A Testing of Lead-lag Relationship between Nifty Spot and Futures Index Returns and Volatility

Transcription

1 A Tesing of Lead-lag Relaionship beween Nify Spo and Fuures Index Reurns and Volailiy 3 A Tesing of Lead-lag Relaionship beween Nify Spo and Fuures Index Reurns and Volailiy Govind Chandra Para, Shaki Ranjan Mohapara Absrac I has been almos a decade since he inroducion of derivaives insrumens in Indian bourses like Opions and Fuures rading replacing hereby age old Badla ransacions and almos wo decades since he inroducion and implemenaion of liberalizaion, privaizaion and globalizaion policies in Indian economy. This has resuled in a sea change in growh and developmen of Indian economy and enhanced aciviy and rade in Indian sock markes. This paper examines and compares he reacion of fuures and cash markes o he flow of informaion and ries o esablish a lead-lag relaionship beween he wo markes in erms of reurns and volailiies being experienced by NIFTY and NIFTY fuures indices in wo differen markes. Our resuls suggess ha hough here is a srong conemporaneous and bi-direcional relaionship among he reurns in he spo and fuures marke, he spo marke has been found o play comparaively sronger leading role in disseminaing informaion available o he marke, and herefore said o be more efficien. Apar from his, here is also inerdependence (in boh direcion) and herefore symmeric spillovers among he sock reurn volailiy in he spo and fuures marke. Keywords: Lead-lag, VAR model, GARCH model JEL Classificaion: G Inroducion Indian capial markes have winessed major ransformaions and srucural changes since pas one or wo decades as a resul of iniiaion of liberalizaion, privaizaion and globalizaion policies and consequenial financial secor reforms. Inroducion of derivaives insrumens in Indian sock exchanges is one such imporan sep in righ direcion replacing age-old Badla ransacion, he aim of which was o esablish greaer sabilizaion in markes and o inroduce sophisicaed risk managemen ools. Worldwide, he fuures rading in sock markes has grown rapidly since heir inroducion because i has conribued in achieving economic funcions such as price discovery, liquidiy enhancemen, porfolio diversificaion, speculaion and hedging agains he risk of adverse price movemens. Movemens in cash marke ges grealy affeced by speculaion, hedging and arbiraging aciviies in fuures marke. Thus, i becomes imporan o undersand he influence of one marke over he oher and heir reacion o flow of informaion. Whichever marke reacs faser o he news is said o lead he oher marke. In an efficien capial marke where all available informaion is fully and insananeously uilized o deermine he marke price of securiies, price of derivaives and spo marke should move simulaneously wihou any delay. However, due o marke fricions such as ransacion coss, capial marke microsrucure effecs ec., significan lead-lag relaionship beween he markes has been observed. Wih he advancemen in echnology, invesor awareness, consciousness, involvemen and excessive greed of earning Govind Chandra Para is Assisan Professor a Regional College of Managemen Auonomous, Bhubaneswar. govindpara@yahoo.com Shaki Ranjan Mohapara is Dean, MBA Deparmen, Biju Panaik Universiy of Technology. shaki.r.mohapara@gmail.com

2 4 Inernaional Journal of Financial Managemen superior reurn, greaer reach of markes o widely scaered invesors, i is foolish o believe ha any marke can lead he oher in erms of number of days. If a all a marke leads he oher, i will be hardly for a few minues. Thus, we have regressed high frequency daa, i.e., one- minue reurns and volailiy here in cash and fuures markes o esablish he lead-lag relaionship beween he wo. The uncerainy of exising heoreical lieraure implies ha he issue of wheher derivaives marke leads or lags he underlying spo marke remains an empirical one. Thus, he aim of his sudy is o esablish lead-lag relaionship beween spo and fuures markes hrough regression of fuures and spo NIFTY index reurn and volailiy uilizing Vecor Auo Regression (VAR) model and ime varian Generalized Auo Regressive Condiional Heeroskedasiciy (GARCH) class of models. Lieraure Review As far as he emporal relaionship among he spo and derivaives viz., fuures and opions (call and pu) marke is concerned, several sudies have aemped o examine he lead-lag relaionship beween he spo and he fuures marke boh in erms of reurn and /or volailiy. These sudies include Ng.(987), Kawaller, Koch and Koch (987), Harris (989), Soll and Whaley (990), Chin, Chan & Karolyi (99), Chan (992), Abhyankar (99), Koumos (996), Jong and Nijman (997), Choudhury. T (997), Pizzi (998), De Jong (998), Charah (998), Abhyankar (998), Min (999), Tse (999), Frino (2000), Cellier (2003), Thenmozhi (2002), Anand Babu (2003), Liena and Yang (2003), Simpson (2004) ec. Almos all of hese sudies have concluded ha here is a significan lead-lag relaionship among he spo and fuures and / or opions marke, and also have ried o provide he possible explanaion behind his. Mos of he sudies have suggesed ha he leading role of fuures / opions marke varies from five o hiry minues, while he spo marke rarely leads he oher markes beyond five minues. While explaining he causes behind such relaion, Kawaller e al.(987) aribue he sronger leading role of he fuures marke o he infrequen rading of componen socks. Though a he same ime, Soll & Whaley (990), Chan (992) ec., proved he exisence of such relaion even in case of highly raded socks or afer adjusing for infrequen rading of componen socks. Chan (992) have invesigaed he inraday lead-lag relaionship beween MM cash index and MM and S&P fuures index reurns under differen siuaions. Their resuls confirmed he leading role of he fuures marke even agains all componen socks. They have also empirically proved he leading role of he fuures marke for he release of any marke-wide informaion. Charah (998) had examined he inraday behaviour of he spo and fuures marke following he release of informaion and also invesigae he role of such informaion in he volailiy spillover among he wo markes. Their resuls have suppored ha one marke leading o greaer volailiy in he oher is parly driven by informaion; herefore he leading role played by he fuures marke may be he resul of new informaion efficienly refleced in he fuures marke. Abhyankar (998) had ried o capure he linear and nonlinear casual relaionship beween he index fuures and spo marke. Their resuls evidenced ha he index fuures end o lead he spo index by abou five o fifeen minues. The linear lead-lag relaionship was found o persis even afer he reurn series were adjused for volailiy persisence. Their mos imporan finding was ha if non linear effecs are aken ino consideraion, neiher marke was found o lead or lag he oher. De Jong (998) have confirmed ha even in he presence of significan conemporaneous correlaion among he spo, fuures and he opions marke, he fuures price changes lead boh he changes in he cash index and index opion by five o en minues. Bu, among he cash and he opions marke, he relaions are largely symmerical and neiher marke consisenly leads he oher. Pizzi M.A.(998) had aemped o invesigae he relaionship beween S&P 00 sock index and hree and six monhs fuures conracs over he same ime period. By applying he Engle-Granger wo sep procedure, hey have found a significan co-inegraion among he spo index wih boh he hree and six monh fuures index. Their resuls clearly revealed ha boh he hree and six monhs fuures marke lead he spo marke by a leas 20 minues. Min and Najand (999) had invesigaed he possible leadlag relaionship in reurn and volailiies beween cash and fuures marke in Korea. Their resuls have suggesed ha unlike he lead-lag relaionship in he reurns of spo and fuures markes, here is significan bu ime-dependen bidirecional casualy beween he markes, as far as volailiy ineracion among he markes is concerned.

3 A Tesing of Lead-lag Relaionship beween Nify Spo and Fuures Index Reurns and Volailiy Frino (2000) had examined he emporal relaionship among he spo and fuures marke around he release of differen ypes of informaion. They had found ha he lead of he fuures marke srenghens significanly around he release of macro-economic informaion. While, he leading role of he fuures marke weakens around sock specific informaion release. Therefore, according o hem he disinegraion in he relaionship beween he wo markes is mainly driven by noises associaed wih rading aciviy around he release of differen ypes of informaion. By looking a he Indian markes, Thenmozhi (2002), Anand Babu (2003) ec., had found ha he fuures marke in India has more power in disseminaing informaion and herefore has been found o play he leading role (for one or wo days) in he maer of price discovery. Anand Babu and Bhole (2003) aemped o examine he emporal relaionship beween he index fuures and is underlying cash index by using daily price observaions. Their resuls had suppored he fac ha he index fuures marke in India leads he underlying Nify index marke and he lead-lag paern beween hose wo markes keeps changing over differen periods. Research Objecives The presen research is being conemplaed wih he following specific objecive: To examine he lead-lag relaionship (if any), boh in erms of reurn and volailiy, among Indian spo and derivaives viz., fuures marke. If such relaionship exiss, hen he focus will be o es which marke leads or lags he oher marke and by how much ime gap. Sample Daa In order o examine he lead-lag relaionship beween he underlying spo and fuures marke, he basic daa used are inraday price hisories for he nearby conrac of CNX NIFTY index fuures and CNX NIFTY spo index raded and recorded in a frequency of one minue inerval during a period of welve monhs for he calendar year 200. Each day rading hour has been pariioned ino one minue inervals. The las price observaion of each one minue inerval has been picked up from he rading daa of spo and fuures index. Daa on fuures index comprise price series only for he near monh conrac. If here is any missing observaion due o non rading in any inerval, he common pracice is o remove ha specific inerval from he sample. All he relevan daa relaing o he spo and fuures marke in India has been colleced from NSE websie, i.e., www. nseindia.com and also he CD-ROM provided by NSE, Mumbai. The inraday price series boh in he spo and fuures marke have been sored ou in MATLAB version 6. and in MS-EXCEL. Mehodology Generally, as he previous sudies sugges, some lead-lag relaionship exiss in spo and derivaives markes. Thus, here we ried o derive he inraday lead-lag relaionship among CNX NIFTY cash and fuures index reurns and volailiy hrough he models as described below: To find ou he significan lengh of leads or lags, we ran a cross correlaion es among he reurns in spo and fuures markes in order o deermine he exen o which he wo markes are correlaed o each oher. In order o ge he lengh of leads (b +k ) and he lengh of lags (b -k ), we have examined he cross correlaion coefficien beween he curren spo reurns (R S, ) and pas fuures reurns (R F,k) and beween he pas cash reurns (R S,-k ) and curren fuures reurns (R F, ) respecively. The significan lengh of lead or lag will be deermined hrough he cross correlaion coefficiens as deailed above based upon he sudies made by Soll and Whaley (990), Abhyankar (99), Min and ohers (999). Now, he lengh of lead or lag can be deermined by he -es. Afer deermining he lead-lag lengh, he nex sep is o examine he lead-lag behaviour beween he cash and fuures markes by esimaing he following regression equaions: n R = a + b R + dz + C () S, k F, + k - k =-n Wherein, R S, and R F, represen inraday reurns in cash and fuures markes a ime, colleced a one minue inerval each. The coefficiens wih negaive subscrips (b -, b , b -n ) are lag coefficiens and hose wih posiive subscrips (b, b , b n ) are lead coefficiens. If he lag coefficiens become significan, hen from he above equaion, i can be inferred ha lef hand side reurn, i.e., spo reurn lags he righ hand side reurn, i.e., fuures reurn. In oher words, significance of lag coefficiens

4 6 Inernaional Journal of Financial Managemen in he above menioned equaion reveals ha fuures lead he cash index reurn. On he oher hand, if he lead coefficiens become significan, hen from he above equaion, i can be inferred ha lef hand side reurn, i.e., spo reurn leads he righ hand side reurn, i.e., fuures reurn. In oher words, significance of lead coefficiens in he above menioned equaion reveals ha spo index leads he fuures index reurn. If he conemporaneous b coefficien (b 0 ) shows he maximum value among all oher lead-lag coefficiens, hen i can be inferred ha he wo markes move simulaneously wihou any lead or lag ime. Again, along wih he highes value of conemporaneous b coefficien (b 0 ), if boh lead and lag coefficiens are found o be significan, hen neiher marke is said o lead or lag he oher and boh he markes reac simulaneously o flow of informaion. Z - is an error correcion erm aken o be he firs lag of conemporaneous difference beween he wo price levels o accoun for he possibiliy ha he wo reurn series are co-inegraed as per he sudy made by Engel and Granger (987). ECT = Y - a - a X (2) The above-menioned equaion is he equaion for error correcion erm represening he residuals from he equilibrium equaion lagged by one period indicaing ha wheher he proporion of disequilibrium from one period is correced in a laer period and he relaive magniude of adjusmens in each marke owards equilibrium. Again, he inraday lead-lag relaionship among he spo and fuures index reurns is also esed hrough anoher imporan and reliable model called Vecor Auo Regression (VAR) model. I is basically an economeric model used o capure he inerdependence beween muliple ime series, generalizing he univariae AR models. All he variables in a VAR model are reaed symmerically by including for each variable an equaion explaining is evoluion based upon is own lags and lags of all oher variables in he model. The model is delineaed below. S, 0 i S, - i F, - - F, 0 i F, - i S, - - (3) (4) where, R S, and R F, represen inraday reurns in spo and fuures markes. The value of ime lags aken o be here. Now, he lead-lag relaionship beween spo and fuures markes in erms of inraday reurn volailiy, popularly known as volailiy spillover, has been esed hrough anoher VAR model as shown below : s = a + a s + b s + C () S, 0 S, - j F, - j sf, = a 0 + ass, - + b jsf, - j + C (6) Here, GARCH(,) residuals as he proxy measure of volailiy are incorporaed in he above VAR model. The GARCH residuals are generaed boh for spo and fuures index reurn series separaely. The value of lags are also aken o be here and one minue inerval reurns idenical wih previous calculaions are also considered. Empirical Findings The descripive saisics of inraday CNX NIFTY index reurns in cash and Fuures marke for he sample period from s January 200 o 3s December 200 are shown in Table. The able reveals ha he mean inraday reurns has been found o be significanly close o zero. The difference beween he maximum and minimum value of NIFTY reurns (range) in cash marke is higher han fuures marke. The range of variaions of reurn and sandard deviaion are almos similar in boh cash and fuures markes which may help o believe ha fuures marke reduces he reurn variaion in spo marke. Now, if we look ino he skewness figures ha represen he asymmery in reurn series, i can be seen ha boh he reurn series in cash and fuures markes are negaively skewed. This negaive skewness reveals ha he chances or he probabiliy of negaive reurn deviaion from he average reurn is higher han ha of a posiive deviaion. A he same ime, kurosis figures represen ha he value is more han hree and herefore all reurn disribuions are lepokuric in naure or fa ailed. This represens ha he probabiliy of large reurn deviaions are comparaively higher which indicaes he level of desabiliy in he marke. The Jarque-Bera saisics and heir probabiliy show ha he reurn series in boh cash and derivaives markes are non-normal. The auocorrelaion and parial auo correlaion figures for one minue cash and fuures markes index reurns are represened in Table 2 and 3. The auocorrelaion and parial auo correlaion coefficiens for NIFTY cash and fuures markes have been compued up o enh

5 A Tesing of Lead-lag Relaionship beween Nify Spo and Fuures Index Reurns and Volailiy 7 order, seleced randomly. The serial correlaions of he cash and fuures marke s index reurns for he firs lag are significanly large and slowly reduces for oher lags. Though relaively small in magniude, he auo correlaion figures of he cash and fuures index reurns are significan up o six lags. Consisen wih previous sudies, our auo correlaion esimaes in he cash index reurn are found o be posiive a he firs hree lags and hen shifed o a negaive serial correlaion afer lag 2. The difference in he resul of auo correlaion of cash and fuures index reurns may be aribued o he non-synchronous rading of underlying NIFTY socks in boh he markes. The basic sep for deermining he lead-lag relaionship beween wo differen markes hrough regression equaion is o deermine he significan lengh of leads and lags proposed o be included in he equaions. By looking ino he cross correlaion among he one minue reurns of wo differen markes, e.g. spo and fuures markes, we can assess he possible lead-lag relaion among wo markes. The cross correlaions among wo one minue NIFTY reurn series are presened in Table 4. The significan cross correlaion figures can sugges he number of leads and lags expeced o be included in he regression analysis. The cross correlaion figures have been esimaed up o en leads and lags. The resuls presen ha hough he conemporaneous correlaion among he NIFTY reurn series are found o be highly significan, boh he lead and lag coefficiens are also found o be significan o some exen. Apar from using only a muliple regression model o analyse he inraday lead lag relaionship among he spo and fuures markes, anoher aemp has also been made o explore he inerrelaionship using VAR model. Inraday inerrelaionship among he index reurns in cash and fuures markes along wih volailiy spill over in he markes are described in he following secions. Lead-Lag Relaionship among Cash and Fuures Index Reurns Lead lag relaionship among cash and fuures markes for NIFTY index reurns have been measured wih minue by minue rading daa. In curren capial marke scenario wih echnological innovaions and efficien markes, no marke is expeced o lead or lag by a day or wo. If a all lead or lag effec exiss beween differen markes, i will be for a maximum period of few minues. For spo marke, he lead-lag relaionship has been esimaed for boh simple reurn and cash reurn innovaions derived from he AR() process as indicaed by he significan auocorrelaion in he spo index reurn. Inraday lead-lag relaionship among he spo and fuures index reurns for boh spo reurn and spo reurn innovaions are repored in Table. The able comprise regression resuls where he presen spo reurn is regressed on he pas and fuure reurn and a lagged error correcion erm aking ino consideraion he possible co-inegraion among he spo and fuure index reurns. Regression resuls, as shown in cross correlaion figures, reveal ha boh lead and lag coefficiens in he index fuures marke in India are found o be significan. I is observed from he able ha he conemporaneous b coefficien b 0 exhibis highes value boh for spo reurn and spo reurn innovaions. This indicaes ha boh spo and fuures markes reac simulaneously o mos of he news flow. The able also reveals ha lag coefficiens are found o be significan up o one lag wherein lead coefficiens are significan up o wo lags. Again, he join significance ess (F and LR es) reveal ha he join significance of he lag coefficiens are sronger han ha of lead coefficiens and vice versa for spo reurn innovaions. Whereas, he fuures marke leads he spo marke by one minue only, he spo marke leads he fuures marke by wo minues. Anoher imporan dimension of his sudy is o uilize bivarie VAR model on he inra day spo and fuures index reurn series in India as shown in Tables 6 and 7, one for spo and fuures index reurn and anoher for spo reurn innovaion and fuures index reurn series. As in case of previous regression model, here also lags of five inervals are considered for boh he reurn series. This model also considers error correcion erm as an exogenous variable and herefore have been aken ino accoun in boh he equaions of he model. The VAR resuls reveal ha he lagged fuure coefficiens in spo reurn and lagged spo coefficiens in fuures reurn are found o be significan up o fourh and firs order respecively. Also, he overall significance es, i.e., Chi-square es reveals ha he lagged NIFTY spo reurn coefficiens are comparaively sronger han he NIFTY fuures reurn coefficiens. Apar from his, Granger casualy es resuls provide he informaion ha hough boh he null hypohesis (fuures does no Granger cause spo and spo does no granger

6 8 Inernaional Journal of Financial Managemen cause fuures) are rejeced, he power of rejecion is more sronger in case of spo does no granger cause fuures, hus revealing he fac ha spo marke is more sronger in disseminaing informaion and he discovery of prices. The same calculaion for spo reurn innovaions and fuures marke also reveals he same resul, i.e., sronger role of spo marke in Granger causing he fuures marke. Lead-Lag Relaionship among Spo and Fuures Index Reurn Volailiy Apar from he inerdependence in erms of only reurns in differen markes, here also exiss inerrelaionship among volailiy of differen markes. In oher words, here is a volailiy spillover from one marke o anoher marke. This invesigaion has been carried ou by using differen proxy measures simulaneously in a similar kind of VAR framework. The resuls owards he inraday volailiy spillover considering differen proxy measures in spo and fuures marke in India are shown below: The inraday inerrelaionship among he spo and fuures index reurn volailiy is presened in Table 8 uilising GARCH(,) framework basing upon a series of spo and fuures reurn residuals as a proxy for he volailiy measure. The resuls clearly reveal ha four ou of five lagged volailiy in one marke can significanly explain he volailiy in he oher marke. The individual significance of lagged spo reurn volailiy in explaining he volailiy in fuures marke and a he same ime, he significan role of lagged fuures reurn volailiy in describing he volailiy in spo marke, can reveal he fac ha here is a srong bidirecional inerrelaionship among he spo and fuures index reurn volailiy. Therefore, i is difficul o predic which marke leads he oher marke. This problem can be resolved by looking a he join significance es on he lagged coefficiens of spo reurn volailiy and fuures reurn volailiy in explaining he inraday volailiy of he oher marke. I should be noed here ha he join significance ess are carried ou only o es he significance of he lagged coefficiens in he couner marke, no he own lagged coefficiens of any marke. No only he individual es of significance, bu he join significance es also exhibis he same picure. The lagged coefficiens in any couner marke are also found o be joinly significan as refleced in Chi-square es. Here, he inraday volailiy in spo index reurn are found o play sronger leading role in predicing he fuure movemens of he inraday volailiy in he fuures marke going by he residuals from he GARCH(,) model. Since he sronger leading role of he spo reurn volailiy is suppored by a VAR framework, i is expeced o be robus in Indian markes. Thus, we can conclude ha here is a sysemaic paern in he inraday volailiy spillover among he spo and fuures marke in India. Table Descripive Saisics of Inraday Spo and Fuures Index Reurns NIFTY SPOT Fuures Index Mean Median Maximum Minimum Sd. Deviaion Skewness Kurosis Jarque Bera Probabiliy Sum Sq. Deviaion No.of Observaions Table 2 Auo-Correlaion Coefficiens of Inraday Reurns in Spo and Fuures Marke Auo-Correlaion Tes No. of Lags NIFTY Spo Fuures 0.23 ** ** ** 0.04 ** ** * ** ** ** ** ** ** ** ** * * * * * * No.of Observaions

7 A Tesing of Lead-lag Relaionship beween Nify Spo and Fuures Index Reurns and Volailiy 9 Table 3 Parial Auo-Correlaion Coefficiens of Inraday Reurns in Spo and Fuures Marke Parial Auo-Correlaion Tes No. of Lags NIFTY Spo Fuures 0.23** 0.067** ** ** ** ** ** ** ** ** ** -0.00** ** ** 8-0.0** ** ** ** * 0.00* No.of Observaions Noe : ** and * represen significan a % and % level of significance. Above wo measures are required o find ou he significan number of lags in an ARMA framework Table 4 Cross Correlaion Coefficiens of One Minue Reurns among NIFTY Spo and Fuures Markes No. of Lags Coefficien values Table Lead-lag Relaionship among NIFTY Spo and Fuures Index Reurns NIFTY Spo Reurn Consan a (0.083) FUTIDX( ) b (0.672) FUTIDX( 4) 0.06 b 4 (.338) FUTIDX( 3) b 3 (2.666) FUTIDX( 2) b 2 (.348) FUTIDX( ) 0.32 b (4.408) FUTIDX 0.46 b 0 (7.894) FUTIDX() b (.7869) FUTIDX(2) b 2 (2.498) FUTIDX(3) b 3 (3.76) FUTIDX(4) 0.07 b 4 (.479) FUTIDX() b (0.989) ECT( ) d n NIFTY Spo Reurn Innovaions RS, = a + bk RF, + k + dz- + C (.43) F Lag LR Lag F Lead LR Lead k =-n (0.76) (.963) (2.897) (0.283) (0.873) (.676) (.8973) (.378) (0.9847) 0.08 (.476) (.983) (0.9283) (.7892) Noe: F saisics and log likelihood raio saisic are used o es he join significance of he lead and lagged coefficiens of fuures reurns.

8 20 Inernaional Journal of Financial Managemen Table 6 VAR Resuls among NIFTY Spo and Fuures Index Reurns NIFTY Spo and Fuures Reurn S, 0 i S, - i F, - - F, 0 i F, - i S, - - NIFTY FUTIDX NIFTY( ) ** 0.27 ** (9.468) (.4733) NIFTY( 2) ** ** (2.348) (2.9867) NIFTY( 3) 0.44 ** ** (3.986) (0.7464) NIFTY( 4) ** ** (8.946) (0.3) NIFTY( ) ** 0.02 ** (8.6672) (.0767) FUTIDX( ) 0.38 ** ** (76.844) (29.946) FUTIDX( 2) ** ** (43.899) (6.744) FUTIDX( 3) 0.09** ** ( ) (7.7968) FUTIDX( 4) ** 0.020** (6.82) (.8498) FUTIDX( ) ** * (9.874) (0.7698) Consan (0.886) (0.8492) ECT( ) Chi Sq FUTIDX Chi Sq NIFTY (.97) (2.368) FUTIDX does no Granger Cause NIFTY NIFTY does no Granger Cause FUTIDX ** ** ** ** Table 7 VAR Resuls among NIFTY Spo Reurn Innovaions and Fuures Index Reurns NIFTY Spo Reurn Innovaions and Fuures Reurn SI, 0 i SI, - i F, - - SI, 0 i SI, - i F, - - NIFTYIN( ) NIFTYIN( 2) NIFTYIN( 3) NIFTYIN( 4) NIFTYIN( ) FUTIDX( ) FUTIDX( 2) FUTIDX( 3) FUTIDX( 4) FUTIDX( ) Consan ECT( ) Chi Sq FUTIDX Chi Sq NIFTYIN NIFTY FUTIDX ** ** ( ) (62.978) ** ** (3.6667) (4.8434) ** ** (8.64) (3.876) 0.24 ** ** (9.36) (0.92) ** ** (2.9867) (4.2739) 0.24 ** ** (42.969) (60.432) ** ** (29.843) (3.948) 0.98 ** 0.04 ** ( ) (3.2693) ** (3.9862) (.9873) ** (8.89) (0.833) (0.43) (0.9678) ** ** (.8746) (2.777) FUTIDX does no Granger Cause NIFTYIN NIFTYIN does no Granger Cause FUTIDX ** ** ** **

9 A Tesing of Lead-lag Relaionship beween Nify Spo and Fuures Index Reurns and Volailiy 2 Table 8 VAR Resuls among Volailiy of Spo and Fuures Index Reurn Through GARCH Model NIFTY VOL( ) NIFTY VOL( 2) NIFTY VOL( 3) NIFTY VOL( 4) NIFTY VOL( ) FUTIDX VOL( ) FUTIDX VOL( 2) FUTIDX VOL( 3) FUTIDX VOL( 4) FUTIDX VOL( ) Consan Chi Sq. NIFTY Chi Sq. FUTIDX s S, = a 0 + Sa s S,-i + Sb j s F,-j +e s F, = a 0 + Sa s S,-i + Sb j s F,-j +e NIFTY VOLATILITY FUTIDX VOLATILITY ** ** (40.362) (43.864) ** 0.64 ** (3.876) (20.92) ** ** (9.28) (9.267) ** ** (0.876) (.42) ** ** (4.342) (2.873) 0.34 ** 0.92 ** (72.434) (3.6740) ** ** (4.976) (7.62) ** ** (30.482) (8.43) ** 0.02 ** (2.6789) (.978) ** ** (.447) (0.386) (0.896) (.0783) ** ** Noe: ** and * represen significan a % and % level of significance. This able shows volailiy inerrelaionship among NIFTY Spo and Fuures index reurns where he residual derived from a simple GARCH(,) model is used as a proxy for volailiy in boh he markes. VOL represens volailiy. Chi-square es saisics represen he join significance of lagged spo (fuures) reurns in explaining he movemen of fuures (spo) reurns. Conclusion The curren research had conduced a series of mehods and ess such as descripive saisical measures o describe he basic characerisics of Spo and fuures markes, muliple regression analysis and Vecor Auo Regression (VAR) model o analyze he inerrelaionship among he markes and ARCH family of models o measure condiional volailiy in differen markes, individual and join ess of significance and Granger casualy ess ec. The lead-lag relaionship among he spo and fuures markes are esed for NIFTY indices in wo differen markes for boh reurns and volailiy of reurns. The primary idea abou he inerrelaionship among he inraday price series in wo markes are generaed hrough he cross correlaion es resuls. This clearly reveals ha apar from being conemporaneously correlaed, he indices are leading or lagging he oher index up o some exen. These resuls prove he presence of some leadlag relaionship among he inraday index reurn and he volailiy of inraday index reurn. This basic es is hen followed by modeling of inerrelaion in a muliple regression framework and hen in a VAR framework. I has been commonly found ha hough he lead or lag coefficiens are found o be significan up o a cerain exen, he conemporaneous coefficien exhibis he highes value, hus represening a sronger conemporaneous correlaion among he wo markes. Boh he muliple regression and VAR analysis provides he overall significance of spo index, hus depicing sronger leading role of spo marke over fuure marke; in oher words, spo index reurns Granger cause he fuures index reurn. Apar from examining he inraday lead-lag relaion among he index reurn series, an effor has been made o deermine he inraday inerrelaion among he volailiy of index reurns in hese wo markes. These resuls depic he inraday volailiy spillover from one marke o oher, and only based upon VAR models bu wih differen proxy measures of volailiy. As far as inraday volailiy spillover is concerned, he lagged coefficiens in boh he markes are found o be significan in explaining he fuure volailiy movemens in he oher marke. In oher words, a srong bidirecional inerrelaion among he volailiy of spo and fuures index reurn has been observed and also he same observaion has been made for differen proxy measures of inraday volailiy. Apar from being individually significan in boh he markes, he join significance of lagged coefficiens reveal ha he lagged volailiy in spo marke has proven o play a sronger leading role over he fuures index reurn volailiy.

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