relaxaion of he up-ick rule largely eliminaes he posiive bias in NYSE order imbalances ha are signed using he Lee and Ready (1991) algorihm. Given ha Boehmer, Jones, and Zhang (2005) and Dieher, Lee, and Warner (2005) show ha shoring selling is beween 13 and 25% of NYSE volume and Boehmer, Jones, and Zhang (2005) show ha shor selling conains informaion abou fuure price movemens, his misclassificaion of shor selling is of significan poenial concern. We discuss his and relaed issues furher in Secions 5 and 6. 3

To examine he relaionship beween invenory reversals and simple reurn-reversals, we repea our daily sor procedure using reurns. Soring on oday s price change yields no evidence of reurn reversals he nex day. However, a 5-day horizons we find he usual significan reurn reversals of 59 basis poins. The reurn and invenory measures complimen each oher. A double sor of pas reurns and invenories shows ha he reurn reversals a 5 days are roughly wice as large in socks where invenories are large. The 5-day reurn of a porfolio long high-invenory/low-reurn socks and shor low-invenory/high-reurn socks is 105 basis poins. Order imbalances he difference beween buyer-iniiaed and seller-iniiaed rading volume as deermined by he ransacion prices and quoes are posiively correlaed wih conemporaneous reurns as in Chordia and Subrahmanyam (2004). Order imbalances are negaively correlaed wih invenories and changes in invenories. Order imbalances do no predic reurn reversals he nex day, bu do predic reversals of 32 basis poins over he nex 5 days. A double sor of pas order imbalances and invenories gives a 5-day reurn of 55 basis poins on a porfolio long high-invenory/low-order-imbalance socks and shor low-invenory/high-order-imbalance socks. To aemp o disenangle order imbalances, pas reurns, and invenories we run crosssecional (Fama-MacBeh) regressions. As wih single sors a one-day horizons, he invenory measure is individually significan and pas reurns are no significan. Unlike he single sors, order imbalances predic reversals over he nex day. All hree measures are individually significan a a one-week horizon. When all hree measures are combined a a one-week horizon, he invenory and order imbalance measures significance declines. When predicing reurns wo weeks ahead, all hree variables predic reversals individually wih reurns being saisically significan, order imbalances being marginally significan, and invenories no being saisically significan. When all hree variables are combined, reurns predic reversals wo weeks ahead while invenories and order imbalances do no. We find ha specialis invenory posiions are asymmeric. Specialiss ake larger long posiions when prices fall han shor posiions when prices rise. Alhough his is somehing no found in invenory models, i is consisen wih he empirical findings ha large buys have a larger price impac han large sells (Kraus and Soll (1972) and ohers). The average invenory posiion is posiive and he exreme long posiions are several imes as large as he exreme shor posiions. The asymmery in he long versus shor invenory posiions also appears in he reurn reversals. The 10-day reurn for he long porion of he porfolio where specialis invenories are highes is 18 basis poins above he marke while he 10-4

day reurn for he shor porion of he porfolio where specialis invenories are lowes is 27 basis poins above he marke. The highes- and lowes-invenory porfolios also exhibi asymmery prior o formaion day wih he highes porfolio falling 1.29% and he lowes porfolio rising 1.48%. Togeher hese findings sugges ha specialiss prefer o be long shares because eiher hey or oher raders face shor sale consrains. Examining invenories and reurns ogeher shows ha specialis invenories can forecas nex day price coninuaions as well as reversals. When reurns are low oday and he specialis is already shor shares, reurns are low on average omorrow. Similarly, when reurns are high oday and he specialis is long shares, reurns are high omorrow. This is he opposie of he reversals ha occur when reurns are low (high) and he specialis is long (shor). 5 A horizons greaer han one day, he specialis invenories do no forecas coninuaions, bu do forecas he size of he reversals. This suggess ha he specialis is informed abou price movemens a one-day horizons, bu no necessarily beyond, alhough we canno idenify wheher he specialiss are skilled raders independen of heir unique posiion a he NYSE. The remainder of he paper is organized as follows. Secion 2 provides a general descripion of our daa and sample. Secion 3 examines he correlaion beween specialis invenories and pas price changes. Secion 4 sudies he relaionship beween specialis invenories and fuure price changes. Secion 5 discusses how invenories relae o approaches ha infer liquidiy demands from signed order flow and pas price changes. Secion 6 invesigaes how invenories inerac wih pas reurns and order imbalances in predicing fuure price changes. Secion 7 concludes he paper. 2 Daa and Descripive Saisics Several daa ses are used o consruc our sample of daily specialis invenories and prices from 1994 hrough 2004. CRSP is used o idenify firms (permno), rading volume, marke capializaion, sock splis/disribuions, closing prices, and ransacion reurns. The Trades and Quoes (TAQ) daabase is used o idenify he closing quoes (MODE=3 in TAQ). Inernal NYSE daa from he specialis summary file (SPETS) provide he specialis closing 5 The reurn coninuaions are consisen wih he Llorene, Michaely, Saar, and Wang (2002) finding ha he Campbell, Grossman, and Wang (1993) reversal effec is aenuaed by informed rading. 5

invenories daa for each sock each day. 6 Throughou we simply refer o he specialis invenory a he end of he NYSE rading day as invenory. The TAQ maser file (MAST) provides he CUSIP number ha corresponds o he symbol in TAQ on each dae and is used o mach wih he NCUSIP in he CRSP daa. 7 We consider only common socks (SHRCLS=10 or 11 in CRSP). This provides a sample of more han four million sock-day observaions. To remove bid-ask bounce, close-o-close reurns are calculaed using bid-ask quoe midpoins. On days when he closing quoes are no in TAQ (0.57% of he sample) and on days wih disribuions (0.97% of he sample), we use he CRSP prices/reurns. The paper s resuls are no sensiive o wheher or no we discard hese observaions. We eliminae firms wih share price over $500 (0.17% of he sample). 8 We begin by presening aggregae marke invenory levels which are he sum over specialiss closing invenories in each sock. Figure 1 graphs aggregae marke invenory levels and he oal marke capializaion of all socks in our sample beween 1994 and 2004. The aggregae marke invenory averages abou $200 million a he end of each day, bu declines somewha saring in lae 2002. The volailiy of he invenory levels increases over he beginning of he sample period. As can be seen in he figure, aggregae invenory levels reach a billion dollars (long) and drop below $200 million (shor). [ Inser Figure 1 Here ] Panel A of Table 1 provides ime series saisics on he aggregae invenory. The invenory level flucuaes wih a daily sandard deviaion of $137 million and he sandard deviaion 6 The specialis has informaional and las mover advanages over oher marke paricipans. He can arguably be considered he marginal liquidiy provider in he marke. Such advanages make specialis invenories well-suied for sudying he price effecs of invenory. The specialis also has obligaions. The specialis is discouraged from demanding liquidiy and he specialis mus rade afer public limi orders a every price see Coughenour and Harris (2004). Planned reorganizaion of he NYSE o increase fully-elecronic rading may change he specialis s role. While he proposed plan coninues o provide he specialis wih a cenral role in rade rading algorihmically agains incoming order flow he specialis role could be diminished making i more difficul o idenify he marginal liquidiy provider. 7 The symbol in TAQ and icker in CRSP only mach 90% of ime in our CUSIP mached sample, suggesing ha using he TAQ maser file o obain CUSIPs is useful. 8 The high price crieria eliminaes Berkshire Hahaway which has quoes and closing prices differing by a facor of 10 on days in he early par of he sample period. The papers resuls are also no sensiive o he inclusion of low-priced socks. 6

of invenory changes is $107 million. Absolue changes in he invenory posiion average $77 million each day wih a sandard deviaion of $75 million. [ Inser Table 1 Here ] Panel B of Table 1 provides cross-secional saisics on invenories and invenory changes a he individual sock level on a daily basis. Median invenories are $41,180 per sock, which is only 1% of average daily rading volume. The mean per-sock invenory is $119 housand, which corresponds o 24% of average daily rading volume. The 1 s and 99 h perceniles show ha specialiss occasionally have closing posiions more han a million dollars long or shor, which represen 1.13 days (4.61) average rading volume for shor (long) posiions. The posiive mean invenory and large exreme long posiions indicae ha specialiss possibly face asymmeric coss of long versus shor posiions. The mos naural explanaion is ha when specialiss are shor hey need o be a buyer o reurn heir invenory o is desired level, requiring oher raders o be sellers. If some raders face shor-sale consrains, he specialis can anicipae ha unwinding large shor posiions is more difficul han unwinding large long posiions. A relaed shor-sale consrain explanaion is ha he NYSE up-ick rule effecively forces shor sellers o provide liquidiy via limi orders. These shor-sale limi orders increase compeiion a he ask Dieher, Lee, and Werner (2005) poenially making he liquidaion of large shor posiions more cosly. 3 Invenories and Pas Reurns Figure 2 plos pas reurns and ne invenory changes a he marke level. As suggesed by he changes in Figure 1, aggregae marke invenory can move up or down by hundreds of millions of dollars during a given day. The negaive slope of he scaer plo indicaes ha specialiss ac as dealers and emporarily accommodae buying and selling pressure. The one oulier (-$849 million change in invenory and -3.65% marke reurn) comes from a day when several specialiss accumulae several hundred million dollar shor posiions in socks ha wen up when he res of he marke was falling. Panel A of Table 2 shows ha changes in aggregae invenory has a -0.71 correlaion wih conemporaneous reurns. Because invenories ypically sar he day above or below heir average level, he correlaion of reurns over a day and invenory levels a he end of he day is somewha lower a -0.57. [ Inser Figure 2 Here ] 7

Panel B of Table 2 provides he cross-secional mean of individual socks ime series correlaion beween invenory changes and reurns. The mean correlaion beween dollar invenory level and reurns is -0.23. The fac ha correlaion is closer o zero wih individual sock daa han wih aggregae marke daa is consisen wih noise in individual sock reurns (and possibly invenories) ha averages ou when aggregaed. This also suggess ha refining our measure of invenory from simple dollar invenory may be beneficial. [ Inser Table 2 Here ] Oher possible measures of specialis invenory accoun for he disance from a arge invenory level as in Madhavan and Smid (1993) and variaions in he riskiness of invenory posiions. To allow for a ime-varying arge invenory level, a each dae we calculae he moving average of each sock s invenory level over he pas 3 monhs beginning 10 days ago, i.e., days -11 o -70, and refer o his as µ INV. We require 30 days of daa o calculae he arge invenory level based on he lagged moving average. Subracing his from he invenory level does no significanly affec he correlaion wih reurns. The same dollar amoun of invenory may pose differen levels of risk o specialiss due o differences in sock volailiy, average rading volume, compeiion for liquidiy provision, specialis paricipaion raes, and oher facors ha are difficul o measure direcly. Raher han posi a funcional form for he amoun of risk per dollar of invenory, we aemp o direcly infer i from changes in he specialis s pas invenory levels. Invenory levels ha hisorically vary up and down more sugges ha specialiss are willing o carry more invenory in ha sock because hey believe larger posiions in ha sock are less problemaic o liquidae. Therefore, we use he sandard deviaion of pas invenory (calculaed over he same ime period as µ INV ) o sandardize he curren invenory posiion. We refer o he sandardized invenory as z INV INV µinv. This sandardized invenory is backward looking version of σ INV he sandardized invenory measure used by Hansch, Naik, and Viswanahan (1998). The correlaion across invenory measures is high wih he correlaion wih reurns being slighly more negaive for he sandardized invenory. 4 Invenories and Fuure Reurns Figure 2 and Table 2 show ha, consisen wih invenory models, he specialis s invenory a hen end of he day is negaively correlaed wih price changes over ha day. We now es 8

he oher invenory model predicion ha invenory levels forecas fuure reurn reversals. The reversal predicion is commonly used o jusify and examine he relaionship beween liquidiy and prices. Table 3 sudies he impac of invenories on subsequen prices. Following he sandard soring and porfolio-formaion approach, we sor socks ino quiniles each day of our sample period based on he hree invenory measures. Panel A is dollar invenory levels and labeled INV ; Panel B uses deviaions of invenory from he specialis s arge invenory and labeled INV µ INV ; Panel C uses deviaions from arge invenory sandardized (divided) by invenory volailiy and labeled z INV. Porfolios are formed each day and reurns are calculaed using closing mid-quoe reurns wih marke capializaions as weighs. We use mid-quoe reurns, value weighing, and quiniles o minimize he impac of small illiquid socks. [ Inser Table 3 Here ] Given he correlaion beween he hree invenory measures, i is no surprising ha all sors pu larger values of each invenory measure in he ouer quiniles. As in Panel B of Table 1, he highes-invenory posiions are roughly wice as posiive, and he lowesinvenory posiions are negaive. Soring by dollar invenory (Panel A) pus he highes urnover, leas volaile, and larges marke capializaion socks in he ouer quiniles. This suggess ha invenory is more manageable in larger, more acive socks, so specialiss are willing o ake larger posiions in hose socks. While his is expeced, i leads quinile porfolios o have differen sock characerisics. Subracing he arge invenory reduces he marke capializaion differences across quinile somewha. Sandardizing by pas invenory volailiy helps o even ou he marke capializaion differences across quiniles more. Noe ha in Panel C, he larger, more acive, less volaile socks appear slighly more frequenly in he cener quiniles. Given ha we are rying o isolae invenory effecs from oher sock characerisics, we will focus on he sandardized invenory measure for he res of he paper, alhough he oher invenory measures yield similar resuls. All hree invenory sors provide qualiaively similar resul in erms of predicing reurns: he low-invenory porfolios have reurns he nex day close o or below zero while he highinvenory porfolios have reurns beween 8 and 10 basis poins he nex day. Therefore, a porfolio long on he highes-invenory socks and shor he lowes-invenory socks yields beween 7.70 and 10.25 basis poins he nex day. All have -saisics greaer han nine. The raw reurns demonsrae ha he invenory posiions of liquidiy providers forecas fuure prices. The fac ha soring on dollar invenory, where he large, acively raded firms are 9

in he ouer porfolios, shows reversals indicaes ha he invenory/reversal effec is presen in large socks as well. Conrolling for he marke, he Fama-French size facor, he Fama- French marke-o-book facor, and a momenum facor has lile effec on he reurn of he high invenory minus low invenory porfolio. To quanify he duraion of invenory effecs on prices, Figure 3 shows he reurns ne of he marke for he 12 days afer porfolio formaion. The highes-invenory porfolio increases by 5 basis poins (over he marke) on he firs day, four basis poins on he second day, and levels off a 18 cumulaive basis poins hereafer. The nex highes-invenory level porfolio (labeled P4 ) increases by 3 basis poins he firs day, increases by 1.5 basis poins on day wo, increases by approximaely 1 basis poin a day on days 3 hrough 8, and levels off a 10 cumulaive basis poins hereafer. The middle porfolio ( P3 ) drifs up somewha. The second-lowes invenory porfolio ( P2 ) declines by 2.6 basis poins he firs day, decreases by 1.3 basis poin a day on days 2 hrough 3, before i levels off a -8 cumulaive basis poins hereafer. The lowes-invenory porfolio declines by 5 basis poins each of he firs 2 days and decreases by approximaely 3 basis poins a day on days 3 hrough 6. Unlike he ohers, he lowes-invenory porfolio coninues o drif afer day 6, declining o a low of -27 cumulaive basis poins on day 11. The cumulaive 5-day reurn difference beween he long- and shor-invenory porfolios is 32.99 basis poins and he cumulaive 10-day reurn difference is 41.12 basis poins. [ Inser Figure 3 Here ] The asymmery beween he reurns on he highes and lowes porfolios suggess ha he specialis s willingness o ake larger long posiions han shor posiions ranslaes ino differences in fuure prices. The larges posiive posiions lead o less mean reversion han he mos negaive posiions. The difference in reurns beween he highes-invenory and 2 nd highes-invenory posiion is also smaller han he difference in reurns beween he lowesinvenory and 2 nd lowes-invenory posiion. When he specialis is shor, oher raders mus sell for he specialis o reduce his posiion (buy back shares). Traders who do no already own he sock face shor-sale consrains, poenially limiing he number of sellers. In addiion, he NYSE up-ick rule effecively requires shor sellers o provide liquidiy via limi orders. Shor-sale limi orders increase compeiion a he ask, poenially making he liquidaion of large shor posiions more cosly. Specialiss ofen give a differen explanaion for he long-shor asymmery: ha hey are more sensiive o prevening downward sock price movemens and, herefore, ake large long posiions when ohers invesors are ne sellers. 10

Given ha here is lile long-shor asymmery in he changes in invenory in Panel B of Table 1, his laer explanaion seems unlikely because he asymmery appears in invenory levels, bu no in changes in invenory. Long (shor) invenories resuling from negaive (posiive) reurns and causing posiive (negaive) reurns he nex day is consisen wih invenory and liquidiy provision models. To examine he pre- and pos-formaion price changes, Figure 4 exends he reurns in Figure 3 back six days in ime by adding he porfolio formaion day as well as he prior five days. Noe ha reversals in reurns swich he ordering of he high- and low-invenory porfolios. The highes-invenory porfolio is on op in Figure 3, while he highes-invenory porfolio is on he boom in Figure 4. The middle-quinile porfolio remains close o zero over he enire ime. The 2 nd highes porfolio based on day 0 invenory declines abou 7 basis poins a day he hree days prior o formaion, drops 30 basis poins on formaion day for a oal decrease of 50 basis poins, and reverses by 10 basis poins as described above. The graphs are consisen wih he specialiss acquiring heir posiions as hey accommodae he liquidiy demands of oher raders. The specialiss hen unwind heir posiions as prices reverse. [ Inser Figure 4 Here ] The highes- and lowes-invenory porfolios exhibi asymmery prior o formaion day wih he high-invenory porfolio falling 1.29% and he lowes porfolio rising 1.48%. The highes porfolio hen reverses 17 basis poins over 6 days while lowes porfolio reverses 28 basis poins and akes abou a week longer o level off. The pre- and pos-formaion reurns show ha price changes prior o porfolio formaion are many imes larger han he reversal. Jus as he asymmery beween he sizes and pos-formaion reurns of he longes- and shores-invenory posiions (Table 1) do no naurally arise in invenory models, neiher do he asymmeric price movemens in he pre-formaion periods. The asymmery in long and shor invenory size and pre- and pos-formaion reurns all poin o he specialis preferring long posiions o shor posiions. This preference leads o smaller downward price changes and smaller subsequen reurn reversals. While he reurn difference of he ouer-quinile porfolios are significan, in Table 4 we es ha hese are no due o risk by performing he sandard procedure of regressing he reurns of he long-shor porfolio on he marke and Fama-French facors. We use pos-formaion reurns for days +1, +2, +3, +4, +5, and +10. The long-shor porfolio loads posiively on he marke on mos daes and posiively on he momenum facor on he firs days, bu 11

he alphas in hese regressions do no differ noiceably from he simple differences in raw reurns. Each of he firs 5 days risk-adjused reurn (alpha) is significan. Day 10 s alpha remains posiive a 2.07 basis poins, bu he -saisic is only 1.83. [ Inser Table 4 Here ] To examine he pre- and pos-formaion invenories Figure 5 provides he sandardized invenory levels corresponding o he reurns in Figure 4. As wih he reurns, mos of he pre-formaion change in invenories occurs on he porfolio formaion day wih he larges long and shor porfolios having sandardized invenory levels of abou +/-1.8. Invenory levels on day +1 are quie similar o hose a day -1, showing ha invenories exhibi large mean reversion over relaively shor horizons. Comparing Figures 4 and 5 shows ha he price effecs and mean reversion in invenories move ogeher, alhough he relaionship is no sricly linear. While our resuls show ha he marginal addiional invenory aken on appears profiable, mos of he large long (shor) invenory posiions occur on days when prices fall (rise). Prices hen show small mean reversion relaive o he pre-formaion reurn, making hese large invenory posiions appear unprofiable overall for he specialis. This is consisen wih he Hasbrouck and Sofianos (1993) and Coughenour and Harris (2004) evidence ha he specialiss make mos of heir money a shor horizons and are no profiable a longer horizons. [ Inser Figure 5 Here ] Finally, we briefly examine day of he week effecs in he invenory induced reversals. Forming invenory porfolios on Wednesday and calculaing weekly reurns from Wednesday o Wednesday gives a reurn of 28.5 basis poins on he high invenory minus low invenory porfolio (resuls no shown in any able.) Forming invenory porfolios a he end of he rading week and calculaing reurns from hen unil he end of he subsequen rading week gives a reurn of 44.4 basis poins on he high-invenory minus low-invenory porfolio (resuls also no shown.) A he end of he rading week he specialiss bear he risk of holding heir invenory over he weekend. The sronger desire o be fla over he weekend resuls in invenory posiions more srongly predicing fuure reurns. 12

5 Invenories and Measures of Liquidiy Demand Linking liquidiy provision and sock price movemen is firmly grounded in models wih liquidiy supplier invenories and/or limied arbirageur risk-bearing capaciy. Empirical invesigaions are challenging because he liquidiy suppliers and arbirageurs are ypically no idenified in daa. Therefore, researchers consruc proxies for poenial liquidiy supply based on measures of he demand for liquidiy. Such measures include order imbalances and liquidiy shocks. If all rading akes place wih a marke maker, order imbalances accumulae ino invenory. Chordia, Roll, and Subrahmanyam (2002) exend he shor-run microsrucure idea of order imbalances roughly caegorizing he amoun of rading above he quoe midpoin price as buying and caegorizing he amoun of rading below he quoe midpoin as selling wih he ne of hese wo being he imbalance o he daily horizon. They show ha daily order imbalances (aggregaed across socks) are posiively correlaed wih he conemporaneous marke reurns. Imbalances are negaively correlaed wih he subsequen day s marke reurn, alhough he correlaion wih he subsequen day s marke reurn is only saisically significan for negaive imbalance days. These reurn reversals are generally consisen wih invenory models and our resuls. Compared o our direc measure of specialis invenories, using order imbalances has he advanage of poenially measuring liquidiy supplied by marke paricipans oher han he NYSE specialis. 9 Chordia and Subrahmanyam (2004) show ha order imbalances for individual socks are posiively auocorrelaed as are marke-wide imbalances. Posiive auocorrelaion in order imbalances can no easily be accommodaed by marke makers who have limied risk bearing capaciy and wan o mean rever heir invenories o a desired level. Chordia, Roll, and Subrahmanyam (2005) address his by poining ou ha order imbalances are posiively correlaed wih conemporaneous price changes and are also highly persisen from day o day. However, daily reurns for NYSE socks are no serially dependen. They reconcile posiive imbalance auocorrelaion, posiive order imbalance correlaion wih conemporaneous reurns, and no reurn auocorrelaion by showing ha afer imbalances occur sufficien counervailing rades arrive wihin he day o remove any daily serial dependence in reurns. 9 Dieher, Lee, and Warner (2005) show how he NYSE up-ick rule for shor selling causes order imbalances o be posiive on average using he Lee and Ready (1991) algorihm. Dieher, Lee, and Warner (2005) and Boehmer, Jones, and Zhang (2005) show ha shor selling is beween 13 and 25% of NYSE volume and ha shor selling predics fuure price changes. These findings sugges ha using aggregae signed (using only quoes and rades) order imbalance daa for individual socks is poenially problemaic. 13

This illusraes ha some complex and suble dynamics in he rading process are a work and suggess i may be difficul o measure invenories by accumulaing order imbalances. The need o infer from he daa when liquidiy is being demanded can be avoided by finding raders whose moives are known and whose posiions daa are available. Coval and Safford (2005) do his by using muual fund ouflows and inflows. Andrade, Seasholes, and Chang (2005) idenify a large group individual invesors whose rades cause reurn reversals a daily, weekly, and monhly frequencies. Campbell, Ramadorai, and Vuoleenaho (2005) use 13-F filings and TAQ daa o idenify insiuional rading. Barber, Odean, and Zhu (2005) use rading aciviy by rade size o idenify noise raders. These papers provide evidence abou he compensaion required o provide liquidiy. However, hese papers resuls res on heir idenificaion sraegy and i is difficul o know how heir resuls generalize. Garleanu, Pedersen, and Poeshman (2005) is perhaps he closes paper o his one in erms of he compleeness and precision of he daa. They use wo sources of daa on open ineres posiions in opions o measure he posiion of opions marke makers from 1996 o 2001. They show ha end-cusomer demand impacs opion prices and can explain a number of opion pricing puzzles. 5.1 Reversals When sudying reversals, a goal of researchers is o idenify socks, indexed by i, ha are rading a prices p i differen from heir fundamenal values v. i Once socks wih large deviaions from fundamenals (labeled ɛ i = p i v) i have been idenified, he socks should (evenually) rever back o heir fundamenal values. 10 If differen socks rever o heir fundamenal values a differen raes i may be useful o normalize deviaions: p i v i σ ɛ i (1) To implemen empirical sudies of reversals, researchers have approached Equaion (1) from wo differen direcions. The firs approach ceners on prices and reurns; he second on rading imbalances. 10 This example considers log sock prices, denoed by lower case leers, and consan fundamenal values. Similar logic applies o examples ha consider prices in levels and/or ime-varying fundamenal values. 14

5.2 Prices, Reurns, and Reversals Esimaing a sock s fundamenal value, v i, is fraugh wih difficulies. There is lile consensus abou he correc valuaion model o use. Thus, any ess are subjec o dual-hypohesis esing problems. Also, financial daa are released quarerly in he Unied Saes. This makes sudies a higher (daily or weekly) frequencies impracical. To ge around problems associaed wih esimaing v i, researchers ypically make wo assumpions (implicily or explicily). They assume ha prices were equal o fundamenal values k days ago. They also assume ha fundamenal values remain consan over shor horizons i.e., beween -k and oday (dae ). In oher words, v i = v k i. These wo assumpions imply p i k = vi. Sock prices oday are simply heir pas prices adjused by he inervening reurns: p i = p i k + 0 τ=k 1 ri τ. Researchers are hen able o subsiue he following ino he numeraor of Equaion (1): 0 τ=k 1 r i τ p i v i. (2) Equaion (2) serves as he basis for many reurn/reversal soring sudies. Socks are sored on he basis of pas reurns. High-reurn socks are likely o be rading above fundamenal values and low-reurn socks are likely o be rading below fundamenal values. Indeed, porfolios of high-reurn socks underperform porfolios of low-reurn socks over periods of wo days o several monhs. 11 Noe ha mos sudies focus on he numeraor in Equaion (1) and do no consider a normalizaion facor (such as he σ ɛ i shown in he denominaor.) No including a normalizaion essenially assumes all socks rever o heir fundamenal values a he same rae. 5.3 Trading Imbalances, Invenories, and Reversals A second approach used in empirical sudies of reversals focuses on proxies for he price deviaions shown in Equaion (1). Invenories are a logical choice. Microsrucure models 11 There is a separae line of research ha uses pas reurns o sor socks by expeced reurns. Socks wih low pas reurns are hough o have higher expeced reurns han socks wih high pas reurns. This phenomenon, someimes called he leverage effec, leads o observaionally similar reversals. Specifically, researchers find highreurn socks underperform low-reurn socks over shor horizons. Our double-sor resuls in Secion 6 using boh invenories and pas reurns provide direc evidence (which are no sensiive o excluding socks wih prices less han $5) ha liquidiy in he form of invenories is par of he explanaion for shor-horizon reversals. 15

provide a clear mapping beween price deviaions and marke maker invenory levels. When invesors are selling, prices prices fall, marke makers buy shares, which leaves marke makers wih posiive invenory levels. When invesors are buying, prices rise, marke makers sell shares, which leaves hem wih negaive (shor) invenory levels. Researchers can also sor socks by disance from arge invenory levels: INV i µ INV,i. As discussed in he inroducion, daa on invenories have no been readily available, so researchers have searched for proxies. Recen work uses rading imbalances in a manner similar o using reurns as in Equaion (2). Firs, invenories are assumed o have been a a arge level k days ago. In oher words, INV i k = µinv,i k. An invenory level oday is simply is pas level adjused by he inervening rades of he marke maker. Under a second assumpion ha he marke maker akes he oher side of all iniiaed buys and sells, we can wrie INV i = INV k i + 0 is assumed no o change over shor horizons: µ INV,i consruc he following: 0 τ=k 1 τ=k 1 Selli τ Buy τ. i Third, he arge invenory level = µ INV,i k. These allows researchers o Sell i τ Buy i τ INV i µ INV,i. (3) Marke makers may conrol heir invenories differenly across socks. Thus, he speed a which prices reverse may depend on invenory conrol policies. Invenory conrol policies depend on rading aciviy, sock volume, and marke maker paricipaion raes. This implies ha imbalance measures of invenory can be sandardized. Chordia and Subrahmanyam (2004) sandardize by dividing by rading volume. If we assume ha he expeced imbalance is zero, he specialis akes on all buy/sell imbalances, and he sandard deviaion of specialiss invenory is proporional o rading volume, hen he sandardized imbalance and invenory measures can we wrien as: 0 τ=k 1 Selli τ Buy i τ 0 τ=k 1 Buyi τ + Sell i τ INV i µ INV,i (4) σ INV i If all rades are iniiaed by invesors wih a marke maker, hen he order imbalance correcly measure changes in invenory. However, he NYSE s up-ick rule requires shor sellers o use limi orders, causing hese rades which are as much as 25% of rading volume (Dieher, Lee, and Warner (2005)) and correlaed wih fuure price changes (Boehmer, Jones, and Zhang (2005)) o be classified as buys. In addiion, if invenories were no a heir arge 16

level as of dae -k, hen invenory changes measure invenory levels wih some error. Given he rae a which invenories mean rever in our daa (Figure 5) and he up-ick shor-sale rule, order imbalances are likely o be a noisy and poenially biased measure of specialis invenory levels. However, order imbalances have he advanage ha hey may capure marke making aciviy and invenory by raders oher han he specialiss. 6 Fuure Reurns and Invenories, Pas Reurns, and Order Imbalances Lehmann (1990), Jegadeesh (1990), and ohers sudy reurn reversals by soring socks based on pas reurns. 12 While hese papers focus on he implicaions of reversals for marke efficiency, if liquidiy suppliers are no perfecly compeiive or have limied risk bearing capaciy, liquidiy supplier invenories may predic reurn reversals. In his secion we invesigae he abiliy of invenories o predic reversals over and above any predicabiliy conained in pas reurns. Our mehodology employs condiional double-sors in which we firs sor socks ino quiniles based on one variable. Wihin each quinile, we hen sor socks ino quiniles based on a second variable. The resul is a se of weny-five, evenly-populaed bins. 13 In Table 5, Panel A we firs sor based on pas reurns and nex sor by our sandardized invenory measure (z INV ). We hen measure reurns over he following day (+1 ). The double sor resuls confirm he exisence of invenory-based reversals as seen in he single sor resuls. Condiional on yeserday s reurn, high (long) invenories oday predic high reurns omorrow: average reurns are beween 6.02 and 13.49 basis poins per day. Low (shor) invenories oday predic low reurns omorrow as reurns are beween 1.62 and -3.86 basis poins per day. Noe, he average reurn of he CRSP value-weighed index is 4.71 basis poins per day over he same period. The difference beween high and low invenory bins condiional on reurn quinile ranges beween 7.85 and 16.33 basis poins. 12 For evidence on shor-run reversal sraegies and heir profiabiliy see Conrad, Hameed, and Niden (1994), Ball, Kolhari, and Wasley (1995), Cooper (1999), Avramov, Chordia, and Goyal (2005), and ohers. See Avramov, Chordia, and Goyal (2005) for evidence ha reurn reversals are due o illiquidiy, which provides indirec evidence o suppor he hypohesis ha reurn reversals are due o invenory effecs. 13 Invenories and reurns are negaively correlaed as can be seen in Table 2 and Figure 2. A condiional double soring mehodology ensures evenly-populaed bins while independen sors would leave cerain bins e.g., lowinvenory/low-reurn and high-invenory/high-reurn sparsely populaed. 17

[ Inser Table 5 Here ] In Table 5, Panel B we firs sor based on sandardized invenories and we hen sor by pas reurns. I is clear ha reurns do no predic reversals a a one-day horizon. Wihin each invenory quinile, high reurn socks ouperform low reurn firms by 1.90 o 5.35 basis poins per day (calculaed as he difference beween sock reurns in he high-reurn column and socks in he low-reurn column). Table 5 highlighs he reurns of he porfolio one expecs o exhibi he mos larges reversals. The difference beween he high-invenory/low-reurn porfolio and he lowinvenory/high-reurn porfolio is 15.43 basis poins per day in Panel A and 12.78 basis poins per day in Panel B. When we compare wih he 10.25 basis poins from he singlesoring (Table 3, Panel C), we conclude ha a he 1-day horizon, invenories predic reversals over and above pas reurns (Table 5, Panel A), bu reurns do no predic reversals over and above invenories (Table 5, Panel B). 6.1 Shor-Term Coninuaion (Momenum) Table 5 shows ha specialiss appear o have informaion abou which socks experience shor-erm reurn coninuaions (momenum) and which socks experience shor-erm reurn reversals. In boh Panel A and Panel B, specialiss wih high invenories in socks ha have high reurns oday see he socks go up an addiional 13.49 and 13.24 basis poins he following day. Specialiss wih low (shor) invenories in socks ha have low reurns oday see he socks reurn 0.75 and -3.47 basis poins he following day. Thus, a porfolio long high-invenory/high-reurn socks and shor low-invenory/low-reurn socks has reurns of 12.74 and 16.70 basis poins he following day. However, here is no evidence ha specialiss invenory level predic reurns a longer (weekly) horizons. 6.2 Invenories, Pas Reurns, and Reurns a 1, 5, and 10 Days Table 6 repors resuls of reurn/invenory sors a a 1-day, 1-week, and 2-week horizons. We define one week ahead (w+1 ) o be rading days +1 hrough +5 and wo weeks ahead (w+2 ) as rading days +6 hrough +10. To avoid difficulies in calculaing saisical significance in samples wih overlapping observaions Valkanov (2003) for he 1- and 2-week reurns we only calculae variables every 5 rading days and calculae reurns for 18

week 1 and week 2 separaely. For hese nonoverlapping periods, in Panel A we carry ou single-sors based on boh invenories and pas reurns. The 1-day resuls based on soring socks ino quiniles based on curren invenory levels come direcly from Table 3, Panel C. Invenories and curren reurns predic reversals of 32.99 and 58.78 basis poins, respecively, over a 5-day period. 14 For he second five day period, he average reversals are 8.10 and 25.15 basis poins based on invenories and reurn respecively. All reurns in Table 6 are from zero-cos/long-shor porfolios. Boh invenories and pas reurns predic economically and saisically significan reversals a 5-day horizons. The resuls for he second week are smaller and of less saisical significance, especially for invenories. [ Inser Table 6 Here ] To deermine wheher invenories and reurns are complemenary or overlapping when predicing reurns, Table 6 summarizes condiional double-sor resuls. Panel B firs sors by reurns and finds ha, condiional on pas reurns, porfolios of high-invenory socks ouperform porfolios of low-invenory socks by 7.85 o 16.33 basis poins a a 1-day horizon (as in Table 5, Panel A). High-invenory socks ouperform low-invenory socks by 4.34 o 26.98 basis poins over he firs five days. Noice ha socks wih more exreme prior reurns exhibi larger reversals based on heir invenories. The 1-day and 5-day resuls show ha invenory effecs exis in addiion o reversals based only on pas reurns. However, reurn reversals based upon invenories are weak in he second week. We also repor reurns of he zero-cos porfolio ha one expecs o exhibi he larges reversal. A a 5-day horizon, he high-invenory/low-reurn bin ouperforms he low-invenory/high-reurn bin by an average of 75.94 basis poins. This value is abou 50 percen larger han he 5-day reurn-only reversal. Table 6, Panel C summarizes he second se of condiional double-sor resuls. We firs sor by invenories and show ha porfolios of high-reurn socks do no ouperform porfolios of low-reurn socks a a 1-day horizon. In fac, shor-erm coninuaions (negaive reversals as in Table 5, Panel B) of -1.90 o -5.35 basis poins exis for all invenory quiniles. Lowreurn socks ouperform high-reurn socks by 33.42 o 76.65 basis poins over he following five days. The 5-day reversals are almos wice as large for he more exreme invenory quiniles, suggesing ha par of he uncondiional reurn reversals of 58.78 basis poins in Panel A is due o invenory effecs. A a 5-day horizon, he high-invenory/low-reurn 14 Our reurn-only reversals are smaller han hose found by Lehmann (1990) and Avramov, Chordia and Goyal (2005) due o he use of value-weighed reurns. 19

porfolio ouperforms he low-invenory/high-reurn porfolio by an average of 105.22 basis poins. This value is almos double he 5-day reversal from reurns alone and more han riple he 5-day reversal from invenories alone. Reversals based on reurns are significan in he second week, bu do no depend on invenory levels/quiniles. We began his secion by asking if invenories can predic reversals over and above pas reurns. A a 1-day horizon, reurns have no forecasing power, bu invenories predic reurn reversals. Invenories also conain informaion abou 1-day price coninuaions (momenum). A a 5-day horizon, condiioning on invenories (afer soring on reurns) increases he abiliy o predic reversals by 29% (75.94 basis poins versus 58.78 basis poins.) Condiioning on reurns (afer soring on invenories) increases he abiliy o predic reversal by 218% (105.22 basis poins versus 32.99 basis poins). Invenories have lile abiliy o predic reversals more han one week ahead, especially afer conrolling for pas reurns. Overall he resuls sugges ha invenories induce reversals, bu ha invenories do no fully explain reversals. I could be ha specialis invenories are an incomplee measure of marke-wide liquidiy supplier invenories or ha reversals are also due reversions in beliefs (overreacion). Finally, he fac ha invenories predic reversals beyond pas reurns is consisen wih Avramov, Chordia and Goyal s (2005) resuls ha reurn reversals are relaed o liquidiy. 6.3 Invenories, Order Imbalances, and Reurns a 1, 5, and 10 Days To aemp o capure marke-wide liquidiy supplier invenories (via liquidiy demand) we calculae order imbalances from ransacion daa (TAQ). We follow he sandard rade signing approach of Lee and Ready (1991) by using quoes from 5 seconds ago for daa up hrough 1998. Afer 1998, we use conemporaneous quoes o sign rades see Bessembinder (2003). We calculae all imbalance measures using only NYSE rades and quoes. As expeced he NYSE up-ick rule for shor sales resuls in order imbalances being posiive on average a resul consisen wih Chordia, Roll, and Subrahmanyam (2002), Chordia and Subrahmanyam (2004), and Chordia, Roll, and Subrahmanyam (2005). 15 Panel A of Table 7 presens he cross-secional average of each socks daily ime-series conemporaneous correlaion beween order imbalances, reurns, invenories, and changes in invenories (similar o Panel B of Table 2.) We presen wo measures of order imbalances: $OIB which is he daily buyer-iniiaed dollar volume minus he seller-iniiaed 15 Dieher, Lee, and Warner (2005) how Regulaion SHO s relaxaion in 2005 of he up-ick rule largely eliminaes he posiive bias in NYSE order imbalances ha are signed using he Lee and Ready (1991) algorihm. 20

dollar volume and OIB which is he ne dollar imbalance divided by he day s or week s dollar rading volume. As in Chordia, Roll, and Subrahmanyam (2002) and Chordia and Subrahmanyam (2004), imbalances are posiively correlaed wih conemporaneous reurns. The scaled/normalized order imbalance measure, OIB, is more highly correlaed wih conemporaneous reurns and invenories. For his reason and because we do no wan he order imbalance ranking o be heavily deermined by sock size, we use he normalized order imbalance hroughou he paper. In general, resuls using $OIB are qualiaively similar. Consisen wih he discussion in Secion 5.3, order imbalances are negaively correlaed wih he level of, and changes in, invenory. However, he correlaion beween OIB and INV is only -0.17, suggesing ha specialis invenories are no highly correlaed wih invenories of oher marke makers or ha he measure of order imbalance is noisy due o difficulies in signing order flow using only rades and quoes (discussed above). [ Inser Table 7 Here ] Panel B of Table 7 presens he cross-secional average of each sock s weekly ime-series conemporaneous correlaion beween order imbalances, reurns, invenories, and changes in invenories. For he weekly measures we calculae weekly reurns and order imbalances over he prior 5 rading days. Weekly invenory is simply he closing invenory on he final day of he 5-day week, alhough using only one invenory daa poin per week poenially reduces he power of he invenory measure. The correlaion of OIB wih he oher variables is similar a daily and weekly horizons. The weekly correlaion beween reurns and invenories is also similar o he daily correlaions in Panel B of Table 2. In Panel A of Table 8 we firs sor based on pas order imbalances and nex sor by sandardized invenories. We hen measure reurns over he following day (+1 ). The posiive correlaion beween OIB and reurns suggess ha he double sors on order imbalances and invenories may be similar o he double sors on invenories and reurns (Table 5). In Panel B we reverse he sor order. We firs sor by invenories and hen on order imbalances. As wih reurns, order imbalances offer lile evidence of predicing reversals one day ahead. 16 As wih reurns, he porfolios of high-oib/high-invenory socks and low-oib/low-invenory 16 Due o he posiive auocorrelaion in order imbalances, in ime series regressions Chordia and Subrahmanyam (2004) show ha oday s order imbalances for a sock is posiively correlaed wih he nex day s reurn for ha sock. If he nex day s order imbalance is included in he regression as well, hen oday s order imbalance is negaively relaed o he nex day s reurn. 21

socks exhibi coninuaions: 6.87 and 9.78 basis poins for order imbalances versus 12.74 and 16.70 basis poins for reurns. These coninuaion are smaller han hose from he double sors using reurns. Unlike reurns, double sors using order imbalances show no increase in one-day reversals beyond he 10.25 basis poins available from invenory single-sors. In fac, when soring on invenories firs, he reversal porfolio of low-oib/high-invenory socks and high-oib/low-invenory socks shows a reversal of only 4.10 basis poins. The lack of reversal evidence a a one-day horizon from order imbalances may be due o informed raders spliing heir rades across days so imbalances help forecas coninuaions, bu no reversals. [ Inser Table 8 Here ] Table 9 repors single and double sor resuls using order imbalances. Panel A conains single-sors based on boh invenories and order imbalances. The single-sor resuls using curren invenory levels maches Panel A of Table 6. The single sor resuls based on order imbalances do no predic reversals one day ahead (as in Table 8), bu do predic reversals of 32.03 basis poins over he nex week. 17 Order imbalances also predic reversals in he second week, bu he saisical significance is marginal. [ Inser Table 9 Here ] To analyze common and complemenary predicabiliy based on invenories and order imbalances, Table 9 summarizes condiional double-sor resuls. Panel B firs sors by order imbalances and finds ha, condiional on order imbalances, porfolios of high-invenory socks ouperform porfolios of low-invenory socks by 7.07 o 13.75 basis poins a a 1-day horizon (as in Table 8, Panel A). High-invenory socks ouperform low-invenory socks by 8.58 o 44.65 basis poins over he firs five days. A a 5-day horizon, he high-invenory/low-oib porfolio ouperforms he low-invenory/high-oib porfolio by 55.37 basis poins, which is abou wo hirds larger han he 5-day reversal based on soring by invenories or order imbalances alone. Invenories coninue o have lile forecasing power in he second week. Table 9, Panel C reverses he order of soring from ha in Panel B. As in Table 8, condiional on invenories, order imbalances predic coninuaions over he nex day. Over he nex week, 17 See Subrahmanyam (2005) for a more deailed examinaion of he impac of order imbalances a longer (monhly) horizons. Given ha order flow and reurns are public informaion, i is surprising ha hese can predic fuure reurns. However, Avramov, Chordia and Goyal (2005) show ha because he predicable reurns are concenraed in illiquid socks, rading coss are likely larger han he rading profis from he reurn predicabiliy. 22

condiional on invenories, order imbalance predic reversals of 8.34 o 27.03 basis poins. The forecasing power of boh imbalances and invenories is weak for reurns wo weeks ahead. The porfolio ha one expecs o exhibi he larges reversals, high-invenory/low- OIB socks minus he low-invenory/high-oib socks, reurns 49.77 basis poins over he nex week, which is roughly 50% larger han he reversal based on invenories or order imbalances alone. The double sors of invenories and order imbalances sugges ha boh measures predic reversals over he nex week. There appears o be some commonaliy in he predicive power of invenories and order imbalances in ha double sor reurns are less han he sum of single sor sor reurns. However, he reurns on he double-sor reversal porfolio are a leas 50% higher han he single-sor reversals, suggesing ha he invenories and order imbalances also complemen each oher. 18 6.4 Invenories, Order Imbalances, and Reurns The prior secion demonsraes ha invenories, pas reurns, and order imbalances all predic fuure reurns, alhough a differen horizons and wih differen levels of significance. To es all hree facors ogeher in a regression framework and accoun for conemporaneous correlaion in reurns across socks we run Fama and MacBeh (1973) cross secional regressions and use he ime series properies of he esimaed coefficiens o calculae sandard errors. To keep he Fama-MacBeh regressions consisen wih our value-weighed sors, we use weighed leas-squares where he weighs are proporional o marke capializaion he previous day. Table 10 summarizes he cross-secional Fama-MacBeh regressions for reurns one day ahead (Panel A), one week ahead (Panel B), and he second week ahead (Panel C). For each horizon we run four regressions, one wih each facor individually and one wih all hree facors ogeher. Wih few excepions, he resuls in Table 10 are consisen wih wha he non-parameric soring procedure found in Tables 5, 6, 8, and 9. [ Inser Table 10 Here ] Panel A of Table 10 shows ha invenories predic he nex days reurn and he -saisic 18 See Chordia and Subrahmanyam (2004) and Subrahmanyam (2005) for analysis of he commonaliy and complemenariy of reurns and order imbalances. 23

of 9.80 is similar o he single sor -saisic of 9.34 in Table 6. In Regressions A2 oday s reurns predic small, bu no saisically significan, coninuaions he nex day, as in Panel A of Table 6. However, in Regression A3 order imbalances predic a reurn reversal wih a -saisic of 2.83. This differs from he no saisically significan resul in he single sor on order imbalances in Panel A of Table 9. Regression A4 includes all hree variables in he regression. The coefficien on invenories coninues o be negaive wih boh he magniude of he coefficien and is -saisic increasing over he univariae regression. Reurns now predic coninuaions. The coefficien on OIB remains negaive, bu falls and becomes less saisically significan wih a -saisic of 2.39. These resuls sugges ha invenories and order imbalances predic reversals he following day, while, condiional on hese, reurns coninue in he same direcion. Panel B of Table 10 repeas he regressions in Panel A on a weekly basis, where, as in he single sors, he weeks are non overlapping. A a one-week horizon, all hree variables predic reversals individually wih -saisics beween 5 and 7. The -saisics are close o hose found in he weekly single sors in Tables 6 and 9. When he hree variables are all included in Regression B4, he coefficiens all remain he same sign, bu decrease in magniude and saisical significance. The coefficien and -saisic on reurns fall he leas and he coefficien and -saisic on order imbalances fall he mos. The weekly resuls sugges ha invenories, reurns, and order imbalances each predic reversals. Condiional on he oher variables, reurns have he mos significan predicive power and order imbalances have he leas power. Panel C repeas he weekly analysis in Panel B wih a wo-week horizon (reurns from rading days +6 hrough +10 ). As wih he single sors all hree variable predics reversals individually wih reurns being saisically significan, order imbalances being marginally significan, and invenories no being saisically significan. When all hree variables are combined in Regression C4 invenories and order imbalances become effecively zero and only reurns remain significan. 7 Conclusion Liquidiy and limis o arbirage argumens regarding asse prices rely on he idea ha cerain marke paricipans accommodae buying or selling pressure. These liquidiy suppliers/arbirageurs will only bear he risk of holding undiversified posiions if hey are compen- 24

saed by favorable subsequen price movemens. Thus, when invenories are large, liquidiy suppliers have aken on risk, and prices should subsequenly reverse. Using a unique 11-year sample of NYSE specialis invenories, his paper ess and confirms he underlying causal mechanism liquidiy supplier invenory linking liquidiy and sock reurn reversals. Consisen wih specialiss acing as dealers and emporarily accommodaing buying and selling pressure, specialis invenories are negaively correlaed wih conemporaneous reurns a boh a he aggregae marke level and individual sock level. We find ha specialiss are compensaed for he invenory risk by reurn reversals. While pas reurns also predic reversals, invenories conain orhogonal informaion and a porfolio long high-invenory/lowreurn socks and shor low-invenory/high-reurn socks earns more han porfolios using only invenories or only pas reurns. Order imbalances calculaed from signing rades (as buyer-iniiaed or seller-iniiaed using rades and quoes) also predic reversals and are complemenary o invenories and pas reurns. Finally, specialis invenories are able o predic coninuaions over a one-day horizon. Subsanial work remains o be done in order o undersand he dynamics of marke maker invenories and sock prices. While papers on liquidiy and asse prices have discovered imporan relaionships beween hem, e.g., Amihud and Mendelson (1986), Pasor and Sambaugh (2003), Acharya and Pedersen (2005), and ohers, a beer undersanding of heir dynamics may help guide fuure research. In paricular, exacly why price impac and oher ransacion coss differ across socks and differ in heir sensiiviy o marke liquidiy has ye o be fully addressed. By showing he marke maker invenories impac prices a he daily and weekly horizons his paper helps formalize a causal link beween liquidiy and sock prices. A possible sep in beer undersanding liquidiy varies across socks is o sudy marke maker risk managemen. Invenory risk managemen may occur on a sock-by-sock basis, across socks raded an individual marke maker, or across socks raded by a firm employing muliple marke makers. The organizaional srucure of specialiss on he NYSE can help o disenangle where risk managemen akes place because an individual specialis has exclusive responsibiliy for a group of socks referred o as a panel. Given he srucure of specialis firms and our resuls linking invenories o pas and fuure reurns, he manner in which specialiss manages risk may have cross-sock pricing implicaions, i.e., Do specialiss hedge posiions in one sock wih oher socks in heir panel? Do firms hedge individual sock posiions wih oher socks?, ec. The lengh and breadh of our daa can help esimae invenory managemen via mean reversion raes boh cross secionally and over ime. 25

A second line of research is o deepen our undersanding of he commonaliy of liquidiy (Chordia, Roll, and Subrahmanyam (2000), Coughenour and Saad (2004), and ohers) and is relaionship o commonaliy in sock reurns (Hasbrouck and Seppi (2001)). In paricular, if invenories drive he liquidiy commonaliy hen he pricing effecs should be sronger when invenories are moving ogeher a he panel level and firm level. For example, a large sell order in a given sock ypically increases he specialis s holdings in ha sock and limis his abiliy/desire o buy more of he sock. The large sell order may also limi his abiliy o purchase oher socks. Thus, he price effecs of a emporary buy-sell imbalance migh be ransmied o anoher sock, even when he wo socks are no subjec o he same (original) buy-sell imbalance. Addiionally, socks which are more likely o have buy-sell imbalances a exacly he same ime as oher socks suffer large buy-sell imbalances could lead o he liquidiy risk facor sudied by Pasor and Sambaugh (2003). A hird line of research is o invesigae layers of liquidiy provision in he sock marke. Given he specialiss unique posiion in he rading process, hey represen he firs level of liquidiy provision. However, if heir risk bearing capaciy is limied, he specialiss holdings are an imperfec measure of available marke-wide liquidiy. Oher invesors such as hedge funds and invesmen banks are willing o provide liquidiy and ake on undiversified posiions, provided hey are sufficienly compensaed via fuure price movemens. The specialis invenories predic reurns over a one- o wo-week horizon even hough he specialiss end upwind heir posiions quickly (Figure 5). To reduce heir invenories he specialiss may be rading wih secondary and eriary layers of liquidiy providers. An empirical sraegy o idenify liquidiy provision by oher invesors/arbiraguers would provide insigh ino how long markes ake o fully share risk afer liquidiy shocks. Undersanding he implicaions of a marke no being able o share risk immediaely or fricionlessly will deepen our knowledge of how long and o wha magniude asse prices migh deviae from fundamenal values. 26

References [1] Acharya, Viral, and Lasse Pedersen (2005), Asse pricing wih liquidiy risk, Journal of Financial Economics 77, 375410. [2] Amihud, Yakov, and Haim Mendelson, 1980, Dealership marke: Marke making wih invenory, Journal of Financial Economics 8, 31-54. [3] Amihud, Yakov, and Haim Mendelson, 1986, Asse pricing and he bid-ask spread, Journal of Financial Economics 17, 223249. [4] Andrade, Sandro, Mark Seasholes, and Charles Chang, 2005, Predicable reversals, cross-sock effecs, and he limis of arbirage, working paper, Universiy of California, Berkeley. [5] Avramov, Doron, Tarun Chordia, and Ami Goyal, 2005, Liquidiy and auocorrelaion of individual sock reurns, Journal of Finance, forhcoming. [6] Ball, Ray, S. P. Kohari, and Jay Shanken, 1995, Problems in measuring porfolio performance: An applicaion o conrarian invesmen sraegies, Journal of Financial Economics 38, 79-107. [7] Barber, Brad, Terrance Odean, and Ning Zhu, 2005, Do noise raders move markes? Working paper, Universiy of California. [8] Bessembinder, Hendrik, 2003, Issues in assessing rade execuion coss, Journal of Financial Markes, Journal of Financial Markes 6, 233-257. [9] Boehmer, Ekkehar, Charles Jones, and Xiaoyan Zhang, 2005, Which shors are informed? working paper, Columbia Universiy. [10] Campbell, John, Sanford Grossman, and Jiang Wang, 1993, Trading volume and serial correlaion in socks reurns, Quarerly Journal of Economics 108, 905-939. [11] Campbell, John, Tarun Ramadorai, and Tuomo Vuoleenaho, 2005, Caugh on Tape: Insiuional order flow and sock reurns, working paper, Columbia Universiy. [12] Cao, Henry, Marin Evans, and Richard Lyons, 2006, Invenory Informaion, Journal of Business 79, 325-364. [13] Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2000, Commonaliy in Liquidiy, Journal of Financial Economics, 56, 3-28. 27

[14] Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2002, Order imbalance, liquidiy and marke reurns, Journal of Financial Economics 65, 111-130. [15] Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2005, Evidence on he speed of convergence o marke efficiency, Journal of Financial Economics, forhcoming. [16] Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2005, Liquidiy and marke efficiency, Working paper, Emory Universiy. [17] Chordia, Tarun, and Avanidhar Subrahmanyam, 2004, Order imbalance and individual sock reurns, Journal of Financial Economics 72, 485-518. [18] Conrad, Jennifer, Allaudeen Hameed and Cahy Niden, 1994, Volume and auocovariances in shor-horizon individual securiy reurns, Journal of Finance 49, 1305-1329. [19] Cooper, Michael, 1999, Filer rules based on price and volume in individual securiy overreacion, Review of Financial Sudies 12, 901-935. [20] Coughenour, Jay, and Lawrence Harris, 2004, Specialis profis and he minimum price incremen, Working paper, Universiy of Souhern California. [21] Coughenour, Jay, and Mohsen Saad, 2004, Common marke makers and commonaliy in liquidiy, Journal of Financial Economics 73, 37-69. [22] Coval, Joshua, and Erik Safford, 2005, Asse fire sales (and purchases) in equiy markes, Working paper, Harvard Universiy. [23] Dieher, Karl, Kuan Lee, and Ingrid Werner, 2005, I s SHO ime! Shor-sale price-es and marke qualiy, working paper, Ohio Sae Universiy. [24] Fama, Eugene, and James MacBeh, 1973, Risk, reurn, and equilibrium, Journal of Poliical Economy 33, 3-56. [25] Garleanu, Nicolae, Lasse Pedersen, and Allen Poeshman, 2005, Demand-based opion pricing, Working paper, New York Universiy. [26] Grossman, Sanford, and Meron Miller, 1988, Liquidiy and marke srucure, Journal of Finance 43, 617-633. [27] Hansch, Oliver, Narayan Naik, and S. Viswanahan, 1998, Do invenories maer in dealership markes? Evidence from he London Sock Exchange, Journal of Finance 53, 1623-1655. 28

[28] Hasbrouck, Joel, and Duane Seppi, 2001, Common facors in prices, order flows, and liquidiy, Journal of Financial Economics 59, 383-411. [29] Hasbrouck, Joel, and George Sofianos, 1993, The rades of marke-makers: An analysis of NYSE specialiss, Journal of Finance 48, 1565-1594. [30] Ho, Thomas, and Hans Soll, 1981, Opimal dealer pricing under ransacions and reurn uncerainy, Journal of Financial Economics 9, 47-73. [31] Lee, Charles, and Mark Ready, 1991, Inferring rade direcion from inraday daa, Journal of Finance 46, 733-747. [32] Lehmann, Bruce, 1990, Fads, maringales, and marke efficiency, Quarerly Journal of Economics 105, 1-28. [33] Llorene, Guillermo, Roni Michaely, Gideon Saar, and Jiang Wang, 2002, Dynamic volume-reurn relaion of individual socks, Review of Financial Sudies 15, 1005-1047. [34] Lyons, Richard, 2001, The Microsrucure Approach o Exchange Raes, MIT Press: Cambridge, MA. [35] Jagadeesh, Narasimhan, 1990, Evidence of predicable behavior of securiy reurns, Journal of Finance 45, 881-898. [36] Kraus, Alan, and Hans Soll, 1972, Price impacs of block rading on he New York Sock Exchange, Journal of Finance 27, 569-588. [37] Madhavan, Ananh, and Seymour Smid, 1993, An analysis of daily changes in specialis invenories and quoaions, Journal of Finance 48, 1595-1628. [38] Madhavan, Ananh, and George Sofianos, 1998, An empirical analysis of NYSE specialis rading, Journal of Financial Economics 48, 189-210. [39] Mann, Seven, and Seven Manaser, 1996, Life in he pis: Compeiive marke making and invenory conrol, Review of Financial Sudies 9, 953-975. [40] Naik, Narayan, and Pradeep Yadav, 2003, Do dealer firms manage invenory on a sockby-sock or a porfolio basis? Journal of Financial Economics 69, 325-353. [41] Pasor, Lubos, and Rober Sambaugh, 2003, Liquidiy risk and expeced sock reurns, Journal of Poliical Economy 111, 642-685. 29

[42] Reiss, Peer, and Ingrid Werner, 1998, Does risk sharing moivae iner-dealer rading? Journal of Finance 53, 1657-1704. [43] Roll, Richard, 1984, A simple implici measure of he effecive bid-ask spread in an efficien marke, Journal of Finance 39, 1127-1139. [44] Spiegel, Mahew and Avanidhar Subrahmanyam, 1995, On inraday risk premia, Journal of Finance 50, 319-339. [45] Subrahmanyam, Avanidhar, 2005, Lagged order flows and reurns: A longer-erm perspecive, Working paper, UCLA. [46] Valkanov, Rossen, 2003, Long-Horizon regressions: Theoreical resuls and applicaions, Journal of Financial Economics 68, 201-232. 30

Table 1 Descripive Saisics of Invenory Posiions This able gives descripive saisics of NYSE specialiss invenory posiions. Panel A gives ime-series saisics for he aggregae marke invenory as shown in Figure 1. Aggregae marke invenory levels are calculaed as he sum, across all socks in our sample, of each specialiss invenory a he close of each rading day. Panel B gives cross-secional saisics a he individual sock level. Invenories are measured a he end of each day. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. Panel A: Time-Series Measures of Aggregae Marke Invenory mk INV mk INV mk INV ($ million) ($ million) ($ million) Average 196.16-0.03 76.59 Sdev 136.78 106.96 74.65 # Days 2,731 2,730 2,730 Panel B: Daily Cross-Secional Measures of Invenory and Changes of Invenory INV INV INV MA Vol INV INV ($ 000) ($ 000) ($ 000) ($ 000) INV MA Vol Average 119.08 305.66 0.24 0.07 239.91-0.00 1 s -ile -1,478.58 0.37-1.13-1,647.70 0.11-0.51 5 h -ile -459.26 4.60-0.20-570.81 1.91-0.17 10 h -ile -227.64 11.15-0.08-307.46 5.25-0.09 25 h -ile -39.00 37.72-0.01-82.37 21.88-0.03 50 h -ile 41.18 113.30 0.01 0.18 80.21 0.00 75 h -ile 185.54 294.76 0.09 80.70 237.75 0.03 90 h -ile 490.10 672.10 0.40 302.22 564.64 0.09 95 h -ile 858.40 1,112.66 0.91 560.74 921.32 0.16 99 h -ile 2,429.61 2,929.24 4.61 1,548.25 2,256.27 0.46 31

Table 2 Correlaion of Variables This able shows cross-secional averages of ime-series correlaions. We consider reurns based on close-o-close prices r (close) and reurns based on closing midquoe prices r (mid q). In Panel A, aggregae marke invenory levels labeled INV mk are calculaed as he sum of each specialiss invenory, across all socks in our sample, a he close of each rading day. INV mk is he daily change in he dollar invenory level. In Panel B, we measure he correlaion of variables for each sock and repor an average measure across socks. Addiional variables are INV - µ INV, which is he dollar invenory level minus a moving average invenory level; z INV is a sandardized invenory level equal o he dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. The number in parenheses shows he fracion of firms wih a correlaion of opposie sign o ha of he average. Panel A: Aggregae Marke r mk ( mid q) r mk (close) r mk (close) 1.00 r mk ( mid q) 1.00 1.00 mk INV mk INV mk INV -0.57-0.57 1.00 mk INV -0.71-0.71 0.39 1.00 Panel B: Individual Socks r (close) 1.00 r (close) ( mid q) r INV INV µ INV INV z INV r ( mid q) 0.96 (0.00) 1.00 INV -0.23 (0.02) -0.24 (0.02) 1.00 INV µ INV -0.23 (0.03) -0.23 (0.02) 0.86 (0.00) 1.00 INV z -0.24 (0.03) -0.25 (0.03) 0.76 (0.00) 0.86 (0.00) 1.00 INV -0.31 (0.03) -0.31 (0.03) 0.38 (0.00) 0.39 (0.00) 0.37 (0.00) 1.00 32

Table 3 Sor Resuls This able shows resuls of a single soring procedure based on NYSE specialis invenory posiions in individual socks. A he end of each rading day for each sock we calculae hree measures of invenory levels: Panel A) The dollar invenory level labeled INV ; Panel B) The dollar invenory level minus a moving average invenory level labeled INV - µ INV ; and Panel C) The sandardized invenory level equal o he dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels labeled z INV. The moving average and sandard deviaion use invenory levels over he pas 60 rading days and are described in he ex. We place socks ino one of five quiniles based on he invenory measures saring wih lowes (shor) posiions o highes (long) posiions. We hen measure he value-weighed reurn of socks in each quinile over he following day. Alphas are he consan from regressing he high-invenory minus low-invenory porfolio on he marke s reurn, Fama-French size facor, Fama-French marke-o-book facor, and he momenum facor. Reurns are calculaed using closing mid-quoes. T-saisics are based on Newey-Wes sandard errors ha are robus o heeroscedasiciy and auocorrelaion. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. Panel A: Sor by INV Sor INV Turnover Reurn MkCap r +1 H L (bp) Alpha Quinile ($ 000) INV - µ INV z INV (bp) Sdev (%) ($ bn) (bp) (T-sa) (T-sa) Lo (-) 1-441.14-473.28-1.31 45.22 2.18 7.66 0.15 8.47 8.66 2-212.84-66.86-0.52 39.87 2.81 2.26 2.54 (9.67) (10.09) 3 42.97-13.88 0.04 38.22 2.78 1.94 4.47 4 148.81 61.64 0.55 41.81 2.44 3.00 7.55 Hi (+) 5 863.61 490.13 1.22 49.37 2.25 9.78 8.62 Panel B: Sor by INV - µ INV Sor INV Turnover Reurn MkCap r +1 H L (bp) Alpha Quinile ($ 000) INV - µ INV z INV (bp) Sdev (%) ($ bn) (bp) (T-sa) (T-sa) Lo (-) 1-301.01-603.51-1.42 49.02 2.25 9.16 0.92 7.70 7.18 2-0.94-92.15-0.73 41.48 2.52 2.57 2.94 (9.23) (8.76) 3 43.57-6.07-0.09 36.59 2.99 1.58 5.54 4 134.49 81.27 0.71 39.58 2.50 2.52 7.23 Hi (+) 5 717.16 617.74 1.51 47.82 2.20 8.81 8.62 Panel C: Sor by z INV Sor INV Turnover Reurn MkCap r +1 H L (bp) Alpha Quinile ($ 000) INV - µ INV z INV (bp) Sdev (%) ($ bn) (bp) (T-sa) (T-sa) Lo (-) 1-286.06-482.97-1.74 39.75 2.50 4.17-0.60 10.25 9.96 2-28.23-182.56-0.54 44.97 2.58 4.89 2.06 (9.34) (9.18) 3-20.29-20.29-0.05 45.73 2.50 5.84 4.99 4 230.20 171.50 0.47 44.00 2.43 5.46 7.51 Hi (+) 5 512.02 512.02 1.84 40.04 2.45 4.28 9.65 33

Table 4 Risk-Adjused Reurns Reurns of zero-cos sor porfolios called r H-L in basis poins are regressed on he marke s reurn and oher facors reurns. The zero cos porfolio is formed by soring on NYSE specialiss curren invenory posiions. We use a sandardized measure (z INV ) described in he ex. We measure closing mid-quoe o mid-quoe reurns of he zerocos porfolio on he k h day following he soring day. The size facor (SMB), he marke-o-book facor (HML), and he momenum facor (UMD) are from Ken French s websie. Reurns are calculaed using closing mid-quoes. T-saisics are based on Newey-Wes sandard errors ha are robus o heeroscedasiciy and auocorrelaion. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. m f SMB SMB HML HML UMD UMD ( r + k r + k ) + β r + k + β r + k + β r + k k H L MKT r + k = α + β + ε + Regression Uses ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) H L r H L +1 r H L +2 r H L +3 r H L +4 r H L +5 r +10 Consan ( α ) in bp 9.960 10.146 5.009 5.174 3.430 2.072 ( T-sa ) (9.18) (9.44) (4.64) (4.63) (3.03) (1.83) Marke ( β MKT ) 0.031 0.059 0.032 0.050 0.027 0.031 ( T-sa ) (1.41) (3.27) (1.58) (2.11) (1.25) (1.93) SMB ( β SMB ) 0.009 0.009 0.001 0.045-0.012 0.013 ( T-sa ) (0.28) (0.34) (0.03) (1.69) (-0.44) (0.39) HML ( β HML ) -0.087-0.038-0.038-0.007-0.063-0.044 ( T-sa ) (-1.95) (-0.88) (-0.82) (-0.15) (-1.34) (-1.19) UMD ( β UMD ) 0.081 0.079 0.018 0.045 0.014 0.036 ( T-sa ) (3.22) (3.49) (0.64) (1.99) (0.46) (1.29) N 2,730 2,729 2,728 2,727 2,726 2,721 34

Table 5 Double Sor : Curren Invenories and Curren Reurns as Predicors of Reurns on Day +1 This able shows he resuls of a double soring procedure based on NYSE specialis invenory posiions and reurns. z INV is he sandardized invenory level equal o he end of day dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. In Panel A, we firs sor socks ino quiniles based on reurns. Wihin each quinile, we hen sor by specialis sandardized invenory posiions. In Panel B, we firs sor socks ino quiniles based on specialis sandardized invenory posiions. Wihin each quinile, we hen sor by reurns. Boh panels show he value-weighed reurn one day following he sor dae. Reurns are calculaed using closing mid-quoes. T-saisics are based on Newey-Wes sandard errors ha are robus o heeroscedasiciy and auocorrelaion. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. Panel A: 1 s Sor Sock Reurns; 2 nd Sor Specialis Invenory Shown Reurns on Day +1 (bp) Lo (-) z INV Hi (+) z INV Reversal Coninuaion 1 2 3 4 5 Porfolio Porfolio Hi (+) r -2.84 4.65 5.33 7.52 13.49 Long: Lo r & Hi z INV 4 1.62 2.73 4.89 7.53 9.46 Shor: Hi r & Lo z INV 3-2.28 1.62 6.03 7.43 8.51 2-3.86-0.39 4.78 4.85 6.02 Lo (-) r 0.75 2.01 5.30 9.34 12.59 Long: Hi r & Hi z INV Shor: Lo r & Lo z INV 15.43 12.74 (6.32) (5.04) Panel B: 1 s Sor Specialis Invenory; 2 nd Sor Sock Reurns Shown Reurns on Day +1 (bp) Hi (+) r Lo (-) r Reversal Coninuaion 5 4 3 2 1 Porfolio Porfolio Lo (-) z INV -1.56 0.37 1.56-2.95-3.47 Long: Hi z INV & Lo r 2 5.22 4.06 2.53-1.23-0.12 Shor: Lo z INV & Hi r 3 6.91 5.64 4.51 2.83 4.46 4 9.45 8.73 6.35 5.98 5.73 Hi (+) z INV 13.24 8.63 6.97 9.71 11.21 Long: Hi z INV & Hi r Shor: Lo z INV & Lo r 12.78 16.70 (4.35) (7.33) 35

Table 6 Soring Resuls Based on Invenories and Reurns a 1-Day, 1-Week, and 2-Week Horizons This able shows he resuls of soring procedures a 1-day, 5-day, and 10-day horizons. Panel A shows he resuls of wo singlesors based on sandardized invenory levels and reurns. z INV is he sandardized invenory level equal o he end of day or week dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. Panel B shows double-sor resuls. We firs sor socks ino quiniles based on reurns. Wihin each quinile, we hen sor by sandardized invenory levels. Panel C also shows double-sor resuls where we firs sor socks ino quiniles based on specialis sandardized invenory posiions. Wihin each quinile, we hen sor by reurns. One week head reurns (r w+1 ) are reurns for rading days +1 hrough +5 and 2-week ahead reurns (r w+2 ) are for rading days +6 hrough +10. Reurns are calculaed using closing midquoes. T-saisics are based on Newey-Wes sandard errors ha are robus o heeroscedasiciy and auocorrelaion. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. Sor Porfolio + 1 Panel A: Single Sors r r w+ 1 r w+ 2 Hi z INV Lo z INV 10.25 32.99 8.10 (T-sa) (9.34) (6.68) (1.49) Lo r Hi r 0.42 58.78 25.15 (T-sa) (0.23) (6.32) (2.33) Panel B: Double Sor on Reurns hen Invenories 1 s Sor Variable 2 nd Sor Porfolio + 1 r r w+ 1 r w+ 2 Hi r Hi z INV Lo z INV 16.33 12.33-1.94 4 Hi z INV Lo z INV 7.85 4.34 10.02 3 Hi z INV Lo z INV 10.80 11.62 4.04 2 Hi z INV Lo z INV 9.88 20.09-6.02 Lo r Hi z INV Lo z INV 11.84 26.98-5.50 Hi z INV / Lo r Lo z INV / Hi r Reversal 15.43 75.94 18.25 (T-sa) (6.32) (6.99) (1.36) Panel C: Double Sor on Invenories hen Reurns 1 s Sor Variable 2 nd Sor Porfolio + 1 r r w+ 1 r w+ 2 Lo z INV Lo r Hi r -1.90 67.20 23.00 2 Lo r Hi r -5.35 33.42 25.03 3 Lo r Hi r -2.45 38.25 23.45 4 Lo r Hi r -3.72 54.18 26.73 Hi z INV Lo r Hi r -2.04 76.65 20.05 Hi z INV / Lo r Lo z INV / Hi r Reversal 12.78 105.22 14.13 (T-sa) (4.35) (7.73) (0.88) 36

Table 7 Correlaion of Order Imbalances This able shows cross-secional averages of each sock s daa series ime-series correlaions. r (close) is he close-o-close reurn. r (mid q) is based on closing mid-quoe prices. INV is he end of day or week dollar invenory level. INV - µ INV is he end of day or week dollar invenory level minus a moving average invenory level. z INV is he sandardized invenory level equal o he end of day or week dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. INV is he daily or weekly change in he dollar invenory level. $OIB is he daily or weekly ne dollar order imbalance (buys minus sells); OIB is $OIB divided by he daily or weekly dollar rading volume. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. The number in parenheses shows he fracion of firms wih a correlaion of opposie sign o ha of he average. Panel A: Individual Socks Daily r (close) ( mid q) r INV INV µ INV OIB OIB INV z INV $ $ OIB 0.20 (0.07) 0.20 (0.08) -0.15 (0.06) -0.14 (0.05) -0.14 (0.05) -0.17 (0.05) 1.00 OIB 0.29 (0.00) 0.29 (0.00) -0.17 (0.04) -0.16 (0.02) -0.17 (0.02) -0.19 (0.01) 0.57 (0.00) 1.00 Panel B: Individual Socks Weekly r w (close) 1.00 r w (close) ( mid q) r w INV w INV µ w INV OIB OIB INV z w INV $ w w w r w ( mid q) 0.99 (0.00) 1.00 INV w -0.25 (0.04) -0.25 (0.04) 1.00 INV µ w INV -0.24 (0.05) -0.24 (0.05) 0.86 (0.00) 1.00 INV z w -0.25 (0.06) -0.25 (0.06) 0.76 (0.00) 0.86 (0.00) 1.00 INV w -0.24 (0.06) -0.24 (0.05) 0.54 (0.00) 0.56 (0.00) 0.52 (0.00) 1.00 $ OIB w 0.21 (0.10) 0.21 (0.10) -0.15 (0.12) -0.13 (0.12) -0.12 (0.11) -0.11 (0.13) 1.00 OIB w 0.29 (0.01) 0.29 (0.01) -0.17 (0.06) -0.16 (0.05) -0.17 (0.05) -0.14 (0.06) 0.66 (0.00) 1.00 37

Table 8 Double Sor : Curren Invenories and Ne Order Imbalances as Predicors of Reurns on Day +1 This able shows he resuls of a double soring procedure based on NYSE specialis invenory posiions and ne order imbalances. z INV is he sandardized invenory level equal o he end of day dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. OIB he daily ne dollar order imbalance (buys minus sells) divided by he daily dollar rading volume. In Panel A, we firs sor socks ino quiniles based on ne order imbalance. Wihin each quinile, we hen sor by specialis sandardized invenory posiions. In Panel B, we firs sor socks ino quiniles based on specialis sandardized invenory posiions. Wihin each quinile, we hen sor by ne order imbalances. Boh panels show he value-weighed reurn one-day following he sor dae. Reurns are calculaed using closing mid-quoes. T-saisics are based on Newey-Wes sandard errors ha are robus o heeroscedasiciy and auocorrelaion. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. Panel A: 1 s Sor Order Imbalances; 2 nd Sor Specialis Invenory; Shown Reurns on Day +1 (bp) Lo (-) z INV Hi (+) z INV Reversal Coninuaion 1 2 3 4 5 Porfolio Porfolio Hi (+) OIB -0.20 4.43 5.32 7.26 6.87 Long: Lo OIB & Hi z INV 4-1.31 3.83 3.90 6.71 9.52 Shor: Hi OIB & Lo z INV 3 0.96 0.63 4.14 6.73 9.88 2-2.24 3.96 6.26 10.53 11.50 Lo (-) OIB 0.00 3.30 4.75 7.55 9.22 Long: Hi OIB & Hi z INV Shor: Lo OIB & Lo z INV 9.42 6.87 (4.95) (3.09) Panel B: 1 s Sor Specialis Invenory; 2 nd Sor Ne Order Imbalances; Shown Reurns on Day +1 (bp) Hi (+) OIB Lo (-) OIB Reversal Coninuaion 5 4 3 2 1 Porfolio Porfolio Lo (-) z INV 3.13-1.10 1.15-1.91-0.40 Long: Hi z INV & Lo OIB 2 5.11 4.38 0.98 1.87 1.00 Shor: Lo z INV & Hi OIB 3 7.04 4.90 3.80 6.51 3.29 4 5.87 7.74 7.61 10.37 5.91 Hi (+) z INV 9.38 9.85 10.50 10.55 7.23 Long: Hi z INV & Hi OIB Shor: Lo z INV & Lo OIB 4.10 9.78 (2.22) (4.84) 38

Table 9 Soring Resuls Based on Invenories and Ne Order Imbalances Reurns a 1-Day, 1-Week, and 2-Week Horizons This able shows he resuls of soring procedures a 1-day, 5-day, and 10-day horizons. Panel A shows he resuls of wo singlesors he firs based on sandardized invenory levels and he second based on order imbalances. z INV is he sandardized invenory level equal o he end of day or week dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. OIB is he daily or weekly ne dollar order imbalance (buys minus sells) divided by he daily or weekly dollar rading volume. Panel B shows double-sor resuls. We firs sor socks ino quiniles based on order imbalances. Wihin each quinile, we hen sor by sandardized invenory levels. Panel C also shows double-sor resuls. We firs sor socks ino quiniles based on specialis sandardized invenory posiions. Wihin each quinile, we hen sor by order imbalances. One week ahead reurns (r w+1 ) are reurns for rading days +1 hrough +5 and 2-week ahead reurns (r w+2 ) are for rading days +6 hrough +10. Reurns are calculaed using closing mid-quoes. T-saisics are based on Newey-Wes sandard errors ha are robus o heeroscedasiciy and auocorrelaion. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. Sor Porfolio + 1 Panel A: Single Sors r r w+ 1 r w+ 2 Hi z INV Lo z INV 10.25 32.99 8.10 (T-sa) (9.34) (6.68) (1.49) Lo OIB Hi OIB 0.52 32.03 12.26 (T-sa) (0.48) (5.66) (2.01) Panel B: Double Sor on Order Imbalances hen Invenories 1 s Sor Variable 2 nd Sor Porfolio + 1 r r w+ 1 r w+ 2 Hi OIB Hi z INV Lo z INV 7.07 8.58 0.51 4 Hi z INV Lo z INV 10.83 26.00 9.66 3 Hi z INV Lo z INV 8.91 22.79 11.68 2 Hi z INV Lo z INV 13.75 44.65-6.74 Lo OIB Hi z INV Lo z INV 9.22 25.22-3.06 Hi z INV / Lo OIB Lo z INV / Hi OIB Reversal 9.42 55.37 2.42 (T-sa) (4.95) (6.74) (0.42) Panel C: Double Sor on Invenories hen Order Imbalances 1 s Sor Variable 2 nd Sor Porfolio + 1 r r w+ 1 r w+ 2 Lo z INV Lo OIB Hi OIB -3.53 27.03 9.07 2 Lo OIB Hi OIB -4.12 23.67-2.65 3 Lo OIB Hi OIB -3.75 17.48 5.99 4 Lo OIB Hi OIB 0.04 8.34 13.15 Hi z INV Lo OIB Hi OIB -2.15 21.43 15.10 Hi z INV / Lo OIB Lo z INV / Hi OIB Reversal 4.10 49.77 8.79 (T-sa) (2.22) (6.21) (0.91) 39

Table 10 Fama-Macbeh Regressions This able shows he resuls of Fama-Macbeh regressions a 1-day, 1-week, and 2-week horizons. Each day or week we run cross-secional regressions using weighed leas squares where he weighs are equal o each sock s previous day s marke capializaion. Panel A uses one day ahead reurns (r +1 ); Panel B uses one week ahead reurns (rading days +1 hrough +5 and labeled r w+1 ); Panel C uses he 2 week ahead reurns (rading days +6 hrough +10 and labeled r w+2 );. Reurns are calculaed using closing mid-quoes. z INV is he sandardized invenory levels described in he ex. OIB is he daily or weekly ne dollar order imbalance (buys minus sells) divided by he daily or weekly dollar rading volume. Repored coefficiens are based on he ime series averages of esimaed coefficiens. T-saisics are based one ime series sandard deviaions. Newey-Wes sandard errors are robus o heeroscedasiciy and auocorrelaion. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. INV ( z ) + β ( r ) + β ( OIB ) α β + ε + 1 2 3 Panel A: LHS variable r +1 (daily) Reg A1 Reg A2 Reg A3 Reg A4 Consan α (10-4 ) 4.95 3.96 5.32 4.47 (2.54) (2.06) (2.75) (2.34) z INV β 1 (10-4 ) 2.63 2.92 (9.80) (11.54) r β 2 (10-3 ) 1.97 6.99 (0.70) (2.39) OIB β 3 (10-4 ) -5.29-4.02 (-2.83) (-2.39) Panel B: LHS variable r w+1 (weekly) Reg B1 Reg B2 Reg B3 Reg B4 Consan α (10-4 ) 2.54 2.63 3.23 2.98 (2.77) (2.93) (3.59) (3.40) z INV β 1 (10-4 ) 6.98 4.13 (5.50) (3.33) r β 2 (10-3 ) -4.13-3.67 (-6.69) (-5.68) OIB β 3 (10-4 ) -9.44-3.10 (-5.70) (-2.11) Panel C: LHS variable r w+2 (weekly) Reg C1 Reg C2 Reg C3 Reg C4 Consan α (10-4 ) 2.58 2.41 2.85 2.47 (2.82) (2.71) (3.10) (2.86) z INV β 1 (10-4 ) 1.23-0.03 (0.93) (-0.03) r β 2 (10-3 ) -1.98-1.98 (-2.88) (-2.72) OIB β 3 (10-4 ) -3.11-0.37 (-1.92) (-0.27) 40

Figure 1 Aggregae marke invenory levels in millions of dollars (LHS) and aggregae marke capializaion in billions of dollars (RHS) are graphed from January 3, 1994 o December 31, 2004. Aggregae marke invenory levels are calculaed as he sum of each specialiss invenory, across all socks in our sample, a he close of each rading day. Aggregae marke capializaion is he sum of he marke capializaion of each sock in our sample a he close of rading each day. Our sample consiss of New York Sock Exchange-lised, common socks, which can be mached wih CRSP daa. Aggregae Marke Invenory (LHS, $ million) 1,200 Marke Capializaion (RHS, $ billion) 12,000 1,000 800 600 10,000 8,000 400 6,000 200 0-200 4,000 2,000-400 0 Jan-94 May-94 Sep-94 Jan-95 May-95 Sep-95 Jan-96 May-96 Sep-96 Jan-97 May-97 Sep-97 Jan-98 May-98 Sep-98 Jan-99 May-99 Sep-99 Jan-00 May-00 Sep-00 Jan-01 May-01 Sep-01 Jan-02 May-02 Sep-02 Jan-03 May-03 Sep-03 Jan-04 May-04 Sep-04 41

Figure 2 A scaer plo of changes in aggregae invenory (shown in millions of dollars on he Y-axis) and conemporaneous daily marke reurns (X-axis). Changes in aggregae invenory levels are calculaed as he daily changes of each specialis s invenory summed across all socks in our sample. Our sample consiss of New York Sock Exchange-lised, common socks, which can be mached wih CRSP daa. Reurns are calculaed using closing mid-quoes. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. 1,000 800 600 Change in Agg. Invenory (Daily $ million) 400 200 0-200 -400-600 -800-1,000-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% Reurn on Marke (Daily) 42

Figure 3 This figure shows he resuls of a single soring procedure based on NYSE specialis invenory posiion in individual socks. A he end of each rading day (=0) for each sock we calculae he sandardized invenory level (z INV ) equal o he dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. The moving average and sandard deviaion measures consider invenory levels over rading days -11 o -70 and are described in he ex. We place socks ino one of five quiniles based on he sandardized invenory measures (on dae =0). Our procedure sors socks wih quiniles from he lowes (shor) posiions o he highes (long) posiions. We hen measure he value-weighed reurn of socks in each quinile over he following welve rading days. Reurns ne of he marke are calculaed using closing mid-quoes. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. 0.30% 0.20% Hi (+) Zinv Cumulaive Porfolio Value 0.10% 0.00% -0.10% 0 1 2 3 4 5 6 7 8 9 10 11 12 P4 P3 P2-0.20% Lo (-) Zinv -0.30% Days From Sor 43

Figure 4 This figure shows he resuls of a single soring procedure based on NYSE specialis invenory posiion in individual socks. A he end of each rading day (=0) for each sock, we calculae a sandardized invenory level (z INV ) equal o he dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. The moving average and sandard deviaion measures consider invenory levels over rading days -11 o -70 and are described in he ex. We place socks ino one of five quiniles based on he invenory measures (a day =0). Our procedure sors socks wih quiniles from he lowes (shor) posiions o he highes (long) posiions. We hen measure he value-weighed reurn of socks in each quinile over he five previous days and he welve following days. Reurns ne of he marke are calculaed using closing mid-quoes. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. 1.50% 1.00% Lo (-) Zinv Cumulaive Porfolio Value 0.50% 0.00% -0.50% -5-4 -3-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 P2 P3 P4-1.00% Hi (+) Zinv -1.50% Days From Sor 44

Figure 5 This figure shows he resuls of a single soring procedure based on NYSE specialis invenory posiion in individual socks. A he end of each rading day (=0) for each sock, we calculae a sandardized invenory level (z INV ) equal o he dollar invenory level minus a moving average invenory level all divided by he sandard deviaion of invenory levels. The moving average and sandard deviaion measures consider invenory levels over rading days -11 o -70 and are described in he ex. We place socks ino one of five quiniles based on he invenory measures (a day =0). Our procedure sors socks wih quiniles from he lowes (shor) posiions o he highes (long) posiions. The sample period sars 03-Jan-1994 and ends 31-Dec-2004. 2.00 1.50 Lo (-) Zinv Invenory Level (Sandardized) 1.00 0.50 0.00-0.50-1.00-5 -4-3 -2-1 0 1 2 3 4 5 6 7 8 9 10 11 12 P2 P3 P4-1.50 Hi (+) Zinv -2.00 Days From Sor 45