Information transmission between U.S. and China index futures markets: An asymmetric DCC GARCH approach

Economic Modelling 52 (2016) 884–897

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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod

Information transmission between U.S. and China index futures markets: An asymmetric DCC GARCH approach☆ Yang Hou a,⁎, Steven Li b a b

Department of Finance, Waikato Management School, University of Waikato, Private Bag 3105, Hamilton, 3240, New Zealand Graduate School of Business and Law, RMIT University, 379-405 Russell St., Melbourne, VIC 3000, Australia

a r t i c l e

i n f o

Article history: Accepted 23 October 2015 Available online 10 November 2015 Keywords: Information transmission Asymmetric DCC GARCH Stock index futures market Chinese and U.S. stock markets

a b s t r a c t The Chinese stock market and its impacts on other stock markets have attracted a lot of attention and have been of a great concern to many countries. This paper aims to shed light on the issue by examining the information transmission between the S&P 500 and the CSI 300 index futures markets. The empirical results reveal that news from one market significantly affects the volatilities of open prices of the other and the impact from U.S. to China is stronger than the other way round. Further, past news of the U.S. has a significant impact on the volatilities of daily trading in China, but not vice versa. These findings indicate that the U.S. stock index futures market is more efficient in impounding information from other markets. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The informational linkages between stock markets in developed economies are widely observed in the literature (Antoniou, Pescetto, and Violaris, 2003; Eun and Shim, 1989; Hamao, Masulis, and Ng, 1990; King and Wadhwani, 1990; Koutmos and Booth, 1995). It is generally agreed that pricing behavior of domestic securities is determined not only by domestic information but also by news generated internationally (Koutmos and Booth, 1995). News generated in one market may transmit into another one via return and volatility spillovers, resulting in the prices of the latter being partially determined by international risk factors. However, the patterns of informational linkages observed in the developed economies may not hold for the Chinese stock market due to its short history and some unique features. These features pertain to the ownership types of instrument suppliers, the proportion of different types of investors, and the trading mechanisms. First, securities of the Chinese stock market are mostly supplied by the stateowned enterprises (SOEs). Unfortunately, the tradable shares only account for a small proportion of total shares of SOEs, resulting in the scarcity of security supplies due to the limited number of SOEs in China. This makes the stock market vulnerable to speculation (Chen, Han, Li, and Wu, 2013). Second, the individual and retail investors are the major force driving stock market movements (Chen

☆ The authors would like to thank Sushanta Mallick (The Editor) and three anonymous referees for their comments and suggestions which have been helpful in improving the quality of this paper. ⁎ Corresponding author. Tel.: +64 7 8379402. E-mail addresses: [email protected] (Y. Hou), [email protected] (S. Li).

http://dx.doi.org/10.1016/j.econmod.2015.10.025 0264-9993/© 2015 Elsevier B.V. All rights reserved.

et al., 2013; Ng and Wu, 2007; Yang, Yang, and Zhou, 2012). Third, a T + 1 trading rule applies in the Chinese stock market. Those who trade stocks in one trading day cannot do another trade until the next trading day. Thus, the possibility of intraday trading is precluded. In addition, short-sale transactions are difficult to implement due to high transaction costs and a lack of lenders (Chang, Luo, and Ren, 2013; Chen et al., 2013; Xie and Mo, 2014). Finally, the Chinese stock market contains two types of stocks that are available to trade. One type is called ‘A-shares’ and the other is called ‘B-shares’. When domestic investors in China can trade both A-shares and B-shares, foreign qualified investors are only allowed to trade B-share stocks. To clarify how the Chinese stock market interacts with developed markets given the characteristics above, this study examines the information transmission in terms of daily return and volatility spillovers between the renowned stock index futures market, the Standard & Poor's (S&P) 500 stock index futures market in the U.S., and the recently established China Securities Index (CSI) 300 stock index futures market in China. In this study, we utilize a bivariate Vector Autoregression (VAR) model with a bivariate asymmetric Dynamic Conditional Correlation (A-DCC) Generalized Autoregressive Conditional Heteroskedasticity (GARCH) error structure to estimate the interdependencies of first and second moments of futures returns distributions. The bivariate A-DCC GARCH model can simultaneously capture the time-varying covariance matrix of error structure of the VAR model and the asymmetry of the correlation matrix of error terms. It should be noted that examining the interaction between the S&P 500 and the CSI 300 stock index futures markets is nearly equivalent to examining the interaction between U.S. and Chinese stock markets. The underlying spot asset of the CSI 300 stock index futures is the CSI 300 stock index, which accounts for approximately 70% of the market capitalization of the Chinese stock market. It is well acknowledged that

Y. Hou, S. Li / Economic Modelling 52 (2016) 884–897

the CSI 300 index is deemed representative of the total performance of the Chinese stock market (Yang et al., 2012). Thus, the CSI 300 index futures market is used as a proxy for the Chinese stock market in this study.1 In addition, using index futures data is advantageous over spot data to study international information transmission, according to Wu, Li, and Zhang (2005). This is because futures markets appear to impound new information into security prices faster than spot markets. Lower transaction costs and less regulation increase transactional efficiency in the futures market (Chan, 1992).2 Although a few studies have been devoted to understanding how the stock market in China interacts with its neighbors and with leading world markets, the conclusions are still not clear. Some studies conclude that information linkages between Chinese and world stock markets are weak and correlations between them are low (Li, 2007; Lin, Menkveld, and Yang, 2009; Long, Tsui, and Zhang, 2014). Others argue that pricing behavior of the Chinese stock market can be affected by international markets while the Chinese market also exerts an important interregional impact (Allen, Amram, and McAleer, 2013; Chow, Liu and Niu, 2011; Guo, Han, Liu, and Ryo, 2013; Johansson and Ljungwall, 2009; Moon and Yu, 2010; Nishimura, Tsutsui, and Hirayama, 2015; So and Tse, 2009). Although there is evidence on information transmission between Chinese and international stock markets, it was obtained based on spot equity data.3 The recently introduced CSI 300 index futures market provides a new perspective through which this issue can be revisited. This study enriches the literature by unveiling new evidence in terms of the interdependency between the CSI 300 and the S&P 500 stock index futures markets. Although Li (2007) and Moon and Yu (2010) find little evidence of the interdependence of the first moment of returns distributions between the two markets, there is clear evidence in our analysis. The finding is somehow consistent with Chow et al. (2011), who find significant cross-market spillover effects of returns between the Shanghai and New York stock exchanges. Furthermore, neither Li (2007) nor Long et al. (2014) find significant evidence on volatility spillovers between the Chinese and U.S. stock markets. This study reveals significant evidence of volatility spillovers between the two markets, where the U.S. market plays a dominant role in the process. The finding partially agrees with Moon and Yu (2010) and Allen et al. (2013). However, compared to Moon and Yu (2010) and Allen et al. (2013), this paper further divides return and volatility spillovers into contemporaneous and lead–lag ones by taking into account closeto-open and open-to-close returns separately.4 We find significant evidence that daytime trading of the U.S. stock market has an important influence on both the opening prices and the subsequent pricing behavior of the Chinese stock market. This paper employs a bivariate GARCH framework instead of a univariate GARCH framework for investigating the daily relationship between the U.S. and Chinese stock index futures markets where their trading hours are not overlapped. The literature always employs a univariate GARCH model to examine the interdependence of the developed stock markets that have no overlapping of trading hours. A two-stage estimation procedure is utilized to estimate the spillovers of daily return and volatility (see, e.g., Hamao et al., 1990; Lin, Engle, and Ito, 1994; Pan 1 There was no stock index to comprehensively reflect the performance of A-shares stocks in China until the China Securities Index (CSI) 300 index was established in 2005. The CSI 300 index is the largest stock index of the Chinese A-shares market. It is regarded as a good reflection of the overall performance of the Chinese stock market (Chen et al., 2013; Yang et al., 2012). 2 Although the CSI 300 stock index futures market is newly established, it has grown rapidly (Chen et al., 2013; Yang et al., 2012). Chen et al. (2013) report that the introduction of the index futures market in China enhances the information content of spot index prices and helps to stabilize the Chinese stock market. Hou and Li (2013, 2015) reveal that the CSI 300 index futures market provides a better price discovery function in light of price and volatility levels after one year's development. 3 Guo et al. (2013) investigate the price discovery and volatility transmission between the CSI 300 and the SGX FTSE Xinhua A50 index futures using intraday data. 4 In Moon and Yu (2010) and Allen et al. (2013), daily close-to-close returns are analyzed instead of close-to-open and open-to-close returns.

885

and Hsueh, 1998; Moon and Yu, 2010) .5 Compared to the univariate GARCH model, the bivariate GARCH model can capture the linkages between the error terms of return processes, which the univariate model fails to address (Bollerslev, 1990; Engle, 2002). That is, the correlation structure of asset returns is gauged simultaneously with the individual heteroskedastic process. The correlation structure needs to be accounted for because it is one of the core questions to be investigated in this study. Moreover, according to Koutmos and Booth (1995), there are a few advantages to employing a bivariate model over a univariate one for studying international information transmission. First, it avoids problems associated with estimated regressors in the twostage procedure. Second, it improves the reliance of the tests for crossmarket return and volatility spillovers. Third, it is consistent with the notion that the essence of international return and volatility spillovers is the impact of global news on any given market. The asymmetric DCC (ADCC) GARCH model is superior to the widely employed BEKK and CCC GARCH specifications for the following reasons. First, previous literature has found that the DCC GARCH model yields more accurate estimates of conditional variances than the BEKK GARCH model (Engle, 2002; Tse and Tsui, 2002). Cappiello, Engle, and Sheppard (2006) further unveil that the asymmetric DCC GARCH model outperforms the DCC model in terms of higher log-likelihood value and lower value of the Bayesian information criterion (BIC). Second, the ADCC model can capture the time-varying market integration by obtaining estimates of the dynamic correlation as conditional correlations change over time. Modeling the dynamic correlation structure can provide insight on both markets' synchronization and volatility clustering in financial series. Hence, the ADCC model is more advanced than the CCC model (Lean and Teng, 2013; Majdoub and Mansour, 2014; Syriopoulos, Makram, and Boubaker, 2015). Third, compared to the BEKK model and the symmetric DCC GARCH model proposed by Engle (2002), the ADCC GARCH model allows for conditional asymmetries in correlations of financial series that can be reasonably observed in a world characterized by the capital asset pricing model (CAPM) (Cappiello et al., 2006). The DCC model can be perceived as a special case of the ADCC model without taking into account asymmetries in the dynamic correlation structure. Thus, the ADCC model can provide more accurate estimation of the dynamic correlation structure than the DCC model (Cappiello et al., 2006). The remainder of this paper is organized as follows. A brief literature review is provided in Section 2. The data and sample statistics are described in Section 3. The methodologies and empirical results are presented in Section 4 and Section 5, respectively. Concluding remarks are made in Section 6.

2. Literature review Early studies of information transmission across international stock markets primarily focused on developed economies. It is generally agreed that the interdependencies of first and second moments of returns distributions between developed stock markets exist. This has been extensively documented by Eun and Shim (1989), Barclay, Litzenberger and Warner (1990),; King and Wadhwani (1990), Hamao et al. (1990), Koutmos and Booth (1995), Pan and Hsueh (1998), Sim and Zurbreugg (1999), Fratzscher (2002), Antoniou et al. (2003), Wu et al. (2005), Otsubo (2014), Kao, Ho, and Fung (2015), among others. However, some studies, including Lin et al. (1994) and Susmel and Engle (1994), argue that the effect of interdependence is existent but rather weak.

5 In these studies, daily close-to-close returns are divided into close-to-open and opento-close components to separate the spillover effect on the opening price of the domestic market from that on the price after market opening. In the two-stage estimation process, foreign shocks of daytime trading are estimated in the first stage; then, spillover effects to the domestic market are estimated by using estimated foreign daytime shocks.

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In recent years, emerging stock markets have become increasingly important in the global stock markets. Recent studies have been devoted to the information interaction between developed and emerging stock markets. It is revealed that information flows from developed stock markets to emerging ones. Evidence is found between the U.S. and Taiwan markets (Chou, Li, and Wu, 1999), the U.S. and Hong Kong markets (Chan, Lien, and Weng, 2008), the Singapore and Taiwan markets (Roope and Zurbruegg, 2002), and Japan and other Asian markets (Miyakoshi, 2003). Informational linkages between the U.S. and BRIC countries (Brazil, Russia, India, and China) also exist (Bekiros, 2014; Kenourgios, Samitas, and Paltalidis, 2011; Syriopoulos, Makram, Boubaker, 2015). The information impacts from developed stock markets are also evidenced in other stock markets of continental regions such as Asia, Africa, Latin America, the Mediterranean, and the Middle East (see, e.g., Yilmaz, 2010; Awokuse, Chopra, and Bessler, 2009; Sugimoto, Matsuki, and Yoshida, 2014; Bekaert and Harvey, 1995, 1997, and 2000; Bekaert, Harvey and Ng, 2005; Beirne, Caporale, Schulze-Ghattas, and Spagnolo, 2010; Chen, Chen, and Lee, 2014). As the Chinese stock market has been gradually integrated into the global financial system, it is of academic interest to explore how it is affected by international information. There are a few studies investigating this issue by modeling the interdependency of first and second moments of returns distributions between the Chinese and U.S. markets. The findings thus far, however, are not conclusive. Li (2007) finds that there is little evidence of informational linkage between the Chinese and U.S. stock markets. Lin et al. (2009) claim that correlations between the Chinese and world stock markets are not high, which have no increasing trend from 1993 to 2006. Moon and Yu (2010) reach the conclusion that stock markets interact in terms of second moments of returns distributions between the stock markets of China and the U.S. They find evidence of asymmetric volatility spillovers from the U.S. to China, but symmetric volatility spillovers from China to the U.S. during 2005–2007. Chow et al. (2011) find evidence of cross-market spillovers effects between the U.S. and China. The effects were quite significant after China joined the WTO. The effects were interrupted by GFC but still remained reasonably high between the two markets. Long et al. (2014) find no evidence of volatility spillovers between the Chinese and U.S. stock markets from 2000 to 2013; however, they detect an increasing trend of correlation between the two markets after the Global Financial Crisis (GFC). Moreover, there is evidence of informational linkages between Chinese and other regional markets. Johansson and Ljungwall (2009) find that the Chinese stock market has strong linkages with the Hong Kong and Taiwan stock markets in the short term. So and Tse (2009) provide evidence of interdependencies of asset returns of stock markets between Hong Kong, mainland China, Taiwan and Singapore. Allen et al. (2013) find evidence of volatility spillovers between the Chinese and world stock markets before GFC but little evidence after the crisis. Guo et al. (2013) investigate price discovery and volatility transmission between the CSI 300 and the SGX FTSE Xinhua A50 index futures by using intraday data. They find that the CSI 300 index futures market dominates the price discovery process. There is evidence of volatility spillovers from the CSI 300 to the Xinhua A50 index futures. Nishimura et al. (2015) conclude that there is a strong linkage between the Chinese and Japanese stock markets. China has a large impact on Japanese stocks via China-related firms in Japan.

3. Data and sample statistics To examine the return and volatility spillovers between the U.S. and Chinese stock index futures markets, we use daily prices of the S&P 500 stock index futures contracts traded at the Chicago Mercantile Exchange (CME) and the CSI 300 stock index futures contracts traded at the China

Financial Futures Exchange (CFFEX). Specifically, daily open and close futures prices are obtained to construct the sample.6 The sample period is from 16 May 2010 to 31 July 2013. Price records of the CSI 300 index futures in the first month of futures trading (i.e., from 16 April 2010 to 16 May 2010) are excluded from the sample because this period is regarded as the learning stage where the market is not stable. The data are obtained from Thomson Reuters Tick History (TRTH). The S&P 500 index futures contracts expire in March, June, September, and December. Day trading starts at 8:30 a.m. and ends at 3:15 p.m. Central Standard Time (CST). The contract multiplier is $250. The maturity date of the S&P 500 stock index futures contract is the third Thursday of the maturity month. On the maturity date, the futures contacts are cash settled. The CSI 300 index futures contract, which was newly introduced in China's financial markets, started to trade on 16 April, 2010. With the CSI 300 stock index as the underlying spot asset, trading of the CSI 300 index futures contracts is deemed a milestone for the development of the Chinese stock market. Maturity months of the CSI 300 index futures contracts traded in each calendar month include the current month, the next month, and the two nearest quarter-end months (i.e., March, June, September, and December). For instance, futures contracts traded in the calendar month of May include contracts expiring in May, June, September and December. Day trading of the CSI 300 index futures contracts is from 9:15 a.m. to 11:30 a.m. and from 1:00 p.m. to 3:15 p.m. Beijing Time. The contract multiplier is RMB 300. The maturity date is the third Friday of the maturity month. On the maturity date, the index futures contracts are cash settled. To construct continuous time-series data, we select prices of the most liquid futures contracts on the S&P 500 index and the CSI 300 index in each calendar month.7 For the CSI 300 stock index futures contracts, the most liquid contract in each calendar month is the contract that expires in this month. To avoid biases caused by irrational trading behavior when the maturity date approaches, we roll the contract over to the next ten working days before the contract expires.8 For example, in the calendar month of May, we select the CSI 300 May contract and shift it to the CSI300 June contract ten working days before the May contract expires. For the S&P 500 stock index futures contracts, because they have a cycle of maturities, the most liquid futures contract in each calendar month is the contract expiring in the closest month. Still, we roll the contract over to the next one ten working days before the contract expires to avoid biases. For instance, in the calendar month of May, we select the S&P 500 June contract. Note that we do not shift the June contract to the September contract until ten working days before the June contract expires in the calendar month of June. After eliminating the data that are missing for either of the two markets, we end up with 750 daily price observations for each series in the sample. The time difference between Chicago and Beijing is 13 h. Thus, the trading hours of the S&P 500 index futures market and the CSI 300 index futures market do not overlap. Fig. 1 depicts the trading hours for the two markets. It should be noted that the daytime segment of each market is a subset of the overnight segment of the other. Thus, it is interesting to investigate whether information in the daytime trading of one market can influence the other market as important ‘overnight’ news.

6 It should be noted that daily open prices collected for the sample are the first transaction prices recorded at the start of each trading day. 7 Note that this paper only accounts for the spillover effects between the most liquid futures contracts on the S&P 500 index and the CSI 300 index. 8 The biases are the expiration-day effects. The effects mean that an abnormal volatility of futures prices occurs in the last weeks of life for futures contracts (Samuelson, 1965). If futures price records of this period are employed for analysis, results concluded from statistical inferences could be distorted from the abnormal volatility (Carchano and Pardo, 2009). Ma, Mercer, and Walker (1992) suggest that futures prices around the expiration date should be avoided, as they always have excessive volatility. Factors causing such effects are discussed in Stoll and Whaley (1997).

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Beijing

----t-1---Trading 9:15

Chicago

--------------------t---------------------No Trading

15:15

-----------t-1----------No Trading

--------t-----Trading

9:15

-----t-1----Trading 8:30

887

---------------------t+1-----------------No Trading 15:15

9:15

----------------------t---------------------No Trading 15:15

----t+1--Trading

-------t-----Trading

8:30

15:15

-----------t+1----------No Trading

15:15

Fig. 1. Exchange trading hours.

Fig. 2. Daily returns of the CSI 300 and S&P 500 index futures.

The daily open and close prices of the S&P 500 and CSI 300 index futures are all taken in the form of natural logarithms. The daily returns are normally calculated as the first-order difference in the close prices. We further divide daily returns (close-to-close) into daytime returns (open-to-close), which is the difference between the open price and the close price on a trading day, and overnight returns (previous close-to-open), which is the difference between the open price on a trading day and the close price on the previous day. Hence, daily close-to-close returns Ri of the S&P 500 index futures (SP) and the CSI 300 index futures (CS) on day t can be expressed as follows: Rit ¼ RNit þ RDit

ð1Þ

where i = sp or cs.9 RNit and RDit denote overnight returns and daytime returns at date t, respectively. Dickey and Fuller (1981) and Phillips and Perron (1988) stationarity tests confirm the stationarity of RNit and RDit (i = sp or cs).10 It should be noted that the futures prices used in our analysis are all recorded in the local currencies. The reason why we do not transform prices into one currency (either U.S. dollars or Chinese RMB) is that the incorporation of the foreign exchange (FX) rate might result in additional

9 sp denotes the S&P 500 stock index futures, whereas cs denotes the CSI 300 stock index futures. 10 Test results are available upon request.

volatility arising from the foreign exchange markets. The additional volatility in foreign exchange markets might be unrelated to volatility within the stock index futures markets (Sim and Zurbreugg, 1999). In addition, it is agreed that currency hedging on the forward markets can mitigate pure currency risk. Thus, the incorporation of FX changes within domestic prices is not required (Cheung and Ho, 1991; Eun and Resnick, 1988). Movements of daily returns of the CSI 300 and the S&P 500 index futures markets during the sample period are depicted in Fig. 2. It can be observed that the CSI 300 index futures returns are all more volatile than the S&P 500 ones. Movements of returns of the two markets seemingly have different patterns. This is especially the case for overnight returns. In addition, as seen in Fig. 2, volatility clustering may exist in returns of both markets where large returns are always followed by large ones during some periods while small returns are in tandem with small ones during other periods. This phenomenon will be further explored in our analysis. Table 1 summarizes the descriptive statistics of daily returns, daytime returns, and overnight returns of the S&P 500 stock index futures and the CSI 300 stock index futures, respectively. The mean of daily returns of the CSI 300 stock index futures is negative, reflecting a bear market in China during the sample period. In contrast, the mean of daily returns of the S&P 500 stock index futures is positive, revealing a bull market in the U.S. during the same period. The standard deviation of daily returns of the CSI 300 stock index futures is higher than that of daily returns of the S&P 500 stock index futures. Hence, the Chinese market is more volatile than the U.S. market during the sample period.

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Table 1 Descriptive statistics of daily rates of return for S&P 500 index futures and CSI300 index futures for May 2010–July 2013. S&P 500

Nobs Mean Std. Skewness Kurtosis

CSI 300

Rt

RDt

RNt

Rt

RDt

RNt

750 5.47 × 10−4 0.012 −0.357 7.895

750 5.43 × 10−4 0.011 −0.279 6.126

750 4.55 × 10−6 0.004 0.289 26.799

750 −3.48 × 10−4 0.015 0.021 5.236

750 −5.65 × 10−4 0.014 0.235 5.771

750 2.17 × 10−4 0.006 −0.407 13.412

Notes: Daily returns (Rt) are calculated as the first-order difference in the natural logarithms of daily closing futures prices. Daytime returns (RDt) are calculated as the difference between the natural logarithms of the closing price and the open price on one trading day. Overnight returns (RNt) are calculated as the difference between the natural logarithms of the open price on one trading day and the closing price on the previous day. Std. denotes the standard deviation. S&P 500 denotes the S&P 500 stock index futures; CSI 300 denotes the CSI 300 stock index futures.

Furthermore, for both stock index futures, the standard deviation of daytime returns is higher than overnight returns. In addition, returns for both stock index futures have excess kurtosis. The distribution of returns has excess kurtosis compared to a standard normal distribution. Panel A of Table 2 reports autocorrelations in each market's daily and daytime returns. The values of the correlation coefficients between daytime and overnight returns in each market are also reported. The firstorder autocorrelations in daily and daytime returns only exist in the S&P 500 futures market. For the same market, the correlation coefficient between daytime returns and overnight returns is significant at the 10% level and is positive (0.063). It suggests that overnight news may influence daytime trading in the U.S. market. In contrast, for the CSI 300 index futures, the correlation coefficient between daytime and overnight returns is not significant at any conventional level. Hence, the effect of overnight news is negligible in China's market. Moreover, overnight returns have a significant correlation with daytime returns of the previous day in both CSI 300 and S&P 500 markets. Such correlation will be accounted for in the VAR model in Section 4. Panel B of Table 2 reports cross-correlations of index futures returns between the Chinese and U.S. markets. The cross-correlations are divided into contemporaneous and lead–lag ones. Contemporaneous crosscorrelation is the correlation between one market's daytime returns and the other market's overnight returns. The correlation between overnight returns of the two markets is partially contemporaneous due to an overlapping of time between them, as shown in Fig. 1. Lead–lag crosscorrelation is the correlation between the past daytime returns of one market and the daytime returns of the other market. As seen from the table, all cross-correlations are significantly different from zero, indicating a close relation between the CSI 300 and the S&P 500 index futures markets. Significant cross-correlations indicate a potential informational linkage between the two markets, which will be focused afterwards.

4. Methodology 4.1. Model specification of contemporaneous spillovers As seen from Fig. 1, the spillovers effect from daytime returns of the foreign market to overnight returns of the domestic market is contemporaneous.11 The effect can be interpreted as the effect of the foreign index futures trading on the domestic market's open price. Such effect is examined in two steps. First, the contemporaneous spillovers of returns between the Chinese and U.S. index futures markets are specified in a bivariate vector autoregression (VAR) model. Second, the contemporaneous spillovers of volatility are specified by extending the VAR model to a bivariate asymmetric dynamic-conditional-

11 Contemporaneous spillovers are defined as the interdependence of first and second moments of returns distributions between open-to-close returns of foreign market and close-to-open returns of domestic market within the same time regime.

correlation (A-DCC) GARCH model. The bivariate GARCH model system is used to account for the conditional asymmetric covariance matrix of overnight returns. Dynamic correlation between the Chinese and U.S. overnight returns is estimated.12 The conditional mean of the VAR (1) model is specified as follows: RNt ¼ Φ þ ARNt−1 þ B⊙RD1;t−1 þ C⊙RD2;t−1 þ et

ð2Þ

where RNcs;t  is a 2 × 1 vector of overnight returns of CSI 300 and S&P RNsp;t 500 futures at date t; Φ Φ ¼ ½ 11  is a 2 × 1 vector of the intercept for each equation; Φ21 RNcs;t−1  is a 2 × 1 vector of lagged overnight returns with a RNt−1 ¼ ½ RNsp;t−1 A12 A ; coefficient matrix A ¼ ½ 11 A21 A22 RD B RD1;t−1 ¼ ½ cs;t−1  with a coefficient vector B ¼ ½ 11 , whereas RDsp;t−1 B21 RD C RD2;t−1 ¼ ½ sp;t−1  with a coefficient vector C ¼ ½ 11 ; RDcs;t C 21 ⊙ is the Hadamard product of two identically sized matrices, which is computed by element-by-element multiplication; e et ¼ ½ 1;t  is a vector of error terms following a bivariate distribution with e2;t mean zero and conditional variance–covariance matrix Ht13. RD1,t − 1 is included in Eq. (2) to examine the predictive effects of lagged daytime returns on overnight returns. RD2,t − 1 is incorporated in Eq. (2) to estimate how foreign daytime returns affect domestic overnight returns in both CSI 300 and S&P 500 futures markets at date t, i.e., the contemporaneous spillovers of returns. Coefficient C11 accounts for U.S.-to-China return spillovers, whereas coefficient C21 accounts for China-to-U.S. return spillovers.14 To further investigate cross-market informational linkages in terms of the second moment of returns, Eq. (2) is extended to have a bivariate conditional heteroskedasticity error structure, by which the conditional variance–covariance matrix of overnight returns is extrapolated. We employ an asymmetric Dynamic-Conditional-Correlation (A-DCC) model, proposed by Cappiello et al. (2006), to explain this structure. A-DCC GARCH model accounts for not only the time-varying correlation between assets but also the asymmetric response of correlation to RNt ¼ ½

12 The cointegration between closing prices of the CSI 300 and S&P 500 index futures markets is tested by the Johansen cointegration test. The test result is shown in Table A1 in Appendix A. The result shows that there is no cointegration between the two markets. Thus, the VAR model is used instead of the vector error correction model (VECM) for this paper. 13 For the bivariate VAR (p) model, p is selected to be 1 based on the Akaike information criterion (AIC). 14 Because of the time difference between China and the U.S., as shown in Fig. 1, the appropriate pairing for examining the spillover effect from China to the U.S. is time t for both China and the U.S., whereas it is time t − 1 for the U.S. and time t for China for the spillover effect from the U.S. to China.

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889

Table 2 Autocorrelations (and correlations of returns) within S&P 500 and CSI 300 index futures markets. Panel A : autocorrelations within S&P 500 and CSI 300 index futures markets S&P 500

Rt − 1 RDt RDt-1

CSI 300 Rt

RDt

RNt

−0.118** – –

– 1.000 −0.096**

– 0.063* −0.071*

Rt − 1 RDt RDt − 1

Rt

RDt

RNt

−0.020 – –

– 1.000 −0.035

– −0.022 0.063*

Panel B: cross-correlations between S&P 500 and CSI 300 index futures markets Contemporaneous

Lead–lag

RDcs,t & RNsp,t

RNcs,t & RDsp,t − 1

RNcs,t & RNsp,t − 1

RNcs,t & RNsp,t

RDcs,t & RDsp,t − 1

RDcs,t & RDsp,t

0.072**

0.509**

0.155**

0.113**

−0.070*

0.149**

Notes: Daily returns (Rt) are calculated as the first-order difference in the natural logarithms of daily closing futures prices. Daytime returns (RDt) are calculated as the difference between the natural logarithms of the closing price and the open price on one trading day. Overnight returns (RNt) are calculated as the difference between the natural logarithms of the open price on one trading day and the closing price on the previous day. CS denotes the CSI 300 stock index futures market. SP denotes the S&P 500 stock index futures market. Panel A reports autocorrelations of return series within the S&P 500 and the CSI 300 stock index futures markets, respectively. Panel B reports cross-correlations of return series between the S&P 500 and the CSI 300 stock index futures markets. ** and * indicate that the null of zero correlation can be rejected at the 5% and 10% levels, respectively.

positive and negative shocks. The error structure of Eq. (2) is specified as follows:
et ¼

 e1;t  Ω  Student−t ð0; Ht ; vÞ; e2;t  t−1

where H t ¼ Dt Rt Dt ;

ð3Þ

with n 1 o 1 Dt ¼ diag h211;t ; h222;t ;

ð4Þ

and Rt ¼ diagfQ t g−1=2 Q t diag fQ t g−1=2 :

ð5Þ

Error term et is assumed to follow a bivariate Student's t distribution with mean zero and conditional variance–covariance matrix Ht. The benefit of assuming error terms to follow Student's t distribution is that it accommodates the excess kurtosis of the innovations (Baillie and Bollerslev, 1989; Bollerslev, 1987), and thus, the estimation is robust to deviations from normality (Susmel and Engle, 1994; Tse, 1999b). Ωt − 1 represents available information set at time t − 1. v is the degree of freedom for Student's t distribution. v controls the tail behavior of Student's t distribution. A significant v implies that the return series should follow Student's t distribution. The Student's t distribution approaches normality as v goes to infinity. v is restricted to be larger than 2 to ensure that the covariance matrix exists.The individual conditional heteroskedasticity process in Dt is specified as follows: hii;t ¼ ηi þ α i e2i;t−1 þ βi hii;t−1 þ γ i I i;t−1 e2i;t−1 þ ϕi RD2j; J þ δi I j; J RD2j; J ;

ð6Þ

1; RD j; J b0 1; ei;t−1 b0 , ; I j; J ¼ ½ 0; RD j; J ≥0 0; ei;t−1 ≥0 when i = 1, j = sp, J = t − 1; when i = 2, j = cs, J = t. In Eq. (6), hii,t is a function of lagged squared residuals (new shocks) and lagged conditional variance (persistence of shocks). Moreover, hii,t follows a GJR GARCH process, as in Glosten, Jagannathan and Runkle (1993), to incorporate disparate effects of previous positive and negative shocks to the conditional volatility. The asymmetry of conditional volatility is thoroughly addressed in the literature (Engle and Ng, 1993; Koutmos and Tucker, 1996). Failure to model asymmetries leads to misspecification of the volatility process. Parameter γi is indicative of the asymmetry of overnight volatility. For the stationarity of hii,t, the

sum of αi, βi and γi/2 should be less than unity. And exogenous series RD2j,J and Ij,JRD2j,J are stationary autoregressive processes with strict white noise processes that are independent of the standardized innovation series of ei,t (Nana, Korn and Erlwein-Sayer, 2013).15 Eq. (6) estimates contemporaneous spillovers of daily volatility between the CSI 300 and the S&P 500 futures market. The squared daytime returns of the foreign market (RDj,J2) representing shocks arising from daytime trading is included in hii,t. Parameter ϕi estimates spillovers from daytime shocks of the foreign market to volatility of the domestic market before market opening. ϕ1 accounts for volatility spillovers from the U.S. to China, whereas ϕ2 accounts for volatility spillovers from China to the U.S. In addition, we test whether positive and negative shocks of the foreign market asymmetrically affect overnight volatility of the domestic market. By including a dummy variable Ij,J, the effect of foreign negative shocks is captured by (ϕi + δi), and the effect of positive ones is captured by ϕi.Rt is a 2 × 2 matrix consisting of conditional correlation and unity. The asymmetric conditional correlation is specified in a 2 × 2 symmetric matrix Qt, which can be expressed as   Q t ¼ R−λ1 R−λ2 R−λ3 S þ λ1 ut−1 uT t−1 þ λ2 Q t−1 þ λ3 st−1 sT t−1 ð7Þ where ut denotes a vector of standardized residuals where ut ¼ pffiffiffiffiffiffiffiffi ðu1t ; u2t ÞT ¼ eit = hii;t ði ¼ 1; 2Þ. R ¼ E½ut uT t  denoting a 2 × 2 unconditional variance–covariance matrix of ut. E[.] is the expectation operator. st = I[ut b 0] ⊙ ut and S ¼ E½st sT t . I[.] is the indicating function, and ⊙ is the Hadamard operator. λ1, λ2 and λ3 are scalar parameters. Eq. (7) aligns with a scalar ADCC model, as in Cappiello et al. (2006, pp. 543), given that λ1 = a2, λ2 = b2 and λ3 = g2. The positive definiteness of Qt can be guaranteed if (λ1 + λ2 + ωλ3) b 1 where ω is the maximum −1=2

−1=2

SR eigenvalue of the matrix ½R asymmetry of correlation matrix Rt.16

. Parameter λ3 estimates the

4.2. Model specification of lead–lag spillovers

where i = 1, 2; I i;t−1 ¼ ½

Similar to the contemporaneous return and volatility spillovers, the lead–lag ones are specified by a bivariate VAR-A-DCC GARCH model.17

15 The unit root test suggests that RD2j , J and Ij,JRD2j,J are stationary. The null hypothesis that their standardized innovations have zero correlation with standardized innovations of ei,t is not rejected at any conventional level. Test results are available upon request. 16 Superscript T denotes a transposed matrix or vector. 17 Lead–lag spillovers are defined as the interdependence of first and second moments of returns distributions between past open-to-close returns of foreign market and current open-to-close returns of domestic market.

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The conditional mean equation of the model is expressed as follows:

and the individual GARCH process in D ' t specified as

RDt ¼ Φ0 þ A0 RDt−1 þ B0 ⊙RNt þ C 0 ⊙RD0 t þ et ;

h0 ii;t ¼ η0 i þ α 0 i e0 i;t−1 þ β0 i h0 ii;t−1 þ γ0 i I0 i;t−1 e0 i;t−1 þ ϕ0 i e0 j; J þ δ0 i I0 j; J e0 j; J ; i ¼ 1; 2

0

ð8Þ

2

2

2

0

2

ð13Þ

where RDcs;t RNcs;t 0 ; RNt ¼ ½ ; RD0 t ¼ ½ ; RDsp;t RNsp;t RDcs;t with coefficient matrix 0 0 0 0 0 A0 B0 C0 A0 12 Φ ¼ ½ Φ0 11 ; A ¼ ½ 0 11 ; B ¼ ½ 0 11 ; C ¼ ½ 0 11 ; A 21 A0 22 B 21 C 21 Φ 21 e0 0 and et ¼ ½ 0 1;t  is a vector of error terms following a bivariate Student's t e 2;t distribution with zero mean and conditional variance–covariance matrix H ' t.18RDcs,t and RDsp,t denote daytime returns of the CSI 300 and the S&P 500 futures at date t, respectively.19 RNt is included to detect any mean-reversal effect, corresponding to a significant correlation in the S&P 500 market, as shown in Table 2. RD ' t is included to examine the lead–lag spillovers of returns from the CSI 300 to the S&P 500 futures markets, which is captured by coefficient C ' 21. Meanwhile, coefficient A ' 12 estimates how daytime returns of the S&P 500 futures predict subsequent daytime returns of the CSI 300 futures, implying lead–lag return spillovers from the U.S. to China.20 It should be noted that Eq. (8) contains a structural equation, where RDcs,t is an endogenous variable. Incorporating RDcs,t as a right-hand-side variable allows for exploring the first-moment explanatory power of the Chinese market on the U.S. market. Using time t instead of time t − 1 is determined by the time zone difference between China and the U.S., as shown in Fig. 1. Variable RDcs,t is endogenous in the VAR (1) model because it is both a dependent and an explanatory variable in Eq. (8). This introduces simultaneity in the estimation process where the disturbances e ' 1,t and e ' 2,t are correlated with the endogenous RDcs,t. At the same time, the error terms in the system are expected to be correlated. Hence, the assumption of ordinary least square (OLS) is violated. To overcome this problem, Eq. (8) is estimated by using three-stage least squares (3SLS), which potentially produces unbiased, consistent, and efficient parameter estimates (Wahab and Lashgari, 1993). 3SLS uses an instrumental-variable approach to produce consistent estimates. It employs generalized least squares (GLS) to account for the correlation structure in the disturbances. Compared with OLS and two-stage least squares, 3SLS can generate more accurate, consistent and efficient estimates of parameters for modeling a system of structural equations (Davidson and MacKinnon, 1993, 651–661; Greene, 2008, 381–383). The conditional variance–covariance matrix of e't is specified as RDt ¼ ½

e0 t ¼




   0 e0 1;t  Ωt−1  Student−t 0; H t ; v0 0  e 2;t

and 0

H 0 t ¼ D t R0 t D0 t ;

ð9Þ

n 1 o 1 D t ¼ dig h0 211;t ; h0 222;t ; 0

0

0

−1=2

R t ¼ diagfQ t g

0

T

0

−1=2

Q t diag fQ t g

t−1 :

s ' t = I ' [u ' t b 0] ⊙ u ' t and S0 ¼ E½s0 t s0 T t . λ ' 1, λ ' 2 and λ ' 3 are scalar parameters. Similar to Eq. (7), Eq. (12) aligns with a scalar ADCC model as in Cappiello et al. (2006, pp. 543) given that λ ' 1 = a ' 2, λ ' 2 = b ' 2 and λ ' 3 = g ' 2.21 The positive definiteness of Q ' t can be guaranteed if (λ ' 1 + λ ' 2 + ω ' λ ' 3) b 1 where ω ' is the maximum eigenvalue of the −1=2

−1=2

S0 R0 . λ ' 3 unveils whether conditional correlation bematrix ½R0 tween daytime returns asymmetrically reacts to previous shocks. In h ' ii,t, parameters α ' i and β ' i estimate ARCH and GARCH effects, respectively. γ ' i examines asymmetry of daytime volatility. The lead– lag volatility spillovers between the CSI 300 and the S&P 500 futures markets are explored by ϕ ' i. ϕ ' 1 estimates spillovers from lagged daytime shocks in the S&P 500 market to daytime volatility of the CSI 300 market while ϕ ' 2 estimates volatility spillovers the other way around. δ ' i is indicative of the asymmetry of lead–lag volatility spillovers. Note that we use lagged squared residuals of Eq. (8) to represent lagged daytime shocks of the foreign market, instead of lagged squared daytime returns—that is, lagged daytime shocks of counterpart market are defined as e'2j,J in Eq. (13). In the literature, squared returns are used to measure aggregate shocks from one market (Engle, Ito, and Lin, 1990), whereas squared residuals represent unexpected shocks of a market (Hamao et al., 1990). We examine how aggregate shocks of one market affect overnight volatility of the other in Eq. (6) and how unexpected shocks of one market affect daytime volatility of the other in Eq. (13) .22

4.3. Distribution specification Parameter estimates of the bivariate A-DCC GARCH specification can be obtained by maximizing the log-likelihood of the probability density function of a bivariate Student's t distribution. The contribution of each observation at time t to the log-likelihood can be expressed in general terms as 

  v  vþ2 ðv−2Þ −ð1=2Þ logðjH t jÞ−ð1=2Þ v = ðvπ ÞΓ lt ðΘÞ ¼ log Γ 2h  0 2 i ε =ðv−2Þ :  ðv þ 2Þ log 1 þ ε t H −1 t t ð14Þ

ð10Þ ;

ð11Þ

  T Q 0 t ¼ R0 −λ0 1 R0 −λ0 2 R0 −λ0 3 S0 þ λ0 1 u0 t−1 u0 t−1 þ λ0 2 Q 0 t−1 þ λ0 3 s0 t−1 s0

1; e0 j; J b0 1; e0 i;t−1 b0 , ; I0 j; J ¼ ½ 0; e0 j; J ≥0 0; e0 i;t−1 ≥0 '2 '2 when i = 1, j = 2, J = t − 1, e j,J = e 2,t − 1; when i = 2, j = 1, J = t, e'2j,J = e'21,t. For the specification of Q ' t, u ' t denotes a vector of standardized pffiffiffiffiffiffiffiffiffi 0 residuals where u0 t ¼ ðu0 1t ; u0 2t ÞT ¼ e0 it = h0 ii;t ði ¼ 1; 2Þ. R0 ¼ E½u0 t u T t  denoting a 2 × 2 unconditional variance–covariance matrix of u ' t. with I0 i;t−1 ¼ ½

ð12Þ

18 It should be noted that superscript ′ is used to denote a different scalar, vector or matrix. 19 RD ' t is a 2 × 1 vector consisting of zero and variable RDcs,t. 20 The lag order p in VAR is selected based on AIC.

where Γ(.) is the Gamma function. v is the degree of freedom for Student's t distribution. Ht is a conditional variance–covariance matrix. Θ is a parameter vector with all of the coefficients of the A-DCC GARCH model.

21 Estimates of (a, b, g) and (a′, b′, g′) are not shown in this paper. Instead, estimates of their squares and corresponding statistical significance are reported, following Cappiello et al. (2006). 22 We also include lagged squared daytime returns in Eq. (13) to estimate lead–lag volatility spillovers and find that the results are qualitatively the same as lagged squared residuals.

Y. Hou, S. Li / Economic Modelling 52 (2016) 884–897

Estimates for parameter vector Θ can be obtained by maximizing the log-likelihood over the sample period, which is expressed as LðΘÞ ¼

X

T t¼1 lt ðΘÞ:

ð15Þ

where T is the sample size. 5. Empirical results 5.1. Contemporaneous spillovers Table 3 presents estimates of the bivariate VAR (1) model. Panel B of Table 3 indicates there is no autocorrelation in estimated residuals. Heteroskedasticity is detected in the residuals of the S&P 500 index futures overnight returns by the Ljung–Box Q statistics. The heteroskedasticity will be further addressed in the A-DCC GARCH model. In addition, the JB normality test strongly rejects normality of residuals. Hence, the non-normality assumption for estimation of the conditional variance–covariance matrix is necessary. In Panel A of Table 3, overnight returns of the CSI 300 futures follow an AR(1) process via significant coefficient A11. They can be explained by overnight returns of the S&P 500 futures on the previous day through significant coefficient A12. In contrast, overnight returns of the S&P 500 futures do not follow an AR(1) process; however, they can be explained by their own values of daytime returns on the previous trading day, as suggested by significant coefficient B21. There are significant bidirectional contemporaneous return spillovers between the Chinese and U.S. index futures markets. C11 is significant at the 1% level, while C21 is significant at the 10% level. Both C11 and C 21 are estimated as positive. An increase of 1% in daytime returns of the CSI 300 futures results in an increase of approximately 0.0187% in overnight returns of the S&P 500 futures. An increase of 1% in daytime returns of the S&P 500 futures leads to an increase of approximately 0.2570% in overnight returns of the CSI 300 futures. Contemporaneous spillovers of returns from the U.S. to China are almost 14 times stronger than the other way around. We test the null hypothesis that C11 equals to C21. The test statistic (χ2 (1) = 154.6189) strongly rejects the null at the 1%

Table 3 Estimation results of contemporaneous spillovers of returns. Parameters

RNcs,t

Panel A : estimation results 9.5319 × 10−5 Φ11 (0.5482) −0.0835*** A11 (−2.6672) 0.1955*** A12 (4.2997) B11 −0.0082 (−0.6458) 0.2570*** C11 (15.8883) Panel B: residual diagnosis JB 9385.864*** LB(12) 12.2554 [0.4254] 2 2.5530 LB (12) [0.9980]

Parameters

RNsp,t

Φ21

2.6908 × 10−5 (0.1909) 0.0024 (0.0953) −0.0096 (−0.2600) −0.0235* (−1.8025) 0.0187* (1.8190)

A21 A22 B21 C21

17,480.94*** 7.5087 [0.8223] 24.3832** [0.0180]

Notes: This table reports estimation results of the bivariate VAR (1) model and corresponding residual diagnosis based on Eq. (2). Panel A reports estimation results of coefficients in Eq. (2). Figures in parentheses (.) are t-statistics. Panel B reports results of residual diagnosis. Raw residuals are used for residual diagnostic check. JB denotes the Jarque–Bera test statistic for normality. LB(k) and LB2(k) (with k = 12 ) are the Ljung– Box Q statistics of kth order autocorrelation for residuals and their squares, respectively. Values of Q statistics are reported. Figures in bracket [.] are p-values for Q statistics. ***, **, and * indicate significance at the 1%, 5% and 10% levels, respectively.

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level. Thus, return spillovers are much stronger from the U.S. to China than the other way around.23 To further investigate the contemporaneous informational linkages between the CSI 300 and the S&P 500 futures, we proceed to estimate the bivariate A-DCC GARCH model based on Eqs. (6) and (7). The results are presented in Table 4. Residual diagnosis in Panel B of Table 4 shows that there is neither autocorrelation nor heteroskedasticity in the standardized residuals, suggesting that the A-DCC GARCH model is well specified. Moreover, parameter v is significant at the 1% level; thus, the assumption of Student's t distribution is appropriate for estimating the A-DCC GARCH model. Panel A of Table 4 shows that both overnight volatilities of the CSI 300 and the S&P 500 futures follow an autoregressive conditional heteroskedastic process. Significant αi and βi (i = 1, 2) imply that volatility is affected by not only the arrival of new shocks but also the lagged own values. The persistence of conditional volatility of overnight returns, measured by (αi + βi + γi/2), is calculated as 0.4037 and 0.5293 for the CSI 300 and the S&P 500, respectively. Both the Chinese and the U.S. index futures markets have low persistence of conditional overnight volatility. Moreover, overnight volatility of the S&P 500 futures asymmetrically reacts to different lagged shocks that arise when the market is closed. Lagged negative shocks after market is closed heightens overnight volatility more intensely than positive ones through significant and positive γ2. However, there is no evidence of asymmetry in overnight volatility of the CSI 300 futures, given the insignificant γ1 24 Negative shocks are perceived as bad news, whereas positive shocks are perceived as good news (Engle and Ng, 1993). A positive γ2 suggests that volatility of the S&P 500 index futures could be higher if bad news against the market is released before the market is open on previous trading day. The asymmetry in volatility may be explained by Koutmos and Tucker (1996), who attribute it to an imbalance of investors' sensitivity in response to different types of news. The S&P 500 index futures market is more sensitive to bad news than good news during after-trading hours. In contrast, there are symmetric effects of past bad and good news to overnight volatility in the CSI 300 index futures market. Conditional correlation of overnight returns between the CSI 300 and the S&P 500 futures markets is indicated by significant estimates of λ1 and λ2. λ3 is significant and positive (approximately 0.0715), implying that conditional correlation of close-to-open returns is strengthened when negative shocks arrive in both markets before they open to trade. Hence, asymmetry exists in the correlation between the U.S. and Chinese index futures markets during non-trading hours. Movements of conditional correlation of overnight returns are depicted in Fig. 3. It shows that the overnight correlations between the Chinese and U.S. markets are highly volatile and vary substantially over time. The correlations go through several troughs and peaks and a reverse of sign recurs. The overnight correlation series overall appears to have a rugged declining trend. The contemporaneous spillovers of volatility between the CSI 300 and the S&P 500 futures are indicated by estimates of ϕi and δi. ϕ1 is significant at the 1% level and positive (0.0155). An increase in shocks of the S&P 500 futures market leads to higher volatility of the CSI 300 futures market before its opening. δ1 is not significant at any conventional level. Hence, there is a symmetric response of the CSI 300 overnight volatility to shocks of the S&P 500 market. Estimates of both ϕ2 and δ2 are significant at the 1% level. ϕ2 is estimated as positive (0.0003), indicating that shocks in the CSI 300 index futures market tend to increase the overnight volatility of the S&P 500 index futures. δ2 is positive (approximately 0.0010), implying that

23 Multicollinearity does not exist between exogenous variables in Eq. (2) including RNsp,t − 1, RDcs,t − 1, and RDsp,t − 1 in equation with dependant variable RNcs,t as well as RNcs,t − 1, RDsp,t − 1, and RDcs,t in equation with dependant variable RNsp,t. Test results on multicollinearity are available upon request. 24 Shocks arising after the market is closed can be attributed to all kinds of news, announcements or events breaking when index futures exchanges are closed.

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Table 4 Estimation results of contemporaneous spillovers of volatility. Parameters Panel A : estimation results η1 α1 β1 γ1 ϕ1 δ1 Panel B: residual diagnosis LB(12) 2

LB (12)

h11,t

Parameters

h22,t

Parameters

Eq. (7)

5.2022 × 10−6*** (18.1986) 0.0524*** (6642.3600) 0.3567*** (49.5102) −0.0108 (−0.4994) 0.0155*** (5.3115) 0.0070 (1.2077)

η2

3.8857 × 10−7*** (212.0978) 0.0017*** (15,440.3744) 0.5129*** (382.7513) 0.0294*** (12.1569) 0.0003*** (9.1140) 0.0010*** (11.5047)

λ1

0.0387*** (37.9146) 0.9413*** (1531.6932) 0.0715*** (25.1658) 17.6312*** (56.3092)

α2 β2 γ2 ϕ2 δ2

9.7590 [0.6371] 1.3276 [0.9999]

λ2 λ3 v

5.8306 [0.9244] 4.7369 [0.9662]

Notes: This table reports estimation results of the individual conditional variance equation of Eq. (6) and asymmetric conditional correlation matrix Qt of Eq. (7) in the bivariate A-DCC GARCH model. Panel A reports estimation results of the coefficients of the bivariate A-DCC GARCH model. Estimates are obtained from MLE method assuming a bivariate Student's t distribution. Figures in parentheses (.) are t-Statistics. Panel B reports results of residual diagnosis for A-DCC GARCH model. Standardized residuals are used for diagnostic check. LB(k) and LB2(k) (with k = 12 ) are the Ljung–Box Q statistics of kth order autocorrelation for the standardized residuals and their squares, respectively. Values of Q statistics are reported. Figures in bracket [.] are p-values for Q statistics. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

negative daytime shocks of the CSI 300 index futures market cause higher overnight volatility of the S&P 500 index futures than positive ones. Hence, contemporaneous spillovers of volatility from the Chinese to U.S. market are asymmetric. To sum up, there are bidirectional contemporaneous spillovers of volatility between the CSI 300 and the S&P 500 futures markets. Spillovers from the U.S. to China are symmetric, whereas those from China to the U.S. are asymmetric. We test the hypothesis that ϕ1 is equal to ϕ2. The null is rejected at the 1% level (χ2(1) = 27.0079). The estimate

of ϕ1 is almost 52 times larger than ϕ2. Volatility spillovers are much stronger from the U.S. to China than the other way around. This is consistent with the return spillovers in Table 3. To summarize, the contemporaneous information flow is of a two-way interaction. The U.S. market is more influential in the process. 5.2. Lead–lag spillovers Table 5 presents the estimation results of Eq. (8). The residual diagnosis in Panel B of Table 5 shows that estimated residuals are not autocorrelated but are heteroskedastic. In addition, the JB normality test rejects that residuals follow a normal distribution. Such non-normality is handled by Student's t probability density function for the estimation process.

Table 5 Estimation results of lead–lag spillovers of returns. Parameters

RDcs,t

Panel A : estimation results −0.0006 Φ′11 (−1.1274) −0.0254 A′11 (−0.6923) −0.0951* A′12 (−1.7585) B′11 0.0434 (0.4165)

Parameters

RDsp,t

Φ′21

0.0015** (2.0890) 0.0033 (0.1135) −0.0929** (−2.5250) 0.1575 (1.5353) 1.7490*** (4.6625)

A′21 A′22 B′21 C′21

Panel B: residual diagnosis JB 246.7757*** LB(12) 6.1388 [0.9089] 26.6897*** LB2(12) [0.0086]

Fig. 3. Conditional correlation between the China and the U.S. index futures markets.

108.0193*** 10.1620 [0.6018] 19.8002* [0.0710]

Notes: This table reports estimation results of the bivariate VAR (1) model and corresponding residual diagnosis based on Eq. (8). Eq. (8) are estimated by 3SLS. Panel A reports estimation results of coefficients in Eq. (8). Figures in parentheses (.) are t-Statistics. Panel B reports results of residual diagnosis. Raw residuals are used for residual diagnostic check. JB denotes the Jarque–Bera test statistic for normality. LB(k) and LB2(k) (with k = 12 ) are the Ljung–Box Q statistics of kth order autocorrelation for residuals and their squares, respectively. Values of Q statistics are reported. Figures in bracket [.] are p-values for Q statistics. ***, **, and * indicate significance at the 1%, 5% and 10% levels, respectively.

Y. Hou, S. Li / Economic Modelling 52 (2016) 884–897

In Panel A of Table 5, daytime returns of the CSI 300 futures do not follow an AR(1) process because coefficient A′11 is not significant at any conventional level. In contrast, significant A′22 suggests an AR(1) process of daytime returns of the S&P 500 futures. Neither B′11 nor B′21 is significant at any conventional level. Hence, neither daytime returns of the CSI 300 futures nor those of the S&P 500 futures are affected by their own overnight returns. Thus, there is no evidence of meanreverting effects in either market. Lead–lag spillovers of returns are estimated by coefficients A′12 and C′21. A′12 is significant at the 10% level and is estimated to be negative (approximately −0.0951). Thus, an increase of daytime returns of the S&P 500 futures leads to a drop of daytime returns of the CSI 300 futures of the next day. The negative predictive power suggests an overreaction effect. Investors in the CSI 300 futures market react disproportionately to price movements of the S&P 500 futures market of the previous trading day. It causes prices of the CSI 300 index futures to change dramatically; thus, the prices do not fully reflect the security's true value immediately. The prices' deviation from fundamental values as a result of overreaction does not last for long. The index futures prices eventually return to true values when information is appropriately impounded in prices. Coefficient C′21 is significant at the 1% level and is positive (approximately 1.7490). An increase of daytime returns of the CSI 300 futures leads to higher subsequent daytime returns of the S&P 500 futures. The CSI 300 daytime futures returns have a positive predictive power for the S&P 500 daytime returns. In addition, the estimate of C′21 is almost double that of A′12, suggesting that return spillovers may be stronger from China to the U.S. than the other way around. We test the null hypothesis that A′12 is equal to C′21 and the null that C′21 is equal to the absolute value of A′12. Test statistics reject both the nulls at the 1% level (with χ2(1) = 24.1675 and 19.4386, respectively). Thus, there are bidirectional lead–lag spillovers of returns between the CSI 300 and the S&P 500 futures.25 Spillover power appears stronger from China to the U.S. than the other way around.26 It is worth noting the reasons for the lead–lag return spillovers from the Chinese to U.S. stock index futures markets being stronger than the other way around. On one hand, the institutional investors who have strong connections with the global financial systems and possess international investment perspectives dominate the Chinese index futures market. This enables investors in the Chinese market to promptly follow the U.S. market, resulting in prices of the former fast assimilating information from the latter. Therefore, according to the efficient market hypothesis (EMH), the weak explanatory power of lagged U.S. returns is reasonably observed. On the other hand, the strong predictive power of lagged Chinese returns implies the weak capacity of prices of the U.S. market to update information from the Chinese market. Such weak capacity may be due to the inactive cross-border transactions between the two markets. Return spillovers between international markets are mainly attributed to the cross-border transactions, which has been well documented in the literature (see, e.g. Engle et al., 1990; Lin et al., 1994). The fewer the cross-border transactions, the stronger the inter-regional return spillovers. The capacity of the Qualified Foreign Institutional Investors (QFIIs) in the Chinese stock market to participate in the cross-border transactions involving the Chinese and U.S. stock index futures contracts is highly constrained. According to trading policies on the Chinese stock index futures contracts, the QFIIs are allowed to trade the Chinese index futures contracts for hedging purpose only. The QFIIs are not allowed to

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use the index futures for the other trading strategies such as market speculation and index arbitrage. In addition, the Qualified Domestic Institutional Investors (QDIIs) from China have the limited capability to participate in trading of the S&P 500 index futures contracts and use them to construct international investment portfolios. As a result, the cross-border trading activities between the Chinese and U.S. index futures markets are inactive and thus the strong lead–lag spillovers of returns from China to U.S. make sense.27 The results of the bivariate A-DCC GARCH model for the lead–lag spillovers of volatility are presented in Table 6. As seen from Panel B of Table 6, there is neither autocorrelation nor heteroskedasticity in the standardized residuals. In addition, parameter v′ is significant at the 1% level, suggesting the appropriateness of Student's t distribution for the estimation process. In Panel A of Table 6, α ' i and β ' i (i = 1,2) are significant at the 1% level. Variances of daytime returns are conditioned on past information, being affected by new and old shocks. The persistence of conditional volatility of daytime returns is calculated by (α ' i + β ' i + γ ' i/2). The value is 0.4612 for the CSI 300 and 0.7941 for the S&P 500. Similar to conditional overnight volatility, the persistence of conditional daytime volatility of both markets is low. γ ' 1 is significant at the 5% level, and γ ' 2 is significant at the 1% level. γ ' i (i = 1,2) is estimated to be positive (γ ' 1 = 0.0760 and γ ' 2 = 0.0907). Thus, conditional variances of daytime returns of the CSI 300 (S&P 500) futures react more intensely to past negative shocks in the CSI 300 (S&P 500) index futures market than positive ones. Asymmetry in daytime volatility exists for both markets, where volatility of daytime trading is more sensitive to bad news than good news when the market is open. Koutmos and Tucker's (1996) explanation applies to the S&P 500 index futures market. The asymmetry of daytime volatility of the CSI 300 futures market may be attributed to the restrictive trading policy imposed on the index futures contracts (Hou and Li, 2015). Adjustments in the positions of futures contracts incur significant costs when investors react to the arrival of bad news. Consequently, investors are more vulnerable to price drops than price rises. Similar to the correlation between overnight returns, the correlation of daytime returns is conditioned on past information, as revealed by significant λ ' 1 and λ ' 2. Moreover, asymmetry in daytime correlation exists via the significant estimate of λ ' 3. λ ' 3 is positive (approximately 0.0276), indicating that the correlation of daily trading between the U.S. and Chinese index futures markets is heightened when both markets are entangled in a market downturn. Movements of correlation series are shown in Fig. 3. In contrast to the series of overnight correlation, daytime correlation is less volatile. The conditional daytime correlation is neither increasing nor declining during the whole sample period, in which four volatile periods are observed. The most volatile period is the first half of 2012. Correlation of daytime returns approximately ranges from −0.5 to +0.5. Thus, there is a relatively low connection between the daily trading of Chinese and U.S. index futures markets. This finding is slightly different from Long et al. (2014), who report a low connection that has an increasing trend between the Chinese and U.S. stock markets from 2000 to 2013. Spillovers of volatility of daytime returns are unveiled by estimated ϕ ' i and δ ' i. The estimate of ϕ ' 1 is significant at the 1% level, whereas ϕ ' 2 is not significant at any conventional level. ϕ ' 1 is estimated as positive (approximately 0.0908), indicating that shocks from the S&P 500 index futures market tend to increase the conditional volatility of daytime returns in the CSI 300 futures market. Past shocks originating from daytime trading in the S&P 500 index futures market can spill into the CSI 300 index futures market and escalate the volatility of the latter. However, there is no evidence of spillovers from China to the

25

An overreaction effect exists from the U.S. to China. Multicollinearity does not exist between exogenous variables in Eq. (8) including RDsp,t − 1 and RNcs,t, in equation with dependant variable RDcs,t as well as RDcs,t − 1, RN sp,t − 1 , and RD cs,t in equation with dependant variable RD sp,t . Test results on multicollinearity are available upon request. 26

27 Other possible reasons for stronger lead–lag return spillovers from China to the U.S. will be left to a future study.

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Table 6 Estimation results of lead–lag spillovers of volatility. Parameters Panel A : estimation results η′1 α′1 β′1 γ′1 ϕ'1 δ′1 Panel B: residual diagnosis LB(12) 2

LB (12)

h ' 11,t

Parameters

h ' 22,t

Parameters

Eq. (12)

3.5611 × 10−5*** (18.8775) 0.0975*** (886.6505) 0.3257*** (25.0917) 0.0760** (2.0423) 0.0908*** (8.8276) 0.1060*** (9.9342)

η′2

4.8213 × 10−5*** (31.0060) 0.0967*** (662.4922) 0.6520*** (141.9946) 0.0907*** (13.4352) 0.0030 (0.5367) −0.0044 (−0.6007)

λ′1

0.1606*** (81.7848) 0.8368*** (512.0194) 0.0276*** (60.9718) 3.8064*** (26.2397)

α′2 β′2 γ′2 ϕ'2 δ′2

5.9291 [0.9196] 13.1598 [0.3575]

λ′2 λ′3 v′

7.9008 [0.7928] 16.7633 [0.1587]

Notes: This table reports estimation results of the individual conditional variance equation of Eq.(13) and asymmetric conditional correlation matrix Q′t of Eq. (12) in the bivariate A-DCC GARCH model. Panel A reports estimation results of the coefficients of the bivariate A-DCC GARCH model. Estimates are obtained from MLE method assuming a bivariate Student's t distribution. Figures in parentheses (.) are t-Statistics. Panel B reports results of residual diagnosis for A-DCC GARCH model. Standardized residuals are used for diagnostic check. LB(k) and LB2(k) (with k = 12 ) are the Ljung–Box Q statistics of kth order autocorrelation for the standardized residuals and their squares, respectively. Values of Q statistics are reported. Figures in bracket [.] are p-values for Q statistics. *** , **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

U.S. Hence, one-way lead–lag spillovers of volatility exist. The direction of spillovers is from the U.S. to China. Furthermore, asymmetry exists in the spillovers process from the U.S. to the Chinese index futures markets, given that δ ' 1 is significant at the 1% level, whereas δ ' 2 is not significant at any conventional level. The estimate of δ ' 1 is positive (approximately 0.1060). Past negative shocks from the S&P 500 futures market cause higher volatility of daytime trading of the CSI 300 futures market than past positive ones. It implies that bad news from the U.S. index futures market attracts more attention of active traders in the Chinese index futures market and causes higher variations of risk. In sum, there are one-way asymmetric lead–lag spillovers from the S&P 500 to the CSI 300 index futures market. The one-way spillovers of daytime volatility strongly suggest that information transmits solely from the U.S. to the China index futures markets. Therefore, the U.S. index futures market dominates in the lead–lag international information transmission and exerts a critical influence on daytime pricing behavior of the Chinese index futures market.

5.3. Further discussion 5.3.1. Information asymmetry and impacts of shocks Tables 4 and 6 imply that asymmetries of volatility transmission exist between the S&P 500 and the CSI 300 index futures markets. The asymmetries are reflected in two aspects. First, the arrivals of new shocks from the S&P 500 index futures market have more impacts on the conditional volatility of the CSI 300 index futures market than the other way around. Second, the arrivals of negative shocks of one market have more impacts on the conditional volatility of the other than positive ones. To better understand how information asymmetries influence asset pricing, we evaluate the impacts of an increase in foreign shocks on conditional volatility based on the estimated coefficients of Eqs. (6) and (13). An increase in foreign aggregate shocks in the process of the contemporaneous volatility spillovers is represented by an increase of the squared foreign daytime returns. Meanwhile, an increase in foreign unexpected shocks in the process of the lead–lag volatility spillovers is represented by an increase of the squared foreign innovations in the past. We set the increase as 1%. According to Eq. (6), a 1% increase of the squared negative foreign daytime returns results in a (ϕi + δi) % change

of the domestic overnight variance. In contrast, a 1% increase of the squared positive foreign daytime returns leads to a ϕi% change of the domestic overnight variance. Similar rules apply in Eq. (13). A 1% increase of the squared negative foreign innovations results in a (ϕ ' i + δ ' i) % change of the domestic daytime variance. In contrast, a 1% increase of the squared positive foreign innovations leads to a ϕ ' i% change of the domestic daytime variance. The calculated results are presented in Table 7. In Table 7, the impacts of an increase in shocks generated in the S&P 500 index futures market are impressively reflected in the CSI 300 index futures market. For example, a 1% increase of the squared negative (positive) daytime returns of the S&P 500 index futures at date t − 1 increases overnight variance of the CSI 300 index futures by 0.0155% (0.0155%) at date t, ceteris paribus. The impacts of negative and positive returns are equal. A 1% increase of the squared negative (positive) innovations in the S&P 500 index futures market at date t − 1 increases daytime variance of the CSI 300 index futures market by 0.1968% (0.0908%) at date t, ceteris paribus. The impact of negative innovations is almost double that of positive ones. In contrast, an increase in shocks of the CSI 300 index futures market has weaker impacts on the variance of the S&P 500 index futures market. A 1% increase of the squared negative (positive) daytime returns of the CSI 300 index futures at date t increases overnight variance of the S&P 500 index futures by 0.0013% (0.0003%) at date t, holding the other independent variables in Eq. (6) unchanged. Nonetheless, there are no impacts of an increase of the squared past innovations of the CSI 300 index futures market on daytime variance of the S&P 500 index futures market. To sum up, information flow between the S&P 500 and the CSI 300 index futures markets influences the pricing dynamics of the two markets. The volatility of the Chinese index futures market is affected more intensely by the arrivals of new shocks originating in the U.S. index futures market than the other way around. The impacts of the arrivals of new foreign shocks to the volatilities are strengthened when the shocks are negative.

5.3.2. Pricing efficiency The asymmetries in information transmission between the U.S. and Chinese index futures markets suggest inefficient pricing of the Chinese

Y. Hou, S. Li / Economic Modelling 52 (2016) 884–897

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Table 7 Impacts of shocks on volatility.

Contemporaneous impact

CSI 300 IF

S&P 500 IF

Change of overnight conditional variance

Change of overnight conditional variance

1% increase of squared daytime returns of CSI 300 IF (RD2cs,t) RDcs,t b 0 RDcs,t N 0 1% increase of squared daytime returns of S&P 500 IF (RD2sp,t − 1) RDsp,t − 1 b 0 RDsp,t − 1 N 0

+0.0155% +0.0155%

Lagged impact

Change of daytime conditional variance

1% increase of squared innovations of CSI 300 IF (e ' 21,t) e ' 1,t b 0 e ' 1,t N 0 1% increase of squared innovations of S&P 500 IF (e ' 22,t − 1) e ' 2,t − 1 b 0 e ' 2,t − 1 N 0

+0.0013% +0.0003%

Change of daytime conditional variance 0 0

+0.1968% +0.0908%

Notes: An increase of foreign aggregate shocks is measured by an increase of RD2j,J in Eq. (6) for calculating contemporaneous impact, whereas an increase of foreign unexpected shocks is measured by an increase of e ' 2j,J in Eq. (13) for calculating lagged impact. Estimates of ϕi and δi in Eq. (6) and ϕ ' i and δ ' i in Eq. (13) are used for calculation. Statistically insignificant estimates are set to zero. IF denotes index futures. RDcs,t and RDsp,t − 1 denote daytime returns of the CSI 300 index futures at date t and daytime returns of the S&P 500 index futures at date t − 1, respectively. e ' 1,t and e ' 2,t − 1 denote innovations of the CSI 300 index futures market at date t and innovations of the S&P 500 index futures market at date t − 1, respectively.

market in terms of the assimilation of cross-market information. This may be attributed to the U.S. market being a major exporter of volatility, which has been well documented in the literature (e.g., Bekiros, 2014; Eun and Shim, 1989; and Theodossiou and Lee, 1993). Moreover, the difference in levels of maturity between the two markets could be another reason. It can be illustrated in three aspects. Investors' capacity to incorporate cross-market information into asset pricing of domestic securities matters substantially in the international volatility transmission (Koutmos and Booth, 1995). The higher the capacity, the lower the impact of news from foreign markets is. It is commonly observed that investors in the U.S. index futures market possess better skills and more knowledge about index futures trading than those who are at the learning stage in the Chinese index futures market. Thus, market players in the U.S. are able to analyze cross-market information better and incorporate it into prices of domestic securities faster than those in China. The difference in capacity to make informed trading decisions contributes to the difference in degree of maturity between the U.S. and Chinese index futures markets. Market openness and liquidity of futures contracts could be another aspect (Cai et al., 2013; Martinez and Tse, 2008). Market openness of the CSI 300 index futures market is much lower than the S&P 500 market because the former is stringently monitored by domestic regulators. Restrictive regulations on trading of the CSI 300 index futures contracts result in the small quantity of market participants, high barriers of entry for new participants, harshness of implementing informed trading measures such as index arbitraging, and large contract size. More importantly, those regulations cannot ensure a high liquidity of index futures contracts in China. All of these features handicap the CSI 300 index futures prices' absorption of cross-market news. Finally, compared to the U.S. index futures market, different types of investors in the Chinese index futures market are disproportionate (Yang et al., 2012). Domestic retail investors as well as foreign qualified investors are mainly precluded from index futures trading. The domestic institutional investors dominate the market. The overweight of domestic institutions in the Chinese index futures market may contribute to domestic prices' being overwhelmed by news from the U.S. index futures market.

5.3.3. Implications to policy makers The empirical results thus far reveal that prices of the CSI 300 index futures market fail to handle global news efficiently. Such failure is reflected by the volatility of domestic market being significantly affected by news generated in the U.S. market but not vice versa. This raises criticism of the current trading policy on index futures contracts in China because it fails to protect the market from contagion effects of any news from the U.S. market that is ‘mistaken’ (King and Wadhwani, 1990). New shocks generated in the U.S. index futures market could easily spill into the Chinese market through the information channel, causing the latter to become destabilized. The impact is strengthened when the shocks are negative. Some changes in the current trading policy may help to enhance the efficiency of the CSI 300 index futures market to assimilate global news. First, it may be wise to allow qualified foreign investors to conduct trading strategies other than index futures hedging. This may attract more qualified foreign institutions into the market, which may improve the quality of market participants. Second, policy makers should endeavor to liberalize the market further and increase the degree of market openness. This could be done by reducing high barriers of entry, decreasing contract size, and encouraging informed trading such as index arbitrage. Finally, efforts should be made to adapt the concurrent investor structure. The appropriate proportions of retail and institution investors pertain to enhancing the information content of futures prices (Bohl et al., 2011). The findings of this paper may have some implications for other stock markets in Asia. On one hand, although the Asian stock markets are growing rapidly and have been gradually playing a more important role in global financial markets in recent years, the U.S. stock market is still a major exporter of global news, which substantially affects Asian markets (Awokuse, Chopra, and Bessler, 2009; Bekiros, 2014). This argument is supported by our study. For policy makers of Asian stock markets, it is important to consider the effect of the U.S. stock market in their regulating local markets. The U.S. impact should not be ignored by local investors either. On the other hand, the Chinese stock market has been deeply integrated into the Asian region, and it has significant effects on its neighbors (Allen, Amram, and McAleer, 2013; Guo et al., 2013; Johansen and Ljungwall, 2009; Moon and Yu, 2010; Nishimura,

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Tsutsui, and Hirayama, 2015; So and Tse, 2009; Yilmaz, 2010). As a result, the relationship between the Chinese and U.S. stock markets should be taken into account when Asian investors undertake international portfolio diversification and effective hedging. It is also of significance for market regulators in Asia to consider the evidence on the Chinese stock index futures market as a reference for how a newly established index futures market can be affected by the U.S. under restrictive monitoring. The evidence suggests that it is advisable for them to similarly regulate the markets in their countries. 6. Concluding remarks Although the issue of information transmission between the developed stock markets has been well documented in the literature, the interaction between the U.S. and Chinese stock markets has not been fully explored. This study examines, for the first time, the interdependency of return and volatility between the S&P 500 and the CSI 300 stock index futures markets. A bivariate VAR-ADCC GARCH model is utilized to analyze the sample data from May 16, 2010 to July 31, 2013. Overall, the U.S. index futures market dominates in the process of information transmission between the U.S. and Chinese index futures markets in terms of the interdependence of first and second moments of returns distributions. The contemporaneous return and volatility spillovers are of a two-way interaction where volatility spillovers from the S&P 500 to the CSI 300 index futures markets are symmetric and the other way around are asymmetric. The influence of the S&P 500 is overwhelming in both the return and volatility spillovers process. Meanwhile, the lead–lag volatility spillovers are of a one-way interaction, where information transmits solely from the S&P 500 to the CSI 300. Such one-way volatility spillovers are asymmetric, where past negative shocks generated in the S&P 500 index futures market predict higher volatility of daytime returns in the CSI 300 index futures market than positive ones. It is also evident that a lead–lag explanatory power of the S&P 500 index futures returns to the CSI 300 futures returns is weaker than the other way around. This may be due to regulatory constraints in the CSI 300 futures market that the limit trading activities of foreign investors. Nonetheless, this evidence is too weak to reject the conclusion that the U.S. index futures market plays a leading role in the process of international information transmission. In addition, the A-DCC GARCH model suggests that the correlation between the U.S. and Chinese index futures markets is conditioned on the past information. The correlation is elevated when negative shocks arrive in both markets. The connection between daily trading of the two markets is relatively low, which does not clearly have an increasing or declining trend. At the same time, the correlation between both markets after trading hours varies remarkably over time and has a roughly declining trend. The findings of this paper suggest that the U.S. index futures market is more efficient than the Chinese index futures market in terms of the price adjustment of one market to the information from its counterpart. The intuitive reason is that the U.S. market is more mature than the Chinese one. Furthermore, the inefficiency of the Chinese stock index futures prices specifically relates to the low capacity of investors to handle cross-market information, the low market openness and liquidity, and the disproportion of different types of investors. Because the S&P 500 and the CSI 300 stock index futures contracts are highly correlated, a future study can be conducted to investigate the performance of statistical arbitrage and cross-hedging strategies between these two markets. This will help to illuminate whether it is practical for domestic market participants in the U.S. and the Chinese markets to use foreign securities as another choice for planning investment strategies.

Appendix A Table A1 Cointegration test. Without linear trend

With linear trend

T

CV(5%)

Decision

r

T

CV(5%)

Decision

r

5.9791 0.1626

15.4947 3.8415

F# F

0 1

15.6553 5.1159

18.3977 3.8415

F R

0 1

Notes: This table tests the cointegration between daily closing prices of the CSI300 and S&P 500 index futures markets. r is the number of cointegrating vectors. T is the trace test statistics. CV(5%) is the trace test critical value at the 5% significant level. A testing sequence is followed in which the test starts from without linear trend and r = 0. r indicated that we reject the null hypothesis that the number of cointegrating vectors is less than or equal to r (when T is larger than CV(5%)). F denotes that we fail to reject the null hypothesis that the number of cointegrating vectors are less than or equal to r (when T is smaller than CV(5%)). We stop testing at the first F# as shown in the table. The testing sequence moves from left to right and from top to bottom. The symbol (#) means the stopping point.

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