Dynamic Analysis on the Volatility of China Stock Market Based on CSI 300: A Financial Security Perspective

Transcription

1 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07), pp.9-38 hp://dx.doi.org/0.457/ijsia Dynamic Analysis on he Volailiy of China Sock Marke Based on CSI 300: A Financial Securiy Perspecive Xiongbing Chen,* and Ning Zhang Economics and Managemen school, Wuhan Universiy, 43007, Wuhan, China School of Economics, Renmin universiy of China, Beijing, China * chenxiongbing@homail.com Absrac Wih he acceleraion of informaion disseminaion, he rapid flow of capial will make sock price changes. A he same ime, he change of sock price also affecs he marke; is volailiy is a measure of he qualiy and efficiency of he sock marke. Research on he volailiy of financial markes can effecively preven he generaion of financial risks. In his paper, he auhors make a dynamic analysis on he volailiy of China sock marke based on CSI 300 index. Through he empirical analysis, he resuls show ha he model can reflec he volailiy of he sock marke reurns in our counry, and he accuracy is high. A he same ime, he es resuls show ha he volailiy of he sock price has a leverage effec, and he volailiy caused by bad news will be large han he volailiy caused by good news. Keywords: Sock marke, Volailiy, Financial securiy, GARCH model. Inroducion The sock marke is full of uncerainy, he marke siuaion is in he process of changing. In oday's sociey, rapid disseminaion of informaion, he rapid flow of capial will make sock price changes and changes in sock prices will also affec he marke, boh influence each oher muual conducion and is volailiy is o measure he qualiy and efficiency of he sock marke, he main reference. Flucuaions in he range of normal range is conducive o he acive marke, so ha he marke can coninue o carry ou, bu oo frequen flucuaions in he marke will increase he risk of invesors o judge, is no conducive o he good operaion of he marke[]. China's sock marke belongs o he emerging marke range, has been China's sock marke volailiy and he flucuaion characerisic of high risk is also very obvious, ofen appear he phenomenon of big ups and downs[-3]. All of hese are he mos represenaive characerisics of he sock marke of our counry. Especially afer he spli share srucure reform, he non radable shares are gradually ransformed ino radable shares, which has furher increased he volailiy of China's sock marke. This kind of excessive flucuaion has grea influence on China's financial sysem and he naional economy. Therefore, his paper will focus on China's Shanghai and Shenzhen sock index volailiy, asymmeric volailiy o undersand, grasp he marke of our counry exis leverage effec and so on, o our counry governmen managemen as well as he majoriy of invesors has a srong pracical significance. Volailiy is he basic naure of he sock marke, he volailiy of he sock price is he necessary condiion for he allocaion of resources in he capial marke[4]. For invesors, i can be expeced o measure he volailiy of he risk of exposure o he size, a he same ime, he volailiy of he grasp will help o define he sock price in a range of possible. Therefore, volailiy is also he basis for invesors o gain income. As an invesor, i is concerned wih he analysis of he securiies marke price behavior as accuraely as possible, in order o make a reasonable forecas of he fuure marke yield[5-6]. The ISSN: IJSIA Copyrigh c 07 SERSC

2 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07) Shanghai and Shenzhen 300 index reflecs he sock price changes in China's securiies marke profile and he rend, he sudy of he volailiy of he index reurn, o provide a correc reference for is invesmen decisions[7]. For a long ime, volailiy is an imporan field in he research of financial risk, which is usually measured by he sandard deviaion or variance of he asse reurn rae[8]. Bu a lo of research resuls show ha he volailiy is no simple o show he characerisics of he normal disribuion, and changes wih ime. Economerics is evolving, and a variey of models ha are derived from his model are consanly emerging, rying o explain his volailiy. In his paper, he use of GARCH model on he Shanghai and Shenzhen 300 index daily yield o do research, enrich he heory of volailiy in our counry.. Theoreical Model.. The ARCH Model ARCH model, also known as Condiional Heeroscedasiciy Model Auoregressive, he main core is he ime of he variance is by he ime (-) of he size of he square error and influence, Y 0 X k X k Under all informaion condiions, (-) ime, he inerference is more han one, and he disribuion of he inerference erm is: ~ N0, 0 ARCH (P) process is he exension of he inerference erm: Var p 0 p If here is no self correlaion exiss in he error variance, here will be H0=a=a. resul is he same variance in he variance of he error variance. Engel has used he following regression o es he hypohesis of he above: 0 In he original regression model (), we esimae he OLS residuals obained. () GARCH (,) model Empirical analysis shows ha he GARCH model has a beer grasp of he financial marke daa analysis, he characerisics of financial daa are fully refleced, and is respeced and widely used. The mos simple GARCH model is he sandardizaion of GARCH (,): y x X represens an exogenous or pre - decision variable inroduced in he mean equaion. If we inroduce condiional variance ino he mean equaion, we can ge he M - ARCH model y x The condiional variance is replaced by he condiional sandard deviaion, which is anoher form of M - ARCH model. M - ARCH model is usually used in he financial field of he expeced reurn on asses and he expeced risk relaionship. The esimaed risk is a rade-off beween risk and reurn. () GARCH (P, q) model Based on he arch model Q may be relaively large, bollerslev he arch (P, q) model is exended, an effecive soluion o he number of parameers is usually higher: using GARCH (P, q) model, and he flucuaion of rae by is hyseresis represenaion and is he p p 30 Copyrigh c 07 SERSC

3 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07) same as ha of mean variance and arch model, difference equaion in a slighly differen. High order GARCH model can be esimaed by using more han of P or Q, denoed as GARCH (P, Q). Is variance is expressed as:.. GARCH Model a p a i i j j j The upward movemen of asses is ofen accompanied by a sronger downward movemen, which is a common phenomenon in he financial markes. In order o explain his kind of phenomenon, Engle and ng drawn respecively under he influence of he informaion curve in under he influence of he good news and bad news of he informaion curve combinaion of asymmeric informaion curve, and o deermine in financial markes in he asymmeric effec is he marke on he impac of he basic form, he non symmery effec in he financial markes is he formaion of he "leverage effec", he effec is also a lo of financial asses is he imporan characerisic of fac, flucuaions in he marke fell when he rae of reacion o han rising marke reacion is much sronger, and more quickly[9]. In he acual capial marke, marke analyss ofen found ha here is asymmeric behavior of sock price when he sock produce flucuaions caused by he negaive impac is ofen compared o sock flucuaions caused by he posiive impac is much greaer. Because he share price dropped significanly, reducing he owner's equiy, increased he company's leverage, bu also increased he risk of holding company sock. The TGARCH model and he EGARCH model are he wo main models o describe he asymmeric shocks. () TARCH model The model can beer simulae he "leverage effec" of financial marke, and i has he condiional variance of he following form: d In his model, he effec of good news (> 0) and bad news < on he condiional variance is quie differen: he good news is he impac of a; he bad news is a shock o he is. If gamma >0, we say ha here is leverage effec; if he gamma 0, hen he informaion is asymmerical. TARCH model, which is a leverage effec by he oupu (gamma) in (RESID<0) *ARCH () iem descripion. () EGARCH model Linear GARCH model assumpions: is equal o he absolue value of he posiive facors and negaive facors caused by flucuaions in he same, ha is, he condiional variance is he same, he resuls of he final reacion should be for absolue value equal o he posiive and negaive impac caused yield flucuaions are symmeric and equal. Bu in realiy, especially in he financial marke, he absolue value of equal posiive and negaive impac caused by he flucuaions are ofen differen, as refleced in he sock marke is ofen share price decline is far greaer han he rae of increase, and down he process o be more inense, more volaile. I is obvious ha he volailiy of he sock marke canno be explained by he linear GARCH model before. Nelson (99) proposed he EGARCH or index (Exponenial) GARCH model. Bu he symmeric condiional variance funcion is no compleely accurae, especially in he case of he negaive correlaion beween he reurn rae of he previous period and he marke flucuaion. In order o avoid his kind of siuaion and complee he non negaive hypohesis of he parameers, he condiional variance is specified as he basis of he GARCH model: log log The advanages of his model is ha he condiional variance of he daa as a logarihmic form, so he variance is greaer han 0, hen here is no need for oher Copyrigh c 07 SERSC 3

4 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07) resricions are added o he formula, because here is no any consrain in he model parameers, making he soluion process is simpler, more flexible. 3. The Empirical Analysis 3.. Daa Descripion The China Financial Fuures Exchange in Shanghai and Shenzhen 300 index in January 006 o 05 on he 7h of each rading day closing price as he original daa, in order o sudy he volailiy of he sock marke, in heir esimaes in Shanghai and Shenzhen 300 daily reurn rae as variables o invesigae, in order o reduce he error, he day reurn rae of naural logarihm processing, is he Shanghai and Shenzhen 300 index daily reurn o adjacen wo days of he closing index of he log firs difference said, hen yields he formula: p r log p Figure. The Shanghai and Shenzhen 300 Index Figure for he Shanghai and Shenzhen 300 index daily rae of reurn of RSH flucuaions, he char can be seen ha he daily yield of he volailiy of he performance of he ime variabiliy, sudden and cluser characerisics. Observaion of hese daa, we can find ha he sample period in Shanghai and Shenzhen 300 index reurn rae average RSH %, sandard deviaion for.30%, skewness is , lef Pianfeng degree for far higher han 3, rae of reurn R wih high peak and fa ail characerisic of he kurosis of he normal disribuion of values. The JB saisic is , and is normaliy ess also confirm his feaure, and he yield of R is significanly differen from sae disribuion a he minimum level. I is no possible o es he yield sequence if he sequence of he F es or all he saisical mehods based on normal disribuion are no esed. 3 Copyrigh c 07 SERSC

5 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07) Figure. CSI 300 Index Flucuaions Figure 3. Descripive Saisics of he Shanghai and Shenzhen 300 Index 3.. Sabiliy Tes The mos commonly used mehod in he sabiliy es is he uni roo mehod, which is a mehod o deermine wheher he correlaion coefficien is equal o. Afer nearly 30 years of academic research, his mehod is finally summarized as ADF es, which can be seen from he above descripive saisical analysis, he yield sequence around he volailiy in he mean, here is no rend. Therefore he sequence of ADF uni roo es, selecing lag of order 4, wih inercep and rend. The es resuls are in Table. Table. Uni roo es Lag Lengh: 4 (Fixed) -Saisic Prob.* Augmened Dickey-Fuller es saisic Tes criical values: % level % level % level Copyrigh c 07 SERSC 33

6 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07) 3.3. ARCH Effec Tes In his paper, we use ime series model o analyze, so we should firs choose he lag order of he rae of reurn. The mean equaion of he Shanghai and Shenzhen 300 index reurns akes he following form: r c 0 n c i ir According o he AIC saisic judgmen can be seen lag phase 4 is he bes, of squared residuals do linear graph, visible flucuaions of he regression equaion of he residual has "swarms" phenomenon: very small flucuaions in he longer period of ime, in some oher longer period of ime is very large, ha is obvious ime variabiliy (ime varying) and clusered (clusering), indicaing ha residual series has high level arch effec, suiable for use GARCH model o modeling, and can be observed in he sock index fuures lised his year volailiy significanly weakened. Figure 4. Residual Square Linear Graph Table. ARCH Tes F-saisic Probabiliy Obs*R-squared Probabiliy The residual error of he linear regression is ARCH-LM es, and he F saisic of he es objec is he join significance of he squared residual error. The Obs*R saisic is he LM es saisic, which is he observed value of he number T muliplied by he es regression R. Given significance level a = 0.05 and 0 degrees of freedom, he LM values for , wih probabiliy p for 0, less han 0.05, rejec he null hypohesis, ha yield sequence has obvious heeroscedasiciy phenomena and residuals wih srong arch effec, so his paper adops GARCH model o fi he daa of he Shanghai and Shenzhen 300 index yield rae is reasonable GARCH Model The esimaed CSI 300 index reurn volailiy of he model resuls are shown in Table 3 shows, visible in he Shanghai and Shenzhen 300 index reurn rae in he condiional variance equaion, wheher i is arch or GARCH phenomena were highly significanly. The significan ha rae of reurn volailiy has a se of clusers of feaures. The ARCH erm of he CSI 300 index reurn and he sum of he GARCH iems is and is less han, which mees he consrain condiions of he parameers. Bu because he wo 34 Copyrigh c 07 SERSC

7 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07) coefficiens and very close o, ha impac on he condiional variance of he impac is no shor is ransien bu a persisen process, hrough he feaure inference impac on fuure predicion has an imporan role, so he GARCH (,) is a saionary process. However, condiional variance performance is flucuaions in he pas o a limied exen, is impac on he fuure in he gradual decay o zero, known as mean reversion. Table 3. GARCH (,) Esimae Model Coefficien Sd. Error z-saisic Prob. C index yield Variance Equaion C 6.54E-03.35E ARCH() GARCH() r According o GARCH-M (,) model esimaion resuls, as shown in Table 4. The Shanghai and Shenzhen 300 index yield rae coefficiens in he mean equaion condiional variance GARCH esimaion is and significan. This reflecs he revenue and risk is relaed o ha income is high risk more, income abou risk is small wih o change. I is proved ha he income has a posiive risk premium. And from he empirical resuls can be drawn from he Shanghai and Shenzhen 300 index of he rae of reurn of ARCH iems and he sum of GARCH is and less han, o mee he sable condiions. Table 4. GARCH-M (,) Esimae Model Coefficien Sd. Error z-saisic Prob. GARCH C index yield Variance Equaion C 6.8E-03.36E ARCH() GARCH() r Sudy on he asymmeric volailiy of he Shanghai and Shenzhen 300 index reurns, as shown in Table 5. In he arch, o he erm leverage effec by he RESID<0 *ARCH () o describe, and he coefficien esimaes values for , is significanly posiive, so here are asymmeric effec, a he same ime ha he flucuaions of sock prices in China's Shanghai and Shenzhen 300 index is "leverage effec": and flucuaion caused by he bad news o flucuaions caused by he good news wih he same degree han o much more: when he "good news", he impac of a a= ; and he emergence of he "bad news", is will bring he impac of a+r= = Copyrigh c 07 SERSC 35

8 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07) Table 5. TARCH Esimae Model Resul Coefficien Sd. Error z-saisic Prob. C index yield Variance Equaion C.58E E (RESID<0)*ARCH() GARCH() r Conclusions d GARCH model can be applied o he sock marke of our counry. Alhough he model is made and widely used by sudy he developed counry maure financial markes in he process, bu i does no preven applied o he emerging sock marke, found afer he analysis, he characerisics of he CSI 300 index volailiy condiional heeroskedasiciy is obvious. I is also proved ha he using GARCH model can reflec he rae of reurn of China sock marke volailiy changes, and he analysis and research resuls of high accuracy. From he poin of view of ime series, he Shanghai and Shenzhen 300 index daily yield flucuaions show a significan variabiliy and volailiy clusering. Se of clusers is he relaed influencing facors of he CSI 300 index, such as informaion on he sock index flucuaion showing greaer volailiy ends o hen more subsanial flucuaions, and smaller flucuaions will hen smaller flucuaions. Yields on iself, here is no auocorrelaion, bu reurns he square has such a srong correlaion, and is no in general normal disribuion, bu sequence showing he disribuion of he peak and fa ail characerisics, and here are significan GARCH effec and he volailiy of he pas impac on fuure gradually decay. China's securiies marke volailiy clusering characerisics are obvious, here are a lo of irraional facors in he marke rading behavior, marke price volailiy is more inense. The inefficiency of marke informaion makes i difficul o fully display he funcion of he sock value and he funcion of resource opimizaion. Informaion disclosure sysem, so ha he basic informaion of he securiies marke can fully and fully open, give full play o he role of he marke, o build a reasonable mechanism for he ransmission of informaion, reduce marke speculaion amosphere. References [] S.Hammoudeh and D.Nguyen, Dependence of sock and commodiy fuures markes in China: Implicaions for porfolio invesmen, Emerging Markes Review, vol., (04), pp [] L. Jason and J. Thompson, Edging effeciveness of sock index fuures, European Journal of Operaional Research, vol. 63, no., (005), pp [3] B. Algieri, The influence of biofuels, economic and financial facors on daily reurns of commodiy fuures prices, Energy Policy, vol. 69, (04), pp [4] A.Anoniou and G. Koumos, Index fuures and posiive feedback rading: evidence from major sock exchanges, Journal of Empirical Finance, vol., no., (005), pp [5] I. Francis and S.Kim, Muliscale hedge raio beween he Ausralian sock and fuures markes: Evidence from wavele analysis, Journal of Mulinaional Financial Managemen, vol. 6, no. 4, (006), pp [6] L. Donald, Availabiliy and selemen of individual sock fuures and opions expiraion-day effecs: evidence from high-frequency daa, The Quarerly Review of Economics and Finance, vol. 45, no. 4, (005), pp Copyrigh c 07 SERSC

9 Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07) [7] J. Driffill and Z. Roondi, Moneary policy and financial sabiliy: Wha role for he fuures marke?, Journal of Financial Sabiliy, vol., no., (006), pp [8] F. Chrisos and E. Salvador, Calendar anomalies in cash and sock index fuures: Inernaional evidence, Economic Modelling, vol. 37, (04), pp [9] R. Yang and L. Xiangyang, Analysis of linkage effecs among indusry secors in China s sock marke before and afer he financial crisis, Physica A: Saisical Mechanics and is Applicaions, vol. 4, (04), pp. -0 [0] H. Hongbo and S. Chen, Financial liberalisaion and inernaional marke inerdependence: Evidence from China s sock marke in he pos-wto accession period, Journal of Inernaional Financial Markes, Insiuions and Money, vol. 33, (04), pp [] L. Hong, The impac of China's sock marke reforms on is inernaional sock marke linkages, The Quarerly Review of Economics and Finance, vol. 5, no. 4, (0), pp Copyrigh c 07 SERSC 37

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