The Empirical Economics Leers, 8(5): (May 2009) ISSN 1681 8997 Capial Marke Volailiy In India An Economeric Analysis P K Mishra Siksha o Anusandhan Universiy, Bhubaneswar, Orissa, India Email: ier_pkm@yahoo.co.in K B Das Dep. of A &A Economics, Ukal Universiy, Bhubaneswar, Orissa, India Email: kbdasuu@gmail.com B B Pradhan Siksha o Anusandhan Universiy, Bhubaneswar, Orissa, India Email: regisrar@soauniversiy.com Absrac: The sub-prime crisis of mid 2008 revealed ha financial asse price volailiy has he poenial o undermine financial sabiliy. I is also observed ha he financial sabiliy is endangered more by sudden shifs in volailiy raher han by a susained increase in he level of volailiy. The sudy of volailiy is, herefore, crucial in an emerging capial marke like India. This paper draws heavily on ARCH class models from he lieraure of ime series economerics o sudy fa ails, volailiy clusering, leverage effecs, and persisence of sock marke volailiy in India. The resuls provide evidence of ime varying volailiy; i s asymmeric and leverage effecs. Key Words: Sock Marke Volailiy, Asymmeric GRACH, Exponenial GRACH, Threshold GRACH JEL Classificaion Number: C22, C52, E44, G12 1. Inroducion The volailiy of maured capial markes have been sudied comprehensively since he 1987 sock marke crash. And, he sudy of volailiy of he Asian sock markes gahered momenum afer Eas Asian financial crisis. Empirical evidence suggess ha developed markes provide high reurn wih low volailiy over a long period of ime. Amongs developing economies excep India and China, all oher counries evidence for low reurns (someimes negaive reurns) wih high volailiy. India and China provide evidence for a
The Empirical Economics Leers, 8(5): (May 2009) 470 high reurn as he US and he UK marke, bu he volailiy in boh he counries is higher (Raju and Ghosh, 2004). The sock marke of India is one of he larges and oldes in Asia. And, i is older han NYSE. Esablished in 1875, Bombay Sock Exchange winessed an explosive growh in he capial marke lieraure in India. Over he las decade or so, here has been a paradigm shif in he Indian capial marke. The Table: - 1 compares some key marke saisics for Indian sock marke in 1992 and 2007. Table: - 1 : Sock Marke Saisics Year Marke capializaion ($ billions) Marke capializaion o GDP (%) No. of muual funds No. of Dema A/Cs Value raded o lised sock (%) No. of FIIs Regiserred Turnover raio (%) Marke volailiy (%) Annual derivaive volumes ($ billions) 1992 144.6 57 0 6 0 11 20 3.3 0 2007 987.2 87 987 38 6362845 71 82 1.1 1601 Source: RBI, Handbook of currency & Finance; SEBI, Handbook of Saisics on Indian Securiies Marke, 2007. However, consequen upon he global financial urmoil and slowdown, Indian sock marke is currenly saddled wih low liquidiy and high volailiy. I shows ha he Indian capial marke is no longer isolaed from he global economic evens. India has winessed bous of volailiy in is marke. Some of which may have heir origin in global evens. The recen sub-prime crisis and news of probable recession emerging from he US, are examples of how evens which are inernaional, can cause volailiy in Indian capial marke. Besides, inflaion raes, global energy prices, exchange rae flucuaions, ec. are winessing consan changes in he recen years. These are affecing he volailiy of he capial marke. In his regard, he sudy of volailiy in India is very significan and meaningful. In simple words, volailiy is he degree o which asse prices end o flucuae. Volailiy is he variabiliy or randomness of asse prices. Volailiy is ofen described as he rae and magniude of changes in prices and in finance ofen referred o as risk. 2. Review of Leraure In his secion we survey and review some of he sudies ha are relevan o his work. Chan (1991) used GRACH models o esimae he inra-day relaionship beween reurns and reurns volailiy in he sock Index and sock Index fuures. Their resuls indicae a srong iner-marke dependence in volailiy of spo and fuures reurns. Gregory (1996)
The Empirical Economics Leers, 8(5): (May 2009) 471 used EGRACH model o examine how volailiy and find ha bad news increased volailiy more han good news and he degree of asymmery was higher for fuures marke. Aggarwal, Inclan, and Leal (1999) used GRACH model o explore he sock marke volailiy of 10 larges emerging markes in Asia and Lain America. They found ha shifs in volailiy of considered emerging markes is relaed o imporan counry-specific poliical, social, and economic evens. Kasch-Harouounian and Price (2001), Poshakwale and Murinde (2001) and Murinde and Poshakwale (2002) invesigaed he volailiy of Cenral and Easern European sock markes and found high volailiy persisence, significan asymmery, lack of relaionship beween sock marke volailiy and expeced reurn and non-normaliy of he reurn disribuion o be he basic characerisics of sock marke volailiy in hose counries. Bara (2004) examined he economic significance of changes in he paern of sock marke volailiy in India during 1979-2003. Karmakar (2006) measured he volailiy of daily sock reurn in he Indian sock marke over he period of 1961 o 2005. Using GARCH model he found srong evidence of ime varying volailiy and used TARCH model o es he asymmeric volailiy effec. Khedhiri and Muhammad (2008) sudied he volailiy of he UAE sock marke using GARCH models and swiching regime ARCH models. Their resul cas a beer performance of SWARCH models in represening and forecasing he marke volailiy. They idenified a significan leverage effec on he basis of TARCH models. Rao, Kanagaraj and Tripahy (2008) aemps o deermine he impac of individual sock fuures on he underlying sock marke volailiy in India by applying boh GARCH and ARCH model for a period of seven years from June 1999 o July 2006. The resuls sugges ha sock fuure derivaives are no responsible for increase or decrease in spo marke volailiy. Thus, i is evidenced ha he issue of changes in volailiy of sock reurns in emerging markes has received considerable aenion in recen years. The reasons for his enormous ineres are ha volailiy is used as a measure of risk, needed as an inpu in porfolio managemen and indispensable in opions pricing. Moreover, in he process of predicing asse reurn series and forecasing confidence inervals, he use of volailiy measure is crucial. 3. Daa and Mehodology The objecive of his paper is o invesigae he volailiy characerisics of he Indian capial marke measured by fa ail, volailiy clusering, and leverage effecs. Thus, focus will be on wo quesions: firs, does sock reurn volailiy change over ime? If so, are volailiy changes predicable? Second, does volailiy responds symmerically for posiive and negaive shocks? Wih hese goals effors have given o esimae volailiy of daily sock reurns in he capial marke of India over he period from 1991:01 o 2008: 12. We
The Empirical Economics Leers, 8(5): (May 2009) 472 use daily daa on sock reurns of he BSE sock marke. The daa are colleced from he RBI daa base. The economeric esimaions of he GARCH, EGARCH and TARCH models are performed so as o produce he evidence of ime varying volailiy which shows clusering, high persisence and predicabiliy and responds symmerically for posiive and negaive shocks. 4. Empirical Analysis and Resuls To he requiremen of volailiy modelling, he daily closing prices of he Sensex are used o arrive a he daily sock reurn daa ignoring he days when here was no rading. The price changes are calculaed from he las day he marke was open. Daily sock reurns ( R ) are calculaed by he log difference change in he price index: I R = log (1) I where I and I are he closing value of he Sensex a ime and -1 respecively. Figure.1 summarises he descripive saisics relaing o he Sensex based sock reurns in India. Figure 1: Descripive Saisics (January 1991 o December 2008) 1200 1000 800 600 400 200 0-0.10-0.05-0.00 0.05 0.10 Series: DAILY RETURN (BSE INDIA) Period: 2nd 1991 o 30h Dec 2008 Observaions 4275 Mean 0.000526 Median 0.000938 Maximum 0.123415 Minimum -0.136607 Sd. Dev. 0.018193 Skewness -0.156137 Kurosis 7.647497 Jarque-Bera 3864.732 Probabiliy 0.000000 The basic saisics indicaes ha he mean is close o zero relaive o he sandard deviaion. The reurn series is negaively skewed for he sample period. The mos ineresing feaure is he kurosis, which measures he magniude of he exremes. I is greaer han hree. And, i suggess ha he reurn series has faer ails han he normal
The Empirical Economics Leers, 8(5): (May 2009) 473 disribuion. Tha is, he probabiliy of exreme reurns ha has been observed empirically is higher han he probabiliy of exreme reurns under he normal disribuion. This feaure is referred o as lepo-kurosis, or simply fa ails. The daily sock reurns are hus no normally disribued a conclusion which is confirmed by he Jarque-Bera es. Now, for volailiy esimaion, he GARCH (1, 1) model is used. The model for daily sock reurn is specified as under: Mean Equaion: R = c+ ε (2) 2 2 2 Variance Equaion: σ = ω+ α1ε 1+ βσ 1 1 (3) 2 Since σ is he one-period ahead forecas variance based on pas informaion, i is called he condiional variance. The above specified condiional variance equaion is a funcion of hree erms: a consan erm (ω ), news abou volailiy from he previous period, measured 2 as he lag of he squared residual from he mean equaion ( ε ), and he las period s 2 forecas variance ( σ ). The GARCH (1, 1) model assumes ha he effec of a reurn 1 shock on curren volailiy declines geomerically over ime. This model is consisen wih he volailiy clusering where large changes in sock reurns are likely o be followed by furher large changes. Table 2: GARCH (1, 1) Esimaes of Reurn Daa Coefficien Sd. Error z-saisic Prob. C 0.001065 0.000206 5.178612 0.0000 Variance Equaion ω 7.148347 8.86E-07 8.069614 0.0000 α 1 0.117560 0.007438 15.80511 0.0000 β 1 0.864063 0.007513 115.0086 0.0000 I is clear ha he bulk of he informaion comes from he previous days forecas (around 86%). The new informaion changes his a lile and he long run average variance has a very small effec. I is very apparen ha he ampliude of he daily sock reurns is changing (see Fig.2). The magniude of he changes is someimes large and someimes small. This is he effec ha GARCH is designed o measure and ha we call volailiy clusering. There is anoher ineresing feaure in he fig.2 ha he volailiy is higher when prices are falling han when
The Empirical Economics Leers, 8(5): (May 2009) 474 prices are rising. I means ha he negaive reurns are more likely o be associaed wih greaer volailiy han posiive reurns. This is called asymmeric volailiy effec. And, his is no capured by GARCH (1, 1) model. Hence, we will use Nelson s Exponenial GARCH (1, 1) model for sock reurn volailiy esimaion. In he EGARCH model, he mean and variance specificaions are: Mean Equaion: R = c+ ε ε ε Variance Equaion: log( σ ) = ω+ αlog( σ 1) + β + γ σ σ 2 2 1 1 1 1 (4) (5) Equaion (5) implies ha he leverage effec is exponenial and ha he forecass of he condiional variance are guaraneed o be non-negaive. In his model, α is he GARCH erm ha measures he impac of las period s forecas variance. A posiive α indicaes volailiy clusering implying ha posiive sock price changes are associaed wih furher posiive changes and he oher way around. β is he ARCH erm ha measures he effec of news abou volailiy from he previous period on curren period volailiy. Here, γ is he measure of leverage effec (i.e., γ > 0). Figure 2: Daily Sock Prices (righ panel) and Reurns (lef panel) from Jan 1991 o Dec 2008.15 24000.10 20000.05 16000.00 12000 -.05 8000 -.10 4000 -.15 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 The impac is asymmeric if his coefficien is differen from zero ( γ 0 ). Ideally γ is expeced o be negaive implying ha bad news has a bigger impac on volailiy han good news of he same magniude. The sum of he ARCH and GARCH coefficiens, ha is, α + β indicaes he exen o which a volailiy shock is persisen over ime. The saionary condiion is α + β < 1.
The Empirical Economics Leers, 8(5): (May 2009) 475 Table 3: EGARCH (1, 1) Esimaes of Reurn Daa Coefficien Sd. Error z-saisic Prob. C 0.000769 0.000202 3.812538 0.0001 Variance Equaion ω -0.488195 0.036252-13.46657 0.0000 α 0.245439 0.012510 19.61869 0.0000 β -0.044530 0.006190-7.193377 0.0000 γ 0.963768 0.003799 253.7191 0.0000 Since he value of γ is non-zero, he EGRACH model suppors he exisence of asymmery in volailiy of sock reurns. Bu on he basis of his model we canno say wheher good news or bad news ha increases volailiy. This aspec of volailiy modelling is capured by Threshold GRACH model. The specificaion for condiional variance in Threshold GRACH (1, 1) model is: σ = ω+ ( α + γi ) ε + βσ 2 2 2 1 1 1 Here, he dummy variable I is an indicaor for negaive innovaions and is defined by: I =1, if ε <0 and I =o if ε 0. In his model, good news, ε > 0, and bad news, ε < 0, have differenial effecs on he condiional variance; good news has an impac of α, while bad news has an impac ofα + γ. If γ > 0, hen bad news increases volailiy, and we say ha here is a leverage effec. If γ 0, he news impac is asymmeric. Table 4: TGARCH (1, 1) Esimaes of Reurn Daa Coefficien Sd. Error z-saisic Prob. C 0.00085 0.000213 3.995551 0.0001 Variance Equaion C 8.39E-06 9.47E-07 8.858735 0 ARCH(1) 0.087653 0.00854 10.26439 0 ARCH(1)*(RESID<0) 0.068512 0.010814 6.335267 0 GARCH(1) 0.854549 0.008438 101.278 0 (6)
The Empirical Economics Leers, 8(5): (May 2009) 476 The Table 4 shows ha he good news has an impac of 0.0876 magniudes and he bad news has an impac of 0.0876+0.0685= 0.1561 magniudes. Thus, we conclude ha in he Indian sock markes, he bad news increases he volailiy subsanially. Also, his ime varying sock reurn volailiy is asymmeric. 5. Conclusion In his paper, we sudied he volailiy of he Indian sock marke using ARCH class models, namely GRACH, EGRACH, and TGRACH models. The analysis cas a beer performance of he TGARCH model in esimaing and predicing he marke volailiy. The change in he paern of volailiy and he recen irregular behaviour of he sock marke came as a resul of he global economic evens, paricularly he recen sub-prime crisis and news of probable recession. Our sudy shows ha his has creaed an unprecedened high level of volailiy and could explain o some degree he recen sluggish performance of he marke. References Aggarwal, R C. Inclan and R. Leal,1999, Volailiy In Emerging Sock Markes, Journal Of Financial And Quaniaive Analysis, 34, 33-55. Bara,A., 2003, Sock Reurn Volailiy Persisence in India: 1973-2003, Working Paper ICRIER, New Delhi, India. Chan K, Chan, K. C. and Karolyi,G A. 1991, Inra-day volailiy in he sock Index and sock Index fuures markes, Review of Financial Sudies, 4, 657 683. Gregory, K. and Michael, T. 1996, Temporal Relaionships and Dynamic Ineracions beween Spo and Fuures Markes, The Journal of Fuures Markes, 16, 1, 55 69 Karmakar, M., 2006, Sock Marke Volailiy in he Long Run, 1961-2005. EPW, 1796-1802. Khedhiri, S and N. Muhammad (2008): Empirical Analysis of he UAE Sock Marke Volailiy, Inernaional Research Journal of Finance and Economics, 15, 249-260. Kasch-Harouounian, M. and S. Price, 2001, Volailiy in he ransiion markes of Cenral Europe, Applied Financial Economics, 11, 93-105. Murinde, V. and S. Pashakwale,2002, Volailiy in he emerging sock markes in Cenral and Easern Europe: Evidence on Croaia, Czech Republic, Hungary, Poland, Russia and Slovakia, European Research Sudies Journal, February Issue.
The Empirical Economics Leers, 8(5): (May 2009) 477 Poshakwale, S. And V. Murinde, 2001, Modelling he Volailiy in Eas European Emerging Sock Markes: Evidence on Hungary and Poland, Applied Financial Economics, 11, 445-456. Raju, M T. And Ghosh, A, 2004, sock marke volailiy an inernaional comparision, WPS NO. 8, SEBI, April. Rao, Ramana S. V. A. Kanagaraj and NalinipravaTripahy, 2008, Does Individual Sock Fuures Affec Sock Marke Volailiy in India? Journal of he Indian Insiue of Economics, Volume 50, No.1, 125-135