Mispricing in stock index futures markets - the case of Greece

Transcription

1 Mispricing in sock index fuures markes - he case of Greece AUTHORS ARTICLE INFO JOURNAL Ahanasios P. Fassas Ahanasios P. Fassas (211). Mispricing in sock index fuures markes - he case of Greece. Invesmen Managemen and Financial Innovaions, 8(2) "Invesmen Managemen and Financial Innovaions" NUMBER OF REFERENCES NUMBER OF FIGURES NUMBER OF TABLES businessperspecives.org

2 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 2, 211 Ahanasios P. Fassas (Greece) Mispricing in sock index fuures markes he case of Greece Absrac This sudy invesigaes he pricing efficiency of FTSE/ATHEX-2 index fuures conracs and examines wheher arbirage profis exis in he Greek marke. By comparing ex-pos mispricing wih round-rip oal ransacion coss faced by differen groups of marke paricipans, he empirical invesigaion suggess ha profiable arbirage opporuniies are likely o be common in he Ahens Exchange. The curren paper also documens and ess he facors ha deermine he occurrence and he magniude of he arbirage opporuniies in he Greek fuures marke. The findings sugges ha variables, such as fuures mauriy, dividends, volailiy, liquidiy and shor-selling resricions, explain effecively he cash-fuures mipricing. Keywords: price discovery, fuures, arbirage, cos-of-carry model, Tobi regression, Greek Sock marke, FTSE/ATHEX-2. JEL Classificaion: G1, G13, G15. Inroducion This paper ess and documens he pricing efficiency of he fuures conracs ha are wrien on he big capializaion sock index of he Greek marke and considers wheher index arbirage is feasible. The empirical findings reveal he exisence of significan differences beween acual FTSE/ATHEX-2 fuures prices and he respecive heoreical fair prices derived from he cos-of-carry model. Addiionally, by using daily daa from January 24 o December 29, his sudy deermines ex-pos arbirage opporuniies by calculaing he difference beween he absolue value of he cashfuures mispricing and he oal ransacion coss. Since he inroducion of sock index fuures conracs, academic research has focused on spofuures prices relaionship mainly in hree ways. The firs class of lieraure ess he pracical validiy of he cos-of-carry model and seeks o discover poenial index fuures pricing inefficiencies. The second group invesigaes he lead-lag relaionships beween spo and fuures markes and heir conribuion in he price discovery procedure, while he hird research class examines he volailiy spillover effecs beween he wo markes. This research paper conribues o he firs line of research by esing he pricing efficiency of he FTSE/ATHEX-2 index fuures conracs raded in he Ahens Exchange (ATHEX). FTSE/ATHEX-2 index consiss of he weny larger in erms of marke capializaion companies lised in he Ahens Exchange. I was he firs sock index ha was used as an underlying asse in he Greek derivaives marke in Numerous sudies have examined he efficiency of fuures markes using differen mehodological echniques. Iniially, researchers mosly employed he regression analysis (e.g., Soll and Whaley, 199). However, he cos-of-carry model implies Ahanasios P. Fassas, 211. ha a pair of spo and fuures prices should be coinegraed in he long run (Schlusche, 29). Therefore, he use of some version of he vecor error correcion model (VECM) has become commonplace in he relevan lieraure (indicaively Ghosh, 1993; Tse, 1995). Coinegraion heory implies ha price differences beween markes do no diverge significanly, as here is a long-run relaionship beween prices in parallel markes. The VECM specificaion defines ha prices may deviae from heir common long-run relaion, bu arbirage forces make cerain ha prices converge o heir heoreically fixed relaionship. One limiaion of he sandard linear error correcion model is ha he coinegraion relaion of spo and fuures prices, which is dicaed by he cos-of-carry model, is no consan over ime bu raher changes daily (Schlusche, 29). This is rue because, as Yadav and Pope (1994) demonsrae, ransacion commissions and coss, ineres rae and dividend uncerainy and marke impac risks essenially allow fuures conracs o hover wihin a price range wihou riggering arbirage inervenion. Profiable arbirage is feasible only when he absolue cash-fuures basis sufficienly exceeds he oal coss associaed wih arbirage ransacions. Therefore, he arbiragedriven convergence owards he fair cash-fuures relaionship is disconinuous. Arbirageurs will sep in only when he absolue price discrepancy surpasses he oal ransacion coss. According o Buhler and Kempf (1995) academic research has exensively documened he exisence of mispricing in he fuures markes of he USA, he UK and Japan. The Greek sock marke has been also invesigaed in ha conex, bu all he relevan aemps use a variaion of an error correcion model. Their findings are remarkably consisen. Kenourgios (24) examines he relaionship beween he spo and fuures prices of FTSE/ATHEX- 2 index during he period from Augus 1999 o June 22 using Engle-Granger and Johansen coin- 13

3 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 2, 211 egraion ess and develops an error correcion model. His empirical resuls show ha he wo markes are coinegraed and also indicae he presence of a bi-direcional causaliy beween he wo markes. Floros and Vougas (27) employ a bivariae GARCH (1,1) model and confirm coinegraion and lead-lag relaionship beween spo and fuures for boh FTSE/ATHEX-2 and FTSE/ATHEX Mid Cap indices during he period of Kavussanos e al. (28) also invesigae he lead-lag relaionships in daily reurns and volailiies beween cash and fuures prices in he FTSE/ATHEX-2 and FTSE/ATHEX Mid Cap markes during he period from Augus 1999 o July 21; heir findings sugges ha prices are coinegraed in boh markes and resricions on he coinegraing vecor hold only in he Mid Cap index. Finally, Hourvouliades and Kousenidis (28) find srong evidence of saionariy on firs differences and Johansen coinegraion beween spo and fuures for FTSE/ATHEX-2 index during he period of However, none of he above-menioned Greekrelaed effors akes ino consideraion ha he coinegraing relaion, dicaed by he cos-of-carry model, is no consan over ime. Given ha he Greek marke has developed considerably since he work of Floros and Vougas (27) and Hourvouliades and Kousenidis (28) i is appropriae o revisi he FTSE/ATHEX-2 fuures marke. Furhermore, he invesigaion of he cash and fuures prices relaion is conduced using a ime varian approach depending on he presence or absence of arbirage ransacions, since i is well esablished ha arbirage aciviies affec marke dynamics. The second conribuion of he curren paper is ha i ess and documens he facors ha deermine he occurrence and he magniude of he arbirage opporuniies in Greek fuures markes. Finally, an imporan finding of his sudy relaes o he linkage beween cash-fuures mipricing and he recen shor-selling prohibiion, which was insaed by many inernaional marke regulaory commissions including he Greek one during he recen subprime crisis. The remainder of he aricle is organized as follows. The nex secion describes he calculaion of deviaions from he no-arbirage window and compares hem o poenial arbirage profis. Secion 2 examines he relaion among cash-fuures mispricing and a variey of facors, such as fuures mauriy, dividends, volailiy, liquidiy and shor-selling resricions. The las secion includes he closing remarks. 1. Pricing index fuures conracs and mispricing measures According o he cos-of-carry model he heoreical fair price of an index fuures conrac should be equal o he underlying spo index price adjused for he cos of carrying he spo index over he remaining life of he fuure. These coss consis of he ineres cos on a loan conraced a and redeemed a he fuures mauriy dae, T, minus he presen value of he dividends delivered by he index socks in he conracs mauriy period (, T). In paricular, he heoreical fair price of an index fuures conrac wih mauriy dae T a ime, F *, T ( S F, T *,T ) e, should be such ha: r ( T ), T (1) D in which, S denoes he value of he spo index (FTSE/ATHEX-2) a ime, D,T is he sum of he dividends paid by he index componens in he period (,T) expressed in index poins and r,t is he risk-free ineres rae. Equaion (1) defines he heoreical fair value of he fuures conrac on he assumpion ha here are no ransacion coss and axes and ha all invesors have idenical risk-free ineres raes. Following Buerworh and Holmes (2), I es for he presence of any mispricing by idenifying differences from he heoreical fuures price esimaed in equaion (1). The ex-pos cash-fuure basis series (B ) is calculaed as he deviaion beween he acual fuures price (F,T ) observed a ime and is fair price a ime divided by he value of he FTSE/ATHEX-2 index: B, T * F, T F, T. (2) S The fair value deviaions are normalized by dividing by S. In ha way he basis series is direcly comparable wih he ransacion coss of he poenial arbirageur, which are also expressed as percenage poins of he spo index. Therefore, he basis series consiues he poenial rae of reurn o he arbirageur. The raionale behind his relaionship is he abiliy o replicae he cash flows of he fuures conrac by borrowing money a he risk-free rae and buying he underlying index (eiher buying an exchange raded fund or buying he index componens). Therefore, if he esimaed basis is posiive ha is he fuures conracs rades above is fair value an arbirageur makes a risk-free profi by buying he spo index porfolio and opening a shor posiion in he fuures marke (long arbirage). Conversely, if he esimaed basis is negaive ha is he fuures conracs rades below is fair value he arbirage profis are secured by buying he fuure and shor selling he underlying index porfolio (shor arbirage). In each scenario, he arbirageurs will coninue o rade unil heir sup- 14

4 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 2, 211 ply and demand in boh he cash and he fuures markes forces he prices o rever o values ha are consisen wih he no-arbirage relaionship. Neverheless, in realiy, when we ake ino consideraion he coss ha are involved in he arbirage ransacions, he no-arbirage cash-fuures basis can deviae from zero. Assuming ha here are no rading resricions (e.g., shor-selling is prohibied), he above-menioned arbirage sraegies are only feasible when he absolue value of any cash-fuures basis is sufficienly higher han he coss involved in he required ransacions ( B, T C ). In his case, he poenial arbirage profi,t is equal o he cashfuures basis minus C, which denoes he ransacions cos associaed wih he rading in boh he spo and he fuures markes:, T B T C. (3), Arbirage profis calculaed in equaion (3) are considered o be ex-pos, because hey represen he profiabiliy of an arbirage ransacion assuming ha arbirageurs can execue he required rades a he observed prices. Furhermore, he assumpion is ha he arbirage posiions are held unil mauriy. Transacion coss comprise of several componens: brokerage commissions, selemen fees, samp duy, he bid-ask spread, axes and any poenial marke impac coss ha reflec he size of he rade and he marke liquidiy in boh he equiy and fuures markes. Yadav and Pope (199) esimae ha he round-rip ransacion coss for various arbirageur groups in he UK cash and fuures markes range from.5% o 2%. Using a similar raional in order o deermine he ransacion coss for he FTSE/ATHEX-2 conrac and aking ino consideraion ha he coss have been seadily decreasing over he years, I esimae he oal round-rip coss for arbirageurs in he.5% o 1.5% area. In Ahens Exchange, he mos favorably placed group of arbirageurs is he derivaive marke makers of ype B, who incur he lowes marke commissions Daa. Alhough recen academic aemps have used high-frequency daa, he relaive low liquidiy of he derivaives marke of Ahens Exchange makes he use of inra-day daa unaainable. Thus, he empirical analysis uses daily closing prices for he sock index and selemen prices for he index fuures series (oally 1,491 daily observaions). Unil March 27, FTSE/ATHEX-2 conracs expired every monh (39 conracs), while aferwards conracs expired every quarer; herefore he oal number of conracs under review for he six-year period is 5. The coninuous ime series of he fuures price for he period from January 24 o December 29 consiss of he daily selemen prices of he neares-o-deliver FTSE/ATHEX-2 conrac. From he las rading day onwards, he nex-odeliver conrac is considered. The iming of he rollover in he daase is based on he rading volume and open ineres on he Greek derivaives marke. In addiion, according o Green and Joujon (2) he cos-of-carry heory implies ha he mispricing riggers arbirage ransacions a any ime during he mauriy of a conrac, herefore he daase used should no rollover o he nex conrac before expiraion. The dividend series is calculaed using acual dividend disbursemens of he componen socks of each period 1. All daa were obained from he official websie of Ahens Exchange. The dividends are reaed as discree paymens and expressed in erms of FTSE/ATHEX-2 index poins. This is more appropriae for he Greek marke, as Greek companies pay dividends mainly once per annum and usually during he second and he hird quarer (primarily from April o Augus). Therefore i is no correc o use a dividend yield since mos of he observaions concern fuures conracs wih less han one monh o mauriy. Finally, one-monh Euribor ineres raes are used as he risk-free rae in he fair cash-fuures basis calculaion Resuls. The cash-fuures mispricing is calculaed using equaion (2). The respecive resuls are illusraed in Figure Fig. 1. The FTSE/ATHEX-2 cash-fuures mispricing As shown in Table 1, FTSE/ATHEX-2 fuures conracs seem o be fairly priced on average wih he mispricing deviaions ranging in general be- 1 For he period under review here were 11 addiions/deleions of he consiuen companies and 1 changes regarding he consiuen freefloa weighings. 15

5 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 2, 211 ween.4% and -1%. The mean deviaion is -.666%, while he median is -.542%. The negaive bias of he mispricing is also confirmed by he finding ha he fuures conrac is found o be underpriced on 1,234 occasions (an overwhelming 83%), while i is found o be overpriced only on 257 days (17%). Considering mean price divergence on a conrac-by-conrac basis, only 7 conracs raded on average a a premium, while 43 raded a a discoun. Mispricing is saisically significan a he 5% level for all bu one conrac. 16 Surprisingly, concerning he FTSE/ATHEX-2 fuures conrac here has been a noiceable deerioraion in is pricing efficiency over he period under review. From March 27 onwards he mispricing of he index fuure has increased in magniude and has been seadily in negaive erriories. I seems reasonable o argue ha his finding can be poenially relaed wih he subprime crisis and he subsequen eurozone deb crisis which resuled in an impressive bear marke for he Greek sock marke in general and is big capializaion index in paricular. Table 1. Summary saisics relaing o he FTSE/ATHEX-2 cash-fuures mispricing Conrac Mean -sa Median Sd. dev. Max Min Average absolue # Obs. # pos dev. # neg dev. B > C C =.5% C = 1% C = 1.5% January February March April May June July Augus Sepember Ocober November December January February March April May June July Augus Sepember Ocober November December January February March April May June July Augus Sepember Ocober November December January February March June Sepember December

6 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 2, 211 Table 1 (con.). Summary saisics relaing o he FTSE/ATHEX-2 cash-fuures mispricing Conrac Mean -sa Median Sd. dev. Max Min Average absolue # Obs. # pos dev. # neg dev. B > C C =.5% C = 1% C = 1.5% March June Sepember December March June Sepember December All Finally, he las hree columns in Table 1 repor he ransacion cos violaions for he mispricing series. Three levels of oal round-rip ransacion coss are used as benchmarks:.5%, 1.% and 1.5%. The empirical invesigaion shows ha a he.5% level, he FTSE/ATHEX-2 conrac is associaed wih violaions on 815 days (55%); a he 1% level, i is associaed wih mispricing violaions on 42 occasions (28%). Lasly, a he 1.5% level he big capializaion fuures conrac is associaed wih mispricing violaions on 26 days (14%). By comparison, Buerworh and Holmes (2) show ha for he UK FTSE 1 fuures conrac he.5% ransacions cos level is violaed on only 5% of occasions. Conversely, he 1% level is surpassed in less han 1% of he days under review, while here is no violaion of he 1.5% ransacion coss level. Therefore, he resuls sugges ha he arbirage opporuniies for he Greek benchmark index conrac are much more frequen han for he respecive UK index reflecing in par he illiquidiy and he difficulies of rading in he Ahens Exchange. 2. Which facors explain he spo-fuures price efficiency/inefficiency? A variey of facors, such as dividends, mauriy, volailiy, liquidiy, or general marke condiions and resricions have been found o explain cash-fuures mispricing and arbirage opporuniies in fuures markes (Severac e al., 29). This secion ess wheher differences in he values of hese facors affec he fuures mispricing in he Greek marke. More specifically, six variables are included in he empirical invesigaion: he days unil fuures expiraion, he FTSE/ATHEX-2 dividend yield, he volume of boh he cash and he fuures marke. Addiionally, I include a dummy variable ha akes ino consideraion he ban of shor selling, as he Greek Capial Commission followed he example of oher inernaional Capial Commissions and prohibied shor selling from Ocober 28 unil May 29. The las variable aims a proxying marke urbulence; in paricular, i measures he deviaion of implied volailiy 1 of he underlying 1 Implied volailiy is calculaed from a srip of opions (boh calls and pus) using he new VIX model-free mehodology. spo index from is fify-day moving average. Therefore, I model he daily ex-pos index-fuures mispricing deviaions, B, using he following specificaion: B,T 5 Fma Dshor 1 IV 6 div 2 1 Svol 3 1,T Fvol (4) in which, Fma denoes he number of days unil fuures expiraion in logarihmic form and div is he dividend yield measured as he discouned dividends paid by he FTSE/ATHEX-2 consiuens from dae o he fuures expiraion dae T in percenage of he value of he index. Svol denoes he daily volume (in number of shares) of he spo index in logarihmic form, while Fvol is he number of fuures conracs raded on day (in logarihmic form). Dshor is a binary variable aking he value of 1 on he days ha shor selling was forbidden and oherwise. Finally, IV is he difference of implied volailiy from is fifyday moving average (again in logarihmic form). An ARMA(1,1) model is applied in order o correc a significan degree of auocorrelaion in he error erms. The above mulivariae analysis (equaion (4)) is also conduced on daily pricing deviaions afer aking ino consideraion he round-rip ransacion coss 2. Hence, his specificaion ess wheher arbirageurs rading insananeously can earn arbirage profis. In his case he ex-pos arbirage profis, if posiive, equal o he resul of equaion (3), or else hey ake he value of zero. Since he disribuion of he average deviaions ne of ransacion coss is characerized by a subsanial number of zero values, equaion (4) is esimaed wih a censored Tobi mehodology using he same independen variables. Table 2 lays ou he resuls of he above wo specificaions. Boh models esimaes show ha fuures mispricing increases as he dividend yield of he index consiuens increases. Concerning ime o mauriy, he empirical evidence generally shows ha fuures divergence from is fair value increases signifi- 2 The average round-rip ransacion cos is assumed o be 1%. 17

7 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 2, 211 canly wih ime o expiraion of he conrac (e.g., Yadav and Pope, 199; 1994; Bühler and Kempf, 1995). Confirming exising research for oher markes, he curren sudy confirms ha in he Greek marke cash-fuures mispricing decreases when approaching he conrac expiraion dae. Now, regarding he effec of urnover in boh he cash and he fuures marke, opposie argumens can be pu forward (Severac e al., 29). According o one poin of view he occurrence and he magniude of price divergence increase rading aciviy by riggering more arbirage ransacions. However, here is an opposing argumen ha higher volumes, if iniiaed by arbiragers, may resul in a igher cash-fuures convergence. The findings of he paricular sudy favor he firs argumen, as he coefficien for oal volume in he cash marke is significanly posiive in boh models. Surprisingly, he number of raded conracs in he fuures marke appears o be saisically insignifican in boh specificaions. Anoher conclusion of he empirical invesigaion is ha cash-fuures price deviaions in he Ahens Exchange end o increase in periods of urbulen/bear Dependen variable Inercep Fma div Svol Fvol Dshor IV 1 1 markes. A poenial explanaion of why he cashfuures mispricing may increase in a bear marke can be relaed wih he increased risk associaed wih he arbirage ransacion. This is rue because when prices are falling, on he one hand he buy order for FTSE/ATHEX-2 fuures can be filled relaively quickly, bu on he oher hand he sell order in he cash marke is usually slower o execue. As a resul, i is likely ha he sell orders in he spo marke are filled a a lower price urning he arbirage rade of buying spo and selling fuures unprofiable. The coefficien of he divergence of implied volailiy from is fify-day moving average has a high level of saisical significance in he Tobi regression, bu i is barely insignifican in he ARMA(1,1) OLS model. Finally, an imporan finding of his sudy concerns he relaion beween cash-fuures mipricing and shorselling prohibiion. The coefficien for he binary variable ha relaes o he shor-selling ban is significanly posiive in boh specificaions, proving ha exernal inervenion reduces he price efficiency of he markes. Table 2. Modeling he daily ex-pos index-fuures mispricing deviaions ARMA(1,1) OLS regression Daily ex-pos mispricing before ransacion coss Censored Tobi regression Daily ex-pos arbirage profis afer ransacion coss *** ( ) ( ).16453*** *** (.22121) (.8849).44758*** *** ( ) (.12154).63295*** *** (.21937) (.8292) (.32893) (.15123) * *** ( ) ( ) *** ( ) ( ) *** (.22546) *** (.489) Adjused R % # of observaions 1, Noes: Sandard errors are in parenheses. *** Idenifies coefficien significance a he 1% level. ** Idenifies coefficien significance a he 5% level. * Idenifies coefficien significance a he 1% level. An ARMA(1,1) ordinary leas regression (OLS) is used o invesigae ex-pos cash-fuures mispricing before ransacion coss and a censored Tobi regression is employed o examine ex-pos arbirage profis ne of ransacion coss. Fma is he number of days unil fuures expiraion in logarihmic form. Div is he dividend yield measured as he discouned dividends paid by he FTSE/ATHEX-2 consiuens from dae o he fuures expiraion dae T in percenage of he value of he index. Svol is he daily volume (in number of shares) of he spo index in logarihmic form. Fvol is he number of fuures conracs raded on day in logarihmic form. Dshor is a binary variable aking he value of 1 on he days ha shor selling was forbidden and oherwise. IV is he difference of implied volailiy from is fify-day moving average in logarihmic form. 1 is he AR(1) coefficien and 1 is he MA(1) coefficien. 18

8 Conclusions This sudy invesigaes he mispricing of FTSE/ ATHEX-2 index fuures conracs and he poenial arbirage profis in he Greek marke by comparing expos mispricing wih round-rip oal ransacion coss faced by differen groups of marke paricipans. This sudy confirms he exisence of significan divergence from he no-arbirage window in FTSE/ ATHEX-2 index fuures wih poenial profis for arbirageurs, even when he round-rip ransacion References Invesmen Managemen and Financial Innovaions, Volume 8, Issue 2, 211 coss are aken ino consideraion. This finding shows ha, when he FTSE/ATHEX-2 fuures price deviaes from is fair price he arbirage ransacions which force prices back owards a heoreical equilibrium are no as srong and effecive in he Greek marke as hey are in he case of oher maure markes (e.g., he S&P5 and he FTSE 1 markes). Neverheless, i should be noed ha i is sill quesionable wheher he observed divergences are always feasible arbirage profis or jus he oucome of liquidiy issues and especially regulaory consrains. 1. Bühler, W. and A. Kempf (1995). Dax index fuures: mispricing and arbirage in German markes, Journal of Fuures Markes, 15, pp Buerworh, D. and P. Holmes (2). Mispricing in Sock Index Fuures Conracs: Evidence for he FTSE 1 and FTSE Mid 25 Conracs, Applied Economics Leers, 7 (12), pp Floros, C. and D.V. Vougas (27). Lead-Lag Relaionship beween Fuures and Spo Markes in Greece: , Inernaional Research Journal of Finance and Economics, 7, pp Ghosh, A. (1993). Coinegraion and error correcion models: ineremporal causaliry beween index and fuures prices, Journal of Fuures Markes, 13, pp Green, C.J. and E. Joujon (2). Unified Tess of Causaliy and Cos of Carry: he Pricing of he French Sock Index Fuures Conrac, Inernaional Journal of Finance & Economics, 5 (2), pp Hourvouliades, N. and D. Kousenidis (28). Sock index fuures, rading volume and open ineres: random walk and forecasing in ADEX, Spoudai, 58 (1-2), pp Kavussanos, M.G., I.D. Visvikis and P.D. Alexakis (28). The Lead-Lag Relaionship Beween Cash and Sock Index Fuures in a New Marke, European Financial Managemen, 14 (5), pp Kenourgios, D.F. (24). Price discovery in he Ahens derivaives exchange: evidence for he FTSE/ASE-2 fuures marke, Economic and Business Review, 6 (3), pp Schlusche, B. (29). Price Formaion in Spo and Fuures Markes: Exchange Traded Funds vs. Index Fuures, The Journal of Derivaives, 17 (2), pp Séverac, B., L. Deville and C. Gresse (29). The Inroducion of he CAC4 Maser Uni and he CAC4 Index Spo- Fuures Pricing Relaionship, Open Access Publicaions from Universié Paris-Dauphine. Obained hrough he Inerne: hp://basepub.dauphine.fr/xmlui/bisream/ /2933/1/8784_full.pdf, [accessed 15/7/21]. 11. Soll. H.R. and R.E. Whaley (199). The Dynamics of Sock Index and Sock Index Fuures Reurns, Journal of Financial and Quaniaive Analysis, 25, pp Tse, Y.K. (1995). Lead-lag relaionship beween spo index and fuures price of he nikkei sock average, Journal of Forecasing, 14 (7), pp Yadav, P.K. and P.F. Pope (199). Sock index fuures arbirage: Inernaional evidence, Journal of Fuures Markes, 1 (6), pp Yadav, P.K. and P.F. Pope (1994). Sock index fuures mispricing, Journal of Banking and Finance, 18 (5), pp