Commission Coss, Illiquidiy and Sock Reurns Jinliang Li* College of Business Adminisraion, Norheasern Universiy 413 Hayden Hall, Boson, MA 02115 Telephone: 617.373.4707 Email: jin.li@neu.edu Rober Mooradian College of Business Adminisraion, Norheasern Universiy 413 Hayden Hall, Boson, MA 02115 Telephone: 617.373.5955 Email: r.mooradian@neu.edu W. David Zhang School of Global Managemen and Leadership Arizona Sae Universiy, Phoenix, AZ 85069 Telephone: 602.543.6238 Email: wei.d.zhang@asu.edu Augus 2006 * The auhors wish o hank M. Nimalendran, Andy Naranjo, Jeff Poniff, David Sherman, Jiang Wang, Ber Porer, and Li Wei (NYSE) for helpful suggesions.
Commission Coss, Illiquidiy and Sock Reurns Absrac We develop a quarerly ime series of he aggregae commission rae of NYSE rading for he period 1980-2003. The aggregae commission rae is of significan size, capures rading cos, and reflecs marke illiquidiy. Consisen wih financial heory, we find a posiive relaion beween marke reurns and he aggregae commission rae. This illiquidiy facor also exhibis significan explanaory power on he cross-secional variaion of sock reurns. We find ha he sensiiviies of reurns of size-based porfolios o aggregae liquidiy decrease wih marke capializaion. Overall, our findings sugges ha marke-wide liquidiy is a sae variable imporan for asse pricing. JEL Classificaion: G12 Keywords: Commission, Liquidiy, Reurns, Volailiy, Risk Premium
I. Inroducion Commission coss influence securiy reurns, selecion, and pricing. Commission coss are significan no only o porfolio managers and raders bu also o academicians sudying marke qualiy and efficiency. Marke fricions and rading coss may help o explain some frequenly observed anomalies, such as abnormal reurns for socks of small size or low price. A reliable ime series of he aggregae commission rae serves as a good proxy for aggregae marke illiquidiy and reveals changes in marke qualiy over ime. I is also valuable o asse pricing ess (Jones, 2002). However, due o he lack of comprehensive daa, mos prior research relies on commission coss and oher fricions esimaed over relaively shor ime horizons in empirical ess and calibraion. We rack commission revenue for all NYSE member brokers exchange equiy rading and NYSE public rading volume. For he aggregae commission rae, he raio of commission revenue o volume, we consruc a quarerly ime series for he period 1980-2003. Our commission rae esimae closely maches he esimaes of insiuional commission raes, for shorer ime periods, repored by Berkowiz, Logue and Noser (1988), Keim and Madhavan (1997), Jones and Lipson (2001), and Jones (2002). Our aggregae commission rae is comparable in size o half of he bid-ask spread of Dow Jones socks and is highly correlaed wih he bid-ask spread, he absolue order imbalance, and he proporion of small rades of Dow Jones socks. Commission coss are also comparable in size o marke impac coss (Berkowiz e al., 1988; Jones and Lipson, 2001). Given is srong correlaion wih oher measures of illiquidiy, he aggregae commission rae seems o be a reliable proxy for marke illiquidiy.
We examine he role of he aggregae commission rae in deermining sock reurns. Over ime, he aggregae commission rae is significanly and posiively relaed o he excess reurns of he marke porfolio of all NYSE/AMEX/NASDAQ socks, afer conrolling for rading volume and he ineres rae facors. We also examine he crosssecional sensiiviies of reurns on illiquidiy; we regress he excess reurns of size-based porfolios on he aggregae commission rae, rading volume and he ineres rae facors. The excess reurns of he en decile porfolios are all sensiive o he aggregae commission rae and heir sensiiviies decline wih capializaion size. Consisen wih Amihud (2002) and Pásor and Sambaugh (2003), porfolios of smaller size socks are more sensiive o marke illiquidiy. Conrolling for he marke, HML, SMB, and UMD facors, we demonsrae he robusness of he explanaory power of he aggregae commission rae on reurns. We also find ha average sock reurns are posiively relaed o rading volume and negaively relaed o he variabiliy of rading volume. Trading momenum may explain his resul: higher and persisen volume reflecs marke confidence and drives marke reurns. We conduc vecor auoregression analysis o examine he dynamics among sock reurns, he aggregae commission rae, and rading volume. The resuls show ha he expeced change in he aggregae commission rae and he expeced change in volume are posiively relaed o expeced excess reurns. Furhermore, he unexpeced change in he aggregae commission rae and he unexpeced change in volume are posiively relaed o unexpeced excess reurns. This finding is consisen wih heory and is significan and robus conrolling for he ineres rae facors and seasonaliy. Alhough NYSE share volume and he aggregae commission rae diverge in he long erm, he unexpeced 2
change in volume is posiively relaed o he unexpeced change in commission rae in he shor erm. We also repor ha he changes in volume and in he aggregae commission rae rack pas marke reurns. Higher reurns in he prior quarer arac more buyeriniiaed volume in he curren quarer, which drives up rading coss and hus, he commission rae. This paper complemens prior research examining he deerminans, srucure and informaion conen of commission coss. For example, Edmiser (1978) and Edmiser and Subramaniam (1982) examine he deerminans and srucure of insiuional brokerage commission revenue following he deregulaion of commissions in May 1975. 1 Berkowiz e al. (1988) examine he NYSE commission and execuion coss of insiuional invesors. Brennan and Hughes (1991) develop a model o examine he dependence of he brokerage commission rae on share prices and he incenive for brokers o produce research repors. Brennan and Chordia (1993) model he brokerage commissions as compensaion for broker research from raders wih differenial risk preferences. Recenly, Jones and Lipson (2001) examine he effec of NYSE ick size reducion in June 1997 on he rading cos of insiuional raders. Jones (2002) consrucs an annual ime series of he aggregae commission rae uilizing he NYSE minimum commission schedules for he period 1925-1967, and he NYSE member brokerage commission income scaled by NYSE dollar volume for he period 1968-2000. However, Jones (2002) brokerage commission daa also includes he commission income from equiy rading in oher exchanges, as well he income from rading bonds and oher securiies. In addiion, he NYSE dollar volume Jones uses o scale he brokerage commission income is oal volume, which includes NYSE member rading ha does no 1 Also see Jones (2002) for a discussion on he hisory of commission coss. 3
conribue o NYSE member brokerage commissions. Our measure of he aggregae commission rae is an improvemen over Jones measure and our empirical resuls suppor Jones iniial suggesion ha commission cos is an imporan deerminan of equiy reurns. This paper also complemens he recen developmen of relaively new measures of aggregae marke liquidiy wihin he conex of asse pricing, such as Amihud (2002), Pásor and Sambaugh (2003), Acharya and Pedesen (2005), and Sadka (2005). The marke microsrucure lieraure esablishes ha liquidiy, reflecing asymmeric informaion and rading coss, is an imporan facor in price discovery. 2 Recen empirical sudies documen correlaed movemens in liquidiy. 3 A marke-wide liquidiy shock should affec reurns of all asses and he average reurns of he aggregae marke. For example, Sadka (2005) shows ha unexpeced sysemaic variaions in liquidiy are priced and can explain boh he momenum and pos-earnings-announcemen drif anomalies. Consisen wih prior sudies, our resuls show ha aggregae marke illiquidiy is a sysemaic risk facored in asse pricing, over-ime and cross-secional. The remainder of his paper is organized as follows. Secion II discusses he aggregae commission rae as an alernae liquidiy measure. Secion III presens he empirical mehodology. Secion IV describes he daa. Secion V documens he empirical resuls. Finally, Secion VI summarizes he resuls. 2 See for example, O Hara (2003). 3 See Chordia, Roll, and Subrahmanyam (2000), Hasbrouck and Seppi (2001), and Huberman and Halka (2001). 4
II. Commission Coss and Illiquidiy In financial markes, liquidiy is seen as he degree o which ransacions of large size can be carried ou in a imely fashion wih a minimal impac on prices. A good measure of liquidiy should incorporae key elemens of volume, ime, and ransacion coss. In his secion, we review he lieraure and discuss he relaion beween he aggregae commission rae and marke illiquidiy. A. Deerminans of he Aggregae Commission Rae Commissions vary over ime and are no a consan proporion of sock price (e.g., Jones, 2002). Prior o May 1, 1975, commission charges for rading lised securiies were esablished largely by consensus (Edmiser, 1978). The price srucure changes subsanially afer May 1, 1975, when brokerage companies obain discreion in negoiaing commissions. Prior sudies and published commission schedules no longer presen accurae descripions of curren securiy prices. Boh share price and ransacion size are now imporan deerminans of he commission rae as a percenage of value raded (Edmiser and Subramaniam, 1982). 4 Per-share commissions are he dominan form of paymen beween brokers and heir insiuional cliens. The negoiaed rae per share charged o insiuional invesors is dependen on he rade size and research provided by he broker, which is recenly in he range of several cens per share. 5 The relaive marke power of he broker and he 4 The relaion beween splis and rading coss (e.g., Brennan and Hughes, 1991) is consisen wih his observaion. 5 Goldsein, Irvine, Kandel, and Wiener (2004) repor ha brokers charge a per-share commission o insiuional raders as a convenien way of charging a predeermined fixed fee for broker services. In heir sudy, mos per-share commissions are concenraed primarily a 2 o 6 cens per share for he orders of NYSE-lised socks by 306 insiuional invesors in he firs quarer of 1997. In some exreme cases, commission raes may no reflec he rue coss of rading. For example, Nimalendran, Rier and Zhang (2004) repor ha cliens of an IPO underwrier could pay as high as 2$/share brokerage commission in pre- IPO rading as a means of sharing he abnormal profi from IPO allocaion. 5
clien also deermines he rae charged, which reflecs he demand and supply of marke liquidiy. For profi maximizaion, brokers may charge a higher commission rae when rading volume is persisenly higher and a lower commission rae when volume is persisenly lower. Such a commission quoaion sraegy may in fac encourage rading when liquidiy is lower. And hence, here is a dynamic relaion among marke reurns, rading volume and he commission rae, which we repor laer. Consisen wih his argumen, we find ha boh rading volume and he aggregae commission rae end o fall afer a marke decline, and rise following a marke run-up. Commission raes charged o reail raders differ across brokers, while wo alernaive reail conracs coexis. Firs, discoun brokers charge a marginal per-rade commission. Inerne rading is an example of a fixed cos per ransacion ha applies o reail rades. Second, full-service brokers charge a percenage of asses fee, according o order size and price. Larger rades are execued a lower commission cos per share and per value. Coler and Schaefer (1988) repor ha he discoun broker commission is abou one-hird ha of he full service broker, and for boh ypes of broker he commission charged as a proporion of he rade value declines as a funcion boh of he rade size and he share price raded. Under boh reail commission mechanisms, he commission rae, afer conrolling for he number of shares raded, conveys informaion abou rade size and marke deph. In he conex of marke microsrucure, small rade size is associaed wih low price volailiy. Informed raders, who end o camouflage heir rading aciviy, choose rades close in size o he median size of rades of insiuional invesors (Barclay and Warner, 1993; Chan and Fong, 2000). Chan and Fong also repor a posiive relaion beween rade size and price impac. When he proporion of small rades increases, a 6
liquidiy rader s medium or large size order faces higher price impac. Furhermore, larger rades are execued a lower commission cos per share. Therefore, he higher commission per share due o he presence of more small rades coincides wih higher rading coss and marke illiquidiy. There is also a more direc relaion beween he aggregae commission rae and illiquidiy. The aggregae commission rae proxies for illiquidiy in ha i accouns for he demand and supply of liquidiy as well as ransacion coss. Public orders originaing off he floor, which are subjec o commission charges, reach he specialis eiher elecronically hrough he NYSE s SuperDo sysem or are walked o he pos by floor brokers. Hasbrouck, Sofinaos and Sosebee (1993) repor ha, in 1992, abou 75% of he orders reach he specialiss via SuperDo, which accouns for only 28% of he execued NYSE share volume. Hence floor brokers end o represen larger and more difficul o execue orders. Furhermore, relaively small porfolio adjusmens by large financial insiuions are ofen oo large for a specialis o absorb. These large blocks of rade are ofen brough o he upsairs marke mainained by large broker firms. These blocks are hen chopped and searches are iniiaed for couner-paries. These rades are repored o he relevan specialiss on he floor afer couner-paries are locaed and deals sruck. The fee ha broker firms charge for heir service, hus, should accoun for heir effor (ransacion coss) and he supply and demand for heir service. Overall, he aggregae commission rae (ACR) reflecs (1) rading volume, (2) he proporion of large and small orders (ACR is higher when orders are smaller), (3) he proporion of reail and insiuional orders (ACR is higher when reail invesors consiue a larger proporion of rading), and (4) he proporion of orders enered hrough 7
discoun brokers and full service brokers. All four facors convey informaion abou marke liquidiy and rading coss. Therefore, he aggregae commission rae is an appropriae measure o proxy for he aggregae marke rading coss and illiquidiy. B. The Commission Rae, Bid-Ask Spread and Marke Impac Coss The bid-ask spread has dominaed discussion of liquidiy, ransacion coss and marke efficiency (see e.g. Amihud and Mendelson, 1986; Ho and Soll, 1983; Glosen and Milgrom, 1985). A large componen of he bid-ask spread is associaed wih he adverse selecion cos o he marke dealer, which measures he informaional efficiency of a marke. The bid-ask spread compensaes he marke dealer for he order processing cos and liquidiy risk associaed wih holding an illiquid asse. Hence, he bid-ask spread is posiively relaed o marke liquidiy risk. However, here are a number of shorcomings associaed wih he bid-ask spread as a proxy for liquidiy. Firs, he bidask spread does no incorporae he key elemen of ime or immediacy. The bid-ask spread also needs o be applied a a disaggregaed level for segmened markes. As a pracical maer, consrucing sysemaic liquidiy measures by aggregaing microsrucure daa, such as he bid-ask spread, is cosly and subjec o he availabiliy of ransacion daa. 6 The aggregae commission rae and bid-ask spread are relaed. Boh reflec he cos associaed wih maching buyers and sellers, he cos of adverse selecion, and he order processing cos. The aggregae commission rae accouns for he supply and demand for liquidiy as well as ransacion coss, and is negaively relaed o marke liquidiy. Lee and Swaminahan (2000) sugges ha a suiable proxy for liquidiy should 6 Jones and Lipson (2001) also sugges ha spreads are no a sufficien saisic for marke qualiy. 8
have a high correlaion wih oher liquidiy measures such as rade size and relaive bidask spread. They also poin ou ha rading volume does no mee his requiremen. Jones (2002) assembles an annual ime series of he NYSE commission rae per value and he proporional bid-ask spread of Dow Jones socks. These wo series have a correlaion of 24.3%. Our aggregae commission rae has a subsanially higher correlaion wih he average proporional bid-ask spread of Dow Jones socks. The bid-ask spread exhibis a correlaion of 44.8% wih our aggregae commission rae per share, and 67.3% wih our aggregae commission rae per rade value. Furhermore, our aggregae commission rae is highly correlaed wih absolue order imbalance (72.7%) and wih he proporion of small rades (66%). This suppors our conenion ha he aggregae commission rae is highly correlaed wih order processing coss and asymmeric informaion risk. The aggregae commission rae is comparable in size o execuion cos and he half bid-ask spread. Berkowiz e al. (1988) repor ha commission coss dominae oal NYSE ransacion coss in 1985. The commission coss average 0.18 percen of principal value and he marke impac coss (difference beween volume weighed average price of he day and ransacion price: buy or sell) average 0.05 percen of principal value. Recenly, Sofianos (2001) finds ha insiuional commissions are considerably higher han he marginal cos of rade execuion. Jones and Lipson (2001) examine he bid-ask spread, and insiuional execuion cos and commission rae of a sample of 1690 NYSE socks for he period of 100 days before and afer June 1997, during which he NYSE swiched o quoaion icks in sixeenhs. The average proporional bid-ask spread is 0.934% before he swich, and 0.686% afer. The average half spread during he 200 days is 0.405%. For he same 200 day period, he average insiuional execuion cos 9
(he difference beween ransacion price and price prevailing a he ime he order was released o he rading desk) and one-way commission rae relaive o value (compiled from Table 4 of Jones and Lipson, 2001) are 0.650% and 0.119%, respecively. The oneway insiuional commission rae is hence abou one-hird of he half quoed spread, and one-fifh of execuion cos. In our daa sample, he aggregae commission rae averages 6.39 cens per share and 0.119% per rade value for he second and hird quarers of 1997, while he average quoed bid-ask spread of Dow Jones socks is 0.337% of price. The one-way aggregae commission rae is abou he size of he half spread of he Dow Jones socks. Our resuls show ha he quoed spread of Dow Jones socks is subsanially lower han he average of 1690 NYSE socks in Jones and Lipson s sample while our aggregae commission rae coincides wih heir esimae. Boh he commission rae and bid-ask spreads are declining in he las wo decades. More recenly, i is no unusual o see a bid-ask spread of one cen for a large capializaion sock priced a $50. However, lower bid-ask spreads do no necessarily represen lower rading coss. Jones and Lipson (2001) find ha he NYSE s swich o he sixeenhs quoaion mechanism reduces he bid-ask spread bu increases he oal execuion coss of rades of medium and large sizes (10,000+ shares). One hypohesis advanced by marke paricipans is ha high commission coss lead o low execuion coss and vice versa. A porfolio manager willing o pay high commissions would be able o induce a broker o search more aggressively for he oher side of ransacions ha favor him. This may be a legiimae hypohesis on he relaion beween he marke impac cos and commission cos on ransacion daa (see Berkowiz e al., 1988). Our sudy focuses on he aggregae effec of commission coss. Hence, he 10
subsiuion effec beween he ransacion level commission quoe and he execuion cos is irrelevan o our cenral hypohesis. In summary, he aggregae commission rae reflecs he key elemens of volume, ime, and ransacion coss (boh processing cos and informaion cos), and serves as a useful proxy for rading cos and marke illiquidiy (also see Edmiser and Subramanian, 1982). I is comparable in size relaive o he bid-ask spread and execuion coss. In addiion, i has a high correlaion wih he bid-ask spread and oher marke illiquidiy measures, which are harder o measure over a longer ime period. III. Daa A. The Aggregae Exchange Commission Revenue of NYSE Member Brokers Our sample of aggregae exchange commission revenue of NYSE member brokers is provided by he Securiies Indusry Associaion (SIA). The SIA derives his daa from he SEC's Financial and Operaional Combined Uniform Single (FOCUS) Repor regulaory filings. Alhough he NYSE group is relaively small in number (240 a year-end 2002), i conains all he major U.S. brokerage firms. The SIA daabank is he sole source for imely (quarerly) reporing on he U.S. securiies indusry's financials and also accouns for a majoriy of he oal financials of U.S. securiies operaions. 7 In conras, he SEC repors only annual daa on all broker-dealers and wih a subsanial lag ime. Also, oher han he handful of publicly owned brokerage firms, he U.S. federal securiies regulaor (SEC) does no and canno provide indusry financials a he 7 NYSE brokers accoun for approximaely 70% o 80% of he revenue, capial asses, and oher financial parameers of he 7,000-plus broker-dealers regulaed by and reporing he SEC. 11
worldwide financial holding company level for he 7,000-plus U.S. broker-dealer i regulaes. We rack he ime series daa of exchange commission revenue, which is he oal quarerly commission income of all NYSE member brokers resuling from exchange equiy ransacions. The exchange equiy commission revenue of NYSE member brokers have experienced subsanial growh in he las wo decades, from $1.12 billion in he firs quarer of 1980 o $3.59 billion in he fourh quarer of 2003. The mean is $2.471 billion wih a sandard deviaion of $0.117 billion (see Table 1). B. NYSE Trading Volume We use NYSE share volume o proxy for rading aciviy in he general marke. The exchange equiy commission income and NYSE volume series share a rising ime rend. While he rading volume was 3 billion shares in he firs quarer of 1980, i reached 86 billion shares in he fourh quarer of 2003. The mean share volume is 26 billion wih a sandard deviaion of 27 billion. Since he level of rading volume is nonsaionary in he sample period, he logarihm changes of rading volume beer reveal he direcion and magniude of marke rading aciviy. We employ he logarihm change of NYSE rading volume in our empirical analysis. Turnover is ofen used as he volume measure (i.e., Jain and Joh, 1988; Campbell, Grossman, and Wang, 1993). We also esimae he urnover rae of NYSE socks, which is equal o he quarerly share volume normalized by he quarerly average number of shares of NYSE socks. The average urnover is 0.155 wih a sandard deviaion of 0.049. This urnover is used as an alernae measure of marke aciviy. We use is logarihm change over each quarer in our empirical analysis. 12
Trading volume is volaile. Varying persisence in rading volume may reflec varying marke senimen. We esimae he variabiliy of rading volume by calculaing he coefficien of variaion of daily NYSE rading volume for each quarer. Since each quarer has abou 60 rading days, we have a reasonably large number of observaions for his esimae. The mean coefficien of correlaion is 0.178 wih a sandard deviaion of 0.059. In our empirical sudy, we use he change of he coefficien of variaion o proxy for he change in he second momen of rading volume. C. The Aggregae Commission Rae Our primary ineres lies on he aggregae commission rae of NYSE rading. In order o recover he aggregae commission rae from he aggregae commission revenue, we have o rerieve he rading volume ha conribues o he commission revenue. Since NYSE Members rade for heir own accouns, no all NYSE share volume conribues o exchange commissions. The NYSE provides monhly share and dollar volume on he exchange, and oal members purchases and sales. The oal members volume consiss of specialiss purchases and sales, purchases and sales of non-specialiss originaing on he floor, and purchases and sales of non-specialiss originaing off he floor. We aggregae he NYSE members purchases and sales ino a quarerly measure. We hen subrac he sum of quarerly members purchases and sales from wo imes of quarerly NYSE share volume. This conribuing volume is hen used o scale he quarerly equiy commissions o obain he one-way aggregae commission rae per share as follows: NYSE Member Brokers Exchange Equiy Commissions ACR =. (1) 2 NYSE Share Volume-NYSE Member Purchases and Sales 13
We calculae he volume weighed average execuion price as he quarerly NYSE dollar volume scaled by NYSE share volume. The aggregae commission rae per share divided by his average execuion price is he proporional commission rae on value: ACR Proporional ACR =. (2) NYSE Dollar Volume/NYSE Share Volume The ime series mean of he NYSE commission rae is 11.0 per share, which is 0.236% of price for he sample period 1980-2003 (Table 1). The commission rae exhibis a high sandard deviaion of 6.1 or 0.137%. No surprisingly, he NYSE commission rae is declining hrough he sample period, from 25.1 (0.58%) in early 1980 o 2.9 (0.07%) a he end of 2003. Figure 1 plos he NYSE share volume and he aggregae commission rae. Our aggregae commission rae esimaes are consisen wih he esimaes of insiuional commission raes repored by prior sudies. For example, Berkowiz e al. (1988) esimae he insiuional commission coss on NYSE rading for 1985 as 0.18%, which is comparable o our aggregae commission rae esimae of 0.31%. Keim and Madhavan (1997) find an average insiuional commission rae of 0.20% for rades during he period of January 1991 o March 1993, which is comparable o our esimae of he aggregae commission rae of 0.24% for he same period. Jones and Lipson (2001) find an average insiuional commission rae of 0.119% for NYSE rades for he second and hird quarers of 1997, which coincides wih our esimae of he aggregae commission rae of 0.119% for he same period. 8 Noe ha he prior researchers esimaes of commission coss are based on heir samples of NYSE insiuional rades in differen ime spans, while our esimae of he aggregae commission rae is for all NYSE 8 Jones (2002) repors a similar esimae. 14
rades. The above sudies ogeher wih our research sugges ha reail commission raes have declined more han insiuional commission raes and ha by 1997 boh raes are similar. Our aggregae commission rae is comparable o he half bid-ask spread and price impac repored in prior research. For example, Bessembinder and Kaufman (1997) repor ha he effecive half spread and price impac (measured a one-day horizon) of all NYSE socks in 1994 are 0.394% and 0.297%, respecively. These corresponding esimaes for large NYSE socks are 0.229% and 0.185%. Our esimae of he NYSE aggregae commission cos for 1994 is 0.19% (6.25 /share). From a sample of 238 NYSE socks, NYSE repors ha he mean effecive half bid-ask spread for marke orders is 2.55 /share, which is 0.185% over price, for 2003 (see NYSE Repor, 2004). The mean effecive half bid-ask spread for limi orders is 2.8 /share, which is 0.115% over price. 9 Comparably, our esimae of he NYSE aggregae commission rae for 2003 is 0.075% of rade value (2.05 /share). D. Daa and Saisics reurns ( Now we urn o he daa for our empirical analysis. To esimae marke excess ER ) we subrac he quarerly percenage hree-monh reasury bill rae effecive a he beginning of he quarer from he percenage reurns of he marke porfolio of all NYSE/AMEX/NASDAQ socks, cum dividend. We check he marke porfolio using boh value-weighed and equal-weighed mehods. The disribuion of he value weighed marke reurns is ploed in Figure 2. 9 The limi orders experience a smaller effecive proporional spread for he foregone immediacy relaive o marke orders. Ineresingly, he effecive dollar spread of limi orders is larger han ha of marke orders. I seems ha raders of socks of higher prices, which are usually larger and more liquid, end o use limi orders in rading. 15
Table 1 provides summary saisics of he daa. The mean excess reurn of he value-weighed marke porfolio is 1.755% during he period wih a sandard deviaion of 8.801%. The excess reurn of he equal-weighed marke porfolio is 2.259% wih a sandard deviaion of 11.742%. The higher mean and sandard deviaion of he equal weighed marke porfolio are expeced since smaller socks have higher expeced reurns and risk. NYSE socks also have reurns and risks comparable o hose of he oal marke. The credi spread, he annual BAA raes minus he 10-year Treasury raes, averages 2.164%, while he erm spread, he 30-year Treasury rae minus he 3-monh Treasury bill rae, averages 0.166%. Table 2 repors he auo-correlaion of he key variables up o four lags. The ineres rae variables, NYSE share volume, urnover rae, and he aggregae commission rae are highly persisen over ime. Their auo-correlaions are in he 80s and 90s percen. The coefficien of variaion of NYSE volume also exhibis a high auocorrelaion of 15.7%. We employ he logarihm changes of hese level variables o capure he direcion and magniude of heir dynamic changes. Specifically, he logarihm change of he aggregae commission rae is defined as follows: ACR = log( ACR ) log( ACR 1). (3) These variables display subsanial iner-emporal variaion as represened by heir high sandard deviaions. Table 3 presens he correlaion marix of he key variables. The rading aciviy in NYSE socks is significan and posiively correlaed wih he erm spread and credi spread, and is negaively correlaed wih hree-monh T-bill rae. The aggregae commission rae is posiively relaed o he T-bill rae, wih correlaion of 0.848 a he 1% 16
significance level. The aggregae commission rae is also significanly and negaively relaed o rading volume and urnover. In he long run, higher rading volume leads o higher liquidiy, and lower uni commission cos, oher hings he same. However, he variabiliy of he commission rae is no solely due o he rading volume denominaor. In he VAR analysis, we laer show ha volume and he commission rae demonsrae posiive shor-run covariance. For exposiion, Figure 3 plos he logarihm changes of NYSE share volume and commission rae. The commission rae jumps (drops) coincide wih he volume jumps (drops) in cerain periods. For example, in he firs quarer of 1981, NYSE volume dropped 16% while he aggregae commission rae dropped 14%. In he firs quarer of 1988, subsequen o he marke crash in he fourh quarer of 1987, NYSE volume declined a subsanial 31% while he aggregae commission rae also dropped 14%. Furhermore, in he forh quarer of 1982, NYSE volume increased 25% while he aggregae commission rae jumped 21%. More recenly, in he second quarer of 2003, NYSE volume increased 7% and he aggregae commission rae jumped 5%. E. The Bid-Ask Spread, Order Imbalance, Small Trade Raio, and Commission Rae Marke microsrucure heory predics ha he size of bid-ask spreads is a posiive funcion of asymmeric informaion in marke rading. In order o proxy marke illiquidiy, he aggregae commission rae should covary wih he bid-ask spread. We esimae he average quoed bid-ask spread normalized by he mid-quoe of each Dow sock for each day from NYSE TAQ daa. We aggregae his daily measure ino a quarerly measure for each sock and hen ake he cross-secional average of all 30 Dow socks o proxy he average bid-ask spread for he marke. 17
Previous sudies have found ha order imbalances may conain informaion. Kyle (1985) and Admai and Pfleiderer (1988) show ha price changes are induced by ne order flow. In heir models, marke makers infer asymmeric informaion from he ne order flow. Since informed raders are one-side raders, a higher inensiy of informed rading naurally causes greaer order imbalance. Furhermore, he clusering of one-side rading, informed or no, causes marke illiquidiy and higher rading cos. Therefore, order imbalances may proxy for marke illiquidiy (due o asymmeric informaion or a liquidiy shock). Empirical sudies (see, for example, Chan and Fong, 2000; Chordia e al., 2002) have found ha order imbalances conain informaion ha can explain inradaily price movemens. On he oher hand, here are relaively few sudies on he effec of rade size and empirical findings differ depending on research design. Grundy and McNichols (1989), Holhausen and Verrecchia (1990), and Kim and Verrecchia (1991) have shown ha informed raders prefer o rade large amouns a any given price. Furhermore, Barclay and Warner (1993), and Chan and Fong (2000) find ha informed raders end o camouflage heir rades among median size rading (also see Kyle, 1985; Admai and Pfleiderer, 1988). In he presence of a large number of small rades, marke deph is reduced and commission cos per share increases. Therefore, a higher proporion of small rades ends o coincide wih higher illiquidiy (for medium or large size rading) and higher realized commission cos per share. Trades are classified ino buys and sells using he mehod suggesed by Lee and Ready (1991). Tha is, rades a prices above he midquoe are classified as buys and hose below he midquoe are sells. This mehod classifies all rades excep hose ha 18
occur a he midpoin of he bid and ask (mid-quoe). These rades are furher classified using he ick es. Trades execued a a price higher han he previous rade are classified as buys and hose ransaced a a lower price are sells. The order imbalance is se equal o he oal number of sells minus he oal number of buys. We hen divide he absolue value of he order imbalance by he oal number of rades each day. 10 For he classificaion of small rades, we follow he approach of Barclay and Warner (1993), and Chan and Fong (2000) o define orders wih less han 500 shares as small rades. We hen calculae he raio of he number of small rades o oal rades for each day. We hen aggregae he daily order imbalance and small rade raio of each Dow sock ino quarerly measure and ake he cross-secion average of he 30 Dow socks 11 o obain he quarerly measure of order imbalance and small rade raio of he marke. Table 4 repors he saisics of he hree marke microsrucure variables and heir correlaions wih he aggregae commission rae, rading volume, and urnover, for he period January 1, 1993 June 30, 2001. 12 The average bid-ask spread of he Dow socks is 0.449% wih sandard deviaion of 0.098%. The aggregae commission rae for he same sample period is 6.6 /share wih a sandard deviaion of 1.5. The proporional commission rae is 0.136% wih a sandard deviaion of 0.045%. The spread and commission rae exhibi a similar level of variabiliy measured by coefficien of variaion. 10 Order imbalances can also be calculaed on he basis of he number of shares or he dollar amoun per rade. Previous sudies (see Chordia e al., 2002, p. 117) have found ha he hree order imbalance measures are highly correlaed and ha calculaing order imbalances in erms of he number of rades is superior because i is no affeced by sock splis and he price level of he sock. 11 The 30 Dow Jones Indusrial Average member companies as of 2001 are Alcoa, American Express, Boeing, Caerpillar, Ciigroup, Du Pon, Wal Disney, Easman Kodak, General Elecric, General Moors, Hewle-Packard, Home Depo, Honeywell Inernaional, Inel, IBM, Inernaional Paper, Johnson & Johnson, J. P. Morgan Chase, Coca Cola, McDonald s, 3M, Alria Group, Merck, Microsof Corporaion, Procor & Gamble, SBC Communicaions, AT&T, Unied Technologies, Wal-Mar Sores, EXXON Mobil. 12 We choose his paricular sample period for wo reasons. Firs, he NYSE TAQ daabase commences in he beginning of 1993. Second, we exclude he daa afer mid 2001in order o avoid he poenial afermah of price decimalizaion, which was officially implemened by April 2001. 19
The one-way percenage commission rae is 60% of he half bid-ask spread (0.225%). The commission rae and bid-ask spread share a similar ime rend and heir relaive size remains comparable during his sample period. The bid-ask spreads in he firs quarer of 1993 and he second quarer of 2001 are 0.623% and 0.470%, respecively, while he aggregae commission raes are 0.270% (9.25 /share) and 0.115% (4.13 /share), respecively. Panel B of Table 4 repors he correlaions for our key variables. The aggregae commission rae, as expeced, exhibis srong correlaions wih he bid-ask spread, order imbalance, and small rade raio, wih correlaion coefficiens of 0.448, 0.727 and 0.660, respecively. The correlaion beween he proporional commission rae and bid-ask spread is 0.673. All correlaion coefficiens are significan a he 1% level. This lends srong suppor o he role of he commission rae as a measure of illiquidiy. I also suggess ha he proporional commission rae and bid-ask spread are boh subjec o price variaion. In conras, NYSE rading volume and urnover are significanly and negaively relaed o he bid-ask spread, order imbalance, and small rade raio. The correlaion of he small rade raio wih he commission rae, rading volume and urnover sugges ha he small rade raio is more of a marke deph and illiquidiy proxy. When marke liquidiy is high, i.e. high rading volume and a low commission rae, small rades occupy a smaller proporion of oal volume. IV. Research Design There are several possible ways o develop a reurn generaing process for he aggregae sock marke. Chen, Roll and Ross (1986), for example, price he aggregae 20
equiy marke based on he presen value model. Alernaively, a number of risk facors are expeced o explain he marke reurns in a mulifacor model. In his paper, we follow Chordia, Subrahmanyam and Anshuman (2001) and assume ha reurns are generaed by an L-facor approximae facor model: R L = E R ) + k =1 ( β f + ε, (4) k k where R is he reurn on he aggregae sock marke a ime, and f k is he reurn on he kh facor a ime. The quarerly reurn of he aggregae sock marke may exhibi auocorrelaion. The expeced reurn for each period, E R ), hus should include he risk free reurn and an auoregressive erm from previous quarers. Relaxing he zero mean assumpion on he risk facors, Model (4) is hus expanded o he ineres rae adjused model wih inclusion of N pas reurns and an inercep: K N 0 + β k k + θ iε i + ε k = 1 i= 1 ER = β f, (5) ( where ER = R R is he aggregae marke excess reurn a ime. F We include he logarihm changes of he aggregae commission rae and rading volume as risk facors. Since boh he aggregae commission rae and rading volume are persisen over ime and have a nonsaionary rend, heir logarihm changes represen he direcion and magniude of marke illiquidiy and rading aciviies. We check he conemporaneous effec of he aggregae commission rae on excess reurns. In a raional marke, expeced commission cos and illiquidiy are posiively relaed o expeced reurns, and hence, here is a posiive conemporaneous correlaion beween he wo. Amihud (2002) consrucs an illiquidiy measure from he average across socks of he daily raio of absolue sock reurn o dollar volume. Using monhly daa, he shows ha 21
over ime expeced marke illiquidiy condiional on pas marke illiquidiy posiively affecs ex ane sock excess reurns. He also repors ha he innovaion in curren marke illiquidiy which is no prediced by pas illiquidiy is negaively correlaed wih curren excess reurns. This negaive correlaion beween excess reurns and marke illiquidiy may be due o he scaling of absolue sock reurn by dollar volume. By consrucion, he curren marke price is inversely relaed o Amihud s marke illiquidiy measure and posiively relaed o curren marke reurns. We include oher prevailing risk facors. The ineres rae is a radiional proxy ha capures he sae of invesmen opporuniies (Chen, Roll and Ross, 1986; Ferson and Harvey, 1991). Meron (1973) and Cox, Ingersoll and Ross (1985) have developed models in which ineres raes are sae variables. Fama and French (1993) idenify he erm spread and credi spread as wo bond-marke risk facors. Changes in ineres raes may influence margin requiremens and shor-selling consrains. This implies ha rading aciviies may be relaed o changes in shor-erm ineres raes. Increases in he long-erm Treasury bond yield and he credi spread may also cause invesors o reallocae heir asses beween equiy and deb. To accoun for hese effecs, we include he changes in he erm spread, credi spread and shor-erm ineres rae in addiion o he rading aciviy and liquidiy facors. We include he marke reurn residuals of he previous quarers in he empirical analysis o conrol for he auo-correlaion of reurns. We also include he Fama-French sock marke facors, in addiion o he illiquidiy measure, o examine he cross-secional variaion of socks reurns based on marke capializaion size. The pricing model in equaion (5) resembles hose of Fama and French (1993) and Pásor and Sambaugh (2003). 22
Wheher marke liquidiy is endogenous o marke rading aciviy and reurns is an imporan issue wih respec o marke qualiy. Wha drives rading aciviy and commission cos on a quarerly basis? Since illiquidiy is a subsanial risk facor ha concerns invesors, answers o hese quesions have imporan implicaion in dynamic porfolio managemen. Arguably, liquidiy is driven by he supply of shares. From a shareholder s viewpoin, commission cos is priced in when a buy decision is iniially made. Inuiively, buyers are more sensiive o liquidiy risk. We examine he emporal dynamics among marke reurns, rading aciviy and he commission rae. Toward his end, we perform he vecor auoregression (VAR). Quarer dummies are included o check possible seasonal effecs and we examine he variables of pas quarers in he VAR analysis. The model is consruced as follows: ERVW NYSE = ACR CSPR A + B TSPR TBIL Q2 + C Q3 + Q 4 N i= 1 Θ ξ + ζ, (6) i i where ζ ~ N 0, ) and A is he inercep. The order of lags is chosen by he AIC. ( 3,1 3, 3 Now we urn o empirical resuls. V. Empirical Resuls A. Conemporaneous Relaion beween Aggregae Liquidiy, Trading Aciviy, and Marke Reurns The recen sudies of Hasbrouck and Seppi (2001), Huberman and Halka (2001), and Chordia, Roll, and Subrahmanyam (2000) documen correlaed movemens in liquidiy and sugges ha aggregae liquidiy may be a sysemaic facor ha impacs asse pricing. Theory suggess ha an addiional componen of long-run reurn is 23
required and obained whenever financial asses are influenced by sysemaic and nondiversifiable risks. If here is a common facor ha is associaed wih non-diversifiable liquidiy risk, he long-run aggregae marke reurns need o compensae for such sysemaic risk. In his subsecion, we examine he conemporaneous relaion beween sock marke reurns, rading aciviy and he aggregae commission rae. The aggregae commission rae capures wo componens of illiquidiy. The firs is he exogenous liquidiy shock due o echnology advancemen and marke srucure change. The second is he effecive rading cos endogenous o rading aciviy. I is obvious ha larger rading volume reduces uni commission cos, all else remaining he same. Hence, he aggregae commission rae does capure he liquidiy informaion refleced in rading volume. Table 5 summaries he conemporaneous relaion among NYSE rading volume, he aggregae commission rae, and marke reurns, conrolling for he ineres rae risk facors and pas reurns. We are also ineresed in he impac of he variabiliy of rading volume on marke reurns. Hence, we include he sandard deviaion of daily NYSE volume normalized by he average daily volume of he quarer in he regressions o sudy he influence of he second momen of rading volume on average marke reurns. If rading aciviy proxies marke liquidiy, one would expec a negaive relaion beween he level of rading volume and marke reurns since increases in rading volume would mean lower liquidiy risk, which should command a lower reurn. For example, Chordia, Subramanyam, and Anshuman (2001) documen a negaive cross-secional relaion beween average sock reurns and average urnover. If he variabiliy of 24
liquidiy is o be priced-- i.e., invesors are risk averse and dislike he variabiliy of liquidiy--greaer variabiliy of liquidiy should command a higher expeced reurn. As such, one would expec a posiive relaion beween he second momen of rading volume and he expeced marke reurns. Our resuls show ha rading volume covaries wih marke reurns. Panel A repors he analysis on he excess reurns of he value-weighed marke porfolio. Columns A and B repor he regression focusing on rading volume. They presen a significanly posiive relaion beween he level of rading volume and marke reurns. I is consisen wih he usual observaion ha volume ends o be higher when sock prices are increasing han when prices are falling (e.g., Campbell, Grossman, and Wang, 1993). Complemening he cross-secional resuls of Chordia, Subrahmanyam, and Anshuman (2001), we find a negaive ime series relaion beween he variabiliy of rading volume and marke reurns. The regressions have high R-square raios (0.181 and 0.220) ha indicae a relaively high degree of goodness-of-fi. These resuls sugges ha he shor-run dynamic changes of rading volume are more relaed o marke senimen han o marke liquidiy. I is usually observed ha marke reurns are driven by acive rading. In his conex, he level of rading volume reflecs invesor confidence, and he variabiliy of daily rading volume reflecs he disagreemen in invesor confidence. High and persisen volume represens srong marke senimen, and low and variable volume represens marke pessimism. Thus, we sugges ha marke senimen explains he marke reurns posiive correlaion wih volume and negaive correlaion wih he variabiliy of volume. Our findings are consisen Chordia, Subramanyam, and Anshuman (2001), who focus on he relaion 25
beween he average reurn and he urnover over a long ime span across individual socks. In conras, we focus on he dynamic over-quarer changes of rading volume and commission coss. Column C repors he regression resuls using he aggregae commission rae as an illiquidiy proxy. The aggregae commission rae exhibis a posiive and significan relaion wih marke reurns. The coefficien is 72.008, significan a he 1% level. The R-square raio is 0.360, higher han hose in Columns A and B, indicaing a beer degree of goodness-of-fi. The commission rae is posiively relaed o boh he bid-ask spread and illiquidiy risk, and is negaively relaed o marke liquidiy. I is well known ha bid-ask spreads are posiively relaed o liquidiy risk since dealers expec o be compensaed from a posiive bid-ask spread for he poenial capial loss from holding an illiquid securiy. Hence, a larger bid-ask spread is associaed wih lower liquidiy. A major componen of commission is he cos associaed wih maching buyers and sellers. A larger bid-ask spread would imply a higher maching cos and herefore an increased commission rae. The posiive relaion beween he aggregae commission rae and he marke reurn indicaes ha illiquidiy does impac asse reurns. Greaer illiquidiy risk commands a higher reurn. To give a broader picure of he marke reurn generaors, we include boh rading aciviy and illiquidiy facors in he regression and repor he resuls in Column D. We find ha he effec of he aggregae commission rae remains economically and saisically significan afer conrolling for rading aciviy and oher facors. The sandard deviaion of ACR is 0.065 in he sample and he sensiiviy of reurns o he change in he aggregae commission rae is 65.390 (Table 5, Panel A, Column D). This 26
implies ha, an increase (decrease) of one sandard deviaion in he aggregae commission rae is associaed wih a 4.25% increase (decrease) in he quarerly marke premium. Marke reurns reain a posiive correlaion wih he level of rading volume and a negaive correlaion wih he variaion of rading volume as repored in Column B. The R-square raio is 0.411, which indicaes an improved goodness-of-fi relaive o he regressions in Columns A, B and C. As a robusness check, we run he same model wih he excess reurns of he value weighed NYSE socks as he dependen variable. The resuls repored in Column E are similar o hose of he regression using he oal marke excess reurns as he dependen variable. The resuls in Columns D and E sugges ha an appreciable fracion of he ime-series variaion of marke reurns is capured by rading aciviy and marke liquidiy. Measures of rading aciviy such as rading volume do convey idiosyncraic informaion besides liquidiy, and are endogenous o pas momenum, as we show in he nex subsecion. As a robusness check, we conduc he same analysis on he excess reurns of he equal-weighed oal marke porfolio and NYSE socks, and repor he resuls in Panel B. The explanaory power of rading volume, variabiliy of rading volume and he aggregae commission rae remain significan. The main difference is ha equalweighed porfolios consisenly exhibi a significan relaion wih he ineres rae facors, and he R-squares of he regressions are noiceably higher han hose in Panel A. Turnover is a popular measure o rading volume in previous sudies, especially for cross-secional analysis. We hence replace he logarihm change in NYSE rading volume wih he change in he urnover of all NYSE shares in he preceding regressions. Table 6 repors he resuls of he regressions on he excess reurns of value-weighed and 27
equal-weighed marke porfolios. The coefficien esimaes are consisen wih hose in Table 5. The urnover rae is significanly relaed o marke reurns, while he variabiliy of rading volume is negaively relaed o sock reurns. Afer conrolling for he rading volume variables, he aggregae commission rae is posiively and significanly relaed wih marke reurns. Overall, our resuls show ha sock reurns are posiively relaed o he aggregae commission rae over ime conrolling for rading volume and he ineres rae variables. In conras, sock reurns are posiively relaed o rading volume and negaively relaed o he variabiliy of rading volume. B. Dynamics among Marke Reurns, Trading Aciviy, and Commission Rae As saed earlier, rading aciviy measures such as rading volume are ofen used o proxy for liquidiy in previous sudies. Financial heory is mue on eiher he posiive relaion beween he level of rading volume and marke reurns or he negaive relaion beween he variabiliy of rading volume and marke reurns. Mos previous sudies on he dynamics beween volume and reurns examine he conemporaneous and ineremporal relaions beween rading volume and absolue reurns (volailiy) or beween volume and he auocorrelaion of reurns (e.g., Karpoff, 1987; Jain and Joh, 1988; Gallan, Rossi and Tauchen, 1992; Hiemsra and Jones, 1994). However, here is documened evidence on he dynamic relaion beween rading volume and he level of reurns. For example, using monhly daa, Lee and Swaminahan (2000) documen ha he relaion beween rading volume and expeced reurns depends on how he socks have performed in he pas. Gervais, Kaniel and Mingelgrin (2001) documen ha socks experiencing unusually high (low) rading volume over a period of one day o a week 28