AN EMPIRICAL STUDY OF VOLATILITY AND TRADING VOLUME DYNAMICS USING HIGH-FREQUENCY DATA

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1 The Inernaional Journal of Business and Finance Research Volume 4 Number AN EMPIRICAL STUDY OF VOLATILITY AND TRADING VOLUME DYNAMICS USING HIGH-FREQUENCY DATA Wen-Cheng Lu, Ming Chuan Uniersiy Fang-Jun Lin, Shanghai Commercial and Saing Bank ABSTRACT This paper examines he dynamic relaionship of olailiy and rading olume using a biariae ecor auoregressie mehodology. This sudy found bidirecional causal relaions beween rading olume and olailiy, which is in accordance wih sequenial informaion arrial hypohesis ha suggess lagged alues of rading olume proide he predicabiliy componen of curren olailiy. Findings also reeal ha rading olume shocks significanly conribue o he ariabiliy of olailiy and hen olailiy shocks parly accoun for he ariabiliy of rading olume. JEL: C01, G0, O16, O30 KEYWORDS: Trading olume; Volailiy; Sequenial informaion arrial hypohesis; Mixure of disribuion hypohesis INTRODUCTION Four relean informaion heories in he lieraure relae olume and olailiy, namely, he mixure of disribuions hypohesis (MDH), he sequenial arrial of informaion hypohesis (SAIH), he dispersion of beliefs hypohesis, and he noise rader hypohesis. Informaion mainly deermines he heories of olume and olailiy. For example, according o he MDH, informaion disseminaion is conemporaneous. Sock prices and rading olume change only when informaion arries and eole a a consan speed in een ime. MDH suggess ha daily price changes and rading olume are drien by he same underlying informaion flow. MDH implies only a conemporaneous relaionship beween olume and reurns. The SAIH argues ha each rader obseres informaion sequenially. Hence, differen ypes of raders will receie informaion sequenially. The economeric resuls show ha pas rading olume proides informaion on curren olailiy or absolue reurns. Seeral sudies find ha a posiie correlaion exiss beween olume and olailiy, including Lee and Rui (2002), Andersen (1996), Manganelli (2005), Xu e al. (2006) and Kim (2005). This inesigaion sudies he dynamic relaion beween reurn olailiy and rading olume on he Taiwan sock marke. This sudy differs, as follows, from oher sudies on he olume-olailiy relaionship. Firs, in his paper he measure of olailiy is calculaed by he sum of inraday 1-min reurns. Minue-by-minue ransacion daa are used. The economic raionale is as follows: Marens (2002) shows he sum of squared inraday and inranigh reurns are beer han using he daily reurn o measure sock marke olailiy. Andersen e al. (1999) and Marens (2001) show ha inraday reurns can improe no only measuring of olailiy, bu also he forecasing of olailiy. The remoal of microsrucure bias makes he resuls in his paper more reliable. Second, in addiion o using a ecor-auoregressie (VAR) model o answer he quesion abou he relaionship of rading olume-olailiy, The VAR model can consider he endogeneiy of olume-olailiy relaions and capure he impac of olume (olailiy) shock on olailiy (olume) in he Taiwan sock marke. The proposed model also proides he dynamic inraday-olume relaion. Third, his paper reeals a olume-olailiy relaionship from he Taiwan sock marke, whereas mos empirical sudies come from deeloped counries. Therefore, resuls from his sudy can complemen and conras wih preious sudies o assess wheher he olailiy-olume relaionship is robus in differen markes. Empirical resuls show a significan relaionship beween he pas rading olume and reurn olailiy and curren rading olume or olailiy. The causaliy ess show a clear bidirecional relaionship beween 93

2 WC. Lu, FJ. Lin IJBFR Vol. 4 No rading olume and reurn olailiy. Our resuls suppor he SAIH. The findings presened in his sudy demonsrae ha he shock o rading olume has a significan effec on olailiy. The conribuion of rading olume shock o he ariabiliy of olailiy accouns for 40%. Only abou 8% of changes in olailiy can be aribued o he shock in rading olume. The impulse response funcion shows ha one sandard deiaion increase in rading olume is followed by an increase in olailiy. As regards he effec on rading olume, here is a downward effec of a shock o olailiy. Trading olume responds much more sluggishly. The remainder of his paper is organized as follows. Secion 2 briefly reiews prior lieraure. Secion 3 discusses he empirical model and esimaion mehodology. Secion 4 describes he daa. Secion 5 proides he main resuls including resuls from he analysis of regression parameers, he Granger causaliy es, ariance decomposiion (VDC) and he impulse response funcion (IRF). Secion 6 concludes he sudy. LITERATURE REVIEW Much lieraure exiss on olailiy-olume relaionships in he sock marke microsrucure. Since he original work by Clark (1973), Epps and Epps (1976), and Harris (1986), a number of empirical papers hae examined differen aspecs of he linkage beween rading olume and olailiy. Grammaikos and Saunders (1986), in early sudies, found ha price ariabiliy and rading olume are posiiely correlaed in fuures markes. More recenly, Wang and Yau (2000) repor eidence of a posiie relaion beween rading olume and price olailiy in fuures markes. For a VAR Framwork, Garcia, Leuhold and Zapaa (1986) documen a lead-lag relaionship beween rading olume and olailiy. Luu and Marens (2003) use US sock index fuures marke daa and find a bi-direcional causal relaionship beween olailiy and rading olume. Xu e al. (2006) and Manganelli (2005) also find a srong conemporaneous and dynamic relaionship beween olume and olailiy. Howeer, some dissimilar resuls also appear in preious lieraure. For example, Pilar and Rafael (2002) argue ha a decrease in olailiy and increases rading olume. Waanabe (2001) suggess here is no relaionship beween price olailiy and olume. The dynamic relaionship beween rading olume and olailiy is unclear ha depend on he marke and ime period we sudied Some sudies consider he arious ypes of rader olume and olailiy. For example, Daigler and Wiley (1999) employ ype of rader olume o sudy conemporaneous olume-olailiy relaionships. They primarily focus on he heory of sequence of informaion arrial and how differen ypes of raders inerpre and reac o informaion. Chen and Daigler (2008) proide an inegraed picure of he olume and olailiy relaionship by inesigaing he dynamic linear and nonlinear associaions beween olailiy and he olume of informed and uninformed raders. The resuls of Chen and Daigler (2008) shows a one-way Granger causaion from olailiy o olume. Informed raders reac less o lagged informaion han do uninformed raders for he sequenial arrial of informaion framework, and public s rading olume creaes excess olailiy. Chen (2007) uses he daa of four fuures markes o inesigae he effec of rader ypes on he inraday olailiy-olume relaionship. Chen s (2007) resuls from a VAR model show ha he dynamic olailiy-olume relaionship depends on he rader ypes inoled. The posiie conemporaneous olailiy-olume relaionship is drien mainly by olume from rading beween floor raders and cusomers. Alernaiely, seeral sudies focus on he effec of expeced and unexpeced olume shocks on olailiy. Bessembinder and Seguin (1993) find ha unexpeced olume shocks hae a larger effec on olailiy in fuures markes han expeced olume. Daigler and Wiley (1999) find ha he unexpeced olume series is more imporan han he expeced olume series in explaining olailiy. DATA The daa of he curren empirical sudy consiss of Taiwan sock exchange (TWSE) (hp:// index ransacion prices (represened by marke index) and rading olume for he period 1 s January 2005 o 31 December This sudy deries he daily rading 94

3 The Inernaional Journal of Business and Finance Research Volume 4 Number olume from he TWSE daabase. There are 743 days (obseraions) in our sample. Andersen e al. (1999) and Marens (2001) show ha inraday reurns can improe no only he measuring of olailiy, bu also he forecasing of olailiy. Therefore, our empirical analyses use inraday reurns from each 1-min ineral o measure reurns and aoid marke microsrucure problems. There are inraday 1-min ineral rading daa in our sample. The coninuously compounded reurns of eery minue are calculaed as r i, = 100 (log( P ) log( P 1 )), where r i, and P are he reurn and marke index a ime. The daily reurns are compued as R =,. i r i Unforunaely, olailiy is no direcly obserable. A popular approach o measure daily olailiy is o use he daily squared reurn. Andersen and Bollersle (1998) argue ha in mos financial applicaions, he asse price is assumed o follow a coninuous ime diffusion process, and he correc measure for daily olailiy is 2 = 2 d + τ τ (1) Andersen and Bollersle (1998) show ha he daily squared reurn is an unbiased esimaor of rue olailiy. Marens (2002) also compares arious measures and forecass of olailiy in daily olailiy and find he bes daily olailiy measure is he sum of inraday squared reurns. This implies ha using he sum of squared inraday reurns is beer han using daily squared reurns o measure sock marke olailiy. Hence, we use equaion (1) o compue olailiy. Table 1 proides basic saisics of olailiy and rading olume. Table 1: Basic Saisics of Sample Volailiy( ) Trading Volume( ) Mean Median Maximum Minimum Sandard deiaion Skewness Kurosis Noe: The basic saisics of olailiy ( ) and rading olume ( ) are presened in his able. For he olailiy, we analyzed wih 1-minue inerals. Trading olumes, measured by naure logarihm, are from he TWSE daabase. The descripie saisics hae some clues for he behaiors of Taiwanese sock marke. RESEARCH METHODOLOGY The VAR approach proides a framework and has been used widely in he lieraure for he issue in our research (e.g. Luu and Marens (2003), and Fujihara and Mougoue (1997)). VAR modeling requires ha all imes series be saionary. As a firs sep, rading olume and olailiy and heir firs differences were esed for saionariy using Augmened Dickey-Fuller ess. If he calculaed ADF saisic is less han is criical alue, hen he ariable is said o be saionary or inegraed o he order zero. If hey are non-saionary, hen he issue is o wha degree hey are inegraed. In pracice, a number of economeric packages can perform his es, which gies he criical alue of he ADF saisic. Compuaions were performed using Eiews 6.0 and he number of lags or augmenaion in ADF regressions were seleced by Akaike Informaion Crierion. Table 2 liss he conclusion. As a resul, he following VAR(k) model is esimaed, in which he Akaike Informaion Crierion (AIC) is 95

4 WC. Lu, FJ. Lin IJBFR Vol. 4 No used o deermine he opimal lag lengh (k). The VAR model used in his sudy is shown in equaion (2) and (3) below. = c0 + α α β1-1 + β2-2 + ε1 (2) = a + a + a + b + b + ε (3) Where is he ecor ha represens he olailiy and is he ecor ha represens he rading olume. The opimal lag lengh ( k ) in he VAR model is seleced by he Akaike Informaion Crierion (AIC) (i.e., k = 2 ). The nex sep is o deermine he direcion of Granger causaliy. Under he assumpion of saionariy of ariables and he null hypohesis of no Granger causaliy, he sandard F-es is used o examine Granger-causaliy beween ariables in he VAR sysem. If he F-es rejecs he null hypohesis ha he lag coefficiens of ariable ( ) are joinly zero when ariable ( ) is he dependen ariable in he VAR sysem, hen ariable ( ) Granger-causes ariable ( ). Once he VAR sysem was esimaed, his sudy employed wo shor-run dynamic analyses: ariance decomposiion and impulse response funcions. Forecas error ariance decomposiion separaes he ariaion in an endogenous ariable ino he componen shocks o he VAR sysem. The ariance decomposiion is an esimae of he proporion of he moemen of he n-sep-ahead forecas error ariance of a ariable in he VAR sysem ha is aribuable o is own shock and ha of anoher ariable in he sysem. Howeer, he recursie ordering of he ariables in he VAR sysem for his sudy follows his order. Volailiy is firs and rading olume is ordered nex o olailiy. The ordering reflecs preious sudies such as Chen and Daigler (2008). Forecas error ariance decomposiion can characerize he dynamic behaior of a VAR sysem. In addiion, we derie impulse response funcions, which show he dynamic effecs on olailiy (rading olume) of innoaions o he rading olume (olailiy). We esimae he VAR model and orhogonalize hese shocks by resoring o a Choleski decomposiion of he esimaed ariance-coariance marix of he VAR residuals o generae impulse response funcions. Figures 1 and 2 lis he resuls. ESTIMATION RESULTS As he firs sep, all he wo ariables were esed for saionariy using Augmened Dickey-Fuller ess. Table 2 gies he resuls. I can be seen ha for all of he leel ariable less han criical alue a 95% leel of confidence. An examinaion of es resuls shows ha all he ime series employed in his research are saionary a leel. The null hypohesis of he uni roo is rejeced for all ariables a he 5% significance leel. Table 2: ADF Tess for Uni Roos Variable Wihou rend Wih rend Tes saisic Criical alue Tes saisic Criical alue Volailiy( ) Trading olume( ) Noe: and represens olailiy and rading olume, respeciely. Compuaions were performed by using Eiews 6.0 and he number of lags or augmenaion in ADF regressions are seleced by Akaike Informaion Crierion. The ADF es rejecs he null of a uni roo for boh series in his able. Table 3 shows he VAR esimaion resuls. Resuls indicae ha he pas rading olume and olailiy significanly affec he curren olailiy or rading olume. This conclusion is ery imporan as i gies 96

5 The Inernaional Journal of Business and Finance Research Volume 4 Number useful informaion abou rading olume and forecass of reurns and olailiy. Table 4 presens causaliy es resuls obained by VAR esimaion using equaions (1) and (2). The resuls indicae he rading olume of he Taiwan sock index significanly Granger-causes olailiy. Volailiy also srongly Granger-causes he rading olume of he Taiwan sock index. Furhermore, he Granger-causaliy beween wo ariables is in boh direcions. The resuls also show he pas marke informaion abou olailiy and rading olume has an abiliy o predic he olailiy and rading olume in he fuure in Taiwan. According o some heoreical papers, boh he MDH and he sequenial arrial of informaion hypohesis suppor a posiie and conemporaneous relaionship beween rading olume and absolue reurns. Our resuls suppors he mixure of disribuions hypohesis (MDH). Furhermore, a bi-direcional causaliy es was found beween olailiy and rading olume, which is consisen wih he findings of Luu and Marens (2003) and Chen (2007). Table 3: VAR Esimaion Resuls Dependen ariable Consan E-06 ( )*** ( )*** (1.8581)* 5.80E-12 (6.2697)*** -3.08E (4.1735)*** -7.52E+09 ( )*** 7.14E+09 (5.1885) *** ( )*** ( )*** (8.8062)*** Noe: 1. and represens olailiy and rading olume, respeciely. 2. saisics are indicaed in he parenheses. 3. ***, ** and * indicae significance a he 1, 5 and 10 percen leels, respeciely. Table 4: Granger Causaliy Tess for Volailiy and Trading Volume Causaliy relaion Saisics P-alue (<5%)*** (<5%)*** Noe: 1. and represens olailiy and rading olume, respeciely. 2. means he olailiy Granger-causes olume. denoes he olume Granger-causes olailiy. 3. *** represens he causal relaionship being significan a 1% leel. Table 5 illusraes he esimaion resuls of ariance decomposiion o examine dynamic relaionships in olailiy and rading olume furher. In Table 5, he sock olailiy ariance decomposiion analysis reeals ha he larges share of shock o olailiy, apar from is own shock, rading olume accouned for abou 40% during he 24-day period (abou one monh), while rading olume accouned for 21% of he shock during he 12-day period (abou wo weeks). The shock o rading olume has a significan effec on olailiy. In addiion, he moemen in rading olume is explained by is own shocks raher han by he shocks o olailiy. Clearly, olailiy does no explain a large par of he ariance decomposiion of rading olume. The ariance of olailiy accouns for approximaely 6% during he 4-day period and 8% in he 24-day period. This shows he small proporion of olailiy shocks on he ariabiliy of rading olume. 97

6 WC. Lu, FJ. Lin IJBFR Vol. 4 No Table 5: Esimaes of Variance Decomposiion Lags ( n ) Percenage of he moemen in he explained by shocks o : Percenage of he moemen in he by shocks o : explained Noe: and sand for he olailiy of Taiwan marke index and rading olume, respeciely. To furher examine dynamic relaionships in and, his able proides he percenage of he moemen in he explained by shocks o and he percenage of moemen in he explained by shocks o. The second use o which we pu he VAR model was he deriaion of impulse response funcions, which show he dynamic effecs beween olailiy and rading olume. Figure 1 and 2 depic he esimaed impulse response funcions. The ime horizon exends o 30 days, oer which he dynamic adjusmen pahs of olailiy are ploed following he innoaions o each of he rading olumes. One sandard deiaion increase in he rading olume is followed by an increase in he olailiy. The effecs on olailiy peak afer 17 days. As regards he effec on rading olume, here is a downward effec of a shock o olailiy. Trading olume responds much more sluggishly. One sandard deiaion increase in olailiy is followed by a decrease in he rading olume. The effec on rading olume peaks afer 3 days. The resuls in Figures 1 and 2 show ha pas informaion abou rading olume has an abiliy o predic olailiy. CONCLUSION This paper aimed o inesigae he dynamic relaions beween reurn olailiy and rading olume on he Taiwan sock marke. The use of he VAR model allowed us o race he predicabiliy of olailiy and rading olume, and o accoun for he endogeneiy beween olailiy and rading olume. The VAR model also enabled us o capure he economic ineracions beween hose ariables. We used inraday reurns o measure olailiy and aoid microsrucure bias. This paper sheds furher ligh on he dynamics beween olailiy and rading olume. Firs, we found a general bi-direcional causal relaionship. Because pas marke informaion abou olailiy and rading olume has an abiliy o predic olailiy and rading olume in he fuure, our resuls suppors boh he mixure of disribuions and he sequenial arrial of informaion hypoheses. The forecas error ariance decomposiion was obained wih he aim of assessing how much such shocks conribue o he ariabiliy of he ariables in he sysem. The resul shows he rading olume shocks significanly conribue o he ariabiliy of olailiy by accouning for abou 40% of he shock during he 24-day period. Howeer, he conribuion of olailiy shocks o he ariabiliy of rading olume only accouns for 8% of he shock during he 24-day period. This finding confirms ha he ariabiliy in sock olailiy is subsanially explained by rading olume. 98

7 The Inernaional Journal of Business and Finance Research Volume 4 Number Figure 1:Esimaion of Response Funcion Response of o Response of o Noe: and represens olailiy and rading olume, respeciely. The impulse response funcion show responses of each ariable in he VAR sysem o a one sandard deiaion shock o iself and o he oher series. In his figure, he dynamic inerrelaion of and can be shown. The findings from he impulse response funcion show ha one sandard deiaion increase in he rading olume is followed by an increase in he olailiy. The effec on olailiy peaks afer 17 days. As regards he effec on rading olume, here is a downward effec of a shock o olailiy. Trading olume responds much more sluggishly. One sandard deiaion increase in olailiy is followed by an increase in rading olume. The effec on rading olume peaks afer 3 days. These findings are helpful o financial managers dealing wih he sock index or is deriaions. The limiaions o our model is sample size, addiional research needs o collec differen ypes of raders daa. The differen ypes of raders may hae disinc informaion. Recenly, many sudies begin o inesigae SAIH o focus on he effec of differen ypes of rader. Therefore, furher resuls should need samples ha are more deailed and many kinds of rader judgmens. 99

8 WC. Lu, FJ. Lin IJBFR Vol. 4 No REFERENCES Andersen, T. G. (1996) Long Memory Processes and Fracional Inegraion in Economerics, Journal of Economeircs, ol. 73, p Andersen, T. G. & Bollersle, T. (1998) Answering he skepics: Yes, sandard olailiy models do proide accurae forecass, Inernaional Economic Reiew, ol. 39, p Andersen, T. G. Bollersle, T. & Lange, S. (1999) Forecasing financial marke olailiy: Sampling frequency is-à-is forecas horizon, Journal of Empirical Finance, ol. 6, p Bessembinder, H. & Seguin, P. (1993) Price Volailiy, Trading Volume, and Marke Deph: Eidence form Fuures Markes, Journal of Financial and Quaniaie Analysis, 28(1), p Clark, P. K. (1973) A Subordinaed Sochasic Process Model wih Finie Variance for Speculaie Prices, Economerica, ol. 41, p Chen, H. (2007) Inraday Trading by Floor Traders and Cusomers in Fuures Markes: Whose Trades Drie he Volailiy-Volume Relaionship? Quarerly Journal of Business and Economics, ol. 46(4), p Chen, Z. & Daigler, R. T. (2008) An Examinaion of he Complemenary Volume-olailiy Informaion Theories, The Journal of Fuures Markes, ol. 28(10), p Daigler, R. T. & Wiley, M. K. (1999) The Impac of Trader Type on he Fuures Volailiy-olume Relaion, Journal of Finance, ol. 54, p Epps, T. W. & Epps, M. L. (1976) The Sochasic Dependence of Securiy Price Changes and Transacion Volumes: Implicaion for he Mixure-of-Disribuions hypohesis, Economerica, ol. 44, p Fujihara, R. A. & Mougoue, M. (1997) An Examinaion of Linear and Nonlinear Causal Relahionships beween Price Variabiliy and Volume in Peroleum, Journal of Fuures Markes, ol. 17, p Garcia, P. Leuhold, R. M. & Zapaa, H. (1986) Lead-lag Relaionships beween he Trading Volume and Price Variabiliy: New Eidence, The Journal of Fuures Markes, ol. 6, p Grammaikos, T., & Saunders, A. (1986) Fuures Price ariabiliy: A es of Mauriy and Volume effec, Journal of Business, ol. 59(2), p Harris, L., (1986) "Cross-Securiy Tess of he Mixure of Disribuions Hypohesis," Journal of Financial and Quaniaie Analysis, ol.21, p Kim S. J. (2005) Informaion Leadership in he Adanced Asia-Pacific Sock Markes: Reurn, Volailiy and Volume Informaion Spilloers from he US and Japan, Journal of he Japanese and Inernaional Economics, ol. 19(3), p Lee, B. & Rui, O. (2002) The Dynamic Relaionship beween Sock Reurns and Trading Volume: Domesic and Cross-counry Eidence, Journal of Banking and Finance, ol. 26, p Luu, J. & Marens, M. (2003) Tesing he Mixure-of-Disribuions Hypohesis Using Realized Volailiy, Journal of Fuures Markes, 23(7), p Manganelli, S. (2005) Duraion, Volume and Volailiy Impac of Trades, Journal of Financial Markes, 100

9 The Inernaional Journal of Business and Finance Research Volume 4 Number ol. 8(4), p Marens, M. (2001) Forecasing Daily Exchange Rae Volailiy using Inraday Reurns Model Incorporaing Sysemaic and Unique Risks, Journal of Inernaional Money and Finance, ol. 20, p Marens, M. (2002) Measuring and Forecasing S&P 500 Index-fuures Volailiy using High-Frequency Daa, The Journal of Fuure Markes, ol. 22(6), p Pilar, C. & Rafael, S. (2002) Does Deriaies Trading Desabilize he Underlying Asses? Eidence from he Spanish Sock Marke, Applied Economics Leers, ol. 9(2), Wang, G. & Yau, J. (2000) Trading Volume, Bid-Ask Spread, and Price Volailiy in Fuures Markes, Journal of Fuures Markes, 20(10), p Waanabe, T. (2001) Price Volailiy, Trading Volume, and Marke Deph, Applied Financial Economics, ol. 11, p Xu, X. Chen, P. & Wu, C. (2006) Time and Dynamic Volume-Volailiy Relaion, Journal of Banking & Finance, ol. 30(5), p BIOGRAPHY Dr. Wen-Cheng Lu, corresponding auhor, is an assisan professor of Economics a Ming Chuan Uniersiy in Taiwan. His research ineress include indusrial economics, produciiy, and applied economerics. He can be conaced a deparmen of Economics, Ming Chuan Uniersiy, 5 De Ming Rd., Gui Shan Disric, Taoyuan Couny 333, Taiwan. bunshou.lu@msa.hine.ne bunshou.lu@msa.hine.ne Fang-Jun Lin is a financial consulan a Shanghai Commercial and Saing Bank in Taiwan. His research ineress include financial economics and asse managemen. She can be conaced a Shanghai Commercial and Saing Bank, 69 Chong Cheng Rd., Ban Qian Ciy, Taiwan. cirolian@yahoo.com.w 101