Resiliency, the Neglected Dimension of Market Liquidity: Empirical Evidence from the New York Stock Exchange

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1 Resiliency, he Negleced Dimension of Marke Liquidiy: Empirical Evidence from he New York Sock Exchange Jiwei Dong 1 Lancaser Universiy, U.K. Alexander Kempf Universiä zu Köln, Germany Pradeep K. Yadav Oklahoma Universiy,U.S. Absrac The seminal lieraure on liquidiy (Garbade (1982), Kyle (1985), and Harris (1990)) idenifies hree main dimensions of liquidiy: spread, deph and resiliency. While here has been exensive research focussing on spread and deph, here has been virually no empirical invesigaion on resiliency, even hough resiliency addresses an imporan quesion: when rades, especially hose resuling from relaively large and uninformaive orders, change marke prices and lead o emporary pricing errors, how fas are hese pricing errors eliminaed hrough he compeiive acions of value raders, dealers and ohers marke paricipans. This paper invesigaes, for he firs ime, he main feaures of resiliency as a dimension of liquidiy, and is effec on sock reurns. Specifically, we firs formally define resiliency as he observed mean-reversion parameer in he sock s pricing-error process. Using minue-by-minue daa for a sample of 100 NYSE socks, resiliency is empirically esimaed on a daily frequency for each sock based on Kalman-filer esimaion echniques. Second, we analyse he micro-srucural ime-series and sockspecific facors ha affec resiliency. Third, we examine he relaionship beween resiliency and he oher wo liquidiy dimensions: spread and deph. And finally, we es if resiliency is relaed wih sock reurns. We idenify eigh facors as deerminans of resiliency: ransacion frequency, ick size, average ransacion size, realized spread, adverse-selecion raio, informaiveransacions raio, marke resiliency and unexpeced volailiy. Alhough hese deerminans are also relaed wih spread and deph, resiliency is only weakly relaed wih hese wo liquidiy dimensions, and hence provides significan new informaion on marke qualiy. Finally, and imporanly, we find srong evidence ha resiliency is significanly relaed wih sock s realized reurn. Keywords: Marke Microsrucure, Liquidiy, Resiliency JEL: G10, G14 1 Jiwei Dong is a he Deparmen of Accouning and Finance, Lancaser Universiy Managemen School, Bailrigg, Lancaser, LA1 4YX. England. Alexander Kempf el (0) ) is a he Universiä zu Köln, Seminar für Finanzierungslehre, Alberus-Magnus-Plaz, Köln, Germany. Pradeep Yadav el ), is a he Price College of Business, Oklahoma Universiy, 307 W. Brooks Suie 205A, Norman, OK The auhors hank Louis Ederingon, Rober Engle, Chiru Fernando, Sco Linn, Janya Porniaguina, Bryan Sanhouse, and Sephen Taylor for exremely helpful discussions, and graefully acknowledge he financial and daa suppor of he Scoish Insiue for Research in Invesmen and Finance (SIRIF) a he Universiy of Srahclyde, he Cener for Financial Research a he Universiy of Cologne, and he Deparmen of Accouning and Finance a Lancaser Universiy. The auhors remain responsible for all errors. Page 1 of 47

2 Resiliency, he Negleced Dimension of Marke Liquidiy: Empirical Evidence from he New York Sock Exchange 1. Inroducion I is widely recognised ha he concep of marke liquidiy canno be capured by a single measure. The seminal lieraure on liquidiy (Garbade (1982), Kyle (1985), and Harris (1990)) idenifies hree main dimensions of liquidiy: spread, deph and resiliency. Spread, ofen measured by he quoe-based bid-ask spread or he rade-based effecive spread, measures ransacion coss for public raders. Deph measures he marke s abiliy o absorb and execue large orders wih minimal price impac, and is ofen measured by he quoed deph or by Kyle s Lambda. Resiliency, following e.g. Kyle (1985), is he speed wih which pricing errors caused by uninformaive order-flow shocks are correced or neuralized in he marke. There has been exensive research on spreads. The lieraure is far oo exensive o adequaely summarise here 2. Imporanly, here is evidence ha spreads affecs sock s required rae of reurn. For example, Amihud and Mendelson (1986) and Eleswarapu (1997) found ha higher quoed bid-ask spreads are associaed wih higher required reurns; and Chalmers and Kadlec (1998) also found a posiive relaionship beween effecive spreads and sock reurns. There has also been a large amoun of research on deph. For example, Hasbrouck (1991) and Kempf and Korn (1999) analysed he effec of ransacions on marke prices; and, Glosen and Harris (1988) and Brennan and Subrahmanyam (1996) invesigaed he relaionship beween sock reurns and measures of deph, similar o Kyle s Lambda. Once again, here is evidence ha deph has some pricing relevance. Surprisingly, here has been virually no empirical invesigaion of resiliency, even hough resiliency provides a key insigh ino he naure of he marke. Resiliency addresses a quesion ha is very imporan for marke paricipans and regulaors, i.e., 2 One srand of he lieraure decomposes he spread ino hree componens: one componen reflecing he invenory holding risk of liquidiy suppliers, anoher componen reflecing he adverse-selecion losses ha liquidiy suppliers make o more informed invesors, and he las componen reflecing order-processing coss. See, for example, Huang and Soll (1997), Soll (1989), and Glosen and Milgram (1985). Anoher srand of he lieraure focusses on he individual rade-based effecive spread, and is decomposiion ino he adverse selecion spread and he realised spread. See, for example, Huang and Soll (1996), Bessembinder (1997) and Naik and Yadav (2003). More recenly, Chorida, Roll, and Subrahmanyam(2000) examine co-movemen of quoed and effecive spreads. Page 2 of 47

3 when rades, especially hose resuling from relaively large and uninformaive orders, change marke prices and lead o emporary pricing errors, how fas are hese pricing errors eliminaed hrough he compeiive acions of value raders, dealers and ohers marke paricipans. Given ha he rue price is unobservable, he less resilien a sock is, he greaer is he risk faced by an invesor rading on he assumpion ha price is he bes available signal of rue value. Resiliency is a measure of he ime dimension of liquidiy in he same way as spread is a measure of he price dimension, and deph is a measure of he quaniy dimension. The quesion arises: does resiliency provide new informaion in addiion o ha provided by spread and deph, and is i also relaed wih sock reurns. Ye, we do no know anyhing abou he empirical properies of he resiliency measure. In paricular, we do no know o wha exen micro-srucural facors like ransacion frequency, ransacion size, and informaion asymmery affec resiliency, we do no know if here is significan commonaliy in resiliency across differen socks, we do no know wha sock-specific facors deermine resiliency in he cross-secion, we do no know if resiliency is relaed o he oher dimensions of liquidiy in some way or provides independen new informaion, and we do no know wheher resiliency affecs sock s required rae of reurn. This paper aims o plug hese major gaps in he lieraure. This paper invesigaes, for he firs ime, he main feaures of resiliency as he hird dimension of liquidiy, and is effec on sock s realized reurns. Specifically, we firs address how we can formally define and measure resiliency. Second, we analyse he micro-srucural and sock-specific facors ha affec resiliency. Third, we examine he relaionship beween resiliency and he oher wo liquidiy dimensions: spread and deph. And finally, we es if resiliency affecs sock s realized required rae of reurn. Our empirical invesigaion is based on 100 acively raded socks on he New York Sock Exchange. Following Kyle (1985), we define resiliency as he rae a which pricing errors caused by emporary order-flow shocks are correced in he marke. In his conex, he observed mean-reversion parameer in he pricing-error process is used o empirically measure a sock s resiliency. An esimaion procedure based on he Kalman-filer is used o esimae resiliency for each rading day in he esimaion period for each sock from minue-by-minue high-frequency daa of 100 NYSE socks. We find ha, for our sample of (heavily raded) NYSE socks, he mean value of he esimaed resiliency over a one- Page 3 of 47

4 minue horizon is 0.60, which indicaes ha as much as 60% of he pricing error revers o zero wihin one minue. We analyse eigh micro-srucural and sock-specific facors as deerminans of resiliency. We find ha ransacion frequency, ick size relaive o pricing level, average ransacion size, realized spread, adverse-selecion raio, informaive-ransacions raio, and sock s unexpeced inra-day volailiy are significan deerminans of resiliency, and in he expeced direcion. We invesigae he relaionships among hese hree liquidiy dimensions. Spread, measured by he dollar effecive spread, is highly correlaed wih deph, measured by he inverse of Kyle s Lambda. However, he relaionship beween resiliency and he oher wo liquidiy dimensions, while saisically significan, is much weaker. I appears ha resiliency, as a dimension of liquidiy, is almos independen o he oher wo dimensions of liquidiy, spread and deph. Hence resiliency can poenially provide significan new informaion on he marke qualiy. Finally, we apply he Brennan and Subrahmanyam (1986) mehodology, and he commonly used Fama and MacBeh (1972) and Fama and French(1993) asse-pricing es procedures o es if resiliency affecs a sock s required rae of reurn, and find srong evidence ha i does influence he sock s required rae of reurn, and in he expeced direcion. The res of his paper is organized as follows. Secion 2 defines resiliency and discusses he mehodology for empirically esimaing resiliency. Secion 3 describes he daa, he mehods used o consruc he differen variables used in he research, and he general feaures of he esimaed resiliency. Secion 4 invesigaes he relaionship beween resiliency and is poenial micro-srucural and sock-specific deerminans. Secion 5 analyses he relaionship beween resiliency and oher liquidiy measures. In secion 6, he effec on marke reurns of he differen liquidiy measures - spread, deph and resiliency is esed wih Fama-French variables: size, book-o-marke raio, and bea. Finally, he conclusions are presened in secion 7. Page 4 of 47

5 2 Resiliency: Definiion and Measuremen 2.1 Definiion In previous lieraure, resiliency was described in differen ways. According o Garbade (1982), a marke is resilien if new orders pour in promply in response o emporary order imbalance. Kyle (1985) refers o resiliency as he speed wih which prices end o converge owards he underlying liquidaion value or he rae a which prices bounce back from an uninformaive shock. Harris (2003) refers o resiliency as how quickly prices rever o former levels afer hey change in response o large order flow iniiaed by uninformed raders. These resiliency descripions can be caegorized ino wo ways of looking a resiliency: order replenishmen and price recovery. Empirical analysis based on he order replenishmen approach is feasible in an orderbook marke where orders, liquidiy and he resulan deph are aggregaed in a cenralized locaion. This paper invesigaes he New York Exchange where, for each sock, here is a specialis, here are floor raders, here are oher marke makers, here is an upsairs marke, and he same sock is also raded on oher exchanges. Hence, i is no possible o meaningfully consruc an observed measure based on he order replenishmen approach. Hence, in his paper, we use he price recovery approach o define resiliency. Following he price recovery approach, resiliency is defined as he speed wih which pricing errors caused by emporary uninformaive order shocks are correced or eliminaed hrough marke ransacions. This speed can be measured by he value of mean-reversion parameer, α, in he following pricing-error process : 2 Δ Y( ) = Y( ) Y ( 1) = α. Y ( 1) + φ( ), φ( ) N(0, ) (2.1). 3 σ φ Where Y () is he pricing error a ime, andφ () is a whie noise innovaion wih mean 2 zero and variance σ. The mean-reversion parameer, α, in equaion (2.1) measures how φ much of he pricing error a period -1 is correced in he curren period. If his parameer equals zero, previous pricing errors are no reduced or eliminaed ever. If his parameer equals one, previous pricing errors are oally eliminaed in he nex period. If he value of his parameer is in he range beween zero and one, some bu no all of he previous pricing error is eliminaed in he curren period. If his parameer is higher han 3 There can be alernaive approaches. For example, Damodaran (1993) inroduced a parial price adjusmen model which measures he speed wih which marke prices converge o heir rue economic value. Page 5 of 47

6 one, he previous error is over-correced, creaing a new pricing error in he opposie direcion. Clearly, economic inuiion dicaes ha he value of his mean-reversion parameer, or he esimaed resiliency as defined, should be greaer han zero bu less han one. 2.2 Esimaion mehodology A sock s rue underlying value, and hence is pricing error, canno be observed direcly. So, furher assumpions are needed o specify an underlying value process and hereby esimae resiliency. Following he Hasbrouck (1993) approach, we assume ha he logarihm of he sock s underlying value, F(), follows a random walk wih a drif, 4 μ, every rading day. 2 F( ) = μ + F( 1) + ε ( ), ε ( ) N(0, ) (2.2) 2 Where ε () is whie noise innovaion wih mean zero and variance. Then, he logarihm of a sock s marke price, S(), equals he underlying value plus he pricing error. σ ε σ ε S ( ) = F( ) + Y ( ) (2.3) Combining equaions (2.1), (2.2) and (2.3), we ge: S( ) = μ + (1 α.). S( 1) + α. F( 1) + θ ( ), where θ ( ) = φ( ) + ε ( ) (2.4) In his equaion, curren marke prices can be aken as he weighed average value of previous underlying values and marke prices plus a consan drif. Based on equaion (2.4), wo mehodologies can be developed o esimae he resiliency measure,α, using only high-frequency marke prices as inpus on every rading day. 5 Firs, he Kalman-filer smooh-esimaion procedure, can be used o esimae our resiliency measure,α, using only ransacion prices. In order o apply he Kalman-filer smooh-esimaion mehodology, equaion (2.2) and equaion (2.4) are rewrien ino he sae-space represenaion as follow. 4 In his paper, drif, μ, is added o he Hasbrouck (1993) model o incorporae he up or down rend of a sock s underlying value during he rading day. Such a rend could be caused by public informaion or by leaked privae informaion. 5 More deails on he Kalman-filer smooh-esimaion procedure are provided in Hamilon (1994) chaper 13, pp Page 6 of 47

7 S( ) Observaion equaion: S( ) = [1,0,0]. F( ) (2.5) 1 S( ) 1 α α μ S( 1) θ ( ) Transiion equaion:. = + F( ) 0 1 μ. F( 1) ε ( ) (2.6) The ransiion or sae equaion (2.6) includes boh equaion (2.2) and equaion (2.4) and specifies movemens of boh marke prices and underlying values. The observaion equaion (2.5) indicaes ha he only observed informaion required for he esimaion procedure is he ransacion price. From his sae-space represenaion, all four unknown, ε 2 parameers μ α, σ 2 θ, σ can be esimaed from observed marke prices wih he Kalmanfiler smooh-esimaion procedure. In addiion o marke prices, one se of iniial values of all hese four unknown parameers are also needed o sar he Kalman-filer smoohesimaion procedure. This iniial condiion, which should be in a reasonable range, is criical for he accuracy of he Kalman-filer esimaion resuls. Second, a reduced-form represenaion of marke price changes, ΔS(), can also be used o esimae resiliency. Differencing equaion (2.4), we ge: ΔS( ) = α. ΔF( 1) + (1 α ). ΔS( 1) + θ ( ) θ ( 1) (2.7) Combining equaion (2.7) wih equaion (2.2), we ge: ΔS( ) = α. μ + (1 α ). ΔS( 1) + θ ( ) θ ( 1) + α. ε ( 1) (2.8) Since he whie noise variables θ () and ε () are independen ime-series, we can rewrie equaion (2.8) ino an ARMA(1,1) process of observable marke price changes, ΔS() : ΔS( ) = β + γ. ΔS( 1) + η( ) + θ. η( 1) β = α. μ γ = 1 α (2.9) From equaion (2.9), he mean-reversion parameer,α, can be calculaed by esimaing parameers in his ARMA(1,1) process of marke price changes. Alhough his ARMA(1,1) process esimaion can be easily applied wih no addiional condiions, is Page 7 of 47

8 esimaion accuracy is low when using small daa samples. This weakness will be discussed in deail laer. In his paper, we find i expedien o use a combined esimaion procedure ha incorporaes boh he reduced-form and Kalman-filer esimaion mehodologies using observed marke ransacion prices. Firs, he reduced-form esimaion procedure is used o provide preliminary esimaes. Then he iniial values of he unknown parameers in he sae-space represenaion (equaion 2.6) are se as equal o hese preliminary esimaion resuls, and he Kalman-filer smooh-esimaion procedure is run wih hese iniial parameer values. The final esimae from Kalman-filer smooh-esimaion procedure is aken as he empirical observed resiliency parameer. Simulaion ess are used o es he opimaliy of our combined esimaion procedure relaive o he reduced-form esimaion procedure. In hese simulaion ess, 20,000 daa poins (marke prices) are simulaed from equaion (2.2) and equaion (2.4) wih known parameer values. All hree esimaion procedures are applied on his se of simulaed daa o esimae empirical resiliency. For every esimaion procedure, differen amouns of daa are used o invesigae he relaion beween esimaion accuracy and amoun of daa poins. In order o compare he esimaion precision of differen esimaion procedures, a ˆ αi α0 precision measure, R, is creaed. R i = i, whereα α 0 is he known and se resiliency value, 0 αˆ i is value of esimaed empirical resiliency. Comparison resuls among differen esimaion procedures using differen amoun of daa poins are presened in figure 1. In hese ess, he Kalman-filer smooh esimaion procedure is run wih he known iniial condiion. When he number of daa poins used for esimaion are higher han abou 1,500, all hree esimaion procedures yield similar esimaion precision, around 94%. As he number of available daa poins decreases, he Kalman-filer and he combined esimaion procedure become superior han he reduced-form esimaion procedure. When he number of available daa poins is abou 800, he precision of he reduced-form esimaion procedure and he precision of he Kalman-filer / he combined esimaion procedures sar diverging considerably. As he amoun of available daa decreases furher, he precision difference beween reduced-form esimaion and he oher wo esimaion procedures becomes even larger. Since we use minue- by-minue daa, he Page 8 of 47

9 number of high-frequency price observaions are around 360 per rading day in our case. Thus, we use he combined esimaion procedure in his paper for is higher esimaion precision. 3. Marke Resiliency esimaion 100 sample socks are seleced from he NYSE and heir rade-by-rade raw TAQ daa are merged o consruc one-minue fixed-inerval high-frequency daa for resiliency esimaion. Daily resiliency is esimaed using hese consruced fixed-inerval highfrequency daa for every sample sock hrough 294 rading days from January 2000 o March Sock selecion and daa consrucion The TAQ daabase is he main source of our high-frequency daa. I includes deailed quoaion and ransacion informaion for he common socks raded in he U.S. marke from January 2000 o March In his paper, we limi our analysis o socks, which were mainly raded in he NYSE. There are around 500 socks issued and mainly raded in NYSE. In order o keep he esimaion accuracy and reduced our calculaion burden, we only selec a sample of 100 hundred socks. We define he acive sock as hose socks, which have he average daily number of ransacions higher han 300, and he minimum number of ransacions on any day in he sample period higher 200. Firs, we selec all NYSE socks available from January 2000 o March 2001, and exclude all cerificaes (ADRs, SBIs (shares of beneficial ineres) ec.), all unis (deposiory unis, unis of Beneficial Ineres, unis of Limied Parnership Ineres, Deposiory Receips, ec.), common socks of American Trus componens, closed-end fund and REIT s (Real Esae Invesmen Truss) because of heir special feaures. Thus, only common socks wih CRSP securiy ype code 10, 11, 12 are lef in our sample. Firms wih a sock price of less han $5 are also excluded. Second, daily ransacion saisics are obained from he TAQ daabase for all he NYSE socks lef in he sample from January 2000 o March Socks wih average number of ransacions less han 300, and lowes daily number of ransacion figure less han 200 are excluded. Page 9 of 47

10 Finally, he firs 100 socks wih he highes average daily number of ransacions are kep in he sample. All hese seleced socks are from five main SIC divisions (D, E, G, H, I, G). Around 50% of he sample socks are from division D, he manufacuring indusry secor. All he high-frequency quoaion and ransacion records are exraced from TAQ for every seleced sample sock in he period from 1 s Jan hrough 31 h March Because of some corruped daa disks, we are lef wih 294 rading days in his esimaion period. We hen filer all ransacion and quoaion records using he following rules: i) All ransacion and quoaion records should be aken from he primary marke where he socks is issued and mainly raded. This rule can exclude hose noisy and uninformaive quoaion records inroduced by he auo-quoaion rules. Moreover, his can exclude some exreme ransacion/quoaion records, which are repored wih longer ime-delay from peripheral markes. ii) Transacion and quoaion records, repored ou of he regular rading hours a NYSE (9:30-16:00), are excluded. Many of hese records involve reporing errors, special rading condiions, or oher special ransacion feaures ha are differen from he ransacion/quoaion records repored during regular opening hours. iii) Transacion records wih marked reporing misakes are excluded. Following his rule, all ransacion records wih CORR value oher han 0 and 12 are excluded. Also, all ransacion records wih special ransacion condiions, negaive ransacion size, negaive ransacion prices are excluded. iv) Quoaion records wih negaive quoaion size, negaive or zero bid/ask price, negaive quoed spread are excluded. In addiion, quoaion records wih quoed spread higher han wo dollar are also excluded, for hese exreme spreads are ypically associaed wih reporing errors. Then, all he filered rade-by-rade ransacion records are pooled up in every oneminue period and consruced ino fixed-inerval records wih corresponding quoaion records. Firs, ransacion daa are pooled up wihin every one-minue period. In his sep, he las ransacion record in every minue is aken as he ransacion record for ha period. If here is no ransacion in his one-minue inerval, a virual ransacion is Page 10 of 47

11 creaed, which is assumed o be execued in he las second of his inerval. Second, hese seleced one-minue real or virual ransacion records are merged wih heir corresponding quoaion records. The Lee and Ready (1991) algorihm is used o merge he ransacion records wih quoaion records. Following his algorihm, he las quoaion record, which is a leas five seconds earlier han he repored ransacion ime, is seleced as he quoaion for he ransacion record. For every one-minue inerval, we also aggregae he ransacion daa o calculae he oal rading volume and he oal number of ransacions in ha inerval. When caegorizing he direcion of ransacions, we use Lee and Ready (1991) mehod. If he realized price of a ransacion is higher han is corresponding mid-quoe 6, his ransacion is classified as buyer-iniiaed. If he realized price of he ransacion is lower han is corresponding mid-quoe, i is caegorized as seller-iniiaed. If he ransacion happens a he mid-quoe, i is classified as unknown. For our sample socks, 16.81% of ransacions, 15.38% of rading volume, are lef as unknown. On every rading day, 390 one-minue fixed-inerval records are consruced for he period from 9:30 o 16:00. Because ransacion behaviour can be unusual a he sar and he closing period, we exclude he firs and las 15 minues from regular opening hours. Thus, here are 360 one-minue records lef for resiliency esimaion a every rading day. Marke ransacion prices no only reflec he asse s underlying values bu also vary wih he direcion of he rade. Buyer-iniiaed ransacions are more likely o be execued a a higher price han seller-iniiaed ransacions under similar condiions and a he same ime. This bid-ask spread effec may inroduce large noise in he pricing error correcion process, and reduce he accuracy of resiliency esimaion. In order o exclude his bid-ask spread effec, mid-quoes are used in place of ransacion prices for resiliency esimaion. 3.2 Resiliency esimaion resuls Following he combined resiliency esimaion procedure, daily resiliency is esimaed for every sock for every rading day from 1 s January 2000 hrough 31 h March 2001 (excep for 20 missing rading days involving corruped daa disks) using consruced fixed-inerval mid-quoes resiliency esimaes are hereby produced. The 6 Mid-quoe is he average value of he bid and ask price quoed wihin he same second. Midquoe bid + ask =. 2 Page 11 of 47

12 frequency disribuion of all he esimaed daily resiliency values is shown in Table 1. 94% of he esimaed resiliency values are in he range from zero o one. This is consisen wih our assumpion (equaion 2.1) ha pricing error follows a mean-reversion process. The small fracion of ouliers may be caused by he esimaion errors inroduced by he noisy high-frequency marke daa. Kalman-filer esimaion procedure can also calculae he sandard deviaions of esimaed resiliency values, from which -values of hese esimaed resiliency esimaes could be obained. A small fracion - abou 10% - of he esimaes are no significan a 5% significan level (see Panel B a able 1). These insignifican values are mainly caused by lower ransacion frequency of several socks on some rading days. In he following analyses on he resiliency, we use only hose esimaed values, which are saisically significan a he 5% level, and lie wihin he range from zero o one. Summary descripive saisics of all he esimaed resiliency values are presened in able 2. The mean value of all he resiliency esimaes is 0.60 (0.65 for all significan values), which is economically and saisically differen from one and zero. This indicaes ha, alhough pricing error can exiss for a brief period, he pricing error process is saionary wih a finie mean value. Based on our resiliency se up, around 60% of he pricing error is correced, on average, in every one-minue period. Hence, marke prices rack underlying values closely. 4. Resiliency and is deerminans In his secion, several possible micro-srucural fundamenal facors, sock-specific ime-series and marke-relaed conrol facors are inroduced as possible deerminans of resiliency. They are daily number of ransacions, daily rading volume, daily price level (proxying for inverse of ick size), average ransacion size, daily average realized spread, daily informaive-ransacions raio, daily adverse-selecion raio, sock s marke capializaion, sock s oal risk (sandard deviaion of he daily reurn) and he overall resiliency of he marke as a whole. Time-series and cross-secion analyses are used o sudy he relaion beween hese facors and resiliency. 4.1 Inroducion of poenial deerminans An individual sock s resiliency could be mainly affec by wo groups of facors: micro-srucural fundamenal facors, and sock-specific or marke-relaed conrol facors. Page 12 of 47

13 The firs group of explanaory facors may reflec sock s rading frequency, ransacion size, ick-size effec, informaion asymmery level and liquidiy supplier revenues. Two represenaive variables for he rading frequency are daily rading volume and daily oal number of ransacions. The economic inuiion behind hese is obvious. If one sock is raded heavily and frequenly in he marke, any new informaion in rades will be incorporaed in prices more quickly in he marke hrough hese ransacions. And here are also more raders keeping close wach on i. If here is a emporary pricing error, i will be noiced by value raders and be eliminaed by heir profi-seeking behaviour as soon as possible. Thus, he rading volume and he number of ransacions should be posiively relaed o he sock s resiliency. Daily ransacion numbers and rading volume are calculaed for every sock a every rading day from he TAQ daabase. The main feaures of hese variables can be found in able 3. There is very high posiive correlaion (more han 0.7, see able 5) beween he daily number of ransacions and he daily rading volumes. In he mulivariae regression analysis, hese wo highly correlaed variables canno be used ogeher. Trading volume reflecs boh he sock s rading frequency and he average ransacion size, which will be used as a separae explanaory variable in he resiliency deerminans analysis. Hence, only he daily number of ransacions is seleced as he proxy for marke rading frequency. Price level is a commonly used variable for measuring relaive ick-size effecs. Since dollar ick-size usually remains sable, higher prices mean lower effecive ick sizes relaive o price level, and should arguably lead o value raders jumping in more quickly o neuralise pricing errors. Hence, ceeris paribus, price level should have a posiive relaionship wih resiliency. Neverheless, price level is significanly correlaed wih oher explanaory facors, such as number of ransacions and marke capializaion (see able 5), and his may inroduce confounding effecs. In his paper, he inverse value of price level is used as a measure of ick-size effec. We expec a negaive relaionship beween he inverse value of price level and marke resiliency. I is difficul o have a firm hypohesis on he relaionship beween average ransacion size and resiliency. On one hand, ransacion size can be aken as a proxy of he dealer s invenory risk level. The large average ransacion size is poenially relaed o larger average invenory imbalance of dealers, and may inroduce addiional pricing error caused by a dealer s invenory-risk-conrol managemen. This can make pricing- Page 13 of 47

14 error las for a longer period, and hereby reduce resiliency. A large average ransacion size is also an indicaor of more privae-informaion ransacions, and herefore can lead o a negaive relaionship beween resiliency and ransacion size. However, ransacion size is an indirec indicaor of he sock s aciviy. Bigger ransacion size also indicaes more acive markes and may be relaed poenially o higher resiliency. The acual relaionship beween ransacion size and resiliency is an empirical issue. The logarihm of average ransacion size a every rading day is used o measure ransacion size in his paper. Informaion asymmery is one of he main concerns in relaion o marke liquidiy in he microsrucure lieraure 7. Informaion asymmery is poenially an imporan deerminan in he pricing-error correcion process. Higher levels of informaion asymmery should arguably make value raders more cauious and increase heir uncerainy abou fundamenal values. All of hese can lead o he pricing-error correcion process becoming less responsive, and hereby reduce resiliency. There are several ways o measure he magniude of informaion asymmery. The probabiliy of informaion rade (PIN) is used by Easley, Nicholas and O Hara (1996a)(1996b), and by Easley, Hvidkjaer, and O Hara (2002) o measure informaion asymmery. However, his measure involves massive compuaion, and is dependen on specific heoreical models and sric assumpions. We use compuaionally and concepually simpler measures of informaion asymmery. They are informaiveransacions raio and he adverse-selecion raio. Boh of hese wo informaion asymmery measures are based on decomposing effecive spread ino realized spread and adverse-selecion spread. The informaive-ransacions raio measures he raio of informaive-ransacions o overall ransacion. The adverse-selecion raio is he raio of adverse-selecion spread o he overall effecive spread. Effecive-spread, which measures he explici ransacion cos, is he difference beween he ransacion prices and he corresponding mid-price. Effecive 2* Q *( P Midquoe ) i i i i = where Q i is he rade-direcion Miquoei indicaor, which akes he value 1 for a buyer-iniiaed ransacion, and -1 for a selleriniiaed ransacion. P is he real marke price for ransacion i, and Midquoe is he i i 7 Many heoreical (Kyle (1985), Glosen and Milgrom (1985)) and empirical works (Amihud 2002, Easley, Hvidkjaer and O Hara (2002)) analysed he effec of informaion asymmery on marke fricions, marke liquidiy, and even is relaion wih he marke reurn. Page 14 of 47

15 corresponding mid-quoe for his ransacion. The effecive-spread is he sum of he realised spread and he adverse-selecion spread (see Naik and Yadav, 2003) 8. The adverse-selecion spread is he average amoun los by liquidiy suppliers o informed raders expressed as a proporion of he mid-price, which is advserse 2* Qi *( Midquoei +τ Midquoei ) i =. The realized spread measures he cos of order Midquoe execuion or liquidiy supplying, excluding he effec of adverse-selecion. Re alized 2* Q *( P Midquoe ) i i i τ i = +, where τ is he ime-delay used o esimae he rue Midquoe marke-impac-free price a he ime of he rade. Three ime-lags are used in his paper o calculae boh realized and adverse-selecion spreads: 5-minues, 15-minues and 30- minues. The informaion-asymmery relaed informaive-ransacions raio is calculaed as ITR n i= 1 i = n i= 1 adverse adverse, i, i. The adverse-selecion raio, adversei ADraio i =, is a relaive measure effecivei of he level of adverse-selecion. 9 Higher hese raios, higher are he level of adverseselecion or informaion asymmery. We would expec marke resiliency o be negaively relaed o he informaive-ransacions raio and he adverse-selecion raio. The realized spread reflecs he gross rading revenue of liquidiy suppliers, and should be relaed o invenory risk and liquidiy-providing profi. Realized spread may be negaively relaed wih resiliency, for he invenory risk concerns, or posiively relaed wih resiliency, for he liquidiy-providing profi concerns. Hence, he relaionship beween realized spread and marke liquidiy is an empirical issue. In ables 4.1, 4.2, 4.3 and 4.4, summary saisics of he calculaed realized spread, informaive-ransacion raio, and adverse-selecion raio are presened. The main feaures of esimaion resuls wih hree differen ime-delays, 5-minue, 15-minue and 30-minue, are similar. So, only 15-minue ime-delay esimaion resuls of realized spread, informaive-ransacion raio adverse-selecion raio are used in he subsequen analyses in his paper. Besides hese micro-srucural facors, several sock-specific and marke-relaed facors are used as conrol variables in he muli-variae regression eses. Firs, marke 8 Bessembinder and Kaufman (1997) decomposed effecive-spread ino hree componens: order-processing cos, cos of invenory risk managemens, and adverse-selecion relaed coss. The sum of he firs wo componens can be aken as Naik and Yadav (2003) s realized spread. 9 Huang and Soll (1996), Bessembinder and Kaufman(1997), and Naik and Yadav (2003) also use similar measures of realized spread and adverse-selecion spread o measure he informaion asymmery level. Page 15 of 47

16 capializaion is used as he measure of firm size. Usually, large firms have beer marke ransparency, larger rading volume, and more analyss following. Hence, socks of firms wih larger marke capializaion should arguably be more resilien han socks of small firms. In his paper, marke capializaion for all he sample socks are calculaed using he COMPUSTAT Annual daa for year Second, sock s oal risk, as measured by unexpeced inra-day volailiy, is anoher sock-specific facor ha may affec sock s liquidiy. Higher risk should reduce he effors made by value raders o neuralise pricing errors since i implies greaer uncerainy abou rue fundamenal value. Tha should lead o a negaive relaionship wih resiliency. The unexpeced inra-day volailiy is esimaed as follows. Firs, inra-day volailiy is calculaed as he volailiy of all he available 5-miniue reurns a every rading day for every sock. This high-frequency inra-day volailiy may be overesimaed because of effec of bid-ask bounce. To exclude his bid-ask bound effec, he 5-minue reurns are calculaed from mid-quoe of las ransacion in every 5-minue period insead of real ransacion price. Second, he raw inra-day volailiy is regressed on daily number of ransacion and average ransacion size for every sock in he esimaion period. And residuals of hese ime-series regressions are aken as he unexpeced inra-day volailiy. Hence, his unexpeced volailiy reflecs mainly he firmspecific risk excluding he effec of sock s ransacion aciviy. Third, cross-secional correlaion beween individual sock s resiliencies, or he commonaliy in resiliency across socks, is examined by consrucing a marke resiliency measure. This is he rading-volume weighed average value of all he individual sock resiliencies on every rading day, excluding he sock for which a marke model in resiliency is esimaed. Tha is: Rmarke i, = w j,. R j,, where Rmarke i, is he marke j i resiliency for sock i a day. o he rading volume..r j, w j, is he weigh for sock i a day, and his is proporional is he value of resiliency a day for sock i. If individual sock resiliencies exhibi cross-secional commonaliy, an individual sock s resiliency should show significanly posiive correlaion wih marke resiliency. 4.2 Hypoheses ess Page 16 of 47

17 Bivariae correlaion analysis and muli-varaie regression ess are used o sudy he cross-secional and ime-series relaionships beween resiliency and hese inroduced poenial deerminans. Fama and MacBeh (1973) s cross-secion analyses procedures are used for he cross-secion analysis, and similar mehods are used for he ime-series analysis. Firs, following his procedure, he cross-secion/ime-series correlaion coefficiens/muli-variae regression coefficiens are esimaed for every specific rading day/sock. Then, ime-series/cross-secion average of all cross-secion/me-series correlaion/regression coefficiens calculaed. All bivariae cross-secion and ime-series correlaion coefficiens beween resiliency and all explanaory facors are given in Table 5. Daily number of ransacion is posiively correlaed wih he resiliency as we expeced. This relaion is much sronger in crosssecional analysis, wih larger -values and correlaion coefficien values. Alhough rading volume also shows significan posiive correlaion wih resiliency in crosssecional analysis, he correlaion becomes insignifican in ime-series analysis. Informaive-ransacions raio and adverse-selecion raio show significanly and srongly negaive correlaion wih resiliency boh in cross-secional and ime-series analysis. The inverse value of price level shows negaive relaion wih resiliency, which is consisen wih our expecaion. This relaion is much sronger in cross-secional analysis. The reason for his is ha price level or ick-size does no vary significanly in ime-series as i does in cross-secion. The size of he firm is posiively relaed wih marke resiliency in cross-secional bivariae correlaion analysis. This indicaes ha socks of larger firms are usually more resilien, as we expeced. The srong posiive correlaion beween an individual sock s resiliency wih is corresponding marke resiliency provides srong evidence of commonaliy in resiliencies. The daily average ransacion size shows weak negaive bivariae correlaion wih resiliency. This implies ha ransacion size is mainly an informaion asymmery/ invenory risk indicaor. Unexpeced inra-day volailiy is negaively relaed wih resiliency. When a sock is more volaile and risky, is resiliency is lower. Finally, average realized spread gives us significan posiive bivariae correlaion wih resiliency in ime-series analyses. This implies ha specialiss end o provide more liquidiy for he higher profi. Mulivariae Regression ess (cross-secion, ime-series) are used o make furher inferences on he relaionship beween hese possible deerminans and resiliency. In his Page 17 of 47

18 sep, rading volume is excluded because of is higher correlaion wih number of ransacions and oher explanaory variables. Daily ransacion numbers and average ransacion size are used as rading aciviy proxies. The mulivariae regression resuls are presened in Table 6. Generally, he mulivariae regression es resuls are consisen wih he bivariae correlaion coefficiens analyses resuls. Combining hese wo ables, we can infer ha: i) The price level (inverse of average price) has a negaive effec on resiliency, especially in cross-secion analysis. This indicaes ha lower ick-size leads o more resiliency, which is consisen wih our expecaion. ii) The number of ransacions, which measures he rading aciviy of he sock, has a posiive effec on resiliency. This effec is also much sronger, wih a large -value and parameers, in cross-secion analysis. iii) The average ransacion size has a significanly negaive effec on resiliency in boh cross-secion and ime-series analyses. iv) Individual sock s oal risk has a negaive effec on resiliency. This implies ha volailiy is relaed o more uncerainy on he sock s fundamenal values and reduce he effor of value raders. v) Individual sock s resiliencies display srong commonaliy across socks. And his co-movemen becomes sronger in he mulivariae analyses. vi) The posiive relaion beween he firms marke capializaion and resiliency becomes insignifican in mulivariae analysis. This can be parially explained by he high correlaion beween marke capializaion and oher facors like price level, average ransacion size and number of ransacions. vii) Effec of informaive-ransacions raios and adverse-selecion raios on resiliency becomes weaker and less significan when hey are combined wih realized spread. There is very high correlaion beween hese wo facors and realized spread. (see Table 5). Bu when hese wo facors are combined wih oher facors, hey sill show negaive effec on marke resiliency. Thus, informaion asymmery, which is measured by boh adverse-selecion raio and informaive-ransacions raio, is a significan deerminan of resiliency. Page 18 of 47

19 viii) Realized spread, which measures invenory/informaion asymmery risk, has a posiive effec on resiliency. This resul is robus and indicaes ha higher profi leads more acive liquidiy-providing ransacion of specialiss. Finally, saisically and economically significan inerceps are lef in hese mulivariae regression ess. (see able 6) 5. Combined analysis of marke liquidiy In his secion, we underake a comprehensive analysis of he relaion among he hree liquidiy dimensions: spread, deph and resiliency. Two quesions are addressed. Firs, wha is he relaion among hese hree dimensions? Second, could resiliency be explained in erms of hese oher liquidiy dimensions, or does i provide independen new informaion? 5.1 Descripion of oher liquidiy measures The firs dimension of liquidiy, spread, can be measured by wo kinds of measures: proporional spread and dollar spread. Dollar spreads refer o dollar value of he quoed spread and he effecive spread. Quoed i, = ask i, bid i, effecive (5.1) = 2 * Qi, * ( Pi, midquoei, i, ) (5.2). Where ask, bid are he quoed ask and bid prices, respecively. midquoe is he average of quoed bid and ask prices. P is he real ransacion price. Q i is he rade-direcion indicaor, which ake value 1 for he buyer-iniiaed ransacion and ake value 1 for he seller-iniiaed ransacion. Proporional or percenage spreads refer o raios of quoed/effecive spread o he mid-quoe level. Pr o Pr o ask bid i, i, quoed i, = (5.3) midquoe i, 2 * Q * ( P midquoe i, i, i, effecive i, = (5.4) midquoe i, ) Page 19 of 47

20 Daily average values of all hese four kinds of spread measured are calculaed over he same esimaion period. Summary saisics of daily proporional and dollar spreads are presened in Table 7. For boh proporional and dollar spreads, quoed spreads are higher han effecive spreads, which is consisen wih previous research. As effecive spread is a beer measure for he real ransacion coss, we use boh proporional and dollar effecive spreads in he subsequen analysis on spread in his paper. Marke deph is he measure of he marke s abiliy o absorb large ransacion orders. One direc measure of marke deph is quoed quaniy. Since we do no have access o hese daa, we use anoher deph measure, which is commonly used in marke microsrucure research, Kyle s Lambda value, which is inroduced by Kyle (1985). I reflecs he relaion beween he previous signed marke order-imbalance o he curren ransacion price changes. This Lambda can measure how much marke prices change afer a ransacion. If he Lambda value is higher, a given ransacion size will cause correspondingly bigger price changes, indicaing lower deph. Thus, Lambda is an inverse measure of deph. In his paper, a hree-facor model is used o esimae Kyle s Lambda from consruced one-minue fixed-inerval high-frequency daa. The model is specified as follow: Δ 2 p i, = μ i + α1, i. OIBi, 1 + α 2, i. OIBi, 1 + COIBi, 1 + ε i, (5.5) Where Δpi, = pi, pi, 1 is he price change a ime for sock i, OIB i, 1 is he signed order-imbalance in period -1. COIB i, 1 is he previous signed cumulaive orderimbalance, which is assumed o be zero a he beginning of he rading day. The las wo 2 facors, OIBi, 1 and COIB i, 1 are conrol variables for he non-linear relaion beween order imbalance and marke price changes. Lambda value is equal o value of coefficien on OIB, i, 1 α 1, i. Madhavan and Smid (1991) and Madhavan e al (1997) used unexpeced order imbalance insead of he oal order imbalance when esimaing Lambda values. We use he oal periodic signed order-imbalance o reduce he calculaion burden and avoid large esimaion errors inroduced by calculaing he unexpeced order imbalance. The same ransacion direcion caegorizaion rules, which are specified a secion 3.1, are used in he Lambda esimaion procedure. Mid-quoes are used here in place of real ransacion prices o reduce he effec of bid-ask spread on price changes. Lambda values are esimaed a each rading day for every sample sock. Frequency disribuion and Page 20 of 47

21 summary saisics of all he esimaed Lambda values are given in Table 8.1 and Table 8.2, respecively. From able 8.1, we find ha mos of he esimaed Lambda values are posiive (99.17%) The small fracion of negaive values are inconsisen wih economic inuiion, and may be caused by esimaion error or he noise inroduced by highfrequency daa. So, all hese negaive values are excluded in subsequen analyses. There are also a small fracion of Lambda values ha are insignifican (15.35%). In Table 8.2, he summary saisics of all esimaed Lambda values, which also include insignifican values, are similar o summary saisics of all significan esimaed Lambda values. So, we did no make any adjusmens for hese insignifican Lambda values. 5.2 Relaion among differen liquidiy measures: effecive-spread, lambda, and resiliency The bivariae correlaion coefficiens of all hese liquidiy measures and explanaory facors are calculaed and given in Table 9. Lambda shows posiive correlaion wih resiliency, while his posiive relaion is sronger in ime-series analysis wih boh higher -values and coefficiens. Looking a correlaions beween Lambda and explanaory facors, we find ha Lambda and resiliency are boh significanly affeced by all hese explanaory facors. The effec of price level, average ransacion size on he resiliency and deph, which is proporional o inverse value of Lambda, is opposie. When price level is high, resiliency is high and deph is lower. When he average ransacion size is large, resiliency is lower and deph is higher. Lambda is also highly posiively correlaed wih dollar effecive spread. (see able 9). And his correlaion beween Lambda and dollar effecive spread is much sronger han correlaion beween Lambda and resiliency, which is lower han Dollar effecive spreads also share he same se of explanaory facors wih resiliency. However, price level, average ransacion price, and ransacion number yield differen effec on he firs dimension of liquidiy, which is measured by inverse value of dollar effecive spread, comparing wih heir effecs on resiliency. When ransacion number is higher, marke spread is higher (see able 9) and resiliency is also higher. Correlaion beween dollar effecive spread and resiliency is posiive and sronger in cross-secion analysis. However, compared o correlaion beween dollar effecive spread and Lambda, his correlaion is very weak. Page 21 of 47

22 Proporional effecive spread also shares he same explanaory facors and similar effec of hese facors wih resiliency, especially in cross-secion analyses. Alhough, proporional effecive and dollar effecive spread are boh proxies for he firs liquidiy dimension, hey have very weak posiive cross-secion correlaions. (See able 9) I seems hey are cross-secionally independen, while hey show high posiive ime-series correlaion beween each oher. This can be explained by he fac ha cross-secional variaion of proporional spread is mainly affeced by sock s price level, while imeseries variaion of proporional spread is mainly driven by variaion of real ransacion coss. Correlaion beween Lambda and proporional effecive spread is also much lower han correlaion beween Lambda and dollar effecive spread. In all, we find ha resiliency, Lambda, proporional and dollar effecive spreads could be affeced by he same se of deerminans: daily ransacion number, daily rading volume, adverse-selecion raio, price level and average ransacion size. Variaion in any one of hese microsrucure facors changes all hese liquidiy measures. However, he effec of some explanaory facors, such as price level and ransacion size, varies across differen liquidiy measures. This variaion causes he firs liquidiy dimension, which is measured by dollar effecive spread, and second liquidiy dimension, which is measured by Lambda, o move ogeher. However, resiliency seems o move opposie o deph and spread. The correlaion beween resiliency and he oher wo liquidiy dimensions, dollar effecive spread and Lambda respecively, is very weak. All correlaion coefficiens beween resiliency and any oher liquidiy measure are less han 0.1 in magniude. To furher invesigae he relaion beween resiliency and oher hree liquidiy measures, mulivariae regression ess are used. We firs ran he cross-secion / imeseries regression on resiliency wih Lambda, proporional and marke spreads, combining wih all oher explanaory facors. Then, ime-series/ cross-secion average of regression coefficiens are repored in able 10. Lambda yields significan effec on resiliency, wih significan posiive coefficiens in regression ess. Is effec is sill significan when i is combined wih dollar and proporional effecive spreads. Relaion beween dollar effecive spread and resiliency becomes less significan in mulivariae regression resuls, especially when i is combined wih Lambda and proporional effecive spread. I seems ha main par of is relaion wih resiliency can be explained by he movemen of oher fundamenal marke facors. Proporional effecive spread ge similar relaion wih Page 22 of 47

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