Analysis and Comparison of ARCH Effects for Shanghai Composite Index and NYSE Composite Index

Transcription

1 Vol. 3, No. Inernaional Journal of Business and Managemen Analysis and Comarison of ARCH Effecs for Shanghai Comosie Index and NYSE Comosie Index Xinghao Liao, Guangdong Qi School of Finance, Shanghai Universiy of Finance and Economics Shanghai 439, China Absrac In his aricle, we used ARCH class model o analyze and comare he income flucuaions of Shanghai Sock Marke and NYSE, and obained he characers of flucuaion for wo markes and he models which fied o describe hem. A he same ime, we also analyzed he flucuaion overflow effec of wo markes, validaed he characer ha Chinese sock marke was no relaively maure and ossessed low inernaional marke inegraion degree, and u forward relaive olicy advances. Keywords: Shanghai comosie index, NYSE comosie index, ARCH class model, Flucuaion overflow. Inroducion In he domain of finance, he daa of ime seuence always u u characers such as convergence and lever effec, bu radiional mehod researching financial daa could no consider hese characers, which induce he redicive abiliy of model is bad. Since Engle u forward ARCH model in 98 (Engle, 98, ), he domain of condiional heeroscedasiciy develoed very uickly, and many variaions of ARCH model occurred, and he mos reresenaive model is he generalized ARCH model which was u forward by Bollerslev in 986 (Bollerslev, 986, ), i.e. GARCH model, and i is exensively alied in he financial research and acual oeraion. Since 5, as he emerging marke, Chinese sock marke has been more and more concerned by he world, and in less han wo years, he sock marke values of Shanghai and Shenzhen was doubling more. The increase seed makes mos markes in he world amazing. However, here are many gas beween Chinese markes wih inernaional financial marke, which is undeniable, for examle, he financial roducs in Chinese caial marke is relaively few, and he srucure is oo single, and he flucuaion is large, and he behaviors of marke conrol sill exis. Comaring wih ha, in hose maure inernaional caial markes such as he caial markes in UN, US and many develoed caialism counries, he flucuaion is small, and he financial roducs is very abundan, he marke order is good and he financial suervision sysem is maure. In his aricle, we will use he NYSE as he reresenaion of inernaional maure financial marke and ake Shanghai Sock Exchange as he reresenaion of Chinese markes, analyze and comare he flucuaion of daily yield for wo markes comosie index o ry o find ou he deficiencies and reasons exising in Chinese sock marke relaive o he maure marke.. Inroducion of ARCH class of model One obvious characer of he financial ime seuence is he condiional heeroscedasiciy, and he ARCH class of model has been exensively alied in he domain of financial measuremen. GARCH model is mos exensively adoed in he research of flucuaion, which is defined by he average value euaion and he condiional variance.. Model of ARCH ARCH model is he simles ARCH class of model, and i suoses he condiional variance of erm is he funcion of residual error from - erm o - erm, i.e. he flucuaion is self-correlaive, and he form of ARCH () is i i i and he non-negaive condiion is, ( i,,, ). i. Model of GARCH The GARCH model is generalized ARCH model, and i suoses he condiional variance is former condiional

2 Inernaional Journal of Business and Managemen December, 8 variance based on he simle ARCH model, i.e. he condiional variance is self-correlaive, and he form of GARCH (, ) is i i i Where,,, he non-negaive condiion is, i ( i,,, ), (,,, ), and o make he condiional variance sable, i mus fulfill he condiion (Bollerslev, 986, P.39-37), i i and is value reflecs he duraive of he flucuaion..3 Model of GJR-GARCH GJR-GARCH model (Glosen, 993, P ) overcomes he limiaion ha GARCH model canno describe he osiive and negaive reacion of collision, and is form is i i I i ( ) where, I, and under he same limiaion condiion wih GARCH model, he non-negaive condiion ( ) also reuires..4 Model of EGARCH Like GJR-GARCH model, he EGARCH model also could be used o deal wih he ime seuence obained by he lever effec. I was u forward by Nelson in 99 (Nelson, 99, P ), and is form is log log i i i h h In a comarison among ARCH, GARCH, EGARCH and oher more comlex half-arameer and zero-arameer models, Pagan and Schwer (Pagan, 99, P. 67-9) roved ha simle EGARCH (, ) could imlemen modeling o he financial ime seuence. 3. Daa selecion and basic analysis In his aricle, we selec he daa of Shanghai Sock Exchange from Jan, 3 o Dec 8, 7, and o make he analysis ossess comarison, he daa of NYSE are also in he same eriod. The backgrounds include ha Chinese economy had been develoed very uickly since China oined in WTO, and US basically cas off he shadow of 9. in 3 and is economy begun o recover o sable saus. The comuaion formula of yield used in he aricle is r ln( / ), where, r is he daily logarihm yield (%), and are resecively he index values in erm and - erm. The descriive sa. resuls of wo markes are seen in Table. The daily yield average of Shanghai comosie index is.%, and he daily yield average of NYSE comosie index is.5%, and he former is wice han he laer, which indicaes as he emerging marke, he yield of China sock marke is higher, and i also exlains why inernaional idle money coninually has flowed ino China in recen years. In addiion, we can obviously see ha large flucuaion exised in boh markes, and he resul showed negaive deflecion, and he kurosis exceeded 3, which indicaed he yield disribuions of wo markes were non-normal, and comaring wih NYSE comosie index, Shanghai comosie index had more obvious and larger deflecion and higher kurosis, so he ossibiliy ha he yield of Shanghai Sock Exchange ke away from he average was higher, and higher risk exised in Shanghai sock marke, and he marke was no sable and large deflecion would always occur in he ary wih negaive yield. From he descriive saisic, as he emerging marke, he yield of Shanghai Sock Exchange was obviously higher han such maure marke as NYSE, and he marke of Shanghai was no maure like NYSE, and large flucuaion exised in i. Imlemen ADF es o he daily yield seuence of samles. The es resul showed he ADF es sa. of Shanghai comosie index daily yield seuence is under he significance level of %, and i was obviously lower han

3 Vol. 3, No. Inernaional Journal of Business and Managemen he criical of under he significance level of %. The ADF es sa. of NYSE comosie index daily yield seuence is under he significance level of %, and i was obviously lower han he criical of under he significance level of %. So we reec he original hyohesis, i.e. wo grous of daily yield seuence have no uni roo, and hey are sable seuence. We imlemen self-correlaive and deviaed self-correlaive coefficien analysis wih 5-order o Shanghai comosie index and NYSE comosie index, and he resuls showed ha in all ime lags, he self-correlaive funcion value and he deviaed self-correlaive funcion value of yield were small, and hey were smaller han.7, so he daily yield seuences of Shanghai comosie index and NYSE comosie index were no self-correlaive. Imlemen self-regression wih -order lag iems o he yields of wo markes, and es ARCH effec o he residual error. For he Shanghai comosie index, he F saisic of ARCH effec es is , and he LM saisic is For he NYSE comosie index, he F saisic of ARCH effec es is , and he LM saisic is The saisics of wo markes are very significan, which indicae he ARCH effec exiss in he daily yield daa of Shanghai comosie index and NYSE comosie index. 4. Flucuaion analysis of ARCH model Imlemen modeling o he yield seuence, and resecively use ARCH (), GARCH (, ), GJR-GARCH (, ) and EGARCH (, ) models o describe he daily yield heeroscedasiciy of Shanghai comosie index and NYSE comosie index, and he esimaion resuls are seen in Table (values in he bracke are saisics). From Table, he coefficiens of GARCH model cluser are big and ass he significan es, which indicaes he sock rice flucuaion ossesses long-erm memory, i.e. he flucuaion of as rice is correlaive wih he flucuaion of infinie erm rice. In he euaion of condiional variance, he coefficiens and are significanly osiive, which indicaes as flucuaion has osiive and released influence o he fuure flucuaion of he marke, so he clusered henomena occurs in he sock marke flucuaion. is closed o, which indicaes he reacion funcion of sock flucuaion o he exerior concussion is degressive by a relaively slow seed, and he big flucuaion in he sock marke canno be eliminaed in he shor erm. In addiion, because in ARCH (), GARCH (, ) and GJR-GARCH (, ) are smaller han, so he condiional variance seuence of yield is sable, and he model can be rediced. Esimae wo markes by he GJR-GARCH (, ) model, we find he yield of Shanghai comosie index has no obvious lever effec, bu he negaive concussion brings smaller flucuaion han he osiive concussion. I also indicaes under immaure marke, invesors are no raional enough, and higher average yield and big flucuaion will induce more shor-erm invesors, and when he marke ossesses big osiive yield, invesors will close ou and induce big flucuaion. Comaring wih Shanghai comosie index, NYSE comosie index has obvious lever effec, and is behavior is consisen wih our aniciaion o he maure marke. 5. Exlanaion degree comarison of various models For he regression resul, every model has cerain limiaion, bu we can ry o find ou he bes models for wo markes. The roofs o udge he model include informaion rincile, F saisic and logarihm maximum likelihood mehod. Bu for he nonlinear model, he maximum likelihood mehod is he bes choice, so we ado he logarihm maximum likelihood mehod o rank he model, and he resuls are seen in Table 3. From he informaion rincile mehod and he maximum likelihood mehod, for he Shanghai sock marke, he bes flucuaion descriive model is EGARCH model, which is consisen wih Liing and Zhao, Liia s conclusions (Li, 4,. 3-3), and hough he symbols of he asymmeric iem don accord wih he aniciaion, bu maybe he unconformiy us indicaes he characers of Chinese sock marke, i.e. bigger osiive yield will bring bigger flucuaion. For he NYSE sock marke, he bes model is GJR-GARCH, which indicaes NY sock marke has srong lever effec which doesn exis in Shanghai sock marke. 6. Overflow effec of Shanghai and Shenzhen Sock Markes flucuaion Esimae Shanghai comosie index by EGARCH model and esimae NYSE comosie index by GJR-GARCH model, and resecively obain he condiional variance daa seuence GARCH and GARCH of he residual iem, and imlemen Granger causaliy es o boh seuences and he resuls are seen in Table 4. From he es resuls, we can see ha he influence of Shanghai sock marke on New York sock marke is no noable, and he influence of New York sock marke on Shanghai sock marke is small, which indicaes hough he marke value of Chinese sock marke, bu afer all he caial marke of China is no oening, so he influences wheher from inerior o exerior or from exerior o inerior is very limied, and he invesmen of QDII would obviously reduce he invesmen risk of domesic invesors.

4 Inernaional Journal of Business and Managemen December, 8 7. Conclusion To comare he daily yields of wo markes by he modeling of ARCH class model, we can see ha he lever effec almos doesn exis in Shanghai sock marke, bu he lever effec of NYSE sock marke is more obvious, which reasons are mainly ha Chinese governmen ofen inervenes he sock marke and sabilize he rice, and i also indicaes ariciaors gambling aiudes are srong. A he same ime, from he analysis of ARCH-M class model, we can see ha Chinese invesors could obviously avoid he risk and reuire higher reurn for he invesmen wih high risk, bu US invesors have no same srong avoidance degree o he risk comaraively. The es resul of flucuaion overflow effec is ha he flucuaion overflow effec of wo markes is no obvious, and he influence of Chinese sock marke on NYSE sock marke is sronger. Of course, he Granger causaliy es only checks u he saisical causaliy relaionshi and i doesn indicae he causaliy relaionshi wih acual meanings cerainly exis or doesn exis in boh markes. And he conclusion only could be referred. As he emerging marke, he average income of Shanghai sock marke is higher han NYSE sock marke, bu he sronger flucuaion also indicaes Chinese invesors invesmen conce is no srong, heir invesmen behaviors are easily suffered by all kinds of informaion, and he Shanghai sock marke is no maure. These flucuaion characers of Shanghai sock marke could rovide decision-making references o avoid risks for invesors and imlemen marke suervision for he managemen dearmen. In addiion, he big flucuaions of Chinese sock marke are mainly induced by he olicy inerferences of managemen dearmen, and mos so-called concussions belong o olicy concussion. Therefore, he managemen dearmen should be more careful when coming on olicies, really realize informaion symmery, hold well he adusmen degree of olicy, and consider he marke conrol from long-erm view o make he olicy more reasonable and consecuive. References Bollerslev T. (986). Generalized Auoregressive Condiional Heeroskedasiciy. Journal of Economerics, No. 3, Engle R F. (98). Auoregressive Condiional Heeroskedasiciy wih Esimaes of he Variance of UK inflaion. Economerica, No. 5, Glosen L R, Jagannahan R. and Runkle D E. (993). On he Relaion beween he Execed Value and Volailiy of he Nominal Excess Reurn on Socks. The Journal of Finance, No. 48(5), Li Q and Zhao L J. (4). The Alied Research of he ARCH Model in he Sock Marke in China. Xi an Finance, No., Nelson D B. (99). Condiional Heeroskedasiciy in Asse Reurns: A New Aroach. Economerica, No. 59(), Pagan A R and Schwer G W. (99). Alernaive Models for Condiional Sock Volailiy. Journal of Economerics, No. 45(), Table. Descriive Sa. of wo markes income Descriive Sa. of Shanghai comosie index income Average Median Max. Min. Sandard deviaion Deflecion Kurosis Jarue-Bera Descriive Sa. of NYSE comosie index income Average Median Max. Min. Sandard deviaion Deflecion Kurosis Jarue-Bera

5 Vol. 3, No. Inernaional Journal of Business and Managemen Table. Esimaion resuls of ARCH class model Daily yield of Shanghai comosie index ARCH () (6.67) (4.57) GARCH (,) (.65) (5.866) (69.8) GJR-GARCH (,) (.63) (4.586) (69.5) (-.4) EGARCH (,) (-5.794) (6.9) (6.997) (.53) Daily yield of NYSE comosie index ARCH () (7.339) (3.) GARCH (,) (3.87) (5.79) (6.7) GJR-GARCH (,) (3.898) (-.536) (65.65) (5.39) EGARCH (,) (-4.76) (5.834) (58.9) (-5.457) Table 3. Ranking models by logarihm maximum likelihood mehod Shanghai comosie index Model Log likelihood AIC F-saisic Prob(F-saisic) EGARCH GJR-GARCH GARCH ARCH NYSE comosie index Model Log likelihood AIC F-saisic Prob(F-saisic) GJR-GARCH EGARCH GARCH ARCH Table 4. Flucuaion overflow effec es of wo markes (Granger causaliy es) Zero-hyohesis F-Saisic Probabiliy GARCH is no he Granger reason of GARCH GARCH is no he Granger reason of GARCH