Research design and methodology

2 . 2 . Selected literature on EGARCH models The generalized autoregressive conditional heteroscedasticity GARCH models have been widely applied in different time series studies Cheung and Ng, 1992a; Antoniou and Holmes, 1995; Chan and Wu, 1995; Tse and Booth, 1996; Liu et al., 1996; Song et al., 1998. The GARCH models incorporate time-varying returns and time-varying volatility which can deal with the problem of autocorrelation and heteroscedasticity in the time series data. The GARCH model does not, however, address the issue of asymmetric volatility effects on stock returns. 3 It imposes a non-negativity constraint on the parameters of past conditional variance d and past volatility shock g in the volatility equation such that the sum d + g must be B 1 for the volatility process to be covariance stationary. 4 The Nelson 1991 EGARCH model relaxes the restrictions of the GARCH model and incorporates the asymmetric volatility effect in the volatility equation. There are numerous papers using the EGARCH model to examine the behavior of stock returns of national stock markets, such as Cheung and Ng 1992b, Koutmos et al. 1993, Episcopos 1996 and Booth et al. 1997. They all find that the EGARCH model can adequately capture the stochastic behavior of return and volatility in stock markets.

3. Research design and methodology

3 . 1 . Sample data and study period The data include the four daily indices: H shares HSCEI, red chips HSCCI 5 , Shanghai Composite Index SHI, and Shenzhen Composite Index SZI for the period August 4, 1994 to June 27, 1997. 6 Data on the HSCEI and the HSCCI were obtained from EXTEL Equity Research Database EXTEL, 1998, whereas data on the SHI and the SZI was supplied by the Hong Kong branch of the Taiwan Economic Journal TEJ, 1998. The official definition of H shares from the SEHK is used in the study. That is, H shares refer to ‘overseas listed foreign shares which are listed on the Exchange and subscribed for and traded in Hong Kong dollars’. Specifically, they are ‘foreign shares issued by a PRC issuer under PRC law, the par value of which is denominated in Reminbi and which are subscribed for in a currency other than Reminbi Hong Kong dollars for H shares’. The H-share issuers have to comply 3 The asymmetry effect in several stock markets has been found by Booth et al. 1997 for Denmark, Norway, Sweden and Finland, Koutmos et al. 1993 for Greece, Cheung and Ng 1992b for the US, Koutmos 1992 for Canada, France and Japan and Poon and Taylor 1992 for the UK. 4 See Section 3.3 for details of the models. 5 See Table 1 and Table 2 for the list of H shares and red chips included in the HSCEI and HSCCI, respectively. 6 The sample period ended right before the Hong Kong hand-over on July 1, 1997 and the Asia financial crisis. with additional requirements set by the SEHK SEHK, 1997. H shares are companies incorporated in China and are listed in Hong Kong. They denote the issued shares of China enterprises mainly state-owned China enterprises listed in Hong Kong. The H-share companies are typically concentrated in heavy industries i.e. steel or petrochemicals like Maanshan Iron and Shanghai Petrochemical. Since there is no official definition of red chips announced by the SEHK, the selection criteria for the constituent companies to be included in the HSCCI by Hang Seng Index Services Ltd., are used in this study HSI, 1997b. That is, The company should have at least 35 shareholding directly held by either: a China entities which are defined to include state-owned organizations, provincial or municipal authorities in China; OR b Listed or privately owned Hong Kong companies Hong Kong or overseas incorporated which are controlled by a. above;... Tables 1 and 2 display the composition of the Red Chip and H-Share Indices. The data for the two tables are based on the information provided by HSI 1997a, 1998, SEHK 1999 and HSI web Hang Seng Index Service Ltd. HSI web: www.hsiservices.com. As expected, Tables 1 and 2 indicate that companies included in the H-Share Index are primarily industrial firms while red chips are more diverse and include industrial, consolidated enterprises and financial companies. In addition, red chips appear to be bigger in size compared to the H shares. Table 3 displays the distribution of the four indices Red Chip, H-Share, Shanghai Composite and Shenzhen Composite Indices among different industries over the years 1993 – 1998. The data are collected from annual reports on SHSE 1994, 1996, 1997, 1998, TEJ 1998, Shenzhen Securities Market 1997 and SZSE 1997a,b, 1998. Most of the companies in each of the respective indices, during the period 1993 – 1998, are industrial firms. So, we would expect that these four indices would be closely related and would show common characteristics of information flow over time. 3 . 2 . Descripti6e statistics Table 4 shows descriptive statistics for the return of the four indices: HSCEI, HSCCI, SHI and SZI. The HSCCI, HSCEI, SHI and SZI returns are positively skewed. The excess kurtosis measures indicate that all index returns are highly leptokurtic and do not follow the normal distribution. The Bera – Jarque test statistics rejects normality for all index returns. 7 Ljung – Box [LB Q ] statistics for ten lags on the HSCEI and HSCCI returns indicate the presence of serial correlation. 8 Also, LB Q statistics on all squared index returns show high autocorrelation. 7 The Bera – Jarque statistic is given by n − kS 2 6-K 2 24, where n is the number of observations, k is zero for an ordinary series and equal to the number of regressors when working with the residuals of an equation, S is skewness, and K is excess kurtosis. Bera – Jarque statistic for normality is distributed as a x 2 . See Jarque and Bera 1980. 8 The Ljung – Box [LB Q ] statistics is used to test whether a series is uncorrelated. This is calculated using the formula LBN = TT + 2 k = 1 N r k 2 T − k, where r k , for k = 1, . . , N is lag k sample autocor- relation of the series, and T is the sample size. LBN is asymptotically distributed as x 2 with N dof. W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 322 Table 1 H shares China enterprises included in the Hang Seng China-enterprises index HSCEI Market Company name Industry Security code Total market No. Listing date Total assets US classification capitalization capitalization US 60 887 888 0.018 07-24-97 740 684 535 Angang New Steel Co. Ltd. 1 Industrial 0347 10-21-97 293 207 137 0.012 2 0914 40 074 741 Industrial Anhui Conch Cement Co. Ltd. 0.017 0995 11-13-96 349 589 822 Anhui Expressway Co. Ltd. Industrial 57 911 151 3 429 365 548 Beijing Datang Power Generation 0.125 03-21-97 1 598 265 774 0991 Utilities 4 Co. Ltd. 05-14-97 830 710 286 113 166,647 Properties 0588 Beijing North Star Co. Ltd. 0.033 5 91 441 556 Beijing Yanhua Petrochemical Co. 0.027 06-25-97 918 023 536 0325 Industrial 6 Ltd. 0.002 08-06-93 133 466 423 7 Beiren Printing Machinery Holdings 0187 Industrial 5 485 977 Ltd. 09-29-97 18 463 408 0.004 14 525 577 0161 8 Industrial Catic Shenzhen Holdings Ltd. 10 946 137 Chengdu Telecommunications Cable 0.003 12-13-94 182 187 911 1202 Industrial 9 Co. Ltd. 10 105 177 666 0.031 02-05-97 3 243 390 399 0670 China Eastern Airlines Corp. Ltd. Consolidated enterprises 0.033 11-11-94 1 117 444 369 Others 11 1138 China Shipping Development Co. 112 084 324 Ltd. China Southern Airlines Co. Ltd. Consolidated 18 008 904 12 122 767 672 1055 07-31-97 0.036 enterprises 10-17-97 447 134 076 13 1053 Chongquing Iron and Steel Co. Ltd. Industrial 20 304 404 0.006 0.003 06-06-94 268 548 424 10 094 198 14 1072 Industrial Dongfang Electrical Machinery Co. Ltd. 0038 0.022 06-23-97 380 437 159 First Tractor Co. Ltd. Industrial 15 76 539 061 Guangdong Kelon Electrical 409 340 341 0.119 07-23-96 606 068 902 0921 16 Industrial Holdings Co. Ltd. 05-14-96 1 298 056 487 166 279 316 Utilities Guangshen Railway Co. Ltd. 0.048 17 0525 0874 0.007 10-30-97 374 700 249 Guangzhou Pharmaceutical Co. Ltd. Industrial 18 23 275 774 17 955 678 Guangzhou Shipyard International 0.005 08-06-93 371 193 179 0317 Industrial 19 Co. Ltd. 12-16-94 1 041 348 989 0.010 34 518 551 20 Industrial Harbin Power Equipment Co. Ltd. 1133 W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 323 Table 1 Continued Market Company name Industry Security code Total market No. Listing date Total assets US classification capitalization capitalization US 513 100 230 0.149 01-21-98 4 286 472 572 Huaneng Power International Co. 21 Utilities 0902 06-27-97 1 487 284 848 0.078 22 0177 266 577 190 Industrial Jiangsu Expressway Co. Ltd. 0.019 0358 06-12-97 568 818 429 Jiangxi Copper Co. Ltd. Industrial 65 683 550 23 51 059 471 0.015 05-23-95 1 867 100 225 Jilin Chemical Industrial Co. Ltd. 24 Industrial 0368 02-02-96 135 997 973 0.002 Industrial Jingwei Textile Machinery Co. Ltd. 7 468 157 25 0350 0.001 0300 12-07-93 78 130 554 Kunming Machine Tool Co. Ltd. Industrial 2 559 047 26 8 003 072 0.002 07-08-94 415 920 347 27 1108 Luoyang Glass Co. Ltd. Industrial 78 291 411 0.023 11-03-93 2 161 103 191 28 0323 Maanshan Iron and Steel Co. Ltd. Industrial 05-02-96 449 776 602 0.003 10 933 229 29 Industrial Nanjing Panda Electronics Co. Ltd. 0553 30 16 981 293 Northest Electrical Transmission and 0.005 07-06-95 407 027 561 0042 Industrial Transformation Machinery Manufacturing Co. 08-17-94 1 052 150 274 Industrial 31 172 040 244 0.050 Qingling Motors Co. Ltd. 1122 Shandong Xinhua Pharmaceutical Co. 15 489 818 0.005 12-31-96 150 897 494 0719 32 Industrial Ltd. 07-26-93 2 526 800 609 33 0338 Shanghai Petrochemical Co. Ltd. Industrial 210 532 435 0.061 03-12-97 395 050 268 0.051 34 0548 173 679 576 Industrial Shenzhen Expressway Co. Ltd. 0.023 0107 10-07-97 650 505 020 Sichuan Expressway Co. Ltd. Industrial 78 587 281 35 0.004 05-17-94 833 696 640 36 Tianjin Bohai Chemical Industry 1065 Industrial 14 702 419 Group Co. Ltd. 07-15-93 474 523 728 36 713 062 Tsingtao Brewery Co. Ltd. 0168 Industrial 0.011 37 1171 0.042 04-01-98 566 968 123 Yanzhou Coal Mining Co. Industrial 38 144 829 795 128 307 319 0.037 03-29-94 1 565 858 323 39 1033 Yizheng Chemical Fibre Co. Ltd. Industrial 290 582 738 0.085 05-15-97 1 384 996 912 0576 40 Zhejiang Expressway Co. Ltd. Industrial 0.033 12-02-94 1 130 083 833 111 174 018 41 1128 Industrial Zhenhai Refining and Chemical Co. Ltd. W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 324 Table 1 Continued Market Company name Industry Security code Total market No. Listing date Total assets capitalization US classification capitalization US 36 820 093 495 1.257 4 319 437 561 Total 0.031 898 051 061 Mean 105 352 136 65 683 550 0.019 568 818 429 Median 4 286 472 572 0.149 513 100 230 Maximum 0.001 18 008 904 Minimum 2 559 047 343 578 708 964 1.000 Total market capitalization US The total assets are as at December 31, 1997. The total assets are as at December 31, 1996 because 1997’s financial statements are not available for these firms. W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 325 Table 2 Red chips China-affiliated corporations included in the Hang Seng China-affiliated corporations index HSCCI Market Industry Company name Total market Security No. Listing date Change date † Total assets code US ‡ capitalization classification capitalization US 0.258 1 Aug. 1970 Beijing Development Hong 05-29-98 43 574 113 0154 Industrial 12 730 379 Kong 88 795 410 0.004 05-29-97 08-31-98 1 239 569 663 2 Beijing Enterprises Holdings Consolidated 0392 enterprises Ltd. 0.032 08-11-97 11-30-98 Industrial 91 508 426 3 CASIL Telecommunications 1185 111 526 688 Holdings Ltd. China Aerospace 172 246 091 0.050 08-25-81 06-25-93 959 016 201 0031 4 Industrial International Holdings Ltd. China Everbright 0257 191 364 306 0.056 Feb. 1973 05-07-93 492 708 088 5 Consolidated International Ltd. enterprises 0.155 02-26-73 12-31-97 Consolidated 993 609 142 532 524 710 China Everbright Ltd. 0165 6 enterprises Industrial 107 432 674 0.031 12-10-91 12-31-97 66 987 747 0256 China Everbright 7 Technology Ltd. 0.045 07-18-90 07-23-93 221 909 755 154 287 816 8 Consolidated China Foods Holdings Ltd. 0506 enterprises 0.348 07-15-92 01-04-93 1 188 508 632 9 China Merchants Holdings 0144 Industrial 1 194 235 805 International Co. Ltd. 0.200 08-20-92 01-04-93 2 411 702 195 Properties 686 241 206 10 China Overseas Land and 0688 Investment Ltd. 118 723 688 0.035 06-21-94 06-22-94 163 053 041 11 China Pharmaceutical 1093 Industrial Enterprises and Investment Corp. Ltd. 0.109 11-08-96 03-31-98 Properties 812 592 091 China Resources Beijing 1109 372 809 787 12 Land Ltd. 0.706 Jan. 1973 01-04-93 2 704 374 104 13 China Resources Enterprise 0291 Properties 2 425 687 477 Ltd. 419 659 826 0.122 11-11-92 01-04-93 1 288 025 092 Consolidated 14 0308 China Travel International Investment HK Ltd. enterprises W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 326 Table 2 Continued No. Market Company name Industry Security Total market Listing date Change date † Total assets classification US ‡ capitalization capitalization code US Others 74 544 746 0.022 05-23-97 08-31-98 105 434 560 0560 Chu Kong Shipping 15 Development Co. Ltd. 07-17-80 01-04-93 4 458 600 567 768 115 397 0.224 Finance CITIC Ka Wah Bank Ltd. 0183 16 0.165 0135 03-13-73 07-12-93 129 075 473 CNPC HK Ltd. Others 566 460 570 17 0.027 08-30-73 02-18-93 435 786 223 92 608 921 18 Others 0119 Continental Mariner Investment Co. Ltd. 0.030 02-11-92 05-29-98 290 261 739 19 Cosco International Holdings 0517 Industrial 104 369 923 Ltd. 0.249 12-19-94 12-20-94 Consolidated 1 426 899 000 854 152 479 Cosco Pacific Ltd. 1199 20 enterprises 02-22-93 02-23-93 109 232 739 0.021 72 433 786 21 Industrial Denway Investment Ltd. 0203 177 588 581 0.052 12-21-95 12-22-95 175 879 879 0418 22 Founder Hong Kong Ltd. Industrial 0.010 03-26-97 05-29-98 105 022 063 33 161 915 Consolidated 23 0340 GITIC Enterprises Ltd. enterprises 0.044 08-08-97 11-30-98 243 995 283 24 Guangdong Brewery Holdings 0124 Industrial 151 417 417 Ltd. 0.145 Jan. 1973 01-04-93 Consolidated 3,044 582 506 497 854 031 Guangdong Investment Ltd. 0270 25 enterprises 12-16-96 03-31-98 126 433 862 0.005 17 592 617 26 Industrial Guangdong Tannery Ltd. 1058 180 942 432 Guangnan Holdings Ltd. 0.053 12-09-94 12-31-94 898 845 764 Consolidated 1203 27 enterprises 0.105 12-15-92 01-04-93 1 848 459 956 Properties 0123 Guangzhou Investment Co. 359 701 320 28 Ltd. 1052 0.059 01-30-97 03-31-98 487 899 961 GZI Transport Ltd. Industrial 29 203 562 683 Industrial 29 283 688 0.009 12-20-93 12-21-93 199 685 868 0382 GZITIC Hualing Holdings 30 Ltd. W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 327 Table 2 Continued No. Market Industry Total market Listing date Change date † Total assets Security Company name US ‡ capitalization capitalization code classification US 02-14-94 02-15-94 684 099 085 0.178 31 0992 612 287 934 Industrial Legend Holdings Ltd. 0.013 0222 06-28-82 12-31-97 190 713 658 Min Xin Holdings Ltd. Finance 46 140 869 32 0318 920 863 519 0.268 10-25-95 10-26-95 359 811 721 33 Ng Fung Hong Ltd. Consolidated enterprises 12-20-91 06-15-93 359 628 188 27 908 895 Properties 0.008 34 0230 ONFEM Holdings Ltd. 23 144 351 0.007 12-15-94 12-16-94 397 273 625 35 Oriental Metals Holdings Co. Consolidated 1208 enterprises Ltd. 0.010 04-06-88 09-01-93 Properties 135 760 903 36 045 668 Poly Investment Holdings 0263 36 Ltd. Industrial 1 699 576 061 0.495 05-30-96 05-31-96 1 727 465 364 Shanghai Industrial Holdings 0363 37 Ltd. Feb 1973 08-04-93 218 774 769 26 985 928 0.008 Finance Shenyin Wanguo HK Ltd. 0218 38 70 434 938 0.021 09-25-72 12-31-97 152 169 271 39 Shenzhen International Consolidated 0152 enterprises Holdings Ltd. 17 585 618 0.005 04-09-92 12-02-93 Consolidated 188 061 464 40 Shougang Concord Century 0103 enterprises Holdings Ltd. 0.010 08-08-91 07-20-93 86 159 877 41 Shougang Concord Grand 0730 Properties 34 408 268 Group Ltd. 42 73 542 821 0.021 04-30-91 01-04-93 Consolidated 979 675 412 Shougang Concord 0697 enterprises International Enterprises Co. Ltd. 0.009 12-23-88 05-31-93 43 110 065 091 Shougang Concord 0521 Industrial 29 320 409 Technology Holdings Ltd. 03-07-97 05-29-98 580 998 314 250 434 855 44 0.073 Properties Shum Yip Investment Ltd. 0604 W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 328 Table 2 Continued Market Company name No. Total market Listing date Change date † Total assets Industry Security code capitalization classification capitalization US ‡ US 0.021 45 08-11-93 Stone Electronic 08-17-93 210 439 974 0409 Industrial 73 322 502 Technology Ltd. 272 796 029 0.079 02-28-73 11-26-93 Properties 993 676 065 Top Glory 0268 46 International Holdings Ltd. Union Bank of Hong 240 258 020 0.070 03-14-73 01-04-93 2 766 665 880 0349 47 Finance Kong Ltd. 36 904 672 394 Total 16 026 223 053 4.664 785 205 796 0.099 Mean 340 983 469 0.045 359 811 721 Median 154 287 816 2 425 687 477 0.706 4 458 600 567 Maximum 12 730 379 0.004 43 574 113 Minimum 1.000 343 578 708 964 Total Market Capitalization US † This is the date the company becomes the Hang Seng China-affiliated corporations index HSCCI constituent stocks. ‡ The total assets are as at December 31, 1997. The exact listing date in 1970’s cannot be found. The total asset is as at March 31, 1998 because these companies have different balance sheet dates. W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 329 Table 3 The distribution of H shares, Red chips, Shanghai A- and B-shares and Shenzhen A- and B-shares by industry and year a Panel A Year Red chips H-shares Total Fin Total Con Ind Oth Pro Uti Total Con Ind Oth Pro Uti 2 24 6 7 1993 6 30 2 7 6 9 2 29 14 1 15 44 10 2 1994 7 2 31 16 1 17 1995 48 10 10 2 7 2 32 21 1 1 23 2 55 7 1996 11 10 12 4 36 2 33 1 1 2 39 75 11 2 7 1997 4 47 2 34 1 1 3 1998 41 14 88 17 3 9 Panel B Shanghai B-shares Shanghai composite Shanghai A-shares Year Total Com Com Ind Mis Pro Uti Total Total Ind Mis Pro Uti 8 8 101 1 16 1 3 1 22 123 16 1993 61 8 169 3 24 3 3 1 34 12 32 203 1994 9 21 95 12 33 184 3 26 3 3 1 36 223 104 26 9 1995 22 45 287 3 30 4 3 2 42 329 163 48 9 1996 372 3 37 4 3 3 50 30 1997 422 9 70 214 49 425 3 38 4 3 1998 4 49 52 477 252 82 9 33 Panel C Shenzhen B-shares Shenzhen composite Year Shenzhen A-shares Fin Com Total Com Ind Mis Pro Uti Total Total Ind Mis Pro Uti 1993 1 1 44 1 16 1 3 1 22 66 24 7 7 4 2 88 3 24 3 3 1 9 34 1994 122 6 9 11 51 W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 330 Table 3 Continued Panel C Shenzhen A-shares Year Shenzhen B-shares Shenzhen composite Fin Total Com Com Ind Mis Pro Uti Total Total Ind Mis Pro Uti 2 88 3 26 3 3 9 1 9 36 124 11 51 6 1995 18 15 4 227 2 28 3 3 7 43 270 23 1996 143 24 3 348 2 36 3 3 7 18 51 18 399 1997 36 230 43 3 1998 400 37 2 39 3 3 7 54 454 268 50 18 24 a Con, consolidated enterprises; Com, commercial; Fin, finance; Ind, industrial; Mis, miscellaneous; Oth, others; Pro, property; Uti, utilities. Indicates the highest percentage in the year. The analysis of the preliminary statistics indicates that the distributions of all index returns are more leptokurtic than the normal, the returns exhibit autocorrela- tion, and their conditional variances are heteroskedastic. An EGARCH model along with the generalized error distribution GED is, therefore, recommended for the following empirical analysis. 3 . 3 . Statistical methodology 3 . 3 . 1 . Return and 6olatility beha6ior analysis The daily returns are computed as the change in the logarithm of closing indices. The daily return of the HSCEI is: R t = lnI t − lnI t-1 1 where R t is the return of HSCEI at time t; I t is the level of HSCEI at time t, andI t − 1 is the level of HSCEI at time t − 1. Similarly, the daily returns of other indices are also computed as Eq. 1. A set of equations for the HSCEI described in this section is also applied to the other three indices with different superscripts. The superscripts, †, , are assigned to the same variable or parameter for the HSCCI, SHI and SZI, respectively. The statistical methodology used to explore the return behavior and the volatility of the HSCEI, HSCCI, SHI and SZI is based on Nelson’s EGARCH model Nelson, 1991. A conditional variance is added into the conditional mean equation for testing the relationship between mean and volatility in both index returns known as the EGARCH-in-mean EGARCH-M model. The H-Share Index Table 4 Descriptive statistics a Shanghai composite Red chip index Shenzhen composite H share index Statistics HSCEI HSCCI index SHI index SZI Mean return − 0.0004 0.0016 0.0009 0.0014 0.0010 0.0010 0.0003 Variance 0.0004 0.7122 0.4012 Skewness 0.5085 1.1529 Excess kurtosis 7.0820 8.0707 5.6289 5.3585 − 1793.2883 − 870.9845 − 1406.9349 − 664.8550 Bera–Jarque statistics 6.6427 44.4567 38.9747 6.2472 LB Q 10 LB Q 2 10 113.5329 98.6237 44.8764 35.0966 a LB Q n and LB Q 2 n, Ljung–Box Q statistics following a x 2 with n dof. Denotes significance at the 1 level. W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 332 Table 5 EGARCH-M model-return and volatility without spillover effect The conditional return and conditional variance for R t , R t † , R t ’ and R t ° are: R t = i = 1 5 l i D i + i = 1 n f i R t−i + a h t + o t 2a h t = exp i = 1 5 c i D i + i = 1 p d i lnh t−i + i = 1 q g i gz t−i 2b R t † = i = 1 5 l i † D i † + i = 1 n f i † R t−i † + a † h t † + o t † 2c h t † = exp i = 1 5 c i † D i † + i = 1 p d i † lnh t−i † + i = 1 q g i † gz t−i † 2d R t ’ = i = 1 5 l i ’D i ’+ i = 1 n f i ’R t−i ’ + a’ h t ’+o t ’ 2e h t ’ =exp i = 1 5 c i ’D i ’+ i = 1 p d i ’ lnh t−i ’ + i = 1 q g i ’gz t−i ’ 2f R t ° = i = 1 5 l i °D i °+ i = 1 n f i °R t−i ° +a°h t °+o t ° 2g h t ° = exp i = 1 5 c i °D i °+ i = 1 p d i ° lnh t−i ° + i = 1 q g i °gz t−i ° 2h whereR t , R t † , R t ’, R t °return of HSCEI, HSCCI, SHI, and SZI at day t, respectively; D i , D i † , D i ’, D i °dummy variable representing the day i, i = 1, 2, 3, 4, 5, of the week for return of HSCEI, HSCCI, SHI, and SZI; u, u † , u’, u°, asymmetry parameters of HSCEI, HSCCI, SHI, and SZI, respectively; 6 , 6 † , 6’, 6°, tail thickness parameters. When 6 = 2, the GED becomes the normal distribution. When 6B2, the distribution of o t has thicker tails than a normal distribution. When 6\2, the distribution of o t has thinner tails than a normal distribution. o t , o t † , o t ’ , o t °, conditional error term of HSCEI, HSCCI, SHI, and SZI at day t, respectively; z t , z t † , z t ’ , z t °, standardized residuals HSCEI, HSCCI, SHI, and SZI at day t, respectively; h t , h t † , h t ’, h t , conditional variance HSCEI, HSCCI, SHI, and SZI at day t, respectively. Red chip index Coefficient Coefficient Shanghai composite H-share index Coefficient Shenzhen composite Coefficient index SZI HSCCI index SHI HSCEI Return equation : l 1 l 1 − 0.0022 0.0041 g 1 † 0.0005 l 1 ’ 0.0008 l 2 l 2 − 0.0014 − 0.0009 g 2 † − 0.0010 l 2 ’ − 0.0017 l 3 0.0008 0.0008 0.0028 l 3 ’ l 3 0.0011 g 3 † W .P .H . Poon , H .- G . Fung J . of Multi . Fin . Manag . 10 2000 315 – 343 333 Table 5 Continued l 4 ’ − 0.0019 l 4 − 0.0020 l 4 g 4 † − 0.0018 0.0002 l 5 ’ 0.0026 l 5 0.0042 l 5 g 5 † − 0.0003 0.0007 f 1 − 0.0428 − 0.0679 f 1 ’ f 1 0.1954 f 1 † 0.1793 − 0.3141 0.4950 a 0.2094 a † 0.1718 a a ’ Variance equation : c 1 − 1.2397 c 1 † − 0.5917 − 0.7917 c 1 ’ − 1.0099 c 1 c 2 − 1.8879 c 2 − 0.8146 c 2 † − 1.3599 c 2 ’ − 1.8040 c 3 − 1.4421 − 1.0828 c 3 ’ c 3 − 1.3993 c 3 † − 1.3982 − 0.8121 − 1.4257 c 4 − 1.4161 c 4 † − 1.0881 c 4 c 4 ’ c 5 − 1.7297 − 1.4276 c 5 − 1.1222 c 5 ’ − 1.3913 c 5 † 0.8157 0.8790 d 1 0.7894 d 1 † 0.8534 d 1 ’ d 1 0.4167 0.3548 g 1 0.5385 g 1 † 0.4614 g 1 ’ g 1 u − 0.1124 − 0.2247 u ’ u 0.0959 u † 0.0775 6 ’ 0.9093 6 0.9803 6 † V 1.0282 1.0841 LB Q 10 7.9085 5.3041 LB Q 10 14.2972 LB Q 10 10.7930 LB Q 10 LBQ 2 10 LBQ 2 10 3.5148 11.8271 LBQ 2 10 9.0235 LBQ 2 10 2.4738 Denotes significance at the 10 levels. Denotes significance at the 5 levels. Denotes significance at the 1 levels. HSCEI return process is modeled in Eq. 2a and Eq. 2b and other indices are formulated similarly with the above superscripts †, , . The HSCEI return process is: R t = i = 1 5 l i D i + i = 1 n f i R t − i + a h t + o t 2a h t = exp i = 1 5 c i D i + i = 1 p d i lnh t − i + i = 1 q g i gz t − i 2b where o t , i.i.d. generalized error distribution GED with scaling 6; gz t , uz t + z t − E z t ; Ez t , v2 16 G 26G16; v, [2 − 26 G 16G36] 12 ; z t , o t h t ; R t , return of HSCEI at day t; D i , dummy variable representing the day i, i = 1, 2, 3, 4, 5, of the week for return of HSCEI; u, asymmetry parameters of HSCEI; l, f, h, a, c, d, g, parameters of HSCEI; G., gamma function; 6, tail thickness parameters. When 6 = 2, the GED becomes the normal distribution. When 6 B 2, the distribution of o t has thicker tails than a normal distribution. When 6 \ 2, the distribution of o t has thinner tails than a normal distribution. o t , conditional error term of HSCEI at day t; z t , standardized residuals HSCEI at day t; h t , conditional variance HSCEI at day t. Eq. 2a is the conditional mean function which is specified as a linear function of day-of-the-week effects i = 1 5 l i D i , past returns i = 1 n f i R t − i , and the condi- tional variance ah t . Statistically significant values for f i imply that past informa- tion can be used to forecast current and future movements of the series. The parameter a tests for linkages between the mean and variance conditional moments of the distribution of each return. A significant value for a implies that conditional volatility triggers movements in the return. The conditional variance in Eq. 2b is specified as an exponential function of day-of-the-week effects i = 1 5 c i D i , the natural logarithm of past conditional variances i = 1 p d i lnh t − i and past volatility shocks i = 1 q g i gz t − i . Significant values for d i and g i indicate that the volatility of index returns can be predicted by past volatility information and past unexpected volatility shocks. The normal probability density function has been one of the most popular density functions used to characterize the distribution of financial time-series. 9 However, our preliminary evidence presented in the previous section indicates that all index returns exhibit excess kurtosis beyond that permitted by the normal distribution, i.e. they are leptokurtic. To accommodate this need, the generalized error distribution is used. The EGARCH-in-mean models are estimated by maximizing the following log-likelihood function, L T , Nelson, 1991: L T = t = 1 T ln6v − 0.5 o t v 6 − 1 + 6 − 1 ln2 − ln[G16] − 0.5 ln h t 3 where T is the number of observations. 9 See Jacobs et al. 1998, Tse and Booth 1996, Koutmos et al. 1993 and Cheung and Ng 1992b. 3 . 3 . 2 . Spillo6er effect analysis The spillover analysis in terms of return and volatility among the four markets is investigated by the multivariate-EGARCH-M model. 10 The models of spillovers between the HSCEI return and the other index returns HSCCI, SHI, SZI are written as: R t = i = 1 5 l i D i + f 1 R t − 1 + f 2 R t − 1 † + f 3 R t − 1 ’ + f 4 R t − 1 + a h t + o t 4a h t = exp i = 1 5 c i D i + d lnh t − 1 + g 1 gz t − 1 g 2 gz t − 1 † + g 3 gz t − 1 ’ + g 4 gz t − 1 } 4b The conditional mean return presented in Eq. 4a is specified as a linear function of day-of-the-week effects, past own returns R t − 1 , its own conditional variance h t , and past returns of other three indices R t − 1 † , R t − 1 ’ , R t − 1 . A statistically significant value for f 2 , f 3 and f 4 indicates that the past returns of other indices correlates with the current and future return of the HSCEI, a result indicative of return spillovers from other markets to H share market. The conditional variance h t in Eq. 4b is specified as an exponential function of day-of-the-week effects, natural logarithm of past conditional variance, past volatil- ity shock, and past volatility shocks of other indices. A statistically significant g 2 , g 3 , g 4 implies that there is volatility spillover from the other markets to the H share market. The models of return and volatility spillover for the HSCCI, SHI and SZI follow Eq. 4a and Eq. 4b. We use a two-stage maximum likelihood ML estimation procedure to obtain the parameters of Eq. 4a and Eq. 4b. 11 In stage one, the ML method is used to estimate the four univariate models given by Eq. 2a and Eq. 2b. These models are subsequently used to calculate standardized residuals for the four index returns. In stage two, parameter estimates for Eq. 4a and Eq. 4b are obtained by taking the standardized residuals of the other index returns HSCCI, SHI, SZI as 10 We find that the four index returns are reasonably predicted by an AR1-EGARCH1,1-in-mean for the univariate analysis; thus we continue to use AR1-EGARCH1,1-in-mean in the multivariate framework. 11 We acknowledge the possibility of using truly multivariate EGARCH models suggested by an annoymous referee. However, the multivariate density function for the GED is unknown, the truly multivariate EGARCH model requires stringent assumption of normality and the normality assumption does not hold in our data as shown in Table 4. Given our data characteristics, the EGARCH models with the GED error densities, therefore, appear to be a reasonable choice for our estimation. We do not model the joint distribution of stock returns using a vector autoregression model with errors following a multivariate exponential GARCH process that requires normality assumption like Christofi and Pericli 1999 and Bollerslev and Wooldridge 1992. We also thank the referee for pointing out the potential problems with generated regressors mentioned in Pagan 1984. As the error terms i.e. the conditional variance terms for each index returns are generated from individual univariate EGARCH estimations and then, subsequently used as independent variables in follow-up estimations, the generated conditional variances may be inconsistent estimators of the true conditional variances. independent variables in the conditional volatility equation. A similar procedure is also applied to the other three indices Theodossiou, 1994.

4. Discussion of empirical results