VOLATILITY OF CHINA SHANGHAI STOCK PRICE-EXCHANGE RATE

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1 Page60 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia VOLATILITY OF CHINA SHANGHAI STOCK PRICE-EXCHANGE RATE Ming Fan a, Meng meng Dong b a Naional Universiy of Malaysia, Malaysia b Hangzhou Wanxiang Polyechnic, China Corresponding @qq.com Absrac This paper examines he use of GARCH-ype models for modelling volailiy and explaining relaionship beween sock marke risk and exchange rae risk in CHINA. We use daily daa from China Shanghai A Sock Price and Exchange Rae. Various ime series mehods are employed, including he simple GARCH model, as well as exponenial GARCH, hreshold GARCH. We find srong evidence ha daily reurns can be characerised by he above models. For boh markes, we conclude ha he bes model is GARCH (1,1)and he asymmeric effec is no significan. These findings are srongly recommended o financial managers and modellers dealing wih inernaional markes. Keywords: China Sock Markes, Exchange Rae, GARCH & Volailiy. 1. Inroducion On July 1, 005, he People's Bank of China announced ha he RMB exchange rae was no longer a single pegged o he US dollar, bu wih reference o a baske of currencies o implemen a managed floaing exchange rae sysem. Since hen, China's exchange rae sysem has enered a relaively floaing sae from a relaively fixed sae, and he impac of exchange rae flucuaions on oher pars of he financial marke (he sock marke) is becoming more and more significan. Sock marke and he foreign exchange marke are wo imporan pars of he financial marke. Their coordinaed developmen is direcly relaed o he seady developmen of financial marke. Therefore, i is of grea heoreical and pracical significance o deeply sudy he relaionship beween RMB exchange rae flucuaion and Chinese sock price remuneraion during his period. The second par is he lieraure review. The hird par is he empirical analysis of he relaionship beween RMB exchange rae volailiy and Chinese sock price reward. The fourh par is he empirical analysis. The resul analysis and he explanaion; The fifh par is he conclusion and he suggesion.. Lieraure Reviews For he heoreical aspec, he curren heories on he relaionship beween exchange raes and sock prices are: he flow-oriened model and he balance-of-securiies heory. The flow-oriened model (Dornbusch and Fisher, 1980) emphasizes he curren accoun or rade balance andhe relaionship beween sock prices is uncerain. The heory of porfolio balance (Branson and Henderson, 1985) argues ha, under oher condiions, he holder of securiies will compare he reurns on various securiies invesmens and decide wheher he holdings of he securiies held Proporionaely, invesors will hold a higher proporion of higher-paid asses and lower holdings of lower-paid asses, believing ha exchange rae volailiy (direc price mehod) is inversely relaed o sock price reurns He and Ng (1998) ake Japan's sock price as a sample o explore wheher here is exchange rae risk in he sock price reward, he research resuls show ha he Japanese company's share price reurns include he risk of exchange rae risk, here is a correlaion beween exchange rae and sock price APET, P.G (001) empirical research on he relaionship beween exchange rae and sock markes in India shows ha here is no Granger causaliy relaionship beween exchange rae and sock marke Asia Pacific Insiue of Advanced Research (APIAR)

2 Page61 Quaniles of Normal Quaniles of Normal 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia 3. Daa The sample daa of his paper is from January, 004 o November 30, 016, he Chinese sock price reurns and RMB o he US dollar nominal exchange rae daa for empirical research. The daa are from he websie of he Sae Adminisraion of Foreign Exchange (SAFE), which is omied in his paper because of he large size of he daa. The daa includes wo pars: he exchange rae daa and he Shanghai Composie Index daa, he exchange rae refers o he People's Bank of China announced he RMB agains he US dollar exchange rae (cenral pariy) daily daa; sock index is he Shanghai Composie Index, he index opening, Closing price of he highes and lowes poins, he mos represenaive of he closing price, so he daily index of he Shanghai Composie Index closed as he represenaive of sock price reurns. In erms of daa processing, since China's sock exchanges do no operae on holidays, he exchange rae daa a he same ime will be deleed when he sock marke is closed o mee he common rading days in he sock and exchange markes. The exchange rae of China agains he U.S. dollar means ha how many unis of RMB o buy one uni of U.S. dollar. The daa we used here is he daily saisical record(see figure 1,). 1, Quaniles of EX Figure 1: QQ-PLOT of he daily change of exchange rae 7,000 6,000 5,000 4,000 3,000,000 1, ,000 -,000 1,000,000 3,000 4,000 5,000 6,000 7,000 Quaniles of SP Figure : QQ-PLOT of he daily Sock Price For furher confirmaion of his guess, ADF es is necessary (see Table 1). Asia Pacific Insiue of Advanced Research (APIAR)

3 Page6 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia Table 1: ADF es Variable ADF Level P-Value Firs Differce P-Value rsp rex Mehodology In financial markes, flucuaion of prices (or reurns) goes under he name of volailiy - how much prices (or reurns) are changing over a given period. Linear models are unable o explain a number of imporan feaures common o much financial daa, including lepokurosis, volailiy clusering, long memory, volailiy smile and leverage effecs. Tha is, because he assumpion of homoscedasiciy (or consan variance) is no appropriae when using financial daa, and in such insances i is preferable o examine paerns ha allow he variance o depend upon is hisory. Therefore, o model he non-consan volailiy parameer, we consider GARCH-ype models. Bollerslev (1986) proposed agarch(p,q) random process, which can represen a greaer degree of ineria in is condiional volailiy or risk. Following he lieraure (Akgiray, 1989; Connolly, 1989; Baillie and DeGennaro,1990; Bera and Higgins, 1993; Bollerslev e al., 199; Floros, 007, among ohers), a simple GARCH model is parsimonious and gives significan resuls. GARCH allows he condiional variance of a sock index o be dependen upon previous own lags. The GARCH (p,q) model is given by: R q q ai i j j i 1 j 1 Where, p is he order of GARCH while q is he order of ARCH process. Error, is assumed o be normally disribued wih zero mean and condiional variance,, R are reurns, so we expec heir mean value ( ) o be posiive and small. We also expec he value of o be small. All parameers invariance equaion mus be posiive, and is expeced o be less han, bu close o, uniy, wih,news abou volailiy from he previous period can be measured as he lag of he squared residual from he mean equaion (ARCH erm). Also, he esimae shows he persisence of volailiy o a shockor, alernaively, he impac of old news on volailiy. Financial heory suggess ha an increase in variance resuls in a higher expeced reurn. Toaccoun for his, GARCH-in-Mean models are also considered, see Kim and Kon (1994). Sandard GARCH-M model is given by: R ~ N 0, a i 1 1 if is posiive (and significan), hen increased risk leads o a rise in he mean reurn ( can be inerpreed as a risk premium). Asia Pacific Insiue of Advanced Research (APIAR)

4 Page63 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia Exponenial-GARCH models were designed o capure he leverage effec noed in Black(1976) and French e al. (1987). A simple variance specificaion of EGARCH is given by: log log The logarihmic form of he condiional variance implies ha he leverage effec is exponenial(so he variance is non-negaive). The presence of leverage effecs can be esed by he hypohesis ha 0. If 0,hen he impac is asymmeric. Furhermore, he Threshold-GARCH model was inroduced by Zakoian (1994) and Glosen, Jaganahan and Runkle (1993). The TGARCH specificaion for he condiional variance is given by: q q ai i id 1 j j i 1 j 1 Where, d =1 if <0 and d =0 oherwise. In his model, good news( >0)and bad news ( <0) have differenial effecs on he condiional variance. Good news has an impac of a, while bad news has an impac of a. If >0hen he leverage effec exiss and bad news increases volailiy, while if 0 he news impac is asymmeric. 5. The seps and resuls 5. 1Modelling From resuls of he above ables, boh of hem are indicaing ha wha we guessed is consisen wih he esing resuls and ime series of exchange rae is no saionary. According o he exbook, we have o conver he sequence o be saionary. Therefore, we use he reurn on exchange rae o measure he volailiy. The equaion is as follow: rsp log( sp ) log( sp ) 1 rex log( ex ) log( ex ) rsp rex 1 5. Rae of reurn disribuion From hese graph, we can see i has higher kurosis and fa ail, we can conclude i has arch effec. So nex, we will do he arch es Series: Residuals Sample 1/05/004 11/30/016 Observaions 3135 Mean -.05e-19 Median Maximum Minimum Sd. Dev Skewness Kurosis Jarque-Bera Probabiliy Figure3: Residual nominal disribuion Asia Pacific Insiue of Advanced Research (APIAR)

5 Page64 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia 5.3 Auocorrelaion es The ACF and PAC graph residual phase obained by his equaion are shown in Fig. 4, and he ACF and PAC OF residual square are shown in Fig 5. As can be seen from Fig. 4 and Fig. 5, residual has no obvious auocorrelaion, while residual square has significan auocorrelaion. This shows ha here is a nonlinear relaionship beween he yields of differen imes, and he condiional variance has ime variabiliy, which proves he clusering of he volailiy of he yield.from he arch-lm es (Fig 6),we can conclude i has arch effec and hen we will find which model is bes for our daa. Figure 4: ACF and PAC OF residual square Figure 5: ACF and PAC OF residual square Table : Heeroskedasiciy Tes: ARCH F-saisic Prob. F(,3130) Obs*R-squared Prob. Chi-Square() Garch Family Seup Normally, we use wo informaion crieria such as AIC and SC o make sure of he opimal order of Garch model. The resuls of differen orders we used is as follow. From indicaions of AIC and SC, Garch(1,1) model should be he bes one o esimae he condiional variance which could affec he volailiy of sock price o exchange rae. Cerainly, we ough o noice he LL(Log likelihood Raio) migh provide differen opinions on i, bu since AIC and SC pu forward he agreemen on choosing he opimal orders for Garch model, he convincing power of his agreemen is overwhelming. Table 3: The resuls of differen orders we ake for Garch model (p,q) AIC SC LL (0,1) (1,0) (1,1) (1,) (,1) (,) Asia Pacific Insiue of Advanced Research (APIAR)

6 Page65 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia Table 4: Garh-family Models for Volailiy (Variance Specificaions) Index/Model GARCH (1,1) EGARCH (1,1) TGARCH (1,1) GARCH (1,1)-M TGARCH (1,1) -M ω 1.56E-06 ( ) ( ) 1.6E-06 (4.8990) 1.55E-06 (4.0981) 1.61E ɑ (1.8604)* ( )* ( )* (1.8488)* ( ) * γ ( ( )* )* β ( )* ( )* ( )* (18.01)* (17.916) * ɑ+β ρ (- ( ) )* AIC SIC ll Noe: 1.we repor he resuls from GARCH-TYPE models is under he assumpion ha he errors are condiionally normal disribued.. Z-saisics in he parenheses.3.* significan a 5% level.4.for he individual specific esimaed resuls of all GARCH-ype models, see he appendix. We esimae a number of differen GARCH-family models o explain condiional variance and volailiy clusering. Table 3 repors he parameer esimaes of all condiional volailiy (GARCH-family) models defined in he previous secion. For boh indices, besides EGARCH(1,1), ɑ+β=1.14, which means volailiy shocks are becoming larger, he oher sum of GARCH family coefficiens are very close o one, indicaing ha volailiy shocks are quie persisen. Firs, we see from AIC, SIC and LL index, we could ge GARCH(1,1) is he bes model. And we furher compare beween GARCH(1,1), EGARCH(1,1) and TGARCH(1,1), we could see γ is significan in EGARCH(1,1) and TGARCH(1,1) model, which means bad news has significan effecs han good news in his model; and furher we see he ω in hese hree models are no significan. Furhermore, EGARCH models show a negaive and significan γ parameer, indicaing he exisence of he leverage effec in reurns during he sample periods. However, he TGARCH leverage effec erm is also significan in he case,while he news impac is asymmeric We go furher compare GARCH(1,1)-M and TGARCH(1,1) M, ω in hese wo models are no significan, which means he variance has no significan effec on means equaion; which means hese wo model are no beer han GARCH(1,1) In GARCH(1,1) model, he coefficien β is especially high han he coefficien ɑ, which indicaing a long memory in he variance. Asia Pacific Insiue of Advanced Research (APIAR)

7 Page66 Quaniles of Normal Quaniles of Suden's 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia 5.5 Furher ARCH-LM Tes We coninue o do he ARCH-LM es on he resuls of GARCH (1,1) o see wheher here are sill ARCH effecs. From Figure 7 we can see ha he Chi-Square (1) value is 0.4, which is far more han 0.05, so we conclude he GARCH model has no ARCH effec. We analyzed he residual residuals (see Figure 8.9), and we can see ha he Heeroskedasiciy disribuion has been fulfilled by he suden's disribuion. Table : Heeroskedasiciy Tes: ARCH F-saisic Prob. F(,3130) Obs*R-squared Prob. Chi-Square() Quaniles of RESID Quaniles of RESID01 Figure 8: Heeroskedasiciy Tes: ARCH Figure 9 Heeroskedasiciy Tes: ARCH 6. Conclusion In Table 9, we build up 5 GARCH-ype models. The lagged orders of boh in mean equaion is seleced by he SC, AIC and LL which are same as wha we menioned above. In addiion, since we have already diagnosed ha he residual of reurns is no normally disribued, we assume ha i is demonsraed by suden T disribuion. Table 10 repors he each esimaed parameer of every GARCH-family models o explain condiional variance and volailiy clusering. We should noice ha he sums of ɑ and β of only GARCH model and Garch-M model we es here are close o 1, indicaing ha he volailiy shocks affecing variance would be persisen. Ohers are eiher more han 1, or boh of coefficiens less han 0, which are no qualify he requiremens of saionary sequences. In GARCH(1,1)-M model, he coefficien of he condiional variance in he mean equaion, denoed as ρ, is equal o which is significanly negaive. I indicaes ha here is a relaionship beween variance and reurns of sock price, in oher words, one uni increase in forecasing risk will bring 0.43 uni decrease in reurn on sock price. Asia Pacific Insiue of Advanced Research (APIAR)

8 Page67 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia Furhermore, EGARCH, TGARCH, models all indicae ha here is asymmeric effecs in volailiy shocks, even hough all of hem are no appropriae o be he bes Garch model. I sill means ha leverage effecs are exising. Finally, he mean values of he volailiy (GARCH variance series) from he above GARCH models are 1.56E-06 (variables in form of logarihm in all mean equaions). Asia Pacific Insiue of Advanced Research (APIAR)

9 Page68 3 rd Asia Pacific Conference on Conemporary Research (APCCR- 017), Kuala Lumpur, Malaysia References i. Aggarwal, R., Exchange Raes and Sock Prices: A Sudy of U.S. Capial Marke Under Floaing Exchange Raes[J]. Akron Business and Economic Reviews, Volume 1, pp ii. iii. iv. Aydemir, O. & ErdalDemirhan, 009. The Relaionship beween Sock Prices and Exchange Rae: Evidence from Turkey. Inernaional Research Journal of Finance and Economics, Volume 3, pp Bahmani-Oskooee, M. & AhmadSohrabian, 199. Sock Prices and he Effecive Exchange Rae of he Dollar. Applied Economics, Volume 4, pp Clive, G., HuangBwo-Nung, Yang & Chin, W., 000. Bivariae Causaliy beween Sock Prices and Exchange Raes: Evidence from Recen Asian Flu. The Quarerly Review of Economics and Finance, Volume 40, p v. Gao, F., 01. The Relaionship beween Sock Prices and Exchange Raes and Sock Prices: Evidence from China. 5h ed. s.l.:universiy of Durham. vi. vii. viii. ix. Ki-ho, K., 003. Dollar Exchange Rae and Sock Price: Evidence from Mulivariae Coinegraion and Error Correcion Model. Review of Financial Economics, Volume 1, pp LianOng, L. & Izan., H., Socks and currencies: are hey relaed?. Applied Financial Economics, Volume 9, pp M.Tabak, B., 006. The Dynamic Relaionship beween Sock Prices and Exchange Raes: Evidence for Brazil, Brazil: Banco Cenral Do Brasil. Ming-Shiun, P., Chi-Wing, F. R. & Y.Angela, L., 007. Dynamic linkages beween exchange raes and sock prices:evidence from Eas Asian markes. Inernaional Review of Economics and Finance, Volume 16, pp x. Phylakis, K. & Ravazzolo., F., 005. Sock Prices and Exchange Rae Dynamics. Journal of Inernaional Money and Finace, Volume 4, pp xi. Sekmen, F., 011. Exchange rae volailiy and sock reurns for he U.S. African Journal of Business Managemen, Volume 5, pp Asia Pacific Insiue of Advanced Research (APIAR)