International Business & Economics Research Journal May 2010 Volume 9, Number 5

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1 Inernaional Business & Economics Research Journal May 010 Volume 9, Number 5 Dynamics Of Sock Marke Reurn Volailiy: Evidence From The Daily Daa Of India And Japan Banamber Mishra, McNeese Sae Universiy, USA Maiur Rahman, McNeese Sae Universiy, USA ABSTRACT This paper sudies he dynamics of sock marke reurn volailiy of India and Japan. The TGARCH-M model is implemened. These markes are impaced asymmerically by bad news and good news. The reurn volailiy persiss in boh counries. Keywords: Condiional Heeroskedasiciy, Volailiy, Asymmeric Effecs I. INTRODUCTION T he relaionship beween he sock marke reurns and heir volailiies is usually nonlinear and dynamic. This is a subjec of considerable research ineres. Conjecuraly, a srong posiive relaionship exiss beween sock reurns and volailiies, bu he srengh of such a relaionship varies across counries. The daily informaion shocks, as well as he differences in invesor opinions and expecaions, are he source of sock marke volailiy. A significan rise in sock marke volailiy, due o posiive and negaive informaion shocks, reduces marke efficiency and liquidiy. The disseminaion of informaion is asymmeric and sequenial from informed raders o uninformed raders. Consequenly, an arrival of new informaion o he marke resuls in price movemens. The marke goes hrough a series of sequenial equilibria via porfolio adjusmens before a final equilibrium is aained (Girard and Biswas, 007). Undersanding he sock-marke risk and reurn is imporan because greaer volailiy influences riskaverse invesors o demand a higher risk premium. This, in urn, creaes a higher cos of capial impeding producive corporae invesmen. Thus, he primary focus of his paper is o sudy he dynamics of he sock marke volailiies of India and Japan. India has been seleced for is emerging financial and economic prominence in he world. India's Bombay sock marke has been soaring as India inroduced massive marke deregulaions and liberalizaions since early 1980s. The Bombay sock marke gained enormous liquidiy and sophisicaion over he las wo decades. Japan is he second larges economy in he world and is sock marke as represened by he Nikkei5 is also he second larges sock marke in he world exceeding $.6 rillion in marke capializaion. High frequency daily daa are employed o implemen he empirics as hey deem more appropriae for volailiy analyses as compared o weekly and monhly daa. Daily daa from May 1, 1998 hrough Sepember 30, 006, as obained from are used in his paper. The remainder of he paper is organized as follows. Secion II briefly reviews he prior lieraure. Secion III briefly oulines he empirical mehodology. Secion IV repors resuls. Finally, secion V offers conclusions. II. BRIEF SURVEY OF PRIOR LITERATURE Numerous financial economiss have employed condiional heeroskedasiciy models o describe he volailiy of he world's developed sock markes. The condiional volailiy of sock reurns in he U.S. has been examined, mos noably by French e al. (1987), Nelson (1991), and Baillie and DeGennaro (1990). Masulis and Ng 79

2 Inernaional Business & Economics Research Journal May 010 Volume 9, Number 5 (1995), and Poon and Taylor (199) sudy he volailiy of he Inernaional Sock Exchange of London using GARCH. Couhray and Rad (1994) invesigae he ime series properies of five developed markes (U.K., France, Ialy, Germany and Neherlands). More recenly, Koumous (1998) models he major sock indices of nine indusrialized naions using a hreshold GARCH (TGARCH) mehodology. The GARCH ype models have also been employed o explain he behavior of smaller European as well as Emerging Sock Markes. Cloquee e al. (1995) model daily reurns of he Belgian Sock Marke for he period Leon and Mora (1996) analyze he daily reurn series of he Spanish equiy index, he BEX-35, for he period Choudhry (1996) models he condiional variance of monhly reurns for six emerging markes, and compares he pre-and pos- Ocober 19, 1987 periods. De Sanis and Imrohoroglu (1997) model he condiional variance in nineeen emerging markes. In he las decade, several sudies of he Chinese sock markes have been conduced. Chui and Kwok (1998) repor ha reurns of B-shares lead hose of A-shares. The auhors hypohesize ha his relaionship can be explained by he fac ha informaion asymmery is less pronounced for B-shares. Chakravary e al. (1998) reached he opposie conclusion. Because foreign invesors have less informaion han domesic invesors, B shares rade a a subsanial discoun relaive o A shares. Fung e al. (000) compare he Shanghai and he Shenzhen markes' response o new informaion. Their research indicaes ha Shanghai invesors reac more rapidly han hose of Shenzhen. Xu and Fung (00) examine he paerns of informaion flows for China-backed socks ha are dual-lised on exchanges in Hong Kong and New York by using a bivariae generalized auoregressive condiional heeroskedasiciy (GARCH) model. They conclude ha socks lised on he domesic marke play a more significan role of informaion ransmission in he pricing process, whereas socks lised on he offshore marke play a major role in volailiy spillover. Darra and Zhong (000) es he random-walk process of A shares in he Shanghai and Shenzhen Sock Exchanges by comparing ARIMA, GARCH, and he Arificial Neural Nework models. They conclude ha A-shares do no follow a random walk. Beer, Lin and Chu (006) find evidence of asymmeric effecs on Shanghai A-share and B-share indices wihin TGARCH (1,1) model. The same apply o Shenzhen-A and Shenzhen-B shares. The volailiy persisence is evidenced in all exceping Shanghai B-shares. III. METHODOLOGY In order o model he dynamics of volailiy and ime-varying risk premia, a naural choice would be he GARCH approach inroduced by Bollerslev (1986) and Taylor (l986) as a model wih an alernaive and more flexible lag srucure han he iniial ARCH model. The model no only provides a measure of expeced or ex ane volailiy bu also allows volailiy shocks o persis over ime. The main drawback of his model is ha i requires consrains o be pu on he coefficiens o ensure non-negaiviy. In addiion despie heir populariy and apparen success in pracical applicaions, GARCH models canno capure he asymmeric response of volailiy o news - he fac ha bad news appears o induce more significan reacion han good news. Furher, GARCH models do no accoun for he fac ha invesors would like o ake addiional risk in order o gain higher reurn. To accoun for hese limiaions, Zakoian (1994) inroduces he Threshold GARCH-M (TGARCH-M) model. As denoed in Beer, Lin and Chu (006), he model conains wo equaions: he mean equaion (eq. 1) and he condiional variance equaion (eq. ). They are as follows: Y a n i1 b Y i 1 h 1/ 1 ~ N(O,h ) (1) h p q j j kh k 1d 1 () j1 k1 80

3 Inernaional Business & Economics Research Journal May 010 Volume 9, Number 5 In equaions (1) and (), Y and Y -1 represen he reurns in and -1 respecively. The condiional sandard deviaion of he error erm is denoed by h 1/ and he condiional variance by h and/or σ. As in he majoriy of oher publicaions, ε denoes he error erm. Finally, d -1 is a dummy variable, where d -1 = 1 if ε -1 < 0 and 0, oherwise. In he mean equaion, he risk premium (γ) accouns for he fac ha invesors migh be willing o ake addiional risk o achieve higher reurns. The condiional variance equaion examines he uncondiional sock price volailiy hrough he β coefficien. In he spiri of he GJR model of Glosen, Jagannahan and Runkle (1993), he erm η ε -1 d -1 assures ha he condiional variance is posiive regardless of he sign of he oher coefficiens. Good news (ε > 0), and bad news (ε < 0) impac he condiional variance h differenly. Good news has an impac of α j, while bad news has an impac of α j +η. If η > 0, he model accouns for he leverage effec. This model capures asymmeric characerisics, such as he leverage effec, in which negaive shocks have a greaer effec on condiional volailiy han posiive shocks of he same magniude. This also deals wih volailiy clusering when large (small) price changes end o follow large (small) price changes. Addiionally, i accouns for lepokurosis and skewness which indicae deparure from normaliy of he daily sock reurns. IV. RESULTS For a general undersanding of he naure of each marke reurn, some summary saisics are compued. They include mean, median, sandard deviaion, skewness, kurosis, and Jarque-Bera, as repored in Table 1. Table 1: Summary Saisics R (India) R (Japan) Mean Median Sd. Dev Skewness Kurosis Jarque-Bera Probabiliy The sample means are all posiive. The differences beween means and medians are noable. The coefficiens of skewness show ha India's sock marke reurns are slighly skewed o he lef and he sock marke reurns of Japan are slighly skewed o he righ. Excess kurosis is observed in boh cases. The Jarque-Bera es rejecs he null hypohesis of normaliy in boh reurn series. Nex, he ime series propery of each variable is examined for nonsaionariy by using he augmened Dickey-Fuller (ADF) es. The ADF es resuls are as follows: Table : ADF Tess Raes of Reurn ADF-saisic India Japan * The criical values a 1%, 5% and 10% are , and , respecively. Table shows ha he null hypohesis of uni roo (nonsaionariy) is rejeced a all he above convenional levels of significance. As boh series are saionary, he quesion of long-run convergence in erms of coinegraion does no arise. Subsequenly, he esimaes of equaion (1) are repored as follows: 81

4 Inernaional Business & Economics Research Journal May 010 Volume 9, Number 5 Table 3: Esimaes of Equaion (1) Parameers India Japan a (.168) ( ) b (.753) (0.8536) γ (1.3617) (-1.148) R DW F Noe: Associaed -values are repored in parenheses. Table 3 shows ha pas reurns influence curren reurn in India. Bu his is no he case in Japan since he coefficiens (a 0 and b 1 ) are saisically insignifican in erms of he associaed -values. In oher words, based on he above, he sock marke of India does no follow a random walk while ha of Japan does. In erms of γ, India's sock marke is influenced by posiive informaion shock while ha of Japan is influenced by negaive informaion shock. Finally, he esimaes of equaion () are repored as follows: Table 4: Esimaes of Equaion () Parameers India Japan (4.179) (5.574) α i (1.731) (13.3) (.78) (-.379) β i (3.741) (7.970) R DW F Noe: Associaed -values are repored wihin parenheses Table 4 shows ha all he coefficiens are saisically significan. For India, α is higher han β showing ha predicion of volailiy is dominaed by ARCH-componens. For Japan, he opposie inference is valid. As he η coefficiens are saisically significan, he exisence of asymmeric effec is suppored meaning ha good news and bad news have differen effecs in magniude on expeced reurns. The sum of he esimaed coefficiens of equaion () is close o uniy implying ha he evoluion of volailiy is in a persisen fashion and ha shocks may persis over a longer period of ime boh in India and Japan. V. CONCLUSIONS The sock markes reurns daa of India and Japan are non-normal and saionary. The sock marke reurns of India are more predicable based on he lagged-realized raes of reurn han hose of Japan. The esimaes of he mean-model show ARCH-componens in he raes of sock marke reurn in India while ha is no he case for Japan. They indicae ha he sock marke of Japan is relaively more efficien han ha of India. There are evidences of asymmeric effecs of bad news and good news on sock marke reurns of India and Japan. Apparenly, India's sock marke is influenced more by posiive news and Japan's sock marke is influenced more by negaive news. There is also evidence of volailiy persisence in boh markes. These findings challenge he concep of informaional efficiency. They have hus imporan consequences for invesors and funds managers in erms of profiable arbirages. 8

5 Inernaional Business & Economics Research Journal May 010 Volume 9, Number 5 REFERENCES 1. Baillie, R.T., and R.P. DeGennaro, Sock Reurns and Volailiy, Journal of Financial and Quaniaive Analysis, 5, 03-15, Beer, Fransisca M., Yu-Tsui Lin and Chi-Shun Chu, Sock Reurns and Volailiy: Evidence from he Chinese Markes, Journal of Emerging Markes, 11(3), 40-49, Bollerslev T., Generalized Auoregressive Condiional Heeroskedasiciy, Journal of Economerics, 31, , Chakravary, S., A. Sarkar, and L. Wu, Informaion Asymmery, Marke Segmenaion, and he Pricing of Cross-lised Shares: Theory and Evidence from Chinese A and B Shares, Federal Reserve Bank of New York, Research Paper, 980, Choudhry, T., Sock Marke Volailiy and he Crash of 1987: Evidence from Six Emerging Markes, Journal of Inernaional Money and Finance, 15, , Chui, C. W., and C.Y. Kwok, Cross-auocorrelaion beween A Shares and B Shares in he Chinese Sock Marke, Journal of Financial Research, xxi(3), , Cloquee, J.F., M. Geard and M. Hadhri, An Empirical Analysis of Belgian Daily Reurns Using GARCH Models, Cahiers Economiqeus de Bruxelles, 148(4), , Darra, A.F., and M. Zhong, On Tesing he Random-walk Hypohesis: A Model-comparison Approach, The Financial Review, 35(3), , De Sanis, G., and S. Imrohoroglu, Sock Reurns and Volailiy in Emerging Financial Markes, Journal of Inernaional Money and Finance, 16(4), , French, K.R., G.W. Schwer, and R.E. Sambaugh, Expeced Sock Reurns and Volailiy, Journal of Financial Economics, 19, 3-9, Fung H. G., W. Lee, and W.K. Leung, Segmenaion of he A- and B-share Chinese Equiy Markes, Journal of Financial Research, 3, , Girard, Eric and Ria Biswas, Trading Volume and Marke Volailiy: Developed versus Emerging Sock Markes. Financial Review, 4(3), , Glosen L.R., R. Jagannaahn and D.E. Runkle, On he Relaion beween he Expeced Value and he Volailiy of he Nominal Excess Reurn on Socks, Saff Repor 157, Federal Reserve Bank of Minneapolis, Ho, J., The Legal Environmen and Business Enerprises in he People's Republic of China, Chinese business: Challenges in he 1s cenury (The Chinese Universiy Press, Hong Kong), Jefferson, G.H., and T.G. Rawski, Enerprise Reform in Chinese Indusry, Journal of Economic Perspecives, 8(), 47-70, Koumos, G., Asymmeries in he Condiional Mean and he Condiional Variance: Evidence from Nine Sock Markes, Journal of Economics and Business, 50(), 77-90, Lee, G.O.M., L. Wang, L. and K. Mok, The Decline of Sae Owned Enerprises in China: Exen and Causes, Deparmen of Public and Social Adminisraion, Hong Kong: Ciy Universiy of Hong Kong. Rerieved 03, 08-10, Leon, A., and J. Mora, Modeling Condiional Heeroskedasiciy: Applicaion o Sock Reurn Index IBEX- 35, Working paper (Insiuo Valenciano de Invesigaiones Economicas, S.A.), 3-40, Masulis, R.W., and V.Ng, Overnigh and Dayime Sock-reurn Dynamics on he London Sock Exchange: The Impacs of 'big bang' and he 1987 Sock-marke Crash, Journal of Business & Economic Saisic, 13(4), , Nelson, D.B., Condiional Heersocedasocoy in Asse Reurns: A New Approach, Economerica, 59, , Poon, S.H., and S.J. Taylor, Sock Reurns and Volailiy: An Empirical Sudy of he U.K. Sock Marke, Journal of Banking and Finance, 16, 37-59, Taylor, S., Modeling Financial Time Series. John Wiley and Sons, New York, Xu X.Q., and H.G. Fung, Informaion Flows Across Markes: Evidence from China-backed Socks Duallised in Hong Kong and New York, The Financial Review, 37(4), , Zakoian, J.M., Threshold Heeroskedasic Models, Journal of Economic Dynamics Conrol, 18, ,

6 Inernaional Business & Economics Research Journal May 010 Volume 9, Number 5 NOTES 84