# Price Movements And Discovery In The Hushen Index

Abstract: In this paper, price movements and price discovery in the Hushen 300 index and the futures markets are investigated using the Engle-Granger Augmented Dickey-Fuller test (Engle and Granger, 1987), the Error Correction Model and the Granger Causality Test. Minute-by-minute data from the Hushen 300 index and Hushen 300 index futures show that the movements of the two markets are correlated. Though, in long term, the spot market plays a prime role in price discovering, the futures market contributes more to eliminate the equilibrium errors and they contain the most information in the short-term. The sub-sample results also suggest that the information discovery role of the futures market has strengthened along with the markets’ growth.

## Introduction

Mainland China’s stock market took off in December 1990 with two stock exchanges sequentially open in Shanghai and Shenzhen. On August 25, 2005, these two stock exchanges jointly introduced the Hushen 300 (HS300) Index. The HS300 index is aimed at reflecting the A-share market (both the Shanghai and Shenzhen markets) as a whole. The most recent index includes 300 actively traded shares, of which 179 shares come from the Shanghai market and the remaining are from Shenzhen market, which encompasses 60% of the total market capitalization of A-share markets. All chosen shares are replaceable, which should meet the standards of highly liquidity and great trading volume. Thus the HS300 index has a comprehensive markets representation and can veritably represent the stock price fluctuations in Chinese stock market. The base period is December 31, 2004 and the base point is 1000. By the way, the HS300 index adopts a “T+1” system, that is, the selling of stocks should be practiced at least one day later.

The HS300 future is a cash-settled futures contract on the value of HS300 index and was issued on April 16, 2010. There are four future contracts being traded in each month, which include the contracts that are separately expiring on the third Friday in current month, next-to-current month, last month of next quarter and last month of the second next quarter. It is the only kind of financial futures contract existing in China up to now and contracts of this kind provide Chinese investors with a new set of instruments to manage portfolio risk. Compared with the spot market, the trading hour of HS300 index futures is from 9:15 a.m. to 11:30 a.m. and from 13:00 p.m. to 15:15 p.m., which is different from the index’s trading hour: 9:30 a.m.-11:30 a.m. and 13:00p.m.-15:00p.m. This time arrangement is aimed at stimulating the futures market to achieve price discovering, which is vital for investors to adjust their investment strategies. Another differentia is that futures market has lower transaction costs and adopts the system of day trading, which may encourage it to react to information rapidly. HS300 futures contract has become increasingly popular in China’s financial market and as it is so young, very little research has been done on this important market.

The stock market of China has experienced a lot of growth ever since, even though it is so young when compared with the stock markets of western countries, which have more than 200 years history. This market, however, is experiencing a quite high volatility of share price and most of the individual investors only gain a loss from their investment, which probably indicates the poor quality of regulation that lies behind such high speed of the growth. Therefore, as a new kind of financial derivatives, the HS300 index futures are expected to help the country to promote its financial efficiency and better manage financial risks (Lu, 2007). Especially after China takeovers Japan as world’s second biggest economy, the emergence of the hedging and price-discovering functions of the futures is anticipated anxiously. Similar to the DJIA futures contracts, the performance of the HS300 index futures are primly attempted to track the average index. To achieve an efficient financial market, information should be processed instantaneously and the most efficient market should play the leading role in incorporating new information. Therefore price discovery or information transmission is a good indication to reflect the efficiency of markets. An investigation of the information processing abilities of these two markets will also improve our understanding of price-discovering abilities of different index markets that are connected by the same economic environment (So and Tse, 2004).

This document, by applying the cointegration methodology developed by Engle and Granger (1987), proposes to investigate the competition in price-discovery ability between the spot market and the futures market based on the HS300 index. The Engle-Granger Augmented Dickey-Fuller test shows that both the index spot and the index futures prices adjust toward the long-run equilibrium relationship. The error correction model (ECM) estimation and the Granger Causality Test suggest that there is a two-way feedback relationship and the information flows from the index futures is stronger in the short-run, though the spot price leads futures price in long term. Sub-sample results reveal that the futures market is growing astatically but its price-discovery function has been strengthening. To know how price moves and which market shares more information is significant for investors to determine trade strategies. Investors can potentially make use of these findings to forecast the price movements by combining the long-run equilibrium relationship and short-term dynamics between the HS300 index and the index futures.

The remainder of this paper is organized as follows. Section two briefly reviews some relevant literature. The third section includes a description of the data and describes how the samples are collected. In the fourth section, the details of methodology adopted in this study are explained. In section five, the empirical results of all the tests are presented and an elaborate analysis of the results is given. A brief conclusion and summary are presented in the last section of this article.

## Literature Review

The process that index futures allow market traders to absorb all relevant information to fairly attain the price of securities is called price discovering (Chen& Gau, 2009). It is one of the most important functions of index futures. As many traders may take positions in more than one market simultaneously, they can utilize the difference of response time with respect to new information and the size of the difference between each market to make a crucial profit. (Kim et al, 2006). To know the price movements’ relationship among markets, both the long-run and the short-term, is also crucial to improve the hedging performance and to achieve a better forecast for investors.

In a perfect capital market, as long as the price instantly and effectively reflects information published in the market, it seemingly coincides with the efficient-market hypothesis devised by Engene Fama (1070). Hence new information is supposed to be absorbed simultaneously into the spot and future market. However, the ability that prices react to new information is likely to be affected by several real world factors. Many studies suggest that market with the lowest trading costs tends to react most rapidly to new information (Fleming et al, 1996 cited from Hseu, Chung & Sun, 2007). Specifically, Chen&Gau (2009), Gibson, Singh and Yerramilli (2003) point out that a smaller tick size may lead to lower effective transaction costs. All of them successfully show that a reduction in tick size is likely to drive traders become more incentive to gather information, thus they are more willing to trade in the stock market. Based on these findings, a reduction in tick size can result in an increasing contribution to price discovery. Additionally, the effect of nonsynchronous trading is regarded as another one of the most important explanations for the lead-lag relationship between spot and futures markets. According to Shyy et al (1996), after removing the effect of nonsynchronation, the lead-lag effect from spot market to futures market become significant rather than in the opposite direction. On the other hand, Chan (1992) suggests that nonsynchronous trading cannot effectively explain the lead-lag pattern, and futures market tends to share more information. Studies by Booth et al (1999), however, conclude that the combination of both the costs of trading and the nature of information are the prime causes for the observed lead-lag relationship between the futures market and their underlying assets market. Besides, there are some other factors, including short selling restriction, difference in trading mechanism and information asymmetry (Chen et al, 2002; Seung et al, 2006). Hence it can be concluded that market with fewer real-world restrictions is seemingly anticipated to incorporate information faster than another one. This speed advantage can be effectively used to forecast the price trend of the slower-reacting market, which shares the same underlying asset.

Numerous studies have examined the price-discovery capabilities between the stock index and its derivative securities in different markets of regions. For example, Kawaller, Koch and Koch (1987) studied the S&P 500 index and index futures by using the three-stage least-squares regression method. They find that futures returns generally lead spot returns by 20 to 45 minutes on a minute-to-minute data basis. Stoll and Whaley (1990) use the ARMA (2, 3) model and report that the S&P 500 and the Major Market (MMI) Index futures returns lead spot returns by 5 minutes on average. After using the cointegration test, Chen and Gau (1995) demonstrate that information flow from the Municipal Bond Index (MBI) futures market to its underlying spot market is stronger. Tse (1999) and Lihara et al. (1996), using a sample of data prior to 1992, also claim that Osaka Securities Exchange (OSE) futures lead the underlying index. On the other hand, Swinnerton et al. (1995) find that the OSE Nikkei futures play little role in price discovering, compared with the index spot. Wahab and Lashgari (1993) investigated the relationship for both the S&P 500 and FT-SE 100 indexes. They suggested that the spot market reacts to new information faster than futures market. Abhyanker (1995) also points out that the spot market may accidently lead the futures market when investors recognize that there is information existing in the spot market only. Furthermore, paper such as Lim (1992) concludes that no lead-lag relationship exists between the SIMEX Nikkei 225 futures and the underlying spot. The different conclusions of extensive studies by numerous researchers may be the result of dissimilar properties of various index and futures markets. Another reason for these divergences may be the very methodologies adopted.

Motivated by previous studies on price discovering and price movement in multi-markets that the prices of spot and futures are cointegrated, error correction model (ECM) tends to be a more proper model to examine the lead-lag relationship between the two markets [See Ghosh (1993), Wahab and Lashgari (1993), Koutmos and Tucker (1996), Shyy et al. (1996), Tse (1999)]. The present research will apply the similar approach (Cointegarion test) to study the lead-lag relationship between the HS300 index and the index futures.

## Data

For my experiment, minute-by-minute data of the HS300 index and index futures are obtained from Ghancn. Likewise, as some of the source data is incomplete and to ensure the simultaneity of the two markets’ trading, I abstract the prices of index and futures that are traded during 9:31a.m. to 11:30 a.m. and 13:00 p.m. to 14:59 p.m. to construct the data sample. In addition, the sample period is from the launching date of Hushen 300 index futures (April 16, 2010) to February 25, 2011, with 49712 observations in total for each variable. The spot price variable is built by using the closing price in every minute; the futures price variable is constructed by using the closing price of the contract that has the maximum trading volume in each minute. And from the orderliness of the data in each month, it is generally observed that the contract expiring in current month is traded most frequently one week before its expiration, and the next-month contract starts to take over the position with higher trading volume during the week prior its expiration. Notably, each series andprocessed in this survey are based on the natural logarithm of the price data to avoid the problem of non-liner relationship between the two variables and the problem of inaccuracy. Also, given the large sample employed in the study, the significance level is adjusted downward to 0.1%, instead of the 1% or 5% for the full sample. By the way, STATA 11 is manipulated by this survey to run the tests and to report results.

All tests in this paper are conducted for three different samples: the full period sample and two equally divided sub-samples. The reason for dividing is to investigate whether there are any developments or variation on futures’ price-discovering abilities all along after launch. The facts are that the HS300 index futures contract is developing astatically in early stage and in latter period it does perform better than that in earlier days and the price-discovering capability is appearing gradually. More details will be explained in the fifth part in this document.

## Methodology

Few fundamental definitions are introduced simply. A series is said to be integrated of order 1 or I(1) if Δ is stationary (A stationary time series is said to be integrated of order 0 or I(0)) . Suppose that I(1), ~I(1). Then and are said to be cointegrated if there exists a θ (it is often called the cointegration coefficient) such that -θ is stationary (that is, -θ is I(0)), and the term -θ is called the error correction term or the equilibrium error. Therefore for the very experiment of this article, the major problem we will address is to test whether the spot rice and the futures price can fulfill the condition -θ~I(0).

However prior to testing for a unit root in the error correction term, we first employ unit root tests to check that and are I(1), otherwise it may arise the problem of spurious regression. The Dickey-Fuller (DF) test and the augmented Dickey-Fuller (ADF) tests are used in this part because DF and ADF are considered to be one of the most reliable and are the most commonly used models in practice (Stock& Watson, 2007). The following ordinary least square (OLS) regressions are performed:

DF: Δ=+δ+ (1)

DF with trend: Δ=+αt+δ++ (2)

ADF: Δ=+δ++ (3)

Where Δ=- and t is the deterministic linear time trend. and are said to be i.i.d error terms. The ADF (with more lagged differences in the test) is considered more appropriate if is serially correlated. Both the DF and the ADF statistics are the OLS t-statistic testing δ=0 in equation (1),(2) and (3) for the null hypothesis that has a unit root.

It should be noted here that the foregoing tests are not enough if the hypothesis is simply rejected as expected. The rejection only implies that the two series do not have a unit root, but it does not reveal whether the two series are integrated of order one or more orders. It is really necessary to ensure that the two series are integrated of the same order to apply the cointegration test. Hence the same DF and ADF test is required with respect to Δ to verify that the two differenced series are stationary. Namely, the original series must be I(1).

If it is confirmed that both the spot and futures prices are I(1) series, the next procedure is to estimate the value of θ by OSL estimation of the regression

. =λ+θ+ (4)

Where λ is a constant; θ is the estimator of the cointegration parameter; and is the error term. Under the null hypothesis of non-cointegration, should have a unit autoregressive root. Here I still use the ADF test, as Engle and Granger (1987) suggest several cointegration tests but suggest that it is best to use the ADF test to test for unit root in, which requires the performing of the following OLS model:

Δ=+++ (5)

Where, ,i=0, 1,2,…l, are regression coefficients and is the error term. If the null hypothesis that equals zero is rejected, then and can be modeled as cointegrated. The two-step procedure (4) and (5) is called the Engle-Granger ADF test for cointegration, or EG-ADF test (Engle and Granger, 1987). Critical values of the EG-ADF statistic can be referenced from Stock and Watson (2007, p.660).

Granger representation theorem (Granger, 1983; Engle and Granger, 1987) holds that when and are both I(1) and have a long-run relationship, the equilibrium error must be pulled back towards zero by some force. The vector error correction model (VECM) exactly corresponds to this as it shows how the short-run behavior of and reconcile with their long-run behavior. Here we apply the VECM, that is, if and are cointegrated we can forecast Δ and Δ by using the following equations:

Δ=+ + + + (6)

Δ=+ + + + (7)

where =[]is the error correction term reflecting the deviation from the long-run equilibrium between the two variables in the last period. ,,,,are the short-term adjustment coefficients; and are the error terms and are assumed to be white noise. This model interprets that the change in and is due to the adjustment to the long-run equilibrium and the short-term effects prom past Δ and Δ.

The causality relationship between the spot price and futures price can be found by the ECM. The Granger Causality Test is a useful application of the F-statistic to test whether the lags of one repressor has useful predictive content. The claim that a variable has no predictive content corresponds to the null hypothesis that the coefficients on all lags of that variable are zero. Namely, if the coefficients of Δ not all are zero in the equation (6), we call Granger causes. Similarly, if the null hypothesis that the coefficients on all the values of Δ are zero is rejected in the equation (7), then Granger causes.

## Empirical results

## Summary statistics

## Table I

Summary Statistics for Hushen300 Index and Index Futures series

Series

Mean

STD

Min

Max

Correlation

Panel A: Full Sample, 16/04/2010-25/02/2011, n=49712

Index()

8.006

0.078

7.809

8.177

0.9971

Index Futures()

8.014

0.818

7.816

8.206

Panel B: Sub Sample 1, 16/04/2010-14/09/2010,n=24856

Index()

7.950

0.057

7.809

8.126

0.9957

Index Futures()

7.956

0.060

7.816

8.148

Panel C: Sub Sample 2, 16/09/2010-25/02/2011,n=24856

Index()

8.062

0.052

7.948

8.177

0.9944

Index Futures()

8.071

0.057

7.954

8.206

Panel D:Differenced Series, Full Sample

Index(Δ)

0.000

0.00076

-0.029

0.021

0.2588

Index Futures()

0.000

0.00140

-0.024

0.024

Descriptive statistics of the natural logarithms of the two markets’ prices are shown in Table I. The mean value of futures price is higher than spot price, which implies that it is more expensive, on average, to establish a futures position than cashed position. And after the date of index futures’ launching, the prices of both two markets are raising generally (compare panels B and C). In addition, the prices of the two markets are significantly positively correlated, though the correlation coefficients for the differenced series, Δ and are lower. This fact reveals that there may be a unit root in the two series and.

## Integration Test

## Table II

Test for Unit Root on Hushen 300 Index and Index Futures series

Series

DF Test

DF test (Trend)

ADF Test(p=12)

ADF Test(p=22)

ADF Test(p=32)

Panel A: Full Sample, 16/04/2010-25/02/2011

Index()

-1.468

-3.064

-1.642

-1.653

-1.687

Index Futures()

-2.178

-3.252

-1.710

-1.788

-1.822

Panel B: Sub Sample 1, 16/04/2010-14/09/2010

Index()

-3.120

-2.655

-2.901

-2.860

-2.917

Index Futures()

-3.096

-2.743

-3.127

-3.117

-3.112

Panel C: Sub Sample 2, 16/09/2010-25/02/2011

Index()

-1.492

-1.645

-1.762

-1.794

-1.833

Index Futures()

-2.297

-2.433

-1.654

--1.777

-1.805

Note:

The critical values with and without time trend at the 1% levels are -3.96 and -3.43, respectively. See Stock &Watson (2007, p563).

The DF and ADF tests are based on the following OLS regressions:

DF: Δ=+δ+ (1)

DF: Δ=+αt+δ+ (Trend) (2)

ADF: Δ=+δ++ (3)

Where =

For testing the unit roots of the natural logarithms series of spot and futures’ prices, and, the resulting regression t-statistics are reported in Table II. It can be seen that both the DF and ADF tests disclose that the hypothesis that the two series and have a unit root cannot be rejected for the full and two sub samples. Hence the two series are integrated at least of one order. For the ADF tests, different lags p, from 0 to 32 is tested, and all results are significant at the 1% level. Only the three cases with p=8, p=12 and p=32 are reported.

## Table III

Tests fore Unit Root on Differenced Series

Series

DF Test

DF test (Trend)

ADF Test(p=12)

ADF Test(p=22)

ADF Test(p=32)

Panel A: Full Sample, 16/04/2010-25/02/2011

Index(Δ)

-155.374

-155.380

-62.067

-45.562

-37.724

Index Futures()

-276.284

-276.289

-66.180

-45.509

-37.322

Panel B: Sub Sample 1, 16/04/2010-14/09/2010

Index()

-117.120

-117.151

-43.465

-32.174

-26.623

Index Futures()

-190.295

-190.327

-45.599

-32.530

-25.921

Panel C: Sub Sample 2, 16/09/2010-25/02/2011

Index()

-101.510

-101.510

-44.288

-32.215

-26.686

Index Futures()

-119.235

-199.234

-47.748

-31.586

-26.552

Note:

The critical values with and without time trend at the 1% levels are -3.96 and -3.43, respectively. See Stock &Watson (2007, p563).

The DF and ADF tests are based on the following OLS regressions:

DF: Δ=+δ+ (1’)

DF: Δ=+αt+δ+ (Trend) (2’)

ADF: Δ=+δ++ (3’)

Where =

Table III conveys the results for testing the unit roots on their differenced series, and, by applying the same DF and ADF tests. It can be seen that the unit root hypothesis can be rejected for the two differenced series for each sample. Hence it is obvious that both Δ and are stationary, which implies that both and are I(1) series.

## Cointegration Test

The cointegration test results are reported in Table IV. The high value of regression implies that the variance of the two variables is well explained by each other. As the test statistics for the full sample are significant at 0.1% significance level, and the two sub-samples are separately significant at 1% level, the non-cointegration null hypothesis can be rejected. Therefore, it can be inferred from the results that there exists a long-term equilibrium relationship between and, though these two series are individually nonstationary. Similar result is also true for the two sub-samples. It is interesting to note that the power of the EG-ADF test decreases as a result of the increase of the lags, for which the reason is that the immaterial insignificant parameters are introduced.

## Table IV

Cointegration Tests for Hushen 300 Index and Index Futures Series

Series

λ

θ

t-Statistic t-Statistic

for for

(l=0) (l=12)

t-Statistic

for

(l=32)

Panel A: Full Sample, 16/04/2010-25/02/2011

Index()

0.361

0.954

0.9943

-25.805*

-8.867*

-7.185*

Index Futures()

-0.331

1.042

0.9943

-25.858 *

-8.883*

-7.214*

Panel B: Sub Sample 1, 16/04/2010-14/09/2010

Index()

0.414

0.947

0.9914

-19.408 *

-7.452*

-6.004*

Index Futures()

-0.365

1.047

0.9914

-19.461 *

-7.483*

-6.062*

Panel C: Sub Sample 2, 16/09/2010-25/02/2011

Index()

0.732

-0.908

0.9888

-19.524 *

-6.153*

-4.890*

Index Futures()

-0.706

-1.089

0.9888

-19.607 *

-6.141*

-4.880*

Note:

The cointegration analysis is based on the following regression equations:

=λ+θ+ (4)

Δ=+++ (5)

When is the LHS variable in (4), =, = and the equilibrium error is denoted as subsequently: when is LHS variable in (4), =, = and the equilibrium error is denoted as.

*indicates the test statistic is significant at the 1% level. The value is from Engle and Granger (1987).

## Error Correction Model Estimation and Granger Causality Test

The results of the OLS estimation of the error correction models are reported in Table V. Four error correction regressions are conducted for the full sample and the two sub-samples: (1) differences of spot series are regressed on the lagged spread (the error correction term) of own market and lagged differences in spot and futures series; (2)differences of spot series are regressed on the lagged spread (cross-market) and lagged differences in spot and futures series; (3)differences of futures series are regressed on the lagged spread (own-market)

## Table V

OLS Estimation Results of Error Correction Models

Panel A: Full Sample: 16/04/2010—25/02/2011

(-0.06) (-4.14) (5.13) (-4.22) (-15.89) (-16.72) (-13.80) (-10.63) (-6.53) (-4.18)

(25.08) (24.76) (24.16) (20.84) (17.39) (13.59) (10.81) (8.25) (5.91) (4.03)

(4.24)

=0.2287

(-0.06) (4.08) (5.13) (-4.22) (-15.89) (-16.72) (-13.80) (-10.63) (-6.53) (-4.18)

(25.08) (24.76) (24.15) (20.84) (17.39) (13.59) (10.82) (8.25) (5.91) (4.03)

(4.24)

0.2287

(-0.33) (-4.69) (8.43) (-9.87) (-4.62) (-3.32)

0.0645

(-0.33) (4.69) (8.44) (-9.88) (-4.63) (-3.32)

0.0645

Panel B: Sub Sample 1: 16/04/2010—14/09/2010

(-0.29) (-3.80) (-3.76) (-11.90) (-13.69) (-11.97) (-9.61) (-5.27) (-3.31) (17.19)

(26.01) (22.71) (19.04) (15.72) (12.74) (10.06) (7.95) (6.50) (6.31)

(5.33) (4.92)

0.2200

(-0.29) (3.65) (-3.77) (-11.91) (-13.69) (-11.98) (-9.61) (-5.28) (-3.31) (17.19)

(26.01) (22.69) (19.02) (15.71) (12.73) (10.06) (7.96) (6.51) (6.32)

(5.34) (4.93)

0.2199

(-0.93) (-3.24) (3.52) (-5.59)

0.0399

(-0.93) (3.00) (3.53) (-5.60)

0.0399

Panel C: Sub Sample 2: 14/09/2010-25/02/2011

(0.44) (-3.52) (5.86) (-9.47) (-9.87) (-8.30) (-5.35) (-4.15) (16.81) (13.54)

(14.23) (12.42) (10.47) (8.13) (6.27) (4.33)

0.2535

(0.44) (3.37) (5.86) (-9.47) (-9.88) (-8.31) (-5.35) (-4.15) (16.82) (13.54)

(14.24) (12.43) (10.48) (8.14) (6.27) (4.33)

0.2535

(0.47) (-3.50) (8.12) (-8.31) (-4.59) (-3.35)

0.0999

(0.47) (3.44) (8.13) (-8.32) (-4.59) (-3.35)

0.

0999

Note:

and are residuals from regression equation (4) when and are the LHS variable, correspondingly.

The numbers in parentheses under the error correction equation are the associated t-statistics, and all t-statistics are heteroskedasticity-robust.

All test statistics are significant at the 0.1% level except #, which indicates the specific test statistic is not significant at the 0.1% level. The critical value for 0.1% level is 3.29.

and lagged differences in spot and futures series;(4)differences of futures series are regressed on the lagged spread (cross-market) and lagged differences in spot and futures series. A Granger Causality Test is conducted for the foregoing first and third regression for all the three samples, of which the results are shown in table VI.

Table VI

Test Results of Granger Causality Relationship

Lagged Number

Null Hypothesis

F Statistics

P-value

Panel A: Full Sample, 16/04/2010-25/02/2011

12

=0 (i=1,2,…12)

87.99

0.0000

=0 (i=1,2,…12)

7.17

0.0000

Panel B: Sub Sample 1, 16/04/2010-14/09/2010

12

=0 (i=1,2,…12)

75.81

0.0000

=0 (i=1,2,…12)

2.56

0.0022

Panel C: Sub Sample 2, 16/09/2010-25/02/2011

12

=0 (i=1,2,…12)

32.41

0.0000

=0 (i=1,2,…12)

6.37

0.0000

The error correction model adopted in this experiment includes 12 lagged and lagged. That is because 12 lags are enough to describe the test and to conclude the results, instead of more lags which are expatiatory. The final ECM equations only include those lagged terms with statistically significant regression coefficients. If the cointegrated variable adjusts to the long-run equilibrium, the coefficient on lagged spread is expected to be negative for the own market error correction term and positive for the cross-market error correction term (Hung and Zhang, 1995). The full sample results are presented in Panel A. It can be observed from the result that the OLS regression coefficients for error correction terms and have the anticipated sign, and these coefficients are 0.1% statistically significant, which reveals that both the index spot and index futures prices, on average, adjust towards the long-run equilibrium when disequilibrium occurs. Moreover, It can be seen from the Panel A of Table VI that both the null hypothesis that the coefficients of and ofall are zero are rejected by the test results of Granger Causality, which also imply that there are short-run bidirectional causal relationship between the two markets for full-sample period. Therefore, the prices of both the two markets interact whenever in long run or in short term.

More specifically, it can be inferred from the results that the most of the price discovery takes place at the spot market in long term. When the spot price is beyond the futures price at any instant minute, the spot price will adjust negatively at the next minute until the price moves back to equilibrium; and the futures price will adjust positively until it reaches equilibrium. Interestingly, the coefficient of the error correction term in the spot equation is smaller in magnitude than that of the futures equation: -0.0026 versus -0.0053. These results reveal that when disequilibrium occurs, it is the futures price that makes the greater adjustment in order to reestablish the equilibrium. Namely, the spot price leads the futures price in long term.

Though the long-run lead-lag relationship is stronger in spot market, in short run, it is the futures market that plays a leading role in incorporating new information. It can be seen from Table V that the spot ECM equation (the first and the second equation in each panel) includes more statistical significant lagged differences terms of futures price (than that of the spot price (. It is also noted that the t-statistic for the term is much higher than for the term. Likewise, the futures ECM equation (the third and fourth equation in each panel) only contains the lagged first differences of spot price and a fewterms. These findings highly suggest that, in short run, the information flow from the index futures market to the index cash market is stronger. The ECM explains 22.87% of variations in index spot changes and only 6.45% of the variations in index futures changes. The lower for the futures ECM equations suggests that all the lagged variables of both markets can only explain a small fraction of the current innovations; and the relatively high for the spot ECM equations implies that those lagged terms can well explain the current changes in spot market. Hence with the fact that lagged futures terms contribute more to changes in spot price, we can conclude that the futures market plays a predominant role in price discovering in short run. Combined the results of the Granger Causality Test that both variables are useful predictors of each other, it is also suggested that the past values of the futures’ price contain more information that is useful for forecasting changes in the spot’s price. The results are qualitatively similar when the cross-market error correction terms are used in the ECM equations. The short-run price leading role of futures may be the result of its advantage of lower transaction costs and day trading, as mentioned in the “Introduction” part. With less trading restrictions, consequently, the index futures have a prior reaction to information in short term.

The results are mostly similar among three samples; however, it is notable that the test results for the two sub-samples are a little different from those for the full sample. Firstly in panel B, the coefficients on the lagged spread for the futures ECM equations are not significant at the 0.1% level (marked by #), but are significant for the spot ECM equations. Though they have the expected sign, this still indicates that all the adjustment is made through the spot market when disequilibrium occurs during the first sub-sample period; that is, the short-run disequilibrium does not have an effect on the long-run equilibrium for futures price and the speed of response to new information within the spot market is slower than in the futures market. Combined with the results of the Granger Causality Test, the null hypothesis that the spot price Granger causes futures price is rejected at the 0.1% level, there is not a causal relationship from the spot price to the futures price. Those above results indicate that the futures market price leads the spot market price and not vice versa. Therefore, the futures market plays the role of price discovery in early stage after index futures’ launching. Whereas, this extraordinary price-discovering ability should not be surprising as the futures market is not active enough at that time so that there was no adequate trading volume to achieve error correcting and to react to the price effect coming from the spot market. Hence this result may not reflect a true image of the HS300 index futures market. Secondly, the results for the second sub-sample period are similar to that for the full sample, which are quite different with sub-sample one as well. This back-to-average movement confirms my point of view that the HS300 index futures market develops quite unsteadily.

It shout be noticed that the increase in advocates the fact that the changes in spot price can be explained better by lagged terms of futures; and significance of the coefficients of all the error correction terms still indicate that futures price play the prime role in eliminating the equilibrium errors; compared with sub-sample one, the decrease of Granger statistic of and the raise of Granger statistic of suggest that the strong unidirectional causality from futures market to spot market has transformed to the bidirectional relationship finally. Therefore, we can conclude from the different results between the two sub-samples that the HS300 futures market is developing in a positive direction and the price-discovery ability has emerged and is strengthening.

## Conclusions

This paper examines the price movements and price discovery process in the Hushen300 index and the index futures markets. It is found that both the index spot and index futures are unit-root non-stationary series. The results of the cointegration test suggest that there is a long-run equilibrium relationship between the Hushen 300 index and the index futures. After using the error correction model to investigate the short-run dynamics of the two price series, it is shown that both the two markets adjust towards the long-run equilibrium when disequilibrium occurs and the futures market plays a predominant role in eliminating disequilibrium errors. Even though the spot market plays a more important role in price discovery in the long-term, futures market conveys more information that is significant for predicting the short-term price movement in spot market. Sub-samples results reveal that index futures market is instable but has been growing fast since its launching last year. It does not only take the place of spot market as the main force in eliminating the equilibrium errors, its past values can better explained the changes in spot price, which shows its potential growth in price-discovering ability in the future.

Therefore, these finding are quite useful for China’s investors in stock market. Index futures market can potentially help to track the performance of index market, thus to contribute to hedging and to the regulation of financial efficiency.

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