Evaluation of Hedging Effectiveness for CNX Bank and Nifty Index Futures

Transcription

1 CMDR Monograph Series No Evaluaion of Hedging Effeciveness for CNX Bank and Nify Index Fuures Dr. Barik Prasanna Kumar Dr. M. V. Supriya Sudy Compleed Under Canara Bank Endowmen CENTRE FOR MULTI-DISCIPLINARY DEVELOPMENT RESEARCH

2 Dr. B. R. Ambedkar nagar, Near Yalakkisheer Colony, Dharwad (Karnaaka, India) Phone : , Websie : CMDR Monograph Series No-57 All righs reserved. This publicaion may be used wih proper ciaion and due acknowledgemen o he auhor(s) and he Cenre For Muli-Disciplinary Developmen Research (CMDR), Dharwad Cenre For Muli-Disciplinary Developmen Research (CMDR), Dharwad Firs Published : December 010 Monograph 57

3 Evaluaion of Hedging Effeciveness for CNX Bank and Nify Index Fuures Dr. Barik Prasanna Kumar, Fellow (Projec), Cenre for Muli-disciplinary Developmen Research, R.S. 9A, Plo.8, Ambedkar Nagar, Lakkamanahalli, Dharwad, , Karnaaka, India. Dr. M. V. Supriya, Assisan Professor, Deparmen of Managemen Sudies, Anna Universiy, Chennai, 60005, India. Acknowledgemen: We hank anonymous referee (s) for commens on his paper. We hank each of discussans for his presened work a he workshop Balancing Banking and Social Responsibiliy: Developmen and Challenges Ahead, Cenre for Muli-disciplinary Developmen Research, Dharwad, India, held on June 08, 010. Monograph 57 3

4 Absrac The hedging effeciveness for bank fuures and CNX nify are evaluaed in his sudy. The sudy is based on 9569 observaions of he daily daa for hese index fuures. For evaluaion OLS, co-inegraed OLS, GARCH (1, 1) and consan correlaion GARCH (1, 1) hedging mehods are esimaed and compared. Resul shows ha consan correlaion GARCH (1, 1) is an efficien hedging mehod ha maximizes invesors uiliy funcion considering ransacion coss. Therefore, invesors can rely on his consan correlaion GARCH (1, 1) hedging mehod. Key words: Hedging effeciveness, Consan correlaion GARCH (1, 1) hedging mehod, Bank fuures, CNX nify. JEL Classificaion: G10, G1, G1 Monograph 57 4

5 Evaluaion of Hedging Effeciveness for CNX Bank and Nify Index Fuures 1. Inroducion Marke paricipans make he marke wih marke-making informaion, which are ofen asymmerical in naure. For example in he conex of foreign exchange-rae exposure rading, informaion like firm size and use of ineres-based or commodiy-based derivaives may deermine he probable use of currency derivaives for speculaion in heir (firms ) opimal hedging sraegies (Geczy e al. 1997). Therefore, hedging is ulimaely considered as o minimize risks in rading. Wih his ligh of observaion and using he consan correlaion generalized ARCH (1, 1) hedging model, his sudy aemps o evaluae he uiliy of hedging models in minimizing he risk and maximizing reurns of CNX bank and nify Index fuures 1 invesors. The India Index Service and Produc Limied manage CNX bank Index. I capures he capial marke performance and provides invesors and marke inermediaries wih a benchmark of he Indian banking secor. This Index has welve scrips from banking secor, which is raded in he Naional Sock Exchange of India Limied (NSE). The oal raded value for he las six monhs of CNX bank Index socks is approximaely 96.46% of he raded value of he banking secor. I represens abou 87.9% of he oal marke capializaion of he banking secor as on March 31, 009. The oal raded value for he las six monhs of all he CNX bank Index consiues is approximaely 15.6% of he raded value of all socks a he NSE. CNX bank Index consiues represen abou 7.74% of he oal marke capializaion as on March 31, 009 ( The marke has winessed a seady growh in invesor preference in banking scrips. Consequenly, hese scrips have ofen exhibied high level of volailiy oo. 1 These indices are ou of he join venure beween he Credi Raing and Informaion Services of India Limied (CRISIL) and he Naional Sock Exchange of India Limied (NSE) and hence CNX bank and nify index. Monograph 57 5

6 In his conex, his sudy inends o measure and analyze he economic viabiliy of hedging models for boh CNX bank and nify Index fuures (hereafer bank fuures and CNX nify respecively). This is because, hedging is a prominen mehod used by marke paricipans o minimize risk. Empirical resuls sugges ha consan correlaion GARCH (1, 1) hedge provides an improved hedging mehod where invesors maximize heir uiliy funcions considering ransacion coss. The reminder of he paper is organized as follows. The nex secion presens mehodology. Each of he successive secions presens daa, empirical findings, and discussions. The las secion presens conclusion.. Mehodology This sudy follows he bivariae GARCH (1, 1) model (Bollerslev 1986, 1987, 1988; Park and Swizer 1995; Prasanna and Supriya 007). Hedging models are consruced using a wo-period invesmen decision based on uiliy maximizaion model. Using spo price (S ) and fuures price (F ) for boh hese indices, hedging models are esimaed and analyzed. Fuures price is calculaed by using he cos of carry model where he Mumbai iner-bank call rae is considered he proxy for he financing rae. Tha is fuures price = closing price + [closing price (call rae dividend yield)] (T-/365). Where, T is oal number of rading days for he fuures conrac (i.e. 91/9 days consising of hree monhs) and is he acual rading days for he conrac (i.e. five days in a week so in oal 60 days). The dividend yield is included in he calculaion of fuures price. This is based on he assumpion ha he financial marke and derivaives marke are linked and hereby have a bearing on he bank fuures and CNX nify spo prices. Moreover, he relaionship beween call ineres rae and invesmen decision in he financial marke is fairly inerdependen. Consequenly, hese have a significan impac on invesmen in bank fuures and CNX nify conracs by individuals, banks, and financial See Edwards and Ma (199, p.31 and 3) Monograph 57 6

7 insiuions. I is observed ha boh he ineres ha is paid in he call marke agains he loan for invesmen and he dividend on securiies are no zero over his sudy period. In his sudy, conracs for boh he bank fuures and CNX nify are considered wih he call rae as financing rae. I is furher assumed ha he paricular call rae is same hroughou he conrac period of hree monhs for all hose who have invesed on a paricular rading day. The call rae is subjec o change, in response o he demand and supply pressure in he call money marke. The invesor makes invesmen decisions based on he call-financing rae of he day. Pas and fuure call raes are immaerial o he invesor on accoun of urgency in requiremen of financial resources for purpose of invesmen. I is likely ha hese invesors are ready o inves in derivaives marke for a paricular selemen dae wihou much heed o prospecive call raes. This is because, i is observed in he marke ha even considering oher financing rae e.g. he Treasury bill rae, fuures conrac has been rading irrespecive of is mauring period of hree monhs depending upon he marke condiions. Therefore, o observe he acual marke posiion unil he las monh of he conrac, his sudy has considered expiry wise conracs han conracs of near monh fuures. Again, hese various financing raes are non-sochasic in naure in he marke as far as he invesors invesmen perspecive is concerned. Therefore, he poin is ha any of financing raes in he financial marke suppors for he equal imporance of money sources a he face of is opporuniy cos. Here, here is no issue on wha he conrac period is. A leas his holds good a he invesors psychology as far as invesmen in derivaives marke is concerned (Prasanna, 011). Therefore, he call rae is considered as he financing rae for he period of hree monhs where he cos of carry period is T - = = 31 days. Now, he dynamic reurns for boh indices i.e. S γ F are calculaed considering he imporance of basis 3 in he marke. Here, dividends are suraced from 3 This is because in he conex of expiry conracs (far monh conracs) basis (spo price as premium or discoun o fuures price) should be wih zero value. Tha is he magniudes (in unis) of spo and fuures posiions should promoe fuures-gain (loss) posiion by offseing loss (gain) in he value of spo posiion. Monograph 57 7

8 he spo prices (S ) o represen he accurae cos of carry model of fuure prices. Hence, his sudy has considered his dynamic reurn as he independen variable in he model specificaion 4 where he relevance of i in he conex of evaluaion of hedging effeciveness agains fuures conracs susains. In his case, he GARCH (1, 1) model specifies mean equaions as, S F = α + α 0 = β + β ( S γf ) + ε s ( S γf ) + ε f ε ε s f ψ ( 0, ) 1 ~ N H (1) i.e. ( F ) Boh S = S S -1 and F = F F -1 reurns depend on he dynamic reurns S γ, which shows he dynamic changes in spo and fuures prices. Here, 1 1 ( ε s, ε f ) ~ N (0, H ) and ψ -1 represens he informaion se. This sudy has considered he ime-varying variances and covariances, where second momen is parameerized wih bivariae consan correlaion GARCH (1, 1) model (hereafer CCGARCH (1, 1)). The following model (Equaion 3) has parameerized condiional variances of wo variables as ARMA models in squared residuals. Here, he assumpion is ha here is he consan correlaion beween hese wo. Therefore he variance vecor is, H h = h ss, fs, h h sf, ff, = hs, 0 h 0 f, 1 ρ ρ hs, 1 0 h 0 f, () So ha he price risk eliminaion is also expeced in his ype of conracs. However, one quesion arises here. Do hey (conracs) work in he expeced manner? Answer o his quesion is discussed in he successive explanaions. 4 I is esimaed and observed ha error erms from he regressions of S -1 on F -1 for boh indices are saionary where he esimaed coefficiens of heir one lag erms as independen variables for he dependen firs differenced error erms are negaive a 0.01 level ((Augmened) Dickey - Fuller es). I is also esimaed ha S -1 and F -1 are coinegraed as he one lag error erms (from he iniial regressions of S -1 on F -1 ) in he Error Correcion Models are negaive a 0.01 level. Monograph 57 8

9 wih he condiional variance and covariance equaions as, h h s, f, = c s = c f + a ε s + a ε f s, 1 f, 1 + b h s s, 1 + b h f f, 1 (3) Equaion () shows he srucure of ime varying bivariae condiional variance vecor wih consan correlaion. Equaions (3), represens he bivariae GARCH (1, 1) condiional variance-covariance model. Wih he exisence of long-run co-inegraion relaionship beween spo and fuures reurns (dynamic reurns), he hedge raios are calculaed wih he variance esimaes from Equaion () as, hˆ hˆ ˆ * sf, = (5) b ff, The one period forecased opimal hedge raio b ˆ * is calculaed for he las half of observaions using esimaed hedge raio from he firs half of observaions. In addiion, he OLS hedge raio is defined wih he resricion α 1 = β 1 = a s = b s = a f = f b =0. The OLS hedge raio ha accouns for he long-run co-inegraion beween spo and fuures reurns (dynamic reurns) are defined wih he resricion a s = b s = a f = b f = 0. Afer esimaing opimal hedge raios, he variances of he reurns o he consruced porfolios i.e. σ ˆ* ( S F ) are calculaed and evaluaed over he second half of he oal sample, where b ˆ * is he forecased opimal hedge raio based on he firs half of he oal sample. The hedging models are consruced using a wo-period invesmen decision based on maximizaion of consumpion uiliy in fuure period. This sudy has modeled ha S and F are he spo and fuures reurns, where assumpion is ha only hedging insrumen is available o he invesor. In his case, hedge porfolio consising spo and fuures is consruced. Here, S +1 and F +1 are he changes in spo and fuures reurns beween Monograph 57 9

10 ime and +1 and b represens fuures a ime. The payoff a +1 is x +1 = S +1 b F +1. This implies ha he invesor is purchasing one uni of he spo and going shor in b unis of fuures a ime. Here, opimal hedge raio b ˆ * maximizes he invesors consumpion uiliy and minimizes risk of porfolios. The assumpion is ha fuures prices are maringale i.e. he expeced value of fuures price a is equal o he expeced value a +1. In successive analysis, he firs and second half of daa are considered a ime periods of and +1 respecively. Finally, his sudy has evaluaed he performance of each ype of hedge mehods and compared i by using he mean-variance expeced spo-fuures porfolio uiliy funcion. Here, invesors appear o have maximized heir uiliy hus esablishing he economic sense of he CCGARCH (1, 1) hedging model for boh he bank fuures and CNX nify. 3. Daa, Empirical findings, and Discussions The presen sudy has used he conrac expiry wise daily daa for bank fuures and CNX nify conracs from June 13, 005 o December 1, 010 consising 1367 daily observaions wih he oal of 9569 observaions. Daily spo price daa for boh bank fuures and CNX nify are colleced from he NSE websie. Daily fuures price daa for boh hese indices are calculaed wih he cos of carry model discussed earlier. The call rae daa are colleced from he RBI websie. The dividend yields for boh he index fuures are colleced from he NSE websie. The public secor bank dividend yields daa are included in his sudy as he proxy yields for he bank fuures for sudy period unil November 16, 007. Thereafer, bank fuures dividend yields daa available in NSE websie are used. Dynamic reurns are calculaed for boh he index fuures. This sudy has considered he economeric model specificaion, where all of he variables like spo, fuures, and dynamic reurns are modeled wihou any logarihmic Monograph 57 10

11 ransformaion. The reasons are explained here. Wih logarihmic ransformaion of spo and fuures reurns, i is observed ha auocorrelaion problem exiss in he iniial regression esimaion where spo and fuure reurns are independen and dependen variables respecively. I is observed ha wihou logarihmic ransformaion of reurns, error erms ( ε s and ε f ) in Equaion (1) are saionary where he esimaed coefficiens of heir one lag erms as independen variables for he dependen firs differenced error erms are negaive a 0.01 level ((Augmened) Dickey - Fuller es). In addiion, he long-run relaionship beween spo and dynamic reurns is also esablished wih he Engle-Granger--sep procedure in he following manner. Equaion (6) and (7) represen equilibrium correcion or error correcion models for boh indices respecively. Wih S = S S -1, S n = S n S n-1, D = S γ F, D = n Sn γ Fn, ΔS = (S S -1 ) (S S -1 ) -1, ΔS n = (S n - S n-1 ) n - (S n - S n-1 ) n-1, ΔD = D - D -1, ΔD n = D n - D n-1 he bank fuures equilibrium correcion model is, S S = λ b0 = ζ + λ D b0 b1 b1 + δ uˆ + u + ζ D 1 b + υ (6) and he CNX nify equilibrium correcion model is; S n S = λ n n0 = ζ + λ D n0 n1 n1 n + δ uˆ + u n + ζ D n 1 n n + υ n (7) Here, equilibrium correcion erms like δ uˆ and δ uˆ b1 1 n1 n 1 are included as independen variables, where he co-inegraing vecors are ( 1 ˆ λ ˆ b0 λb 1) ( ˆ λ ˆ λ ) 1 n0 n1 and. From Table (1), i is observed ha esimaed consan and slope coefficiens Monograph 57 11

12 in co-inegraing regressions are posiive respecively. Wih he unresriced u ˆ = c + c + c uˆ + c uˆ e & u n = c + c + c uˆ n + c uˆ n 1 + en resriced ˆ = c + c uˆ e & u n = c + c uˆ 0 3 n 1 + en u + ˆ and ˆ residual regressions, i is esimaed ha he compued F raio saisic values are and respecively. These values are greaer han he (A)DF criical value 8.34 a 1% level wih he resricion of c 0, c 1 = 0, and c = 0 where c = ρ 1 and ρ = 1 (Dickey and Fuller, 1981, Table VI, p.1063). Therefore, his sudy rejecs he residual random walk hypohesis a 1% level. In addiion, DF ess on esimaed residuals (wih consan and rend) show ha absolue esimaed values and are greaer han he criical value a 1% level (Table 1). Therefore, from each of Equaion (6) and (7) he null of a uni roo is rejeced. Therefore, alernaive hypohesis i.e. saionary û and û are acceped. From hese resuls, i is concluded ha S & D and S n & D n are co-inegraed respecively. Wheher he individual variables are saionary is also already esed wih I(0) process (Foonoe 4). n Table 1: Co-inegraing Regressions Esimaors Bank Fuures CNX Nify ˆb0 λ & ˆn λ 0 λ & ˆn λ 1 ˆb1 S D + u = λ b0 + λb 1 S D + u n = λ n0 + λn 1 Esimaes Esimaes F raio es saisic * * DF es saisic on residuals * * * Significan a 0.01 level. S & S n = Spo prices, and D & D n = Dynamic reurns. n n In second sep esimaion (Table ), esimaors like ˆb δ 1 and ˆn δ 1 are significanly negaive and differen from zero by and respecively. This implies ha if Monograph 57 1

13 he difference beween spo and dynamic reurns is posiive in one period, he spo reurns will decrease during he nex period o resore he equilibrium. Similarly, if he difference beween spo and dynamic reurns is negaive in one period, he spo reurns will increase during he nex period o resore he equilibrium. The esimaors like ˆb ζ and ˆn ζ sugges ha he dynamic reurns affec spo reurns posiively in case of boh bank fuures and CNX nify fuures respecively. This long-run equilibrium will be mainained wih efficien call money marke, which is relaed wih liquidiy adjusmen mechanism of he Reserve Bank of India (RBI). I is also examined ha dynamic reurns granger cause spo and fuures reurns for boh indices. In addiion, i is esimaed ha he coinegraing durbin-wason d saisics for boh regressions are greaer han 0.5 a higher significance level. Thus, he long-run relaionship beween spo and dynamic reurns for boh he indices are confirmed. Table : Esimaed Error Correcion Models Esimaors Bank Fuures CNX Nify ζ & ˆn ζ 0 ˆb0 ˆb1 δ & ˆn δ 1 ζ & ˆn ζ ˆb * Significan a 0.01 level. S = b + δ b uˆ ζ b ζ D + υ S n = n + δ n uˆ 0 1 n 1 + ζ n ζ D + υ Esimaes p-values Esimaes p-values * * n n In his secion, he hedging effeciveness wih each of models is compared. The full hedging effeciveness (FHE) is defined as 1 minus he raio whose numeraor is he variance of changes in he difference of spo (S ) and fuures price (dynamic reurn) and whose denominaor is he variance of changes of he spo price (Houhakker and Williamson 1996). Here he calculaed FHE for boh indices are and This Monograph 57 13

14 shows ha hedging is negaive and approaching o zero. Using FHE and respecive parial hedging effeciveness (PHE) i.e and for boh indices, hedge raios are calculaed wih he formula PHE = HR /(HR-FHE). As a resul, respecive hedge raios for boh indices are and Oher roos for boh indices are and respecively 5. I can be observed ha hese hedge raios are negaive and approaching zero. Therefore, his observaion concludes ha he Indian fuures markes have been experiencing inefficien hedging a he face of illiquidiy siuaion. Applying maximum likelihood esimaion OLS, OLS co-inegraion, GARCH (1, 1), and CCGARCH (1, 1) models parameers are esimaed. The hedging effeciveness is measured hrough he dynamic hedging performance of he above models for he ou-ofsample periods. Here he firs 683 daily observaions are used o esimae parameers for all hedging models. Using hese esimaed parameers and las observaion (i.e. 683 rd observaion), he one sep forecas hedge raio is esimaed which is he one-period forecas of covariance divided by one-period forecas of variance. Afer esimaing he opimal hedge raio b ˆ * of each hedge mehod, he variances of he reurns o he consruced porfolios σ ˆ* ( b F ) S are calculaed for he half of he oal sample. Therefore, he porfolios implied by he hedge raios are compared for each hedge mehods. I is observed ha excep CCGARCH (1, 1) hedge raios, oher hedge raios do no show for he perfec hedging. These oher hedge-raio values are oained from one-sep forecas values hose depend on each of 683 rd esimaed variances and covariances. These oher hedge raios imply ha hedging is imperfec by worsening he hedger s posiion. Therefore, surac from (add o) he loss (gain) is no realized where opimal hedge raios ahr + bhr + c =, 5 Roos for boh indices are calculaed from he algebraic quadraic equaion 0 where a = 1, b = -PHE, and c = PHE.FHE. Monograph 57 14

15 for respecive hedging models are imperfec wih he exisence of basis risk 6 which does no help o minimize (maximize) he expeced loss (gain). In his conex, i is already observed ha hedging in near monh fuures conrac is more effecive for some of specific fuures conrac (Ederingon, 1979). However, in his sudy he query on wha abou he case of far monh fuures conrac invesmens is focused having equal imporance of money sources a he face of is opporuniy cos. I is observed ha raional and perfec hedging is implied wih CCGARCH (1, 1) hedge model where CCGARCH (1, 1) hedge raios are 1.0 and 1.01 for boh indices. I seems hese CCGARCH (1, 1) hedge raios show for perfec hedging comparing he paricular GARCH (1, 1) and oher hedge raios. This is because lower hedge raio figures may no be desirable wih he exisence of zerosum game rading wih speculaion or arbiraion in he marke. So hese lower figures may represen as unprofiable speculaion or fuile arbiraion raio as he par of opimal hedging aciviy (Table 3). Therefore, echnically and heoreically i seems CCGARCH (1, 1) hedge raios 7 are more efficien han he GARCH (1, 1) hedge raios. Table 3: Opimal Hedge Raios wih Hedging Models * Hedging Models Bank Fuures CNX Nify OLS Co-inegraed OLS GARCH (1, 1) Consan correlaion GARCH (1, 1) * Hedge raios are esimaed from he raio of one-period forecas of covariance o one-period forecas of variance. 6 I is observed ha he average raes of changes of basis [spo fuures (dynamic reurns) in uni erms] are higher a 13% and 14% for boh indices over he sample period. 7 Here if we consider he original S and F (no dynamic reurns), he FHE for boh indices are Therefore, comparing his we can say here ha CCGARCH (1, 1) hedge mehod is efficien han oher hedging mehods. Monograph 57 15

16 Table 4: Variance Reducion * % Variance reducion of CCGARCH (1, 1) hedge over Bank Fuures CNX Nify OLS hedge Co-inegraed OLS hedge GARCH (1, 1) Consan correlaion GARCH (1, 1) hedge * The esimaion period is from June 13, 005 o March 07, 008. Toal sample considers he period from June 13, 005, o December 1, 010. Percenage variance reducions of CCGARCH (1, 1) hedge over oher hedge models are calculaed as [( σ OTHERS σ CCGARCH ) / σ OTHERS ] 100 using he second half of he oal sample. This is because, i is proved ha CCGARCH (1, 1) hedge raios are efficien. [( The variance reducions of porfolio reurns are calculaed as σ σ σ using he second half of oal sample (March 10, OTHERS CCGARCH ) / OTHERS ] o December 1, 010). Here he porfolio reurns have used hedge raios ( b ˆ * ), which are esimaed from he firs half of he sample (June 13, 005 o March 07, 008). I is observed ha all hedging models reduce he variance of spo porfolio significanly in his second half of he sample. The variance reducion is greaer for CNX nify. Table (4) shows he percenage variance reducions of CCGARCH (1, 1) hedge over oher hedge posiions. This implies ha here is improvemen of hedging effeciveness hrough CCGARCH (1, 1) over oher hedge models in boh cases. Now, he hedging mehods are compared using mean-variance expeced consumpion uiliy funcions. I can be assumed ha he mean-variance expeced consumpion uiliy of spo-fuures hedge porfolio funcion wih given informaion is Monograph 57 16

17 [ ( c )( x ) I ] u = ξ (Grossman and Shiller, 1981). Assume ha invesor relies ( c ) x E u on his mean-variance expeced uiliy funcion where he expeced produc of wo variables is he produc of heir mean and covariances. If reurns are wih high negaive covariances having he marginal rae of subsiuion beween presen and fuure uiliy consumpion (rading wih porfolios), hen hese porfolios are risky in naure. Therefore, he uiliy funcion wih perfec foresigh can be represened as EU x ) = E( x ) λ. Var( x ) where x is reurns from he spo-fuures hedge porfolio and ( λ is he risk aversion parameer (Park and Swizer, 1995). Here, λ = 4 and E(x ) = 0. Now, his mean-variance expeced perfec consumpion uiliy from hedging is y 4 Var(x ). Here, Var (x ) is he one-period forecased variance based on he firs half of he sample. y is he negaive reurn due o he ransacion cos and his is considered as impac cos (%) for boh indices. The monhly nify (individual scrip) impac-cos daa are available in NSE websie and he average percenage rae of change of bank nify selemen price is considered as he proxy for is impac cos. This is because in he absence of daa, i is assumed ha he cos of rading only deviaes conrac s selemen price. For porfolio reurns comparisons, his sudy has considered he oal impac cos of five scrips like HDFC bank, ICICI bank, OBC/AXIS bank 8, PNB, and SBIN of CNX nify 9. For bank fuures, all 1 scrips are considered for he impac cos calculaion 10. Here, he mean-variance hedging usually considers he marke los for boh indices. This is because, lo size and hence he number of marke los deermines he conrac size. In urn, his conrac size deermines he ick value (ick size conrac size) hrough which he fuures hedge 8 I is observed in he daa se ha AXIS bank scrip appears wih he CNX bank nify index in he year of 009 and Orienal Bank of Commerce scrip does no appear wih he CNX bank nify index from he year of Impac cos (for CNX nify) = [(Acual Buy Price Ideal Price)/Ideal Price] 100. Impac coss for considered bank scrips are colleced a heir respecive sample monhs. Then, he oal of each of hese impac coss are aken ino consideraion for he enire sample period i.e. from June 13, 005 o December 0, Impac cos (for Bank fuures) = [{(Selemen Price) (Selemen Price) -1 }/(Selemen Price) -1 ] 100. Monograph 57 17

18 posiion is deermined. Therefore, considering number of marke los, invesor usually akes shor posiions of bank fuures and CNX nify o cover losses or gain wih required number of fuures conracs. The consumpion uiliy funcions for boh firs and second half of he ime-periods wih all hedging models are compared. In he dynamic hedging model, invesors, marke paricipans and oher marke players prefer he consumpion uiliy funcion only if he poenial uiliy gains from he firs half compensaes he losses, which are due o he ransacion coss. Therefore, he consumpion uiliy funcions for he las half of he sample i.e. from March 10, 008 o December 0, 010 are calculaed and compared wih he consumpion uiliy funcions of he sample i.e. from June 13, 005 o March 07, 008 for four hedging models. I is observed ha increased uiliy is wih CCGARCH (1, 1) han oher hedging mehods like GARCH (1, 1) paricularly in he case of CNX nify (Table 5). This is also explained in Table 4. Here, he mean-variance expeced uiliy maximizing invesor should prefer he CCGARCH (1, 1) hedge mehod han oher convenional mehods. Therefore, i can be jusified ha he CCGARCH (1, 1) model provides an efficien hedging mehod. Table 5: Mean-variance Expeced Uiliy Comparisons * Hedge mehods Bank Fuures CNX Nify OLS hedge (1) (5) Co-inegraed OLS hedge -4.4 (1) (5) GARCH (1, 1) (1) (5) Consan correlaion GARCH (1, 1) hedge (1) (5) * One-sep forecas variances from he firs half of sample are used for boh indices. Parenheses (.) indicae he number of scrips, which are considered for he calculaion of impac cos (%) for respecive indices. Monograph 57 18

19 4. Conclusion From his sudy, i is concluded ha here is a long-run relaionship beween he spo and dynamic and hence fuures reurns. Opimal hedge raios were calculaed using all four hedging models. I is observed ha he CCGARCH (1, 1) is an efficien hedging mehod. Considering he mean-variance consumpion uiliy funcion for all hedging mehods, i is also observed ha CCGARCH (1, 1) is an efficien hedging mehod. Togeher his indicaes ha he CCGARCH (1, 1) hedge provides an improved hedging mehod even considering he ransacion coss. This sudy finds ha he esimaed variance coefficien marices for 1, 1, CCGARCH (1, 1) are wih he specificaion ( ) ( ) a, + b, 1 1. In addiion, saionary variance holds as he condiional variance forecas has converged upon he long-erm average value of he variance. Thus suggesing a beer model fi. Monograph 57 19

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