The Dynamic Relationship between Price and Trading Volume: Evidence from Indian Stock Market

Transcription

1 INDIAN INSTITUTE OF MANAGEMENT AHMEDABAD INDIA The Dynamic Relaionship beween Price and Trading : Evidence from Indian Sock Marke Brajesh Kumar Priyanka Singh Ajay Pandey W.P. No December 9 The main objecive of he working paper series of he IIMA is o help faculy members, research saff and docoral sudens o speedily share heir research findings wih professional colleagues and es heir research findings a he pre-publicaion sage. IIMA is commied o mainain academic freedom. The opinion(s), view(s) and conclusion(s) expressed in he working paper are hose of he auhors and no ha of IIMA. INDIAN INSTITUTE OF MANAGEMENT AHMEDABAD-8 INDIA W.P. No Page No.

2 The Dynamic Relaionship beween Price and Trading : Evidence from Indian Sock Marke Brajesh Kumar Priyanka Singh Ajay Pandey Absrac This sudy invesigaes he naure of relaionship beween price and rading volume for Indian socks. Firsly he conemporaneous and asymmeric relaion beween price and volume are examined. Then we examine he dynamic relaion beween reurns and volume using VAR, Granger causaliy, variance decomposiion (VD) and impulse response funcion (IRF). Mixure of Disribuions Hypohesis (MDH), which ess he GARCH vs. effec, is also sudied beween he condiional volailiy and volume. The resuls show ha here is posiive and asymmeric relaion beween volume and price changes. Furher he resuls of VAR and Granger causaliy show ha here is a bi-direcional relaion beween volume and reurns. However, he resuls of VD imply weak dynamic relaion beween reurns and volume which becomes more eviden from he plos of IRF. On MDH, our resuls are mixed, neiher enirely rejecing he MDH nor giving i an uncondiional suppor. JEL Classificaion: C, C, G Keywords: Trading volume, Volailiy, Mixure of disribuions hypohesis, GARCH, Granger Causaliy, VAR, Impulse response funcion, Variance decomposiion Docoral Suden, Indian Insiue of Managemen Ahmedabad, brajeshk@iimahd.erne.in Docoral Suden, Indian Insiue of Managemen Ahmedabad, priyankas@iimahd.erne.in Professor, Finance & Accouning, Indian Insiue of Managemen Ahmedabad, apandey@iimahd.erne.in An earlier version of his paper was funded by Naional Sock Exchange of India under heir Research Iniiaive W.P. No Page No.

3 The Dynamic Relaionship beween Price and Trading : Evidence from Indian Sock Marke. Inroducion In financial economics, considerable aenion has been given o undersand he relaionship beween reurns, volailiy and rading volume. As argued by Karpoff (986, 987), price-volume relaionship is imporan because his empirical relaionship helps in undersanding he compeing heories of disseminaion of informaion flow ino he marke. This may also help in even (informaional/liquidiy) sudies by improving he consrucion of es and is validiy. This relaionship is also criical in assessing he empirical disribuion of reurns as many financial models are based on an assumed disribuion of reurn series. There are numerous empirical sudies, which suppor he posiive relaionship beween price (reurns, volailiy) and rading volume of a radable asse (Crouch, 97; Epps and Epps, 976; Karpoff, 986, 987; Assogbavi e al., 99; Chen e al, ). Various heoreical models have been developed o explain he relaionship beween price and rading volume. These include sequenial arrival of informaion models (Copeland, 976; Morse, 98 and Jennings and Barry, 98), a mixure of disribuions model (Clark, 97; Epps and Epps, 976; Tauchen and Pis, 98; and Harris, 986; Lamoureux and Lasrapes, 99) asymmeric informaion models (Kyle, 98; Admai and Pieiderer, 988), and differences in opinion models (Varian, 98, 989; Harris and Raviv, 99). All hese models predic a posiive relaionship beween price and rading volume. In a similar srand of lieraure, he asymmeric naure of volume response o reurn (volailiy) i.e. he rading volume is higher when price moves up han on he downick is sough o be explained (Epps 97; Karpoff 986, 987; Assogbavi e al., 99). The asymmeric naure is explained hrough heerogeneous expecaions and coss involved in shor selling. Recenly, Henry and McKenzie (6) examined he relaionship beween volume and volailiy allowing for he impac of shor sales in Hong-Kong marke and found ha he asymmeric bidirecional relaionship exiss beween volailiy and volume. Oher han posiive conemporaneous relaionship beween reurns and rading volume and asymmeric relaionship beween level of volume and price changes, some sudies also repor bidirecional causaliy beween reurns and volume (Hiemsra and Jones, 994; Chen, Firh, and Rui, ; Raner and Leal, ). This dynamic relaionship beween reurns and volume is explained by various heoreical models. These include models developed by Blume, Easley, and O Hara (994), Wang (994), He and Wang (99) and Chordia and Swaminahan (). Mos of hese models assume volume as a proxy for qualiy and precision of informaion. I is found ha he informaion conen of volume and sequenial processing of informaion may lead o dynamic relaionship beween reurns and rading volume. Blume, Easley, and O Hara (994) developed a model in which prices and volume of he pas carry informaion abou he value of securiy and explained ha he raders, who include pas volume measures in heir echnical analysis, performed beer. Wang (994) and He and Wang (99) developed a model based on asymmeric informaion and showed ha he rading volume is relaed o informaion flow in he marke and invesor s privae informaion is revealed hrough rading volume. Chordia and Swaminahan () also examined he predicabiliy of shor-erm sock reurns based on rading volume and concluded ha high volume socks respond promply o marke-wide informaion. W.P. No Page No.

4 Similar o reurns and volume, considerable aenion has also been given o undersand he relaionship beween volailiy and rading volume of an asse by he researchers. Mos of he sudies repor he evidence of ARCH effecs in he ime series of reurns. However, very few of hem ry o give any heoreical economic explanaion of he auoregressive naure of condiional volailiy. One of he possible heoreical explanaions is he mixure of disribuions hypohesis (Clark, 97; Epps and Epps, 976; Tauchen and Pis, 98; Lamoureux and Lasrapes, 99). The Mixure of disribuions hypohesis (MDH) explains he posiive relaionship beween price volailiy and rading volume as hey joinly depend on a common facor, informaion innovaion. According o MDH, reurns are generaed by mixure of disribuions and informaion arrival is he mixing variable. This mixing variable causes momenum in he squared residual of daily reurns and hence auoregressive naure of he condiional volailiy. As informaion arrival is unobserved, rading volume has been usually considered as a proxy of informaion flow ino he marke. Any unexpeced informaion affecs boh volailiy and volume conemporaneously and, herefore volailiy and volume are hypohesized o be posiively relaed. While a fair amoun of empirical evidence on he price (reurns, volailiy) and volume relaionship, asymmeric relaionship beween volume and price change, and on he mixed disribuion hypohesis exiss for developed counries, very few empirical sudies have been repored from emerging markes and specifically from Indian sock marke. This paper repors same empirical evidence on hese issues for Indian Sock marke. All he socks of S&P CNX Nify, a value-weighed sock index of Naional Sock Exchange ( Mumbai, derived from he prices of large capializaion socks, for he period of s January o s December 8 are analyzed. We find ha here is a posiive conemporaneous relaionship beween reurns and volume. Furher we ha find ha boh uncondiional as well as condiional volailiies are posiively relaed wih volume. I is also found ha he rading volume depends on he direcion of price change, wih more volume being associaed wih posiive price changes. From he resuls of he VAR and Granger Causaliy i can be seen ha hough bi-direcional causaion is here bu reurns cause volume o a greaer exen han vice versa. I is ineresing o noe ha even afer conrolling for high auoregressive naure of volume, we find significan effec of one day lagged reurns and volume. However, variance decomposiion resuls show ha he effec ha reurns have on volume is a he mos percen only. Similarly volume a mos explains percen of reurns only. On ploing he impulse response funcion, i becomes eviden ha dynamic relaion is very weak beween reurns and volume. We ge a mixed resul on MDH, wih some socks supporing he MDH hypohesis and ohers rejecing i. Given he high auoregressive naure of boh volume and volailiy, i can be said ha informaion is processed sequenially in Indian marke. The remainder of his paper is organized as follows. A brief review of empirical lieraure is given in secion. Secion explains he sample and basic characerisics of he daa. The empirical models of he conemporaneous and dynamic relaionship beween reurns and rading volume, and models of he mixure of disribuions hypohesis are explained in secion 4. Secion discusses he empirical findings and he las secion summarizes hem and concludes.. Lieraure on Relaionship among Trading, s and Volailiy There have been number of empirical sudies in developed markes which provide evidence on he relaionship beween rading volume and sock reurns. Rogalski (978) using monhly sock daa found posiive conemporaneous correlaion beween reurns and rading volume. Using W.P. No Page No. 4

5 nonlinear Granger causaliy es, Hiemsra and Jones (994) analyzed he bidirecional causaliy beween rading volume and reurns for New York Sock Exchange and found suppor for posiive bidirecional causaliy beween hem. In an emerging marke conex, Saacioglu and Sarks (998) examined he relaionship beween price changes and volume for six Lain American markes (Argenina, Brazil, Chile, Colombia, Mexico, and Venezuela) found a posiive conemporaneous relaionship beween reurns and volume. However, upon employing Granger causaliy, hey failed o find srong evidence on reurns leading o volume. Chen e al. () examined casual relaionship beween reurns and volume for nine naional markes. The resuls indicaed ha for some counries, reurns cause volume and volume causes reurns. Assogbavi e al. (7) used vecor auo-regression model o analyze dynamic relaionship beween reurns and rading volume using weekly daa of individual equiies of he Russian Sock Exchange. They found a srong evidence of bi-direcional relaionship beween volume and reurns. The relaionship beween sock reurn volailiy and rading volume has also been analyzed in several sudies. Crouch (97) sudied he relaionship beween daily rading volume and daily absolue changes of marke index and individual socks and found posiive correlaion beween hem. Epps (97) used ransacions daa and found a posiive conemporaneous correlaion beween rading volume and absolue price changes. Harris (987) used he number of ransacions as a measure of volume and found a posiive correlaion beween changes in volume and changes in squared reurns for individual NYSE socks. Smirlock and Sarks (988) analyzed he causal relaionship beween rading volume and volailiy using individual sock ransacions daa and found a posiive lagged relaion beween volume and absolue price changes. Moosa and Al- Loughani (99) examined he dynamic relaionship beween volailiy and volume for four Asian sock markes excluding India and found a srong evidence for bi-direcional causaliy for Malaysia, Singapore, and Thailand. However, Bhaga and Bhaia (996) found srong onedirecional causaliy running from volailiy o rading volume while analyzing he lead-lag relaionship beween rading volume and volailiy using Granger causaliy es. Brailsford (996) for he Ausralian sock marke found a posiive conemporaneous relaionship beween absolue reurns and volailiy. Several empirical sudies have been done invesigaing MDH. In he U.S. sock marke, Andersen (996), Gallo and Pacini (), Kim and Kon (994), and Lamoureux and Lasrapes (99, 994) found suppor for he MDH. In emerging markes conex, Pyun e al. () invesigaed individual shares of he Korean sock marke, Brailsford (996) analyzed he effec of informaion arrivals on volailiy persisence in he Ausralian sock marke and Lange (999) for he small Vancouver sock exchange. All of hem found suppor for he mixed disribuion hypohesis. Wang e al. () examined he Chinese sock marke and invesigaed he dynamic causal relaion beween sock reurn volailiy and rading volume. They found suppor for he MDH as he inclusion of rading volume in he GARCH specificaion of volailiy reduced he persisence of he condiional variance. In general, mos of empirical sudies in he developed and developing marke conex have found evidence ha he inclusion of rading volume in GARCH models for volailiy resuls in reducion of he esimaed persisence or even causes i o vanish. However, Huang and Yang () for he Taiwan Sock Marke and Ahmed e al. () for he Kuala Lumpur Sock Exchange found ha he persisence in reurn volailiy remains even afer volume is included in he condiional variance equaion. The relaionship beween volume and volailiy has also been sudied in he marke microsrucure srand of lieraure. However, he implicaions are no always consisen. For example, he model of Admai and Pfleiderer (988) which assumes hree kinds of raders, W.P. No Page No.

6 informed raders who rade on informaion, discreionary liquidiy raders who can choose he ime hey wan o rade bu mus saisfy heir liquidiy demands before he end of he rading day, and non discreionary raders who ransac due o he reasons exogenous a a specific ime and don have he flexibiliy of choosing he rade ime, predics he posiive relaionship beween volailiy and rading volume. On he oher hand Foser and Viswanahan (99) model implies ha his relaionship does no necessarily follow even when hey use he same classificaion of raders as used by Admai and Pfleiderer. Anoher very imporan issue ha has been has been addressed by researchers is he measuremen of rading volume. Generally, hree kinds of measures, namely, number of rades, volume of rade or oal dollar value of rades have been used as a proxy of volume. The heoreical models of he pas did no suppor he effec of rade size in he volailiy volume relaionship. However, recen models consider he effec of rade size on he volume volailiy relaionship bu repor conradicory resuls. On one hand, some models (Grundy and McNichols, 989; Holhausen and Verrecchia, 99; Kim and Verrecchia, 99) show ha informed raders prefer o rade large amouns a any given price and hence size is posiively relaed o he qualiy of informaion and is herefore correlaed wih price volailiy. On he oher hand, some oher models (Kyle, 98; Admai and Pfeiderer, 988) indicae ha a monopolis informed rader may disguise his rading aciviy by spliing one large rade ino several small rades. Thus, rade size may no necessarily convey adverse informaion. Given he mixed empirical resuls beween price and rading volume especially in emerging markes conex, more empirical research from oher emerging financial markes is needed o beer undersand he price-volume relaionship. Very few sudies have examined he pricevolume relaionship in Indian marke. This paper represens one such aemp o invesigae reurns, volailiy and rading volume relaionship in Indian Sock marke.. The Sample and is Characerisics In his sudy our daa se consiss of all he socks of S&P CNX Nify Index. S&P CNX Nify is a well diversified sock index accouning for secors of he Indian economy. Table provides he lis of hese companies, indusry ype and he period considered in he analysis. Daa has been colleced for he period of s January o s December 8. For companies ha were lised afer s January, he daa has been aken from he lising dae o s December 8. The daa se consiss of 8674 daa poins of adjused daily closing prices and hree differen measures of daily volume (number of ransacions, number of shares raded and oal value of shares). The daily adjused closing prices have been used for esimaing daily reurns. The percenage reurn of he sock is defined as ln p R =, where, R p is logarihmic daily percenage reurn a ime and p and p are daily price of an asse on wo successive days - and respecively. Table presens he basic saisics relaing o he reurns and he squared reurns of each sock in he sample. W.P. No Page No. 6

7 Table : Lis of Consiuens of S&P CNX Nify This able provides he lis of consiuens of large capializaion socks of S&P CNX Nify, a value-weighed sock index of Naional Sock Exchange, Mumbai. Their indusry ype and daa period are also presened. Company Name Symbol Indusry Daa Period ABB Ld. ABB ELECTRICAL EQUIPMENT Jan o Dec 8 ACC Ld. ACC CEMENT AND CEMENT PRODUCTS Jan o Dec 8 Ambuja Cemens Ld. AMBUJA CEMENT AND CEMENT PRODUCTS Jan o Dec 8 Bhara Heavy Elecricals Ld. BHEL ELECTRICAL EQUIPMENT Jan o Dec 8 Bhara Peroleum Corporaion Ld. BPCL REFINERIES Jan o Dec 8 Bhari Airel Ld. BHARTI TELECOMMUNICATION - SERVICES Feb o Dec 8 Cairn India Ld. CAIRN OIL EXPLORATION/PRODUCTION Jan o Dec 8 Cipla Ld. CIPLA PHARMACEUTICALS Jan o Dec 8 DLF Ld. DLF CONSTRUCTION Jul 7 o Dec 8 GAIL (India) Ld. GAIL GAS Jan o Dec 8 Grasim Indusries Ld. GRASIM CEMENT AND CEMENT PRODUCTS Jan o Dec 8 HCL Technologies Ld. HCL COMPUTERS - SOFTWARE Jan o Dec 8 HDFC Bank Ld. HDFC BANKS Jan o Dec 8 Hero Honda Moors Ld. HONDA AUTOMOBILES - AND WHEELERS Jan o Dec 8 Hindalco Indusries Ld. HINDALC ALUMINIUM Jan o Dec 8 Hindusan Unilever Ld. HLL DIVERSIFIED Jan o Dec 8 Housing Developmen Finance Corporaion Ld. HDFCORP FINANCE - HOUSING Jan o Dec 8 I T C Ld. ITC CIGARETTES Jan o Dec 8 ICICI Bank Ld. ICICI BANKS Jan o Dec 8 Idea Cellular Ld. IDEA TELECOMMUNICATION - SERVICES Mar 7 o Dec 8 Infosys Technologies Ld. INFOSYS COMPUTERS - SOFTWARE Jan o Dec 8 Larsen & Toubro Ld. L&T ENGINEERING Jan o Dec 8 Mahindra & Mahindra Ld. M&M AUTOMOBILES - 4 WHEELERS Jan o Dec 8 Marui Suzuki India Ld. MARUTI AUTOMOBILES - 4 WHEELERS Jul o Dec 8 NTPC Ld. NTPC POWER Nov 4 o Dec 8 Naional Aluminium Co. Ld. NALCO ALUMINIUM Jan o Dec 8 Oil & Naural Gas Corporaion Ld. ONGC OIL EXPLORATION/PRODUCTION Jan o Dec 8 Power Grid Corporaion of India Ld. POWER&G POWER Oc 7 o Dec 8 Punjab Naional Bank PNB BANKS Apr o Dec 8 Ranbaxy Laboraories Ld. RANBAXY PHARMACEUTICALS Jan o Dec 8 Reliance Communicaions Ld. RCOMM TELECOMMUNICATION - SERVICES Jul 6 o Dec 8 Reliance Indusries Ld. RELIANC REFINERIES Jan o Dec 8 Reliance Infrasrucure Ld. RINFRA POWER Jan o Dec 8 Reliance Peroleum Ld. RPETRO REFINERIES May 6 o Dec 8 Reliance Power Ld. RPOWER POWER Feb 8 o Dec 8 Sayam Compuer Services Ld. SATYAM COMPUTERS - SOFTWARE Jan o Dec 8 Siemens Ld. SIEMENS ELECTRICAL EQUIPMENT Jan o Dec 8 Sae Bank of India SBI BANKS Jan o Dec 8 Seel Auhoriy of India Ld. SAIL STEEL AND STEEL PRODUCTS Jan o Dec 8 Serlie Indusries (India) Ld. STERLIT METALS Jan o Dec 8 Sun Pharmaceuical Indusries Ld. SUNPHAR PHARMACEUTICALS Jan o Dec 8 Suzlon Energy Ld. SUZLON ELECTRICAL EQUIPMENT Oc o Dec 8 Taa Communicaions Ld. TATACOM TELECOMMUNICATION - SERVICES Jan o Dec 8 Taa Consulancy Services Ld. TCS COMPUTERS - SOFTWARE Aug 4 o Dec 8 Taa Moors Ld. TATAMOT AUTOMOBILES - 4 WHEELERS Jan o Dec 8 Taa Power Co. Ld. TATAPOW POWER Jan o Dec 8 Taa Seel Ld. TATASTE STEEL AND STEEL PRODUCTS Jan o Dec 8 Uniech Ld. UNITECH CONSTRUCTION Jan o Dec 8 Wipro Ld. WIPRO COMPUTERS - SOFTWARE Jan o Dec 8 Zee Enerainmen Enerprises Ld. ZEE MEDIA & ENTERTAINMENT Jan o Dec 8 W.P. No Page No. 7

8 Table : Sample Summary Saisics of and Squared This able provides descripive saisics for reurn and squared reurn of all consiuens companies of NIFTY: Symbol; Mean, Sandard Deviaion, Skewness, and Kurosis over he period from January hrough December 8. Company N Mean SD Skewness Kurosis Mean SD Skewness Kurosis Squared ABB ACC AMBUJA BHARTI BHEL BPCL CIPLA CAIRN DLF GAIL GRASIM HCL HDFC HDFCORP HINDALC HLL HONDA ICICI IDEA INFOSYS ITC L&T M&M MARUTI NALCO NTPC ONGC PNB POWER&G RANBAXY RCOMM RELIANC RPOWER RINFRA RPETRO SAIL SATYAM SBI SIEMENS STERLIT SUNPHAR SUZLON TATACOM TATAMOT TATAPOW TATASTE TCS UNITECH WIPRO ZEE W.P. No Page No. 8

9 The saisics from Table show ha mos of he sock reurns are negaively skewed during he period, alhough he skewness is no large. The negaive skewness implies ha here is higher probabiliy of earning negaive reurns. These sock reurns also show higher kurosis (>). This implies ha he disribuion of reurns have fa ails compared o he normal disribuion. In squared reurn series, he kurosis is much higher han hree. This implies fa ails in volailiy and is an indicaor of ARCH effec. Given he muliple possible measures of rading volume and inconsisen resuls from previous research, we employ hree differen measures of rading volume: Daily number of equiy raded or daily number of ransacions (rade); Daily number of shares raded (volume); Daily oal value of shares raded (value). Table presens he year wise descripion of average daily measuremen of volume of he consiuens of NIFTY socks for each of hree measures. Table 4 repors he basic saisics relaing o he hree measures of rading volume of each sock. For he sample period, he average daily number of ransacions of Nify socks was around 7 wih around.84 million of raded shares. The average value of share raded per day was around Rs. 9. million. Table : Year wise descripion of average daily measuremens of rading volume of Nify socks This able provides he yearly esimaes of hree measures of daily volume i.e, Number of ransacions, Number of shares raded and Value of shares for he daa period. Year N Number of ransacions (Trade) Number of shares raded () Value of shares raded (Value) (Rs. Million) Table presens he Pearson correlaion beween he hree measures of daily rading volume. The hree measures of volume are closely relaed as would be expeced. For mos of he companies we found high correlaion beween all he hree measures of volume: he number of shares raded, he value of rades, and number of ransacions (more han.8). The measures of rading volume have been sandardized for furher analysis. The saionariy of he reurns, squared reurns and all hree sandardized measures of volume is esed using Augmened Dickey-Fuller (979) es. The resuls confirm ha all series used in our sample are saionary 4. 4 Resuls of he Augmened Dickey-Fuller (979) es on he reurns, squared reurns, and sandardized measures of volume (Number of ransacions, Number of shares raded and Value of rades) can be obained from auhors on reques. W.P. No Page No. 9

10 INDIAN INSTITUTE OF MANAGEMENT AHMEDABAD INDIA Table 4: Sample Summary Saisics of Value, and Trade This able provides basic Summary Saisics of daily rading volume. Daily rading volume is measured in hree ways: he daily oal value of shares raded (value), he daily number of shares raded (volume) and he daily number of equiy rades (rade). The mean, sandard deviaion, skewness and kurosis of sandardized value of value, volume and rade are presened. Mean SD Skew Kurosis Mean SD Skew Kurosis Mean SD Skew Kurosis Company N Value Trade ABB ACC AMBUJA BHARTI BHEL BPCL CIPLA CAIRN DLF GAIL GRASIM HCL HDFC HDFCORP HINDALC HLL HONDA ICICI IDEA INFOSYS ITC L&T M&M MARUTI NALCO NTPC ONGC PNB POWER&G RANBAXY RCOMM W.P. No Page No.

11 Mean SD Skew Kurosis Mean SD Skew Kurosis Mean SD Skew Kurosis Company N Value Trade RELIANC RPOWER RINFRA RPETRO SAIL SATYAM SBI SIEMENS STERLIT SUNPHAR SUZLON TATACOM TATAMOT TATAPOW TATASTE TCS UNITECH WIPRO ZEE W.P. No Page No.

12 INDIAN INSTITUTE OF MANAGEMENT AHMEDABAD INDIA Table : Pearson Correlaion beween Measures of Daily Trading This able presens he Pearson Correlaion beween Measures of Daily Trading namely Number of Transacions, Traded Quaniy and Turnover for he whole period. Company Number of Transacions and Traded Quaniy Number of Transacions and Turnover Traded Quaniy and Turnover ABB ACC AMBUJA BHARTI..9.9 BHEL.6.9. BPCL CIPLA CAIRN DLF GAIL GRASIM HCL HDFC HDFCORP HINDALC HLL HONDA ICICI IDEA INFOSYS ITC L&T M&M MARUTI NALCO NTPC ONGC PNB POWER&G RANBAXY RCOMM RELIANC RPOWER RINFRA RPETRO SAIL SATYAM SBI SIEMENS STERLIT SUNPHAR SUZLON TATACOM TATAMOT TATAPOW TATASTE TCS UNITECH WIPRO ZEE W.P. No Page No.

13 . Models for Invesigaing Empirical Relaionships among, s and Volailiy The sudy repored in his paper invesigaes relaionship beween rading volume and reurn, is asymmeric naure, and dynamic relaionship using OLS regression and VAR modeling approach. The relaionship beween volume and uncondiional volailiy and is asymmeric effec is invesigaed using OLS regression. We also es he mixed disribuion hypohesis (MDH) using GARCH model in which conemporary volume is used as an explanaory variable in he GARCH specificaion.. Trading and s The relaionship beween rading volume and price change and asymmeric naure is generally invesigaed hrough esimaing conemporaneous correlaion beween reurns and rading volume by using OLS equaion as follows: V α + β r + β = D r [] where, V = sandardized rading volume a ime, r is he reurn a ime and D = when r < and D = when r. Three alernaive measures of rading volume, daily oal value of shares raded (value), daily number of shares raded (volume) and daily number of rades (rade) have been used in he equaion as he dependen variable. The parameer β measures he parial correlaion beween absolue reurns and volume irrespecive of he direcion of reurn. The parameer β capures he asymmery in he relaionship. A saisically significan negaive value of β would indicae ha he relaion beween reurn and rading volume for negaive reurns is smaller han for posiive reurns.. Causal Relaion beween Trading and s The dynamic relaionship beween reurns and rading volume is esimaed using bivariae VAR model in which reurns and rading volume are used as endogenous variables. In his case also hree alernaive measures of rading volume, daily value of rades, daily number of shares and daily number of ransacions have been used. r = α + V = γ + i= i= α r i i γ V i i + + j= j= β V j δ r j j j [] The coefficiens α i and β j represens he effec of lagged reurns and lagged volume on he presen reurns. If β j = hen i can be concluded ha volume does no cause reurns. Similarly, γ i and δ j represens he effec of lagged volume and lagged reurn on he presen volume. The significance of he parameers δ j indicaes ha he causaliy runs from reurns o volume. If boh parameers β and δ are significan hen here exiss bi-direcional causal relaion beween reurns and rading volume. We repor boh Granger Causaliy es and VAR parameer esimaes o undersand he dynamic relaionship beween volume and reurns. We also invesigae he W.P. No Page No.

14 dynamic relaionship beween reurns and volume hrough impulse response funcion and variance decomposiion echniques... Funcion and Variance Decomposiion of s and Trading One of he well esablished mehods of VAR analysis is he impulse-response funcion, which simulaes he effecs of a shock o one variable in he sysem on he condiional forecas of anoher variable (Sims, 97, 98; Abdullah and Rangazas, 988). I explains he impac of an exogenous shock in one variable on he oher variables of he sysem. We use he impulseresponse funcion o analyze he impac of change in prices on volume and vice versa. Under he VAR represenaion, he variance decomposiion explains he relaive impac of one variable on anoher variable. This analysis measures he percenage of he forecas error of one endogenous variable ha is explained by oher variables.. Trading and Uncondiional Volailiy The relaionship beween rading volume and uncondiional volailiy (measured by eiher absolue reurns or squared reurns) and is asymmeric naure is invesigaed hrough OLS regression as follows: V α + β r + β = D r or, V = α + β r + β D r, [] where V = sandardized rading volume a ime, r is he reurn a ime and D = when r < and D = when r. As explained in secion. he parameer β capures he relaion beween absolue reurns/ squared reurns and volume and β he asymmeric relaionship. The significan and negaive value of he parameer β would indicae ha he relaion beween uncondiional volailiy ( r / r ) and volume would be lesser for negaive reurns han posiive reurns..4. Trading and Condiional Volailiy The condiional volailiy of he reurns is measured hrough GARCH model. Le r is he reurn a ime. The GARCH (,) model is given by: r = a + b r i= i i + ε ε ψ ~ N(, σ ) and [4] q i= i + σ = ω + α ε β σ. i p j= J j The parameers α i and β j measure he dependence of curren volailiy ( σ ) on innovaion erm ( ε i ) and pas volailiy ( σ j ) respecively. The persisence of he condiional volailiy is measured by α i + β j. The relaionship beween condiional volailiy and rading volume is Absolue reurns is a more robus measure of uncondiional volailiy as compared o squared reurns W.P. No Page No. 4

15 modeled by modifying GARCH equaion. The conemporaneous volume is used as explanaory variable in GARCH equaion (Lamoureux and Lasrapes, 99) as given by: r = a + b r i= i i + ε ε ψ ~ N(, σ ) and [] q p = ω + αiε i + i= j= σ β σ + χv J j. The significance of he coefficien esimae ( χ ) of rading volume indicaes he influence of rading volume on he condiional volailiy. 4. Resuls and Discussions on Relaionship beween, s and Volailiy In his secion of he paper we presen empirical resuls on he relaionship beween rading volume, reurns and volailiy (condiional and uncondiional). Firsly we repor he relaionship beween rading volume and price changes. Laer, we repor he relaionship beween volume and uncondiional and condiional volailiy. 4. Trading and s The resuls of he OLS regression using equaion [] o explain he relaion beween volume and price changes and is asymmeric naure are presened in Table 6. The esimaes of β, which measure he relaionship beween price changes and volume irrespecive of he direcion of he price change, are significan and posiive a % level (excep for Idea Cellular Ld., where he coefficien is significan a % level when value is aken as measure of rading volume and Reliance Power, where i is no significan when value and rade is aken as he measure of rading volume) across all hree measures of rading volume. The coefficiens are higher for mos of he companies, when he number of ransacions is aken as a measure of rading volume followed by volume of ransacions. The asymmeric behavior of relaion beween volume and reurns is indicaed by coefficien β. In almos all he cases, β is significan and negaive i.e. for mos socks β is negaive for a leas wo ou of he hree rading volume measures. The negaive value of β indicaes ha he relaion beween price changes and rading volume is smaller for negaive reurns han for posiive reurns. This is consisen wih Karpoff (986, 987) and Assogbavi e al. (99) who relae he observed price-volume asymmery in developed markes o he higher cos of shor sales as compared o margin buying. Only Reliance Power does no show asymmeric behavior in wo of he measure of volume (value and rade where i is insignifican). W.P. No Page No.

16 Table 6: Relaionship beween Sandardized Trading and s This able provides he coefficien esimaes from regressions of rading volume agains he price changes (e reurns) and asymmeric coefficien of he OLS equaion = α + β r + β D r, where V = sandardized rading V volume a ime, r is he reurn a ime and D = when r < and D = when r. Three measures of rading volume, he daily oal dollar value of shares raded (value), he daily number of shares raded (volume) and he daily number of equiy rades (rade) are considered. Parameer esimaes of all companies are presened. Value Trade Company α β β RSQ α β β RSQ α β β RSQ ABB -.74*.6* -.*.4 -.9*.9* -.9*. -.7*.* -.8*. ACC -.68*.7* -.79* *.88* -.84* *.* -.*.4 AMBUJA -.8*.* -.6* * -.8**. -.*.* -.*. BHARTI -.9*.4* -.*. -.9*.4* -.9*.8 -.4*.* -.48*.8 BHEL -.94*.* -.8* *.86* -.6*.8 -.9*.7* -.6*. BPCL -.48*.4* -.* *.4* -.4*.7 -.7*.47* -.46*.7 CIPLA -.6*.* -.44* *.6* -.7* *.48* -.47*.6 CAIRN -.6*.* -.88*.8 -.*.8* -.7*.6 -.*.4* -.*.4 DLF -.7**.7* -.4**.4 -.*.7* -.9* *.4* -.8*.47 GAIL -.97*.7* -.98*. -.7*.8* -.8*.8 -.9*.7* -.*.69 GRASIM -.*.7* -.*.6 -.9*.68* -.6*.6 -.*.4* -.86*.9 HCL -.*.9* -.*. -.9*.* -.*.8 -.4*.9* -.8*. HDFC -.89*.6* -.*.9 -.6**.49* -.7*.6 -.6*.94* -.99*. HDFCORP -.47*.74* -.6*. -.9*.7* -.4* *.* -.469*.86 HINDALC -.68*.4* -.4*. -.49*.* -.4*.8 -.4*.67* -.497*. HLL -.49*.78* -.4*. -.*.* -.6*.7 -.4*.4* -.9*.7 HONDA -.4*.* -.68*.6 -.4*.6* -.66* *.8* -.9*.86 ICICI -.8*.96* -.*.6 -.*.* -.*.8 -.*.8* -.88*. IDEA -.6.7** **.49* -.9**. -.47*.8* -.9*. INFOSYS -.*.6* -.97*.4 -.*.6* -.*. -.94*.9* -.77*.68 ITC -.48*.76* -.6* *.87* -.6*.8 -.4*.8* -.*.78 L&T -.*.9* -.4* *.8* -.6*.97 -.*.9* -.8*.9 M&M -.7**.7* -.67*.7 -.*.8* -.4*.4 -.8*.47* -.96*.6 MARUTI -.6*.6* -.64* *.46* -.6* *.67* -.8*.7 NALCO -.6*.9* -.98*.7 -.4*.4* -.96* *.7* -.8*. NTPC -.7*.* -.4*. -.9*.99* -.*. -.*.87* -.69*.8 ONGC -.48*.9* -.6* *.9* -.9* *.68* -.4*.8 PNB -.*.9* -.89*.7 -.4*.6* -.6*.8 -.4*.* -.77*.96 POWER&G -.4*.6* -.6* *.* -.79*.8 -.4*.* -.*. RANBAXY -.4*.7* -.8*. -.8*.7* -.46*.6 -.8*.9* -.46*.6 RCOMM -.7*.9* -.7* *.6* -.8* *.94* -.*.9 RELIANC -.*.98* -.4*.4 -.*.8* -.7* *.44* -.8*. RPOWER *.4* -.* RINFRA -.*.77* -.4*. -.4*.* -.8*.7 -.7*.88* -.4*.9 RPETRO -.44*.8* -.84*. -.48*.46* -.4*. -.46*.* -.44*.8 SAIL -.6*.* -.4*.8 -.6*.4* -.9*.6 -.4*.4* -.47*. SATYAM -.44*.4* -.64*.6 -.*.* -.* *.7* -.4*.64 SBI -.*.96* -.*.96 -.*.4* -.49* *.8* -.9*.8 SIEMENS -.*.49* -.69*.7 -.*.7* -.8*.4 -.*.67* -.6*. STERLIT -.67*.* -.*.6 -.4*.* -.49* *.97* -.8*.7 SUNPHAR -.*.8* -.44*. -.8*.9* -.4*. -.7*.4* -.4*.8 SUZLON -.*.44* -.*. -.7*.48* -.*.6 -.4*.7* -.*.7 TATACOM -.9*.94* -.6* *.96* -.* *.8* -.47*. TATAMOT -.8*.6* -.77*.9 -.9*.* -.*.9 -.*.9* -.9*.9 TATAPOW -.*.74* -.4*. -.86*.9* -.77*.9 -.*.7* -.6*.4 TATASTE -.6*.44* -.44*.66 -.*.74* -.84* *.96* -.7*.49 TCS -.99**.6* -.6* * -.7*. -.76*.* -.4*.9 UNITECH -.*.8* -.*.49 -.*.99* -.87* *.94* -.8*.89 WIPRO -.7*.7* -.* *.8* -.*.7 -.*.4* -.6*.7 ZEE -.6*.* -.86* *.9* -.*. -.6*.* -.6*.4 W.P. No Page No. 6

17 4. Causal Relaion beween Trading and s In order o invesigae dynamic relaionship beween reurns and rading volume, we analyze hese variables hrough a bivariae VAR model. We also explore lead-lag relaionship beween reurns and rading volume by using Granger Causaliy es (Smirlock and Sarks, (988), and Assogbavi e al. (7). Granger Causaliy es is a F es which checks he block exogeneiy. In equaion given earlier, i ess he null hypohesis ha reurn series is no affeced by pas volume (β j =) and ha he volume is no affeced by pas reurns (δ j =) separaely. Resuls of he es are repored in Table 6. The resuls of he Granger causaliy es indicae mixed resuls on effec of pas reurns on rading volume. When he number of ransacions is aken as a measure of volume, in case of socks he null hypohesis ha pas reurns does no cause rading volume (δ j =) is rejeced a % significance level, and for 7 socks i is rejeced a % significance level. On he oher hand, he null hypohesis ha he pas volume does no cause reurns (β j =) is rejeced in case of 6 socks a % significance level, and for 4 socks a % significance level. Similar 6 kind of resuls are found when oher wo measures of volume, daily number of shares raded and daily value of socks raded are used o es he dynamic relaionship beween reurns and volume. The Granger causaliy resuls show ha reurns cause volume and ha he pas rading volume also Granger causes reurns albei in lesser number of socks. This evidence suppors he sequenial processing of informaion hypohesis argued by Smirlock and Sarks (98). They propose ha he informaion arrives sequenially raher han simulaneously in he marke. The evidence ha volume Granger causes reurns for some socks suppors heoreical models which imply ha here is informaion conen in volume which predics fuure reurns. The difference in direcion of causaliy across socks may be due o naure of he indusry, ypes of invesors ec. The auoregressive coefficien of reurn and parial coefficien of reurn on pas volume and auoregressive coefficien of volume and volume on pas reurns are also esimaed hrough bivariae VAR model as explained in equaion []. In his case also, all he hree measures of volume have been considered and he resuls are repored in Table 8. We find ha he all hree measures of volume are highly auocorrelaed wih pas volume. These resuls provide evidence ha in Indian marke, informaion is processed sequenially. Even afer facoring in high auocorrelaion in volume, he parial correlaion beween volume and pas reurns are significan and mos of he significance is found wih only las day reurn ( socks when number of rades, 6 socks when volume and socks when value is aken as measure of raded volume). The reurn series are also auocorrelaed up o lag or (in mos of he socks) and he coefficiens are small. In some cases, (lesser han dependence of volume on pas reurns) we find significan parial correlaion beween reurns and pas volume and in hese cases, mos of he significan coefficiens are for relaion beween reurn and las day volume (7 socks when number of rades, 4 socks when volume and 6 socks when value is aken). 6 In case of oal number of daily shares raded, socks a % significance level and by 7 socks a % significance level have rejeced he null ha reurns do no cause volume. When he daily value of shares raded is used, socks a % significance level and by 8 socks a % significance level. Granger causaliy from volume o reurns is rejeced by socks a % significance level and by socks a % significance level and 7 socks a % significance level and by 4 socks a % significance level when oal number of shares raded and oal value of shares are considered respecively. W.P. No Page No. 7

18 Table 7: Granger Causaliy Tes (Wald Tes) This able provides he F es resuls of resricion on auoregressive parameers β j = and δ j = of he bivariae VAR model = i= j= r = α + + α ir i β jv j and V + + γ γ iv i i= j= δ r j j.where V is he sandardized rading volume a ime, and r is he reurn a ime. Three measures of rading volume, he daily oal dollar value of shares raded (value), he daily number of shares raded (volume) and he daily number of equiy rades (rade) are considered. Parameer esimaes of all companies are presened. Value Trade Company β j = δ j = β j = δ j = β j = δ j = ABB ACC.87.78*.6.*.7.4** AMBUJA * BHARTI BHEL * * * BPCL 7.* ** **.8 CIPLA.99.6* * CAIRN.8.**.9.9**. 4.** DLF GAIL GRASIM.97.7**.7.8** HCL 9...** 4.8* * HDFC HDFCORP.6*.9**.7.9** * HINDALC.9**.**.** 47.9* 6. 4.* HLL HONDA * ** ICICI.6** ** 9.7* IDEA INFOSYS.7*.9** 6.6.8* * ITC.7* 8.* L&T 6.7.7** ** M&M MARUTI *..9* NALCO.8 7.*.74.8**.8 4.6* NTPC 6.76*.98* *.44 ONGC PNB ** POWER&G RANBAXY ** * RCOMM RELIANC 8.9.4** ** 7.9 RPOWER RINFRA 4.4** * 8.7 RPETRO 7.8.7* **.9.6** SAIL * * 7.6.4* SATYAM.6.6* * * SBI 4.9.9*.8 7.4* * SIEMENS ** * STERLIT * 7.96* SUNPHAR.9** **.7* SUZLON *.9*.8* 8.9* TATACOM TATAMOT.84.** *..8** TATAPOW 4.* 79.4*.* 7.94*.* 4.* TATASTE 6. 7.* * TCS * UNITECH * 6.8* 77.9* WIPRO * ZEE.9*.9* ** ** W.P. No Page No. 8

19 Table 8: Resuls of Bivariae VAR model = This able provides he parameer coefficien esimaes of he bivariae VAR model r + + α αir i β jv j and V = γ + i= γ V i i + j= δ r j j.where V is he sandardized rading volume a ime, and r is he reurn a ime. Three measures of rading volume, he daily oal dollar value of shares raded (value), he daily number of shares raded (volume) and he daily number of equiy rades (rade) are considered. Parameer esimaes of all companies are presened. a) VAR model wih reurns and number of ransacions as volume measure i= j = r = α + αir i + β jv j V = γ + γ iv i + i= j = i= j= δ r j j Company α α α α α 4 α β β β β 4 β γ γ γ γ γ 4 γ δ δ δ δ 4 δ ABB.9.6* *.8*..8*.8* ACC *.7*.6.9*.*.* AMBUJA.. -.* *.*.*.9*.*.* * BHARTI.8* * *.8*.8*.9*.** BHEL * ** *.9*..**.7* -.* -.* -.*.. BPCL..8* * *..9*.*.6*..... CIPLA..8* -. -.* *.4.*.4.6*.* CAIRN * * -.7.* **.. -.* DLF *.8* -.4.8* GAIL *.. -.7* *.6**.4*.9*.6* GRASIM..6* -..6* *.9*.8*..* HCL -.7.7* * -. -.* *.* * -.* -.4.8* -.. HDFC * -. -.* *.6*.*.4*.* ** HDFCORP.*. -.9* -.6* * *..4*.6*.7* -.**. -.* -.* -.* HINDALC -..* * **.7..7*..*.* *. -.6* HLL * *.*.9*.*.7* HONDA * -.* *.4.*..9*. -.* ICICI.8.* -.6* *.7* -..*.8* -.9* IDEA -..** * INFOSYS..8* -.6* * *.4*.*.6*.8* -.* ITC *.8*.* -..4* L&T..8* -.** *.*.8*.*.* * M&M..4* -.** ** *.7*.*.*.* W.P. No Page No. 9

20 company α α α α α 4 α β β β β 4 β γ γ γ γ γ 4 γ δ δ δ δ 4 δ MARUTI *..8* -..* -.* NALCO *..*.6*.7*.*. -.*. -.* NTPC * *.9* -.* * -.8**.8*..6*.** ONGC.67.9* -.69* *.8*.*.*.9* * PNB.6** *.9*..*.4.** POWER&G -.9.* * -.4.8* RANBAXY -..** * *.8*..4.*. -.* RCOMM ** * ** *.9**.*..* * -.4. RELIANC * *..4*.4*.* RPOWER -.9.6* -.4.6** *.*.*..9*.6* RINFRA..6* -.7*. -.4** ** *.*.9* -..6* RPETRO..* **....6*..8* -..8* -..4** SAIL.8.* ** *.6*.4*..*.*..6** SATYAM -..** *.7*.4.4*.4* -.* * -.* SBI.7.6* ** *.*.6*.*.*..9** * SIEMENS.7.* *...6**.9*.*... -.* STERLIT.4.7* *.7*..6*..*..*..4* -..4* -. SUNPHAR *..*..*..4*.* SUZLON * * -..* -.6.* -.7**.7** * TATACOM -..8* ** *.**..*.* TATAMOT -..* *.9*.9*.8*.*.7** * TATAPOW -..4* **. -.**. -.9*.66* *..9*.*.9*.7* TATASTE. -.7.* *.9*.9*.6*.7*. -.* -.* -.*.4 TCS -. -.*. -.* **.*..7** -..* -....**.** UNITECH.** -....**.** ** *.9*.4*.8*.* -.*.6* -.* WIPRO -..* *.*.8*.9*.7* * ZEE -.9.* *.*.9*.*.* * W.P. No Page No.

21 b. VAR model wih reurns and he daily number of shares raded as volume measure r = α + αir i + β jv j V = γ + γ iv i + i= j = i= j= δ r j j Company α α α α α 4 α β β β β 4 β γ γ γ γ γ 4 γ δ δ δ δ 4 δ ABB.9.6* *.*.8*.4* ACC *.6*.*.*.*.7* AMBUJA.. -.6* *..* BHARTI.8* * ** BHEL * *.*.9*.*.** -. -.* BPCL..8* * *..9*.*.8* CIPLA..8* -. -.* *.*.*.**.9*.6** CAIRN * * -.**.*..8.** ** DLF *.*..8* GAIL *.. -.7* *.*.*.7*.* GRASIM..* -.4.6* *.8*.*..6* ** -.6 HCL -.7.7* * -. -.* ** *.*.*..* -.7* -.4.* -.7**. HDFC * -. -.* HDFCORP.*. -.9* -.6* * ** **.....*. -. HINDALC -..* * * *.4.8* * * HLL *.*.*.*.*. -.** HONDA *.8*.8*.*.8*. -.* ICICI.8.* -.6* *.7*.*.*.* IDEA -..** *.6*.** -..* INFOSYS..8* -.6* *.8...9*.4*.8*.6*.6* -.* ITC *.*.9*.4.* L&T..8* * *.*.*.9*.9*. -.9* M&M..* -.* *.*.*.4*.*.** MARUTI *..* -..9* -.6* NALCO *.4*.*.9*.7*.6* NTPC * *.4.*.6.6*.* ONGC.7.9* -.7*....** *.*.*.*.8* PNB.6** * *.7*..7*..* POWER&G -.7.4* ** * -.8*.4* RANBAXY -..4** * *.8*..**.*. -.* W.P. No Page No.

22 company α α α α α 4 α β β β β 4 β γ γ γ γ γ 4 γ δ δ δ δ 4 δ RELIANC *.9*.6*.6* -..* RPOWER -.4.7* *.9.*..*.87* RINFRA..6* -.7* *.*.*.9*.4* RPETRO..* *..6* -..* -..6**.6**.7. SAIL.76.47** ** *..7*..8*.* SATYAM -..** * *.9*..*.7* -.9* * -. SBI.7.* ** *.*.*.*.7*.* SIEMENS.7.* *.9*.4.*.6*.* STERLIT.4.6* -..4** *.9*..46*.9*.9*.4*.6*..4** -.*.* -. SUNPHAR *..6*.6*.* SUZLON * ** * -.9**.* -.6*.* * TATACOM -..8* *.* -.4.*.9* TATAMOT -..* *.8*.7*.7*.* TATAPOW.9.8* -.* ** -.7**.4* -.4*..9*.*.*.*.8*.* TATASTE..7* *.*.*.6*.8* -..9**.. -. TCS * -.* -.* * UNITECH.** -....* **..7*..* -.9*.8* -.*. -.9*. -.6* WIPRO -..* *.*.7*.*.* ** ZEE -.9.* *.*.**.6*.* * W.P. No Page No.