UNIVERSITY of PIRAEUS Department of Banking and Financial Management Postgraduate Program

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1 UNIVERSITY of PIRAEUS Deparmen of Banking and Financial Managemen Posgraduae Program Maser Thesis: Trading aciviy and sock price volailiy: Evidence from he Greek sock marke by Mpoumpoukioi Efichia MXRH/0417 Members of Commiee: Dr. Ch. Chrisou (Supervisor) Dr. D. Maliaropoulos Dr. N. Kourogenis June 006

2 Maser Thesis: Trading aciviy and sock price volailiy: Evidence from he Greek sock marke by Mpoumpoukioi Efichia Members of Commiee: Dr. Ch. Chrisou (Supervisor) Dr. D. Maliaropoulos Dr. N. Kourogenis June 006

3 Trading aciviy and sock reurn volailiy: Evidence from he Greek sock marke. Acknowledgemens I would like o express my graiude firs of all o my supervisor Dr. Ch. Chrisou for her unreserved suppor o complee his disseraion and for he ideal collaboraion we had. Her posiive suggesions and commens were valuable and helped me significanly. I would also like o hank all he Professors eaching a he Posgraduae program in Banking and Finance for providing me wih all he essenial qualificaions needed o be able o develop his sudy. I am also graeful o my colleague Bouras Chrisos, who helped me in various sages in he compleion of his disseraion. This disseraion is dedicaed o my family as graiude for heir uncondiional love and suppor in all my effors. M.Sc. in Banking and Finance Page i

4 Trading aciviy and sock reurn volailiy: Evidence from he Greek sock marke. Conens Pages Lis of Tables iii Absrac iv 1. Inroducion 1. Exising Lieraure.1. Empirical Evidence.. Theoreical Explanaions 3.3. Summary of Theoreical Explanaions Recen Empirical Sudies Measures of volailiy Condiional Heeroskedasic Models The ARCH Model The GARCH Model The Inegraed GARCH Model The GARCH-M Model The Exponenial GARCH Model The Sochasic Model The Long-Memory Sochasic Volailiy Model Realized Volailiy Inraday Reurns Squared Reurns-Absolue Reurns 8 4. Daa and Preliminary Resuls Daa Descripion Descripive Saisics Tesing for uni roo Mehodology Conemporaneous Relaion The heeroskedasic Mixure Model and Arch GMM esimaion Dynamic relaionship Empirical Resuls Conemporaneous Relaionship The heeroskedasic Mixure Model and Arch GMM esimaion Dynamic relaionship 5 7. Summary and Conclusions 54 Appendix A 55 Appendix B 71 References 80 M.Sc. in Banking and Finance Page ii

5 Trading aciviy and sock reurn volailiy: Evidence from he Greek sock marke. Lis of Tables Table:1 Companies included in he sample and period of quoaion Table: Preliminary analysis of daily reurns Table:3 Correlaions coefficiens beween rading aciviy measures Table:4 Maximum Likelihood esimaion of he GARCH(1,1) wihou rading aciviy Table:5 Maximum Likelihood esimaion of he GARCH(1,1) wih rades Table:6 Maximum Likelihood esimaion of he GARCH(1,1) wih value Table:7 Maximum Likelihood esimaion of he GARCH(1,1) wih volume Table:8 Persisence in condiional sock reurn s volailiy Table:9 Regressions of R and various rading aciviy measures Table:10 Regressions of R and various rading aciviy measures Table:11 Regressions of condiional variance and various rading aciviy measures Table:1 Regressions of dayime volailiy and various rading aciviy measures Table:13 Regressions of R and various rading aciviy measures combinaions Table:14 Regressions of R and various rading aciviy measures combinaions Table:15 Regressions of condiional variance and various rading aciviy measures combinaions Table:16 Regressions of dayime volailiy and various rading aciviy measures combinaions Table:17 Number of rejeced null hypoheses based on he Granger causaliy es Table:18 Uni roo ess for rading aciviy measured as he as Table:19 Uni roo es for rading aciviy measured as he number of rades Table:0 Uni roo es for rading aciviy measured as he value of rades Table:1 Uni roo es for rading aciviy measured as he share volume Table: Uni roo es for volailiy measured as he absr ( R ) Table:3 Uni roo es for volailiy measured as he rr (R ) Table:4 Uni roo es for volailiy measured as he condiional variance Table:5 Uni roo es for volailiy measured as he dayime volailiy Table:6 Granger-causaliy es beween absolue reurn ( R ) and number of rades in he FTSE-0 socks Table:7 Granger-causaliy es beween absolue reurn ( R ) and value of rades in he FTSE-0 socks Table:8 Granger-causaliy es beween absolue reurn ( R ) and rading volume in he FTSE-0 socks Table:9 Granger-causaliy es beween condiional volailiy and number of rades in he FTSE-0 socks Table:30 Granger-causaliy es beween condiional volailiy and value of rades in he FTSE-0 socks Table:31 Granger-causaliy es beween condiional volailiy and rading volume in he FTSE-0 socks Table:3 Granger-causaliy es beween squared reurn (R ) and number of rades in he FTSE-0 socks Table:33 Granger-causaliy es beween squared reurn (R ) and value of rades in he FTSE-0 socks Table:34 Granger-causaliy es beween squared reurn (R ) and rading volume in he FTSE-0 socks M.Sc. in Banking and Finance Page iii

6 Trading aciviy and sock reurn volailiy: Evidence from he Greek sock marke. Absrac In his disseraion he relaionship beween rading volume and sock reurn volailiy is examined for he FTSE-0 Greek socks. By using differen measures of reurn volailiy and rading aciviy, his sudy invesigaes he conemporaneous and he causal rading aciviy-volailiy relaion as well. The main purpose of his paper is o explore no only if any relaion beween hese wo variables exiss bu also if his relaion is affeced by he differen measures of volailiy and rading aciviy used. Our calculaions provide evidence for a posiive conemporaneous ineracion and a feedback causal relaionship beween he wo variables. Furhermore, i is esed if volailiy persisence ends o disappear when he rading aciviy proxy is included in he condiional variance equaion. In accordance wih he findings from he US sock marke our empirical resuls show ha in he majoriy of cases GARCH effecs end o disappear when rading aciviy is included in he variance equaion. KEY WORDS: Trading aciviy, sock reurn volailiy, volailiy persisence, GARCH models, VAR, Granger-causaliy, FTSE-0 Greek socks. M.Sc. in Banking and Finance Page iv

7 Inroducion 1. Inroducion In recen years, here has been a renewed ineres in he relaion beween rading volume and he volailiy of share prices. Par of his ineres has been fueled by several episodes of high price volailiy coupled wih heavy rading volume in equiy markes. Anoher source of his ineres has been he emergence of a heoreical lieraure ha examines he ineracions of marke makers and speculaive, informed raders. Mos empirical research abou sock markes focuses on sock price movemens over ime. The sock price of a company reflecs invesors expecaions abou he fuure prospecs of he firm. New informaion causes invesors o change heir expecaions and is he main reason for sock price changes. Indeed, a necessary condiion for price movemen is posiive rading volume. Trading volume can be reaed as descripive saisics, bu may also be consider as an imporan source of informaion in he conex of he fuure price and price volailiy process. Prices and rading volume build a marke informaion aggregae ou of each new piece of informaion. Unlike sock price behavior, which reflecs he average change in invesors beliefs due o he arrival of new informaion, rading volume reflecs he sum of invesors reacions. Differences in he price reacions of invesors are usually los by averaging of prices, bu hey are preserved in rading volume. In his sense, he observaion of rading volume is an imporan supplemen of sock price behavior. However, he release of new informaion does no necessarily induce sock prices o move. One can imagine ha invesors may evaluae he news heerogeneously (as eiher good or bad). Think of a company ha announces an increase in dividend payou. Invesors may inerpre his as a posiive signal abou he fuure performance of he company and raise heir demand prices. On he oher hand, invesors ineresed in capial gains migh wish o sell he sock on he basis of his informaion, raher han receive dividend payous (e.g. due o ax reasons). On average, despie is imporance o individual invesors, such informaion does no noiceably affec prices. Anoher siuaion in which new informaion migh leave sock prices unalered can arise if invesors inerpre he news homogeneously bu sar wih differen prior expecaions (e.g. due o asymmerically disribued informaion). One can conclude ha sock prices do no mirror he informaion conen of news in all cases. Earlier works are moivaed in par by he evens on he sock marke, which sugges ha more can be learned abou he marke and, in paricular, abou volailiy by sudying prices in conjuncion wih volume, insead of prices alone. I is also moivaed by an objecive of providing a full se of sylized facs ha heoreical work will ulimaely have o comfor. Because of he limiaions of exising heory, he empirical work is no organized around he specificaion and esing of a paricular model or class of models. Insead, he empirical effor is mainly daa-based. Knowledge of he dynamic relaionship beween volailiy and volume is essenial for undersanding he informaion assimilaion process, marke efficiency and liquidiy. There are a leas four reasons why he price-volume relaion is imporan. Firs, i provides insigh ino he srucure of financial markes. The empirical models predic various price-volume relaions ha depend on he rae of informaion flow o he marke, how he informaion is disseminaed, he exen o which marke prices convey he informaion, he size of he marke and he exisence M.Sc in Banking and Finance Page 1

8 Exising Lieraure of shor sales consrains. Empirical relaions beween prices and volume can help discriminae beween differing hypoheses abou marke srucure. Second, he price volume relaion is imporan for even sudies ha use a combinaion of price and volume daa from which o draw inferences. If price changes and volume are joinly deermined, incorporaing he price volume relaion will increase he power of hese ess. In oher ess, price changes are inerpreed as he marke evaluaion of new informaion, while he corresponding volume is considered an indicaion of he exen o which invesors disagree abou he meaning of he informaion. The consrucion of ess and validiy of he inferences drawn depend on he join disribuion of price changes and volume. Third, he price-volume relaion is criical o he debae over he empirical disribuion of speculaive prices. Knowledge of he price-volume relaionship can be used in even sudies o measure changes in he variance of he price process from non-even o even ime. And fourh, price-volume relaions have significan implicaions for research ino fuure markes. Price variabiliy affecs he volume of rade in fuure conracs. The price-volume relaion can also indicae he imporance of privae versus public informaion in deermining invesors demands. The objecive of his sudy is very specific. We concenrae on he role of rading aciviy in he process ha generaes sock reurn volailiies on he Greek sock marke. Unlike mos oher sudies on his issue, we use individual sock daa insead of index daa. Our invesigaion covers no only conemporaneous bu also dynamic (causal) relaionships because we are ineresed in wheher rading aciviy can be regarded as a prognosis of sock reurn volailiies. One imporan difference disinguishing his sudy from conribuions in he exising lieraure is he variey of proxies used o approach rading aciviy and reurn volailiy. The remainder of he paper is organized as follows. Secion conains a brief overview of he exising lieraure on he relaionship beween sock reurn prices/volailiies and rading aciviy. The secion afer explains why is imporan o model volailiy and how i can be modeled or measured. The fourh secion describes he daa se and repors some preliminary resuls. In secion 5 he models used in his sudy are specified. Secion 6 presens he empirical resuls on he volailiy-rading aciviy relaion for several alernaive measures of reurn volailiy and aciviy and provides a discussion of he findings and heir implicaions. Concluding remarks are conained in Secion 7.. Exising Lieraure.1. Empirical Evidence I is an old Wall Sree adage ha I akes volume o make prices move. Alhough one can quesion he assered causaliy, numerous empirical findings suppor wha would be could here a posiive volume-absolue price change correlaion. Academic reamen of a price-volume relaion can be raced o Osborne (1959), who aemped o model he sock price change as a diffusion process wih variance dependen on he number of ransacions. This could imply a posiive correlaion beween volume (V) and volailiy ( p ), as laer developed by Clark (1973) and Tauchen and Pis (1983). However, by assuming ransacions are uniformly disribued in ime, Osborne was able o reexpress he price process in erms of ime inervals, and did no direcly address he volume price issue. M.Sc. in Banking and Finance Page

9 Exising Lieraure An early empirical examinaion of he volume price relaion was conduced by Granger and Morgensern (1963). Using specral analysis of weekly daa from , hey could discern no relaion beween movemens in a Securiies and Exchange Commission composie price index and he aggregae level of volume on he New York Sock Exchange. Daa from wo individual socks also displayed no price-volume relaion. In 1964, Godfrey, Granger and Morgensern presened new evidence from several daa series, including daily and ransacion daa for individual socks. Bu once again hey could find no correlaion beween prices or he absolue values of price differences and volume. Anoher finding by Godfrey, Granger and Morgensern is ha daily volume correlaes posiively wih he difference beween he daily high and he daily low. This is suppored by heir laer finding ha daily volume correlaes wih he squared difference beween he daily open and close. The auhors aribue his correlaion o insiuional facors such as sop-loss and buy-above-marke orders ha increase volume as he price diverges from is curren mean. The failure of Godfrey e al. o uncover price-volume relaion moivaed he empirical es of Ying (1966). Ying applied a series of chi-squared ess, analyses of variance, and cross-specral mehods o six-year (1957 o 196), daily series of price and volume. Prices were measured by he Sandard and Poor s 500 composie index adjused for dividend payous, and volume by he proporion of ousanding NYSE shares raded. The following lis is a subse of his findings: A small volume is usually accompanied by a fall in price. A large volume is usually accompanied by a rise in price. A large increase in volume is usually accompanied by eiher a large rise in price or a large fall in price. A large volume is usually followed by a rise in price. If he volume has been decreasing consecuively for a period of five rading days, hen here will be a endency for he price o fall over he nex four rading days. If he volume has been increasing consecuively for a period of five rading days, hen here will be a endency for he price o rise over he nex four rading days. Ying s empirical mehods are easily criicized. One problem arises because he price series (S & P s 500 index) and volume series (NYSE percenage volume) he used are no necessarily comparable. A second problem arises from his adjusmens o he daa for dividends and oal NYSE shares ousanding. Ying s daily price series was adjused by quarerly dividend daa, and he daily volume series was adjused by monhly daa on he number of ousanding shares, each using linear inerpolaions. Also, several of Ying s findings are inconsisen wih weak form marke efficiency. However, iems (1) and () sugges V and p are posiively correlaed, and iem (3) is consisen wih a correlaion beween V and p. Thus, Ying was he firs o documen boh price-volume correlaions in he same daa se... Theoreical Explanaions I is rue ha here is lile evidence in his area. A major limiaion has been he lack of subsanial heory linking rading aciviy direcly o sock reurns. There are wo heoreical explanaions for he observed volume-volailiy relaions of socks. M.Sc. in Banking and Finance Page 3

10 Exising Lieraure An early work dedicaed o he role or rading volume in he price generaing process is ha by Clark (1973). He developed he well known Mixure of Disribuion Hypohesis (MDH). Clark saes ha sock reurns and rading volume are relaed due o he common dependence on a laen informaion flow variable. According o Clark, he more informaion arrives on he marke wihin a given ime inerval, he more srongly sock prices end o change. Clark advises he use of volume daa as a proxy for he sochasic (informaion) process. Under he MDH he daily sock reurn r and he daily rading volume V is he sum of a random number of individual price incremens and volumes. This random number depends on he rae of informaion arrival during he day. Each ime ha informaion arrives o he marke, raders adjus he equilibrium price and here is above average rading aciviy in he marke as i adjuss o he new equilibrium. Assuming each inraday reurn is idenically and independenly disribued (i.i.d.) wih mean zero and variance σ, he join disribuion of daily reurns and rading volume is a bivariae normal condiional on he daily number of informaion arrivals, I, ( 0, ) r Ι ~ Ν σ I (.1) ( bi ci ) V I ~ N, (.) I follows from he above equaions ha he dynamics of he volailiy process of reurns are dependen on he ime series behavior of I which also affecs he dynamics of rading volume. From he MDH assumpion i follows ha here are srong posiive conemporaneous bu no causal linkages beween rading volume and reurn volailiy daa. Under he assumpions of he MDH model, innovaions in he informaion process lead o momenum in sock reurn volailiy. A he same ime, reurn levels and volume daa exhibi no common paerns. The heoreical framework developed by Clark has been generalized among ohers by Epps and Epps (1976), Tauchen and Pis (1983), Andersen (1996) and Lamoureoux and Lasrapes (1990). In a firs form of he MDH, ha of Clark (1973), and Tauchen and Pis (1983) he daily price change p is he sum of a variable number m of independen wih-in day price changes. Thus, he variance of he daily price change is a random variable wih a mean proporional o he mean number of daily ransacions. For a given m, he Cenral Limi Theorem implies ha p is approximaely normal wih variance proporional o m. For a variable m however, he Cenral Limi Theorem is applicable and he disribuion of p is subordinae o he disribuion of m 1 (finievariance subordinaion model). I is inuiively aracive o inerpre m as he number of wihin-day informaion arrivals, so he condiional variance of p is considered o be an increasing funcion of he rae a which new informaion eners he marke. The V, p correlaion resuls because volume is also an increasing funcion of he number of wihin-day price changes. Clark argues ha he rading volume is relaed posiively o he number of wihin-day ransacions, and so he rading volume is relaed posiively o he variabiliy of he price change. The cenral proposiion of he models by Clark, and Tauchen and Pis is ha ransacion ime inervals are variable. There is also some empirical suppor for his 1 See Clark (1973) for discussions of subordinaed process. Loosely, he disribuion of he daily change is subordinae o ha of m because is parameers are funcions of m. M.Sc. in Banking and Finance Page 4

11 Exising Lieraure conenion. Clark s ess use daily daa from he coon fuures markes and volume as a proxy variable for he number of ransacions variable m, and show ha he lepokurosis in he empirical disribuion of daily price changes largely disappears when he changes are grouped by volume classes. The hypohesis ha ransacions ime differs from calendar ime provides insighs ino several relaed marke phenomena. The Tauchen and Pis (1983) model implies ha he volume-volailiy correlaion increases wih he variance of he daily rae of informaion flow, and ha, as he raders number increases, he volume of rade increases and price variabiliy decreases. The reason for his is ha he marke price change during a single marke clearing is he average of he changes in he raders reservaion prices. More erms in he average end o wash ou he effecs of iner-rader differences. This laer predicion is consisen wih evidence from he 90- day Treasury bill fuures marke daily daa. In a second form of he MDH, Epps and Epps (1976) derive a model, which implies sochasic dependence beween ransacion volume and he change in he logarihm of securiy price from one ransacion o he nex since he variance of he price change on a single ransacion is condiional upon he volume of ha ransacion. The change in he logarihm of price can herefore be viewed as following a mixure of disribuions, wih ransacion volume as he mixing variable. For common socks hese disribuions (of which he disribuion of log(p) is a mixure) appear o have a pronounced excess of frequency near he mean and a deficiency of ouliers, relaive o he normal. These findings are consisen wih he hypohesis ha sock price changes over fixed inervals of ime follow mixures of finie-variance disribuions. While heir resuls suppor Clark s view ha he variance of he change in log price depends on volume, i is worh poining ou ha heir findings do no by hemselves rule ou he possibiliy ha he change in log price over fixed inervals of ime (Y) has infinie variance. The Epps and Epps model is similar o he sequenial informaion arrival model, which is discussed below, in ha i places a paricular srucure on he way invesors receive and respond o informaion. Epps and Epps provide empirical suppor for heir conenion ha a volume-volailiy correlaion occurs a he ransacion level by using ransacions daa from 0 N.Y.S.E. common socks. The Clark and Epps and Epps models are complemenary and hey give considerable insigh ino he behavior of speculaive markes. Ye, even when aken ogeher, he wo models provide a descripion of speculaive markes ha is incomplee and can be exended in wo direcions. Firs, boh models work wih he condiional disribuion of he square of he price change over a shor inerval of ime, P, given he volume of rading, V, for he same inerval of ime. Applicaion of eiher model requires he invesigaor o specify in advance or discover by nonlinear regression he funcional form of he condiional expecaion, Ε [ P V ]. On he conrary, he Tauchen and Pis model eliminaes he need for his. The heory gives an explici expression for he join probabiliy disribuion of he price change and he rading volume over any inerval of ime. The join disribuion conains all relevan informaion abou he price variabiliy-volume relaionship. Specifically, i deermines he condiional disribuion of he price change given he volume and he condiional absolue momens of all orders. Second, neiher model considers growh in he size of speculaive markes such as ha experienced by many of he new financial fuures markes. Trading on a new marke is iniially very hin. If he marke is viable, hen he rading volume increases secularly as more raders become aware of he marke s possibiliies. Evenually a seady sae is reached. The empirical resuls of oher M.Sc. in Banking and Finance Page 5

12 Exising Lieraure sudies sugges ha price variabiliy should increase wih he growh in he rading volume. This seems unlikely. In fac, one migh conjecure ha more raders would end o sabilize prices. A major difference beween he Tauchen and Pis model and ha of Epps and Epps is he way in which hey connec he price change o he rading volume. Epps and Epps s key assumpion gives hem a nearly exac posiive relaionship beween he absolue value of he change in he marke price and he rading volume on each wihin day marke clearing. Tauchen and Pis do no invoke heir assumpion. Insead, hey use a variance-componens scheme o model he wihin-day revisions of raders reservaion prices. This allows hem o derive he join probabiliy disribuion of he price change and he rading volume for each wihin-day marke clearing. Adding he random number of wihin-day price changes and volumes gives he daily values of each variable. The resul is a bivariae normal mixure model wih a likelihood funcion ha depends only on a few easily inerpreed parameers. I should be noed ha, while he Epps and Epps (1976) model requires all invesors o receive informaion simulaneously, he Clark, and Tauchen and Pis models can be muually consisen wih sequenial informaion arrival. While hese models imply simulaneous dispersion of an informaion bi, hey do no require i. The successive equilibria presumed by hese models can resul from a gradual disseminaion of a single bi of informaion, as in he sequenial informaion arrival model (SIAM), which is discussed below, or from a process in which invesors receive informaion simulaneously. These models are also more general han he SIAM, for wo reasons. Firs, hey are consisen wih eiher simulaneous or gradual informaion disseminaion, while Copeland s model implies a negaive V, p correlaion when simulaneous informaion arrival is supposed. And second, hey explain greaer number of phenomena. The MDH is consisen wih he empirical disribuion of price changes and he difference in he V, p correlaion over differen frequencies. Laer, Andersen (1996) developed a model of he daily reurn-volume relaionship by inegraing he marke microsrucure seing of Glosen and Milgrom (1985) wih he sochasic volailiy, informaion flow perspecive of he MDH. A firs, he join disribuion is derived via weak condiions on he informaion arrival process. Subsequenly, he model is expanded ino a full dynamic represenaion by providing a specific sochasic volailiy process for he informaion arrivals. Boh represenaions are esimaed and esed for five major individual common socks on he New York Sock Exchange over he period The main conribuions of his aricle are as follows. Firs, he developes modificaions o he sandard MDH ha arise naurally from he microsrucure seing, in which informaional asymmeries and liquidiy needs moivae rade in response o he arrival of new informaion. The specificaion is generally consisen wih he Mixure of Disribuions Hypohesis for asse reurns, alhough he volume equaion differs from sandard specificaions. This is due o an accommodaion of microsrucure feaures as well as a Poisson, raher normal, approximaion o he limiing disribuion of he binomial process ha drives he rading volume. Second, he reinforces he recen empirical findings by resoundingly rejecing he resricions ha he sandard MDH imposes on conemporaneous reurn-volume observaions, while conrolling for he rend in Glosen and Milgrom (1985) develop a sequenial rading model wih informed and uninformed invesors and find ha marke makers and uninformed invesors experience adverse selecion when rading wih informed invesors. By assumpion, each invesor is allowed o ransac one uni of sock per uni of ime, so price changes are compleely independen of rade size. M.Sc. in Banking and Finance Page 6

13 Exising Lieraure volume and using a long sample. In conras his alernaive version of he MDH provides an overall accepable characerizaion of hese feaures of he daa, so he general framework of he MDH may ye provide a useful basis for srucural modeling of he ineracion of marke variables in response o informaion flows and, ulimaely, he sources of reurn volailiy. Third, he demonsraes ha a sochasic volailiy represenaion of he informaion arrival process ha generalized he popular GARCH(1,1) resuls in a dynamic specificaion of he join sysem ha is consisen wih he main conemporaneous as well as dynamic feaures of he daa. Fourh, he documens ha, in spie of he overall saisfacory fi, he simulaneous incorporaion of reurns and volume daa resuls in a significan reducion in he esimaed volailiy persisence relaive o he usual resuls obained from univariae reurns series. Easley and O Hara (1987), also, exends Glosen and Milgrom model o allow raders o ransac a varying rade sizes and inroduced uncerainy in he informaion arrival process of he informed rader. When invesors ac compeiively, Easley and O Hara find ha larger-sized raders end o be execued by beer informed invesors, so ha larger rades exhibi a greaer adverse selecion effec. In paricular, hey showed ha an adverse selecion problem arises because, given ha hey wish o rade, informed raders prefer o rade larger amouns a any given price. Since uninformed raders do no share his quaniy bias, he larger he rade size, he more likely i is ha he marke maker is rading wih an informed rader. This informaion effec dicaes ha he marke maker s opimal pricing sraegy also depends on quaniy, wih large rade prices reflecing his increased probabiliy of informaion-based rading. In heir model, rade size affecs securiy prices because i changes percepions of he value of he underlying asse. Thus, here is a posiive relaion beween rade size and price volailiy. In criically evaluaing he Easley and O Hara model, heoriss have observed ha raders are no allowed o ac sraegically, which could resul in large blocks being broken up ino a number of smaller rades. If informed invesors are allowed o sraegically breakup orders as in Admai and Pfleiderer (1988), hen he effec of rade size on price volailiy is aenuaed and is impac may be shifed o he number of rades. Supporing his view, Barclay and Warner (1993) repor empirical evidence from he NYSE consisen wih informed invesors breaking up large rades so as o beer hide heir informaion moivaed rading aciviy. Their evidence is based on how influenial rades of various sizes are on price changes. Indeed, hey found ha mos of he sample securiies preannouncemen cumulaive sock-price change occurs on medium-size rades. This evidence is consisen wih he hypohesis ha informed rades are concenraed in medium sizes and ha price movemens are due mainly o informed raders privae informaion. These resuls appear more general because hey also apply o a noneven period long before he sample securiies experience sysemaic unusual behavior, and o a sample of all NYSE securiies. Based on Admai and Pfleiderer model, Foser and Viswanahan (1995) presen a model of speculaive rading ha predics condiional heeroskedasiciy in rading volume and he variance of price changes and posiive auocorrelaion in rading volume. They use speculaive rading model in which a lognormal laen variable is used o mix condiionally normal parameers, hereby generaing persisence in rading volume and squared price changes. Using momen condiions from he model, hey esimae is parameers for IBM in Alhough, hey rejec he model, we learn several hings. I appears ha many informed raders pay lile o receive relaively imprecise informaion and ha he bulk of rading comes due o inense compeiion beween hese informaion raders. Hence i may be he case ha M.Sc. in Banking and Finance Page 7

14 Exising Lieraure he maerial informaion abou IBM is revealed hrough public disclosure and here is much less privae informaion for IBM ha is revealed hrough rading. Moreover, i appears ha he model is unable o explain he relaion beween curren rading and lags of rading volume and squared volume s relaion o squared price changes. Afer scaling hese values by heir sandard errors i is less clear ha hese momen condiions are responsible for he model s demise. An imporan model explaining he arrival of informaion on a marke is he sequenial informaion arrival model inroduced by Copeland (1976). I implies ha news is revealed o invesors sequenially (informaion is disseminaed only o one rader a a ime) raher han simulaneously. This causes a sequence of ransiional price equilibrium which is accompanied by a persisenly high rading volume. The mos imporan conclusion from his model is ha here exis posiive conemporaneous and causal relaionships beween price volailiy and rading aciviies. Copeland (1976) presened a new echnique for demand analysis under he key assumpion ha individuals shif heir demand curves sequenially as new informaion is revealed o hem. The informaion causes a one ime-upward shif in each opimis s demand curve by a fixed amoun δ and a downward shif of δ in each pessimis s demand curve. Trading occurs afer each rader receives he informaion, bu uninformed raders do no infer he conen of he informaion from informed raders acions. Also, shor sales are prohibied. Wih N raders, here will in general be k opimiss, r pessimiss, and N-k-r uninformed invesors a any poin in ime before all invesors become informed. The values of k and r depend on he order in which invesors become informed. Because of he shor sales prohibiion, volume generaed by a pessimis is generally less han ha generaed by an opimis (i.e., he pessimis canno sell shor upon receiving he informaion). So he price change and he rading volume when he nex rader becomes informed depend upon boh (i) he previous paern of who has been informed and (ii) wheher he nex rader is an opimis or pessimis. Likewise, he oal volume afer all raders become informed depends on he pah by which he final equilibrium is reached. The expeced volume for each possible sequence beween he iniial and final equilibria is weighed by is probabiliy, and hen he probabilisically weighed pahs are summed in order o derive he expeced number of rades given N, he oal number of rades, S, he number of shares ousanding, δ, he srengh of new informaion, and j*, he number of opimiss among N raders. I was heoreically demonsraed ha he expeced number of rades is a logarihmically increasing funcion of he number of rades and of he srengh of new informaion. I is a concave funcion of changes in he number of shares ousanding, and a U-shaped funcion of he percen of opimiss. By assuming ha he percenage of opimiss was symmerically disribued wih mean 0.5 i was possible o show ha he sequenial informaion model prediced a posiive correlaion beween he absolue value of price changes and volume, posiive skewness in he disribuion of volume, and increasing posiive skewness as a funcion of he srengh of new informaion. Simulaion ess indicae ha volume (V) is highes when invesors are all opimiss or all pessimiss. Also he absolue value of price changes ( p ) is lowes a he same percenage of opimiss a which volume is lowes, and rises wih volume. This suppors a posiive correlaion of volume and volailiy. This model is open o a leas wo criicisms. Firs, is he assumpion ha prohibis raders from learning from he marke price as oher raders become informed. Second is he implicaion ha volume is greaes when all invesors agree M.Sc. in Banking and Finance Page 8

15 Exising Lieraure on he meaning of he informaion. This is conrary o he inference drawn from high measures of volume. Copeland aribues his o he shor sales consrain, bu ha is only par of he sory. Also imporan is raher peculiar inerpreaion of disagreemen among raders, who are forced ino a binary response o new informaion. In an exension of Copeland s model (SIAM) o incorporae real world margin consrains and shor selling, Jennings, Sarks, and Fellingham (1981) provide an alernae heory consisen wih he correlaion beween V and p. In previous informaional sudies using equilibrium analysis, all marke paricipans are assumed o become informed simulaneously. The sequenial informaion arrival model assumes ha only one rader observes he informaion iniially. This rader inerpres he news, revises his beliefs, and rades o arrive o a new opimal posiion. The oucome of his series of evens is he generaion of ransacion volume and a new equilibrium price. Afer he marke arrives a his new equilibrium, he nex invesor becomes informed and, afer a similar sequence of evens, a second emporary equilibrium is achieved. This process coninues unil all raders are informed and resuls in a series of momenary equilibria. When he las rader receives he informaion, he marke reaches a final equilibrium. The sequenial process allows one o observe he pah of rades, prices, and volume. In addiion i provides a more realisic model for mos informaion evens. The key innovaion in heir model is ha shor posiions are possible bu are more cosly han long posiions, which implies ha he quaniy demanded of an invesor wih a shor posiion is less responsive o price changes han he quaniy demanded of an invesor wih a long holding. They showed ha, for many cases, he volume ha resuls when a previously uninformed rader inerpres he news pessimisically is less han when he rader is an opimis. Since price decreases wih a pessimis (who sells) and increases wih an opimis (who buys), i is argued ha volume is relaively high when he price increases and low when he price decreases. While is inconsisen wih he empirical correlaion beween V and p, his model is subjec o he same criicisms as Copeland s. In a framework which assumes sochasic flucuaions of sock prices, recen sudies, e.g. by Blume, Easley and O Hara (1994) and Suominen (001) sae ha daa concerning rading volume deliver unique informaion o marke paricipans; informaion ha is no available from prices. Blume e al. in heir invesigaion over he informaional role of volume develop a new equilibrium model in which aggregae supply is fixed and raders receive signals wih differing qualiy. They argue ha informed raders ransmi heir privae informaion o he marke hrough heir rading aciviies. Uninformed raders can draw conclusions abou he reliabiliy of informaional signals from volume daa ha canno be deduced from he price saisic. They also show ha raders who use informaion conained in marke saisics do beer han raders who do no. Thus, i can be inferred ha volume plays a role beyond simply being a descripive parameer of he rading process. Therefore, reurn volailiy and rading volume show ime persisence even in a case where he arrival of informaion does no show i. As do Blume e al., Suominen (001) applies a marke microsrucure model in which rading volume is used as a signal o he marke by uninformed raders. I explains why rading volume conains useful informaion for predicing volailiy and can help o reduce informaion asymmeries. Specifically, his paper sudies an asse marke where he availabiliy of privae informaion is sochasically changing over ime due o changes in he source of uncerainy in he asse reurns. In equilibrium, liquidiy raders and speculaors use pas periods rading volume o esimae he availabiliy of privae informaion. As he public esimae on he availabiliy of privae informaion increases, liquidiy raders M.Sc. in Banking and Finance Page 9

16 Exising Lieraure become wary and sar posing more conservaive limi orders. Iniially, he number of informed raders increases bu, in response o more conservaive rading by liquidiy raders, i may subsequenly decrease. Because he rading by informed raders reveals privae informaion, here is a posiive correlaion beween price variabiliy and rading volume. He shows ha he condiional variance is auocorrelaed and mean revering and ha i may be eiher posiively or negaively correlaed wih he expeced rading volume and ha price changes are no sufficien saisics o characerize he evoluion of condiional variance, bu ha informaion on rading volume is also needed. In many ways his paper is a heoreical exension of he MDH model. These wo sudies argue ha rading volume describes marke behavior and influences marke paricipan s decisions. Boh auhors sugges srong relaionships, bu no only conemporaneous bu also causal, beween volume and reurn volailiy. These wo papers also develop models in which raders use previous periods rading volume o make inferences abou he qualiy of informed raders signals, which is imporan for esimaing he payoff o he securiy..3. Summary of heoreical explanaions The wo heoreical explanaions for he observed volume-volailiy relaions of socks are he sequenial informaion arrival hypohesis (SIAH) of Copeland (1976), Jennings e al. (1981); and he Mixure of Disribuion Hypohesis (MDH) advanced by Clark (1973), Tauchen and Pis (1983), and Andersen (1996). SIAH assumes ha raders receive new informaion in a sequenial, random fashion. From an iniial posiion of equilibrium where all raders possess he same se of informaion, new informaion arrives in he marke and raders revise heir expecaions accordingly. However, raders do no receive he informaion signals simulaneously. Reacions of differen raders o informaion are pars of a series of incomplee equilibria. Once all raders have reaced o he informaion signal, a final equilibrium is reached. The sequenial reacion o informaion in he SIAH suggess ha lagged values of volailiy may have he abiliy o predic curren rading volume, and vice versa. On he oher hand, he MDH implies an alernaive volailiy-volume nexus, in which he relaion is criically dependen upon he rae of informaion flow ino he marke. The model assumes ha he join disribuion of volume and volailiy is bivariae normal condiional upon he arrival of informaion. All raders simulaneously receive he new price signals. As such, he shif o a new equilibrium is immediae and here will be no inermediae parial equilibrium. This is conrary o he SIAH, which assumes ha here are immediae equilibria en roue o he final equilibrium. Thus, under he MDH, here should be no informaion conen in pas volailiy daa ha can be used o forecas volume or vice versa since hese variables conemporaneously change in response o he arrival of new informaion. While having some success in characerizing he empirical behavior of volailiy and volume, he MDH model has is limiaions. For example, he model does no allow for serial dependence in reurn volailiy and volume, condiional on he underlying informaion flow. Furhermore, he model does no accoun for he effec of ime duraion beween rades. M.Sc. in Banking and Finance Page 10

17 Exising Lieraure.4. Recen Empirical Sudies These heoreical conribuions have been accompanied by a number of empirical sudies which deal wih volume-price relaionships on capial markes. Karpoff (1987) concludes from a review of prior empirical lieraure ha volume and changes in absolue reurns are posiively associaed, bu ha his associaion weakens as he measuremen inerval shorens. More recen suppor for his relaion is found in Jain and Joh (1988), Hiemsra and Jones (1994), Lee and Rui (00), Gallan, Rossi and Tauchen (199), Lamoureoux and Lasrapes (1990), Foser and Vishwanahan (1995) and Andersen (1996). Jain and Joh (1988) analyze hourly rading volume on he New York Sock Exchange and hourly reurns on he Sandard and Poor s 500 index for he years 1979 o 1983 in order o invesigae he join generaing process for hourly common sock rading volume and reurns. The resuls showed a srong posiive conemporaneous rading volume and absolue value of reurns and are consisen wih he MDH (Mixure of Disribuion Hypohesis). The resuls also show ha he average rading volumes across six rading hours of he day and across days of he week differ significanly. Specifically, average volume is highes during he firs hour, declines monoonically unil he fourh hour, bu increases again on he fifh and he sixh hours, while average daily rading volume is lowes on Monday, increases monoonically from Monday o Wednesday, and hen declines monoonically on Thursday and Friday. Moreover, common socks reurns differ across rading hours of he day. On average, larges sock reurns occur during he firs (excep on Monday) and he las rading hours. In heir aricle Hiemsra and Jones (1994) use linear and nonlinear Granger causaliy ess o examine he dynamic relaion beween aggregae daily sock prices and rading volume. They apply he ess o daily Dow Jones sock reurns and percenage changes in NYSE rading volume over he 1915 o 1946 and 1947 o 1990 periods. Their ess provide evidence of significan bidirecional nonlinear Granger causaliy beween sock reurns and rading volume in boh sample periods. They also examine wheher he nonlinear causaliy from volume o sock reurns deeced by heir es could be due o volume serving as a proxy for daily informaion flow in he sochasic process generaing sock reurn variance. Afer conrolling for simple volailiy effecs, he es coninues o provide evidence of significan nonlinear Granger causaliy from rading volume o sock reurns. Their resuls conribue o he empirical lieraure on he sock price-volume relaion by indicaing he presence of bidirecional nonlinear Granger causaliy beween aggregae daily sock prices and rading volume. Using daily daa, Lee and Rui (00) examine causal relaions no only beween sock marke rading volume and price changes bu also beween volume and volailiy of reurns boh in domesic and inernaional markes and invesigae dynamic effecs among hese variables of he hree larges sock markes: New York, Tokyo, and London. They include volailiy in heir analysis as well as reurn and volume in par because i is possible ha he dynamic relaion beween reurn and volume may be affeced by volailiy effecs associaed wih informaion flow and in par because volailiy is a key ingredien of he risk-reurn radeoff ha permeaes modern financial heories. The following bivariae vecor auoregression (VAR) M.Sc. in Banking and Finance Page 11

18 Exising Lieraure model 3 is used o es for causaliy beween he wo variables among rading volume, sock reurns and volailiy of sock reurns: m n = α 0 + α i χ i + β i i i= 1 i= 1 m n = γ 0 + γ i χ i + δ i y 1 + η i= 1 i= 1 χ y + ε y (.3) (.4) Lee and Rui s evidence shows ha rading volume does no Granger-cause sock marke reurns on each of he markes since rading volume does no add significan predicive power for fuure reurns in he presence of curren and pas reurns. However, volume helps predic reurn volailiy and vise versa. Taken ogeher, rading volume helps predic he volailiy of reurns bu no he level of reurns. Gallan, Rossi and Tauchen (199) use a differen approach o invesigae he price and volume co-movemen. They use nonparameric mehods. The main reason for doing his is o avoid bias due o a specificaion error. They uilize daily daa on he S&P composie index and oal NYSE rading volume from 198 o 1987 and found ha he daily rading volume is posiively and nonlinearly relaed o he magniude of he daily price change. This associaion is a characerisic of boh he uncondiional disribuion of price changes and volume and he condiional disribuion given pas price changes and volume consan. Their finding means ha he volume-volailiy associaion is sill observable afer aking accoun of nonnormaliies, sochasic volailiy and oher forms of condiional heerogeneiy. Using daily individual securiy daa ( ), Lamoureoux and Lasrapes (1990) find a posiive condiional volume volailiy relaionship in models wih Gaussian errors and Garch-ype volailiy specificaions. However, hese earlier sudies ypically do no consider compeing measures of rading aciviy, nor do hey examine he number of rades as a measure of rading aciviy, as Jones, Kaul and Lipson do. Findings ha are quie conrary o he old Wall Sree adage ha i akes volume o make prices move are hese of Jones, Kaul and Lipson (1994). Their invesigaion can be viewed as a direc es of he Mixure of Disribuion Hypohesis (MDH), which assers ha volailiy and volume are posiively correlaed only because boh are posiively relaed o he number of daily informaion arrival (he mixing variable). Wih a fixed number of raders who all rade a fixed number of imes in response o new informaion; he number of daily ransacions will be proporional o he number of informaion arrivals [see Clark (1973), and Tauchen and Pis (1983)]. Therefore, he volailiy-volume relaion should be rendered saisically insignifican when volailiy is condiioned on he number of ransacions as well. Jones, Kaul and Lipson (1994) repor a sarling resul concerning sock price volailiy. Afer decomposing rading volume ino wo componens, he number of rades and he average rade size, which hey use as regressors in heir model, hey find ha he firs (rade frequency) is much more imporan han he laer in affecing sock price volailiy. Their evidence is based on an examinaion of a large sample of Nasdaq socks using daily daa over he period and hey use average rade size (oal number of shares raded divided by number of daily ransacions) as he measure of volume. Their resuls, however, are insensiive o he choice of he empirical measure of volume, since alernaive measures like dollar volume, number of shares raded, or urnover (number of shares raded divided by oal number of 3 Mehodology developed by Sims (197, 1980) M.Sc. in Banking and Finance Page 1

19 Exising Lieraure shares ousanding) yield virually idenical inferences. They also measure daily volailiy using he absolue residuals of he following model: R i 5 1 = ˆ ˆ α ˆ ik Dk + β j Ri j + ε i, k = 1 j= 1 (.5) where R i is he reurn of securiy i on day, D k s are he five day of he week dummies used o capure differences in mean reurns. The 1 lagged reurns are used as regressors o esimae shor-erm movemens in condiional expeced reurns. To gauge he relaive imporance of number of ransacions versus volume of rade, hey esimae he following hree ses of regressions for each securiy: ˆ ε ˆ i α i + α imμ + β iαvi + ρij ε i j + ηi, = j= 1 1 (.6a) ˆ ε α + α Μ + γ Ν + ρ ˆ ε + η, i = i im i i ij i j j= 1 1 i (.6b) and ˆ ε ˆ i α i + α imμ + β iαvi + γ iν i + ρij ε i j + ηi, = j= 1 1 (.6c) where εˆ i is he absolue residual from (.5), M is a rading-gap dummy variable ha is equal o 1 for Mondays and 0 oherwise, AV i is he average rade size (oal number of shares raded divided by he number of ransacions for securiy i or day ), N i is he number of ransacions for securiy i on day, and he coefficiens ρ ij s measure he persisence in he volailiy of securiy i. Jones, Kaul, and Lipson s (JKL) evidence shows ha he volailiy-volume relaion ypically disappears when hey conrol for he relaion beween volailiy and number of ransacions. Specifically, daily volailiy is significanly posiively relaed o boh average daily rade size and number of daily ransacions. However, in regressions of volailiy on average rade size and number of ransacions, he volailiy-volume relaion is rendered saisically insignifican while he relaion beween volailiy and number of ransacions remains virually unalered. Average size of rades has a saisically significan posiive relaion wih volailiy only for small firms, bu on average even his saisical relaion seems o be of lile economic significance. Thus, heir evidence srongly suggess ha he occurrence of ransacions per se conains all he informaion perinen o he pricing of securiies. In a summary, Jones, Kaul, and Lipson showed ha he posiive volailiy-volume relaion documened by numerous researchers simply reflecs he posiive relaion beween volailiy and number of ransacions. The mos noable implicaion of his finding is ha on average he size of rades has virually no incremenal informaion conen; any informaion in he rading behavior of agens is almos enirely conained in he frequency of rades during a paricular inerval. This evidence appears o run couner o he dominan marke microsrucure heories of sock price deerminaion, which emphasize he role of rade size as a means of deecing likely informed rading and adverse selecion. M.Sc. in Banking and Finance Page 13

20 Exising Lieraure Huang and Masulis (003) assess he generaliy of he JKL conclusions by sudying his relaion in anoher major compeing dealer marke, he London Sock Exchange (LSE). To examine he quesion of how rading aciviy impacs price volailiy, hey analyze dayime and hourly price changes and rading aciviy for he 100 larger socks, based on equiy capializaion, in he London marke for he year They also explore wo exensions of he basic JKL experimen. Firs, hey consider wheher ime aggregaion of individual rades ino daily sums and averages srongly smoohes he underlying variabiliy of he rade size variable, hereby lowering is informaion conen and significance. Second, hey consider he fundamenal quesion of wheher rades of all sizes have he same effec on price volailiy. If informaion raders break up large rades o gain beer price execuion, hen any remaining large rades are likely o be liquidiy-driven, wih lile impac on price volailiy. Barclay and Warner (1993) as menioned above, presened evidence consisen wih informaion raders inenionally breaking up large orders, hus making large rades less frequen and medium-size rades more informaive. This is referred o as he sealh rading hypohesis. Furher aenuaion of he empirical relaion beween rade size and price volailiy can resul from an infrequency of large rades relaive o small rades, poenial fron running prior o he compleion of large rades, reporing of some conemporaneous small rades as a single large rade and delayed reporing of large rades. Therefore, in analyzing he rading aciviy-price volailiy relaion, hey also invesigae he empirical relevance of rade size caegories and of rade reporing rules. Huang and Masulis (003) use as price volailiy measure he absolue value of he closing price minus he opening price, which represens dayime volailiy raher han daily volailiy. Average rade size is defined as share volume divided by number of rades, where rades are for buy ransacions. They use JKL s linear specificaion in heir saisical model: V = α + βα + γν + ε, (.7) where V represens price volailiy, i i i i i Α represens average rade size and i represens he number of rades, in each case for sock i over he inerval. They esimae his equaion using Hansen s (198) generalized mehod of momens (GMM) 4. For heir overall sample, price volailiy on he London Sock Exchange is direcly relaed o rade frequency and more weakly, bu posiively relaed o rade size. In his regard, hey suppor he general conclusion of Jones, Kaul and Lipson. They also conclude ha small rades are he only ones ha consisenly have a significan impac on price volailiy. Furhermore, for small rades, hey find significan impac on price volailiy from boh rade size and rade frequency, paricularly when we move from dayime o hourly daa. In examining wheher his relaion varies across socks caegorized by equiy capializaion or rading volume, hey find no evidence of significan differences, which indicaes ha he rade size is no acing as a proxy for equiy capializaion or sock liquidiy. Ν i 4 The GMM esimaion mehod imposes weak disribuion assumpions on he observable variables and endogenously adjuss he esimaes o accoun for general forms of condiional heeroskedasiciy and/or serial correlaion ha may be presen in he error srucure. Serial correlaion in sock price volailiy is a paricular concern, given he widely documened srong posiive serial correlaion found in squared sock reurns. In conras, JKL use a wo-sep esimaion procedure and measure price volailiy by he absolues residuals from daily reurns regressed agains five day of he week dummies and 1 lagged reurns o handle he serial correlaion in he residuals. M.Sc. in Banking and Finance Page 14

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