Hội nhập kinh tế và tương tác thị trường chứng khoán - Nghiên cứu trường hợp ECFA

Nội dung text: Hội nhập kinh tế và tương tác thị trường chứng khoán - Nghiên cứu trường hợp ECFA

1. ECONOMIC INTEGRATION AND STOCK MARKET CORRELATION CHANGE-THE CASE OF ECFA HỘI NHẬP KINH TẾ VÀ TƯƠNG TÁC THỊ TRƯỜNG CHỨNG KHOÁN - NGHIÊN CỨU TRƯỜNG HỢP ECFA JEFF T.C. LEE Lunghwa University of science and technology, Taiwan Introduction China replaced the United States and became Taiwan’s largest export market in 2002. To enhance the economic integration with China, Taiwan signed the Economic Cooperation Framework Agreement (ECFA) with China on June 29, 2010 and became effective on September 12, 2010. The spirits of ECFA are to lower the tariff, promote the trade in service and goods and encourage mutual investment between Taiwan and China. Since ECFA became effective¸ the total trade volume between Taiwan and China grew from 525.8 billion in 2010 to 588.1 billion in 2014 in terms of US dollar. Many Taiwanese listed companies have set up plants in China to embrace the opportunity for market opening. The share of total revenue from China for these companies also increases steadily. Business conditions in China start to influence the financial performance for those companies which have big share of total revenue from China. This connection raises our motivation to investigate whether stock market correlation has changed between Taiwan and China since ECFA took effect. Many studies have pointed out that economic integration would not only enforce the economic relationship between counterparties but also increase the correlation between their stock markets. For examples, Aggarwal and Kyaw (2005) believe that stock markets correlations among Mexico, the United State and Canada have increased significantly after North America Free Trade Agreement (NAFTA) took effect in 1994. Bartram, Taylor, and Wang (2007) confirm that stock market correlations among major euro money union countries have change significantly after single money union took effect in 1999. Also, Chuang and Lee (2013) find that correlation between Hong Kong and Chinese stock markets has increased significantly after the Closer Economic Partnership Agreement (CEPA) took effect in 2004. However, these studies consider the date which economic integration took effect as a known correlation change cut point. In fact, the correlation change between stock markets might be unknown. Methodology In this paper, first, we use GJR-GARCH (1,1)-t to fit both Taiwan and Chinese stock markets. Second, we deploy conditional t copula to measure correlation between Taiwan and Chinese stock markets. Finally, we follow the procedure of Gombay and Horvath (1996) and Dias and Embrechts (2004, 2009) to test the unknown correlation change between these two markets. 222
2. GJR-GARCH (1,1)-t Margin Model The GJR-GARCH (1,1)-t margin model is used to capture volatility clustering and heavy tail for both Taiwan and Chinese stock markets. This model is specified as r =+µ ε , (1) i,titit,, 2222 σεσεit,,1,1,1,2,1,1=+ca i i it−− + b i it + aI i it −− it , (2) εψi,1,,t t− = hz it it, zti,tv~, (3) where rit, represents the log return for market i at time t . i =1, 2 stands for the 2 Taiwan and Chinese stock markets, respectively. Conditional variance σ it, is explained by 2 2 the lag-1 square residual εi,1t− and lag-1 variance σ i,1t− . Indication function Ii,1t− is used to detect volatility asymmetry effect. When ε it,1− < 0 , the value of Ii,1t− will be equal to 1 ; otherwise, the value of Ii,1t− will be equal to 0. The standardize residuals zit, are assumed to follow the t distribution with degree of freedom v . Conditional t Copula The bivariate copula function combines two different margin distributions, Fz()1,ttψ 1,− 1 and Gz()2,ttψ 2,− 1 , into a joint distribution, Φ (rr1,ttt,| 2,ψ − 1 ) . The joint conditional cumulative density function (cdf) is defined as rr Cuv CFz Gz (4) Φ( 1,ttt,| 2,ψψ−− 1) ==() ttt ,| 1 ( ( 1, t ψψ 1, t −− 1),( 2, t 2, t 1 )) , where uFzttt= ()1,1ψ − , and vGzttt= ( 2,1ψ − ) . ψ t−1 is the information set at t −1. The probability density function (pdf) of this joint distribution function can be decomposed as a product of a copula pdf and the two marginal pdfs ϕψ( zz1,ttt,,|||, 2,−−−− 1) =×× cuv( ttt ψ 1) fz( 1, t ψ 1, t 1) gz( 2, t ψ 2, t 1 ) (5) where fz( 1,tt|ψ 1,− 1 ) and gz( 2,tt|ψ 2,− 1 ) represent the marginal density functions for the Taiwan and Chinese stock markets. cu( tt,| v ψ t−1 ) is the pdf of copula function. In this paper, we choose t copula as the researched copula function because it has symmetry and heavy tail correlation. The t copula density function is specified as −+[2/2](υ ) ⎛⎞⎛⎞⎛υυ+ 21−1 ⎞ ΓΓ+Ω⎜⎟⎜⎟⎜1 ψψ′ ⎟ 1 22υ cu,, vρυ= ⎝⎠⎝⎠⎝ ⎠ , ()tt t 2 2 −+[1/2]()υ 1− ρ ⎛⎞⎛⎞υ +1 2 ⎛⎞1 2 t Γ 1+ ψ ⎜⎟⎜⎟∏i=1⎜⎟i ⎝⎠⎝⎠2 ⎝⎠υ where ρt is correlation parameter and v is the degree of freedom . To search for correlation change attribute to ECFA, this study assumes ρt as the following model ρt =+ωλDt , (6) where ω and λ are parameters to be estimated in the copula function. Dt is the dummy variable and its value is assumed to be 0 before correlation change; otherwise, it will be 1. However, the existence of correlation change is assumed to be unknown and thus in need of testing. 223
3. Test of Correlation Structure Change Let u,u,12K ,uT be the sequence of an independent random vector with uniformly distributed margins and a copula of C (u1;,θ11η ),C (u2 ;,θ22η ) ,K ,C (uT ;,θTTη ) , where θi (1) (2) and ηi are the copula’s parameters and θi ∈ Θ ,ηi ∈ Θ . Assuming parameter ηi (1,,)iT= K is constant, testing if the correlation parameter has a single correlation change is equal to testing the null hypothesis, which is H01:θ ===θθθ 2L T H :θ ==θθθθ ≠ = = conditional to 11L kkk −+11T η12===ηηηL T . (7) * * If H0 is rejected, k is the change point. If kk= is known, the likelihood ratio test ( LR ) is defined as supc (u ;θη , ) ()θη,∈Θ()12 ×Θ ( ) ∏1≤≤iT i ii Λ= ii . (8) k supcc (uu ;θη , ) ( ; ςη , ) ()112 () ( ) ∏∏1≤<ikiiii kiT ≤≤ ii ()θςηiii,,∈Θ ×Θ ×Θ When Λk is small, the null hypothesis will be rejected easily. Given the copula pdf c(⋅) , the estimate of Λk can be estimated using the following two equations: Lcki()θ,log;,,ηθη= ∑ (u ) (9) 1≤<ik * Lcki()θ,log;,,ηθη= ∑ (u ) (10) kiT≤≤ where Lk ()θ,η is the maximum log likelihood estimate for samples tk=−1, 2,K , 1 , and * Lk ()θ,η is the maximum log likelihood estimate for samplestk= ,,K T. Therefore, the test for asymptotic distribution of LR is −Λ=2log( ) 2⎡⎤LLLθηˆ ,ˆ + θηˆ ,ˆ − θηˆ ,ˆ , (11) kkkkkkkTTT⎣⎦()( ) ( ) ˆ ˆ* where θk and θk represent parameter estimates before and after change point k ˆ respectively. θT and ηˆT are the copula parameter estimates for the entire samples. If k is unknown, a grid is used to search the maximum ZT and testify the significance of correlation change point k . ZT is defined as ZTk=−Λmax 2log() . (12) 1<<kT() When the general conditional holds, the smaller the value of Λk , the larger the value of ZT and the easier of the null hypothesis will be rejected. The p− value for asymptotic 1/ 2 distribution of ZT can be calculated by xxp exp(− 2 / 2) PZ()1/2 ≥≈ x × T 2/2p /2Γ()p (13) ⎛⎞(1−−hlp )(1 ) (1 −− hl )(1 ) 4⎛⎞ 1 ⎜⎟ log−++224 logO ⎜⎟ , ⎝⎠hl x hl x⎝⎠ x where h and l can be taken as hT()== lT () (log) T 2/3 . p is the number of changing parameters under alternative hypothesis. 224
4. Empirical Results Data and Summary Statistics In this paper, we use Taiwan Weighted Stock Index and Shanghai Stock Exchange Composite Index to represent the Taiwan and Chinese stock markets. We collect the daily closing price for about five years before and after ECFA became effective. The source of data is from Datastream. Data period is from January 5, 2006 to December 31, 2014. After deleting the non-common trading days, the daily closing price is converted into the daily log returns. A total of 2,137 return samples are used in this paper. Table 1 is the summary statistics for Taiwan and Chinese stock markets. The mean and standard deviation of return for Chinese stock market are larger than Taiwan stock market. Both Taiwan and Chinese stock markets are skew to the left and have a high kurtosis for the whole samples. Jarque-Bera statistics rejects the null hypothesis of normal distribution meaning that both stock markets are non-normal distribution. Linear correlations between these two markets are 0.322 Pre-ECFA and 0.349 Post-ECFA, respectively. Although the correlation of Post-ECFA is higher than the correlation of Pre- ECFA, the significance of correlation change between these two markets has to be further testified. Table 1. Summary statistics for Taiwan and Chinese stock markets Pre-ECFA Post-ECFA Whole Samples Taiwan China Taiwan China Taiwan China Mean 0.013 0.018 0.018 0.073 0.015 0.047 Std. Deviation 0.977 1.166 1.570 2.085 1.321 1.710 -0.408 -0.147 -0.526 -0.471 -0.538 -0.444 Skewness (0.000) (0.054) (0.000) (0.000) (0.000) (0.000) 3.061 2.062 3.233 2.123 4.356 3.413 Kurtosis (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) 395.9 232.7 Q2 (6) (0.000) (0.000) 425.6 184.0 539.3 251.8 1792.3 1107.2 Jarque-Bera (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Correlation 0.322 0.349 0.328 Note: the number in parentheses is p-value. The parameter estimates for GJR-GARCH (1,1) margin model are presented in Table 2. All the parameters satisfy the conditions of ci > 0 , αi,1 ≥ 0 , βi ≥ 0, αii,1 +<β 1 for the GJR-GARCH (1,1) model. Although the ARCH effect is not significant for Taiwan stock market, the GARCH effect is significant for both markets. That implies volatility clustering is significant for both markets. However, the volatility asymmetry is not significant in Chinese stock market while volatility asymmetry is significant in Taiwan stock market. 225
5. Table 2. Parameter estimates for GJR-GARCH (1,1) margin model Taiwan China 0.031 0.032 µ it, (0.000) (0.005) 0.002 0.002 c i (0.021) (0.081) 0.015 0.041 a i,1 (0.123) (0.000) 0.942 0.953 b i (0.000) (0.000) 0.064 -0.011 a i,2 (0.000) (0.370) 5.573 5.132 ν (0.000) (0.000) Log-Likelihood -1450.0 -2077.2 Note: the number in parentheses is p-value. In this paper, we choose t copula to measure the stock market correlation for the reason of high kurtosis in both Taiwan and Chinese stock markets. We follow the fine-tune procedure of Bai (2007) to find out correlation change. First, we use whole samples to discover the initial correlation change point. Then, we use initial correlation change point to divide whole samples into two subsamples and search for another correlation change point in two subsamples. Finally, we use correlation change point in subsamples to divide subsample further and search for another correlation change point until there is no correlation change point in subsamples. The estimated results for correlation change by using t copula are presented in Table 4. For whole samples (level I), the maximum Zn is 3.9 and is significant to reject the null hypothesis of no correlation change. The date of correlation change is July 28, 2007. The parameter λ is 0.212 meaning the average correlation increases 21.2% after correlation change. The correlation change date of July 28, 2007 was around the time which subprime crisis severely influenced the stock markets around the world. According to Manner and Candelon (2010) and Johansson (2011), extreme volatility in stock market will cause correlation to change significantly. Moreover, the date of July 28, 2007 was about three years before the ECFA took effect. Therefore, this correlation change is not influenced by ECFA. For two subsamples (level II), the maximum Zn are 1.8 and 3.5, respectively. However, these two correlation change points are not significant. Therefore, there are no correlation change points in these two subsamples that imply the influence of ECFA on the correlation change between Taiwan and Chinese stock markets is not significant. 226
6. Table 3. Test for correlation change under t copula Time Zn Date of level Interval ω λ ν p-value Change I 2006/1/5~ 0.149 0.212 13.9 3.9 0.022 2007/7/28 2014/12/31 (0.004) (0.000) (0.000) 2006/1/5~ -0.264 0.433 28.5 1.8 0.657 NO II 2007/7/27 (0.202) (0.042) (0.000) 2007/7/28~ 0.386 -0.215 18.2 3.5 0.117 NO 2014/12/31 (0.000) (0.001) (0.000) Note: the number in parentheses is p-value. Conclusion In this paper, we use GJR-GARCH as margin model to fit the Taiwan and Chinese stock markets and choose t copula to measure the correlation between these two markets. Following the procedure of Gombay and Horvath (1996) and Dias and Embrechts (2004, 2009) to test correlation change, we find the influence of ECFA on correlation change between Taiwan and Chinese stock markets is not significant. The only significant correlation change is influenced by subprime crisis, not by ECFA. This result contradicts to those studies of Bartram, Taylor, and Wang (2007) and Chuang and Lee (2013) who confirmed that economic integration causes stock market correlation change significantly. The reason for the contraction may result from the interruption of Sunflower Movement in 2013. This movement is started by the college students in Taiwan to against the parliament passing the followed-up treaty, the Cross-strait Agreement on Trade in Services and Goods. This interruption blocks the economic integration between Taiwan and China to close further. REFERENCES Bai, J. (1997). “Estimating Multiple Breaks One at a Time.” Econometric Theory 13, 315- 352. Bartram, S. M., Taylor, S. J., and Wang, Y. H. 2007. “The Euro and EuropeanFinancial Market Correlation.” Journal of Banking & Finance 31, no. 5: 1461-1481. Chuang, C. and Lee, J. 2013. “Has CEPA Increased Stock Market Correlation Between Hong Kong and China? The Application of Conditional Copula Technique.” International Journal of Innovative Computing, Information and Control 7, no. 9: 2461- 2466. Dias, A. and Embrechts, P. 2004. “Change-Point Analysis for Correlation Structures in Finance and Insurance.” In G. Szego (ed.), Risk measures for the 21st century(321-35). Chichester: Wiley Finance Series. 227
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