Dynamics and Information Transmission between Stock Index and Stock Index Futures in China

2015 International Conference on Management Science & Engineering (22 th ) October 19-22, 2015 Dubai, United Arab Emirates Dynamics and Information Transmission between Stock Index and Stock Index Futures in China WANG Chao-you,KOU Yi School of Management, Harbin Institute of Technology, Harbin 150001, P.R. China Abstract: This research employs the multivariate GARCH models to investigate the volatility transmission between the stock market and index futures market in China. The daily returns of the latest four years are tested as sample data. Three different multivariate GARCH models (BEKK, CCC and DVEC) are estimated and compared. The BEKK model works best and is able to capture the bidirectional transmission between the two markets. The conditional correlations are close to 1 for most of the time, which shows the strong linkage of the two prices. In addition, we find the variance of the futures is larger than the spot market. Above results indicate the futures perform better compared to its earlier stage. The information transmission between the two markets proves that the futures ability in price discovery. Keywords: multivariate GARCH, volatility transmission, stock index futures 1 Introduction China launched its first stock index futures in 2010. This was the first time that investors could sell short in Chinese market. It also helps the price discovery and provides the tool to hedge risk. Five years later, the index futures is now the mostly traded futures in China As the two markets are highly connected, the information and risk transmission transfer bidirectionally and quickly. The stock futures is designed to improve the price discovery and lower the risk of the spot market. The performance of the futures is of great significance. Therefore, the relationship between the index futures and its underlying spot market attracts many researchers. Abundant researches have been done to investigate the relationship between the index futures and the stock index across the world. The results of different markets differ. Garbade and Silber (1983) [1] test the prediction ability of the basis on the price of spot and futures markets in the U.S. market. They find that the futures dominates cash markets for most commodities. However, the integration of two markets over short times is much weaker in grains than gold and silver. Cakici and Chatterjee (1991) [2] find the S&P500 index futures decreases the volatility of the cash market, which proves the benefit of the futures introduction. The result is also found in the interest rate market. Merton (1995) [3] indicates the futures weaken the asymmetry of the underlying stock market. In addition, the improvements in information technology leads to the structure change in the long run relation. Due to the late introduction of the Chinese index futures, the researches about the Chinese market are relatively deficient. Yang, Yang and Zhou (2012) [4] uses high-frequency data to investigate the relationship. They find the futures is not mature enough in its first year due to the high entry barrier. The cash market still contributes more in the price discovery process, which is different from its foreign counterparts. Yan (2011) [5] find the two markets are not causal related and the futures market does not contribute the price discovery significantly. Wang and Xie (2013) [6] use high frequency data to study the cross-correlations. They find the correlations are strongly multifractal, which also indicates the immaturity of the futures market. These studies provide the discovery about the infancy stage of the Chinese index futures. However, after five years operation, the trading volume grows rapidly and is already the highest of all futures in futures market nationwide. The transaction fee and the entry barrier are much lower now. The effect of the futures should be reinvestigated to see the difference from the earlier years which would be helpful for the development of the markets. The multivariate GARCH model is wildly used to testify the dynamic relationship between multiple financial assets and in different countries [7-11]. For example, stock and index futures markets in Hongkong [12], Korea [13] and UK [14] have been studied. It is also used to compare the price discovery between markets [15-17] and jump dynamics [18,19]. It captures the volatility movements of related assets as well as their correlations and time-varying information transmission. This paper attempts to use three varieties of multivariate GARCH models to test the past four years data. Therefore, the features of different phases can be explored. 2 Model specification The bivariate GARCH models are developed from the univariate GARCH model by Bollerslev (1986) [19] 978-1-4673-6513-0/15/$31.00 2015 IEEE - 1296 -

and it take the interaction of variances into account. The ARCH and GARCH models are the mostly used models in describing the time-varying variance of time series. In this paper, three multivariate GARCH models (BEKK, constant conditional correlation, Diagonal VECH) are used to model the volatility transmission between the CSI 300 index futures and its underlying spot markets. All the three models contain a vector autoregression (VAR) process. The VAR process resembles the ARMA process in univariate GARCH. The BEEK-GARCH proposed by Engle and Kroner (1995) [20] can be specified by the following equations: RμR t = + a t-1 + t (1) m H = AA + A a a A + B H B (2) t i t-i t-i i j t-j j i= 1 j= 1 s The VAR process is depicted by Equation (1). R t is the return series vector of two assets. The a t is a 2 1 vector of residuals. H t is a 2 2 matrix of the variance and covariance of the residuals. The A is a symmetric parameter matrix. A i and B j and coefficient matrices, which capture the moving average and autoregressive effect of the volatility respectively. The off-diagonal elements of matrices A i and B j provide the information transmission across the two assets. The BEKK-GARCH model can capture features of heavy tails and volatility clustering like univariate GARCH model. It also can guarantee that the matrix are positive definite under very weak conditions. The equations for the CCC-GARCH and Diagonal VEC GARCH are similar to the BEKK model. The DVEC is a straightforward generalization of the univariate GARCH model to the multivariate case. Every conditional variance and covariance is a function of all lagged conditional variances and covariances, as well as lagged squared returns and cross products of returns. m H = A + A ( a a ) + B H (3) t 0 i t-i t-i j t-j i= 1 j= 1 s The Equation (3) depicts the DVEC GARCH model and denotes the Hadamard product, that is, element-by-element multiplication. The DVEC model can also be described in Equation (4)-(6) in detail. Equation (5) captures the information transmission process. = A + A a + B (4) = A + A a a + B (5) 2 11, t 11,0 11,1 1, t 1 11,1 11, t 1 21, t 21,0 21,1 1, t 1 2, t 1 21,1 21, t 1 2 22, t A22,0 A22,1a2, t 1 B22,122, t 1 = + + (6) The CCC-GARCH model is relatively simple: 2 11, t a10 a11 a12 a 1, t 1 2 = 22, t a + 20 a21 a 22 a2, t 1 β 11 β12 11, t 1 + β 21 β 22 22, t 1 (7) The coefficient which measure two prices relation α 12 is constant which is not time-varying like BEKK or DVECH. The prices are higher related when α 12 is closer to 1. This simple model can only provide the rough result of the whole sample period. BEKK is the most complicated model of the three. It can capture both the time-varying correlation and asymmetry of the information transmission. The Diagonal VEC and CCC only have one each result. However, the BEKK is less accurate than the other two when focus on only one aspects. Therefore, we employ all the three models in our research. All the three models can be estimated in two steps. Firstly, the GARCH parameters and then correlations are estimated. The BHHH (Berndt, Hall, Hall and Hausman) algorithm is usually employed in the Quasi-Maximum Likelihood estimation. 3 Data description Our data derives from both stock market and futures market. The stock index used in this empirical study is the closing price of CSI300 stock index. The CSI300 index contains 300 biggest shares from both Shanghai and Shenzhen Stock Exchanges. The CSI300 index futures launched in April 2010 which was relatively late. The introduction of the index futures makes the Chinese investors could make profits by selling out for the first time. The expiration day of the futures is the third Friday of the contract s delivery month. And the delivery price is the expiration day s last two trading hours arithmetic average of index points multiplied by RMB 300. Both the Shanghai and Shenzhen stock exchanges trade from 9:30 a.m. to 11:30 a.m. and 1:00 p.m. to 3:00 p.m., while the CSI 300 index futures is traded from 9:15 a.m. to 11:30 a.m. and 1:00 p.m. to 3:15p.m. The data s sample period is from April 19, 2010, the beginning of the index futures, to July 16, 2014, of about1026 trading days. The length of the time is relatively short when compared to other researches. However, it is the best we can do since the late introduction of the index futures. The futures and the underlying index prices are from Resset cooperation. The main contract (most active) often shifts one or two days before the delivery day. Therefore, we change the sample contract in the third Wednesday every month, two days before the delivery day. Fig. 1 presents the whole data's pattern. The price of the index and futures is very close and the basis is under 20 for most of the time, so cannot describe clearly in Fig. 1. The trend of the graph shows the Chinese stock market still suffered the bear market in the last four years after the 2008 globe financial crisis. Tab.1 summarizes the common statistics of the daily returns. The skewness of the stock is less than the futures, which means the futures has a fatter tail and higher peak. The kurtosis of both markets are very high. This means we can view the data are not normally - 1297 -

distributed. The Jarque-Bera test also rejects the hypothesis of normal distribution. Finally, the L-B test shows the autocorrelation of series. Tab.1 Sample statistics of the CSI index and index futures daily return Statistics Stock Futures Mean -0.0002-0.00019 Maximum 0.0214 0.0391 Minimum -0.0283-0.0402 Standard deviation 0.0059 0.0064 Skewness -0.1132 0.1182 Kurtosis 4.9000 8.2095 Jarque-Bera test 156.8177 1164.9 Ljung-Box Q-test 18.6999 27.9901 Fig.1 CSI 300 index and futures movement, 2010-2014 4 Empirical Result 4.1 Cointegration test In efficient markets, arbitrageurs will pair trades to eliminate the statistically abnormal basis of futures and cash markets. Arbitrage trading causes information transmission between the two markets, resulting in an equilibrium relationship. The relationship between the markets must be investigated before modelling them with multivariate GARCH models. The existence of the cointegration relation should therefore be examined. The standard unit root procedure, the augmented Dickey-Fuller test, is used to test the data s stationarity first. The results show that the null hypothesis of a unit root is not rejected. The log prices of cash and futures are non-stationary. However, the null hypothesis is strongly rejected for the first-differenced series. The log prices are I(1) processes. The Johansen trace test is further applied. The results indicate the existence of cointegration relation, regardless of the existence of a linear deterministic trend in the series. Consequently, the two series have a linear combination that is unit-root stationary and there is a long-run equilibrium relationship between the two prices. We therefore expect the two markets are related and their volatilities can be further described by multivariate GARCH models. Tab.2 Stationarity tests on index and futures log prices Lag length ADF statistic Result ln F t 1-1.7162 non-stationary ln S t 0-1.7403 non-stationary ln F t 0-35.1838 stationary ln S t 0-32.1066 stationary Notes: the optimal lags are selected based on the Akaike information criterion. The 1%, 5% and 10% critical values are -3.4365, -2.8641 and -2.5682, respectively 4.2 Conditional variance curves This research uses BHHH algorithm to perform the maximum likelihood estimation in the S-Plus software. Fig. 2 is the conditional variance curves based on BEKK estimation. The curves based on CCC and DVEC models which are not presented since they are similar to the BEKK model. From the curves, we can see the futures has more dynamics than the index in most of the time. This is consistent with the fact that the component stocks of the index often reach the daily limits and stop changing, and the futures price only reached the daily price limit once in the last five years. Therefore, the price movement of the component stocks could be restrained by the daily limits and futures price moves freely. Another possible reason is that futures trades 30 minutes longer than the spot market. Hence, the futures contains more information than the spot market. In addition, the variances of the two assets were higher in the futures infancy stage. This accords with the earlier researches that the futures didn t improve the price discovery process significantly and brought disturbance to the cash market when it s newly launched [4,5]. The long-run trend of the conditional variance is decreasing, which could be a good sign that the futures market matures gradually. Fig. 3 shows the correlation between the CSI 300 index and the futures. As can be seen, the two series are highly correlated when the conditional variance are Tab.3 Johansen trace tests on index and futures prices H 0 No deterministic trend Linear deterministic trend T C (5%) Decision T C (5%) Decision r = 0 76.4027 20.2618 R 75.5772 15.4947 R r 1 3.9215 9.1645 F 3.0965 3.8414 F Notes: C is the critical value. R indicates that we reject the null hypothesis. F indicates a failure to reject. - 1298 -

stable and less correlated when variance has higher peaks. Most of the time, the correlation value is close to 1. This indicates the arbitrage opportunity is rare and the information transmission between the two markets is quick and efficient. Low correlation takes place in the middle of each year. It was even under 0 for a few days in the first year. This could be resulted in dividend paying to the shareholders. Because it s hard to predict the impending dividend, the price of the two series will disperse for weeks before the announcements. This dispersion could be risky for arbitragers. 4.3 Dynamics spillover Tab.4 shows the estimated result from the three multivariate GARCH models. In CCC and BEKK models, A 12 and B 12 indicate the volatility spillovers from the index to the futures, A 21 and B 21 show the volatility spillovers from the futures to the index. The DVEC model is symmetry which cannot distinguish the direction of volatility transmission. Therefore A 12 = A 21 and B 12 = B 21. Most of the estimated coefficients are significant at 0.01 level. Whilst the A 11 and A 21 from the CCC model are not significant. This means the CCC model cannot captures the short-lived information transmission from the futures market to the cash market. The hypothesis that the correlation is constant will lead the overlook of the short-run volatility transmission. It also makes the long-run transmission result stronger and more obvious than in the other two models. However, from the BEKK model we can see the bidirectional influence is significant for both long and short dimensions. The likelihoods of three models also indicate the BEKK fits best. Furthermore, A 21 is bigger than A 12 but B 21 is less than B 12. This diverse result indicates that the two market lead in short-run and long-run respectively. The spot market contains more long-run information. However, the futures market reacts more quickly for short-lived news. From each model, B 11 is larger than B 22, which means that the long-run persistence of the futures is stronger and the spot market is more risky. Also, A ii is much smaller than B ii, which means the long-run volatility is more important. From DVEC, A 12 is much smaller than B 12, which also means long time volatility transmission is more important. Fig.2 Conditional variance of the index and futures Fig.3 Conditional correlation of the index and future - 1299 -

Tab.4 Estimation from three multivariate GARCH models CCC BEKK DVEC coeff sig coeff sig coeff sig C 11 0.0014 0.6607 0.1089 0.0000 0.0300 0.0000 C 21 0.0581 0.0300 0.0299 0.0000 C 22 0.0015 0.5168 0.0453 0.1384 0.0363 0.0000 A 11 0.0050 0.5888 0.3357 0.0000 0.1369 0.0000 A 21 0.0050 0.4224-0.2616 0.0000 0.1385 0.0000 A 12 0.1000 0.0000-0.1831 0.0005 A 22 0.1000 0.0000 0.4059 0.0000 0.1454 0.0000 B 11 0.9799 0.0000 0.8869 0.0000 0.7971 0.0000 B 21 0.9799 0.0000 0.1010 0.0008 0.7928 0.0000 B 12 0.7498 0.0000 0.0843 0.0011 B 22 0.7499 0.0000 0.8818 0.0000 0.7786 0.0000 LogL -1179.74-816.431-855.947 5 Conclusion With three multivariate GARCH models, we examine the volatility spillover between the CSI 300 index futures and its underlying spot market. The dataset contains four years daily returns, which is the longest to our knowledge in Chinese market. The volatility of the futures is higher than the index because the stock index could be restrained by daily price and trade 30 minutes less than the futures. The correlation of the two assets is high for most of the time and lower when shares paying dividend. The BEKK works best for its capturing the bidirectional information transmission between the index and futures. The bidirectional movement is significant. The stock market contains more long-run information. The futures are more sensitive for the sudden news. However the futures play a dominant role in the price discovery process. References [1]K D Garbade, W L Silber. Price movements and price discovery in futures and cash markets. The Review of Economics and Statistics, 1983: 289-297. [2]N Cakici, S Chatterjee, Pricing stock index futures with stochastic interest rates. Journal of Futures Markets, 1991, 11(4): 441-452. [3]R C Merton, Financial innovation and the management and regulation of financial institutions. Journal of Banking & Finance, 1995, 19(3): 461-481. [4]J Yang, Z Yang, Y Zhou. Intraday price discovery and volatility transmission in stock index and stock index futures markets: Evidence from China. Journal of Futures Markets, 2012. 32(2): 99-121. [5]Z Yan, The empirical research of the relationship of spot and future: Based on the data of CSI300 index future. Value Engineering, 2011, 30(33): 126-128. [6]G Wang, C Xie. Cross-correlations between the CSI 300 spot and futures markets. Nonlinear Dynamics, 2013, 73(3): 1687-1696. [7]H Chen, Q Han, Y Li, K Wu, Does index futures trading reduce volatility in the Chinese stock market? A panel data evaluation approach. Journal of Futures Markets, 2012: 1167-1190. [8]C Huang, X Gong, X Chen, F Wen, Measuring and forecasting volatility in Chinese stock market using HAR-CJ-M model. Abstract and Applied Analysis, 2013. 2013: 1-13. [9]M Szymanowsk. An anatomy of commodity futures risk premia. The Journal of Finance, 2014, 69(1): 453-482. [10]S H Poon, Extreme value dependence in financial markets: Diagnostics, models, and financial implications. Review of Financial Studies, 2003, 17(2): 581-610. [11]T Bollerslev, V Todorov, S Z Li, Jump tails, extreme dependencies, and the distribution of stock returns. Journal of Econometrics, 2013, 172(2): 307-324. [12]J Wang, Price behavior of stock index futures: Evidence from the FTSE Xinhua China a50 and H-Share index futures markets. Emerging Markets Finance and Trade, 2011, 47: 61-77. [13]S H Kang, C Cheong, S Yoon, intraday volatility spillovers between spot and futures indices: Evidence from the Korean stock market. Physica a: Statistical Mechanics and its Applications, 2013, 392(8): 1795-1802. [14]P Huang, Volatility transmission across stock index futures when there are structural changes in return variance. Applied Financial Economics, 2012, 22(19): 1603-1613. [15]R F Engle, K Sheppard. Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH. National Bureau of Economic Research, 2001. - 1300 -

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