Intraday return dynamics and volatility spillovers between NSE S&P CNX Nifty stock index and stock index futures

Using 5-min intraday transaction prices, this study investigates the relationship between the National Stock Exchange (NSE) S&P CNX Nifty futures and its underlying spot index in terms of both return and volatility. By applying Johansen–Juselius (J–J) cointegration analysis, we find evidence of single common stochastic trend, to which spot and futures prices move together in a long-run equilibrium path. The vector error correction model (VECM) and Granger causality test find that there is unidirectional causality running from futures to spot market. To examine the volatility spillovers between the markets, this study has used bivariate Generalized Autoregressive Conditional Heteroscedastic (GARCH) (1, 1) model with Baba, Engle, Kraft and Kroner (BEKK) parameterization and finds evidence of bidirectional volatility spillovers between spot and futures markets. However, there is pronounced spillover effect of a previous shock and volatility from the futures market to spot market. Hence, we conclude that Nifty futures prices lead spot prices and futures market largely contributes to price discovery. These findings have significant implications for traders in implementing hedging and arbitrage trading strategies, for portfolio managers in managing risk and also for policymakers in assessing market stability.

Price discovery, besides hedging, is another important economic function of futures markets. Price discovery is about how agents discover the true value of assets among different markets (O'Hara, [19]). It is a dynamic process through which financial markets converge and reach on the efficient equilibrium price (Schreiber and Schwartz, [22]). In a perfectly efficient market, all available information impounds fully and instantaneously into the markets, so that futures prices move concurrently with the underlying spot prices without any lead–lag. However, it does not hold in the real world. The study of price discovery is of interest to academics, practitioners and regulators for many reasons. First, the issue is linked to market efficiency and microstructure design. Second, the arbitrage trading strategies must take into account the lead–lag relationship between spot and futures markets. Third, mispricing of futures prices provides short-run riskless profit-making opportunity to the arbitrageurs and their actions result in correcting the magnitude of basis. A number of studies have examined the relationship between futures and spot market, mostly in the United States and other developed markets. The studies (Kawaller et al., [14]; Cheung and Ng, [6]; Stoll and Whaley, [24]; Chan, [3]; Ghosh, [11]; Wahab and Lashgari, [27]; Tse, [25]; Abhyankar, [1]; Pizzi et al., [20]; Min and Najand, [18]; Frino et al., [10]; Brooks et al., [2]; Chatrath et al., [5]; Roope and Zurbruegg, [21]; Covrig et al., [7]; So and Tse, [23]; Zhong et al., [28]) found evidence that futures returns led spot returns, as well as a strong contemporaneous relationship. This can be traced to market imperfections, transaction costs, liquidity differences, nonsynchronous trading, trading intensity, short-selling restrictions and differences in the frequency of trading of individual stocks within the index portfolio. There is little evidence of spot markets leading futures markets.

The issue of volatility spillovers between markets also plays an important role in managing risk for portfolio managers and assessing market stability for policymakers. The empirical evidence on the volatility spillovers between spot and futures market has been conflicting. The majority of the studies have found evidence that futures volatility led spot volatility (Iihara et al., [12]; Koutmos and Tucker, [15]; Tse, [26]; Zhong et al., [28]). Also some studies have inferred bidirectional volatility spillovers between markets (Cheung and Ng, [6]; Chan et al., [4]; Lee and Linn, [17]; Chatrath et al., [5]; Lafuente, [16]; Zhong et al., [28]). There is no evidence of spot volatility leading futures volatility.

In recent years, the emerging capital markets of India have generated considerable interest among regional as well as global investors and researchers, because of the dematerialization of shares, rolling settlement (T + 1), electronic open limit order book trading, strengthening of corporate governance practices and enhanced transparency and disclosure standards. Analysis of the intraday relationship between spot and futures markets is very limited in India. This study fills that gap by examining the intraday price discovery and volatility spillovers between the S&P CNX Nifty spot and futures.

The outline of this article is as follows: Section II presents data and preliminary analysis. Section III describes the model specifications. The empirical results are explained in Section IV. Section V concludes.

The data consist of 5-min transaction prices for National Stock Exchange (NSE) S&P CNX Nifty futures and spot index from 1 March 2007 to 31 January 2008. We extract 5-min data from the historical data CD-ROMs made available by the NSE and used the last-quoted value of the index at 5-min intervals. Daily trading begins at 9:55 am and ends at 3:30 pm for both the stock and the futures markets. The first 5-min observations of each trading day are excluded to remove the effect of the overnight orders. If no observation occurs in the interval, then the previous period's price is recorded. We remove the problem of nonsynchronous in data by matching each futures price with the spot value observed at the same minute. In this way, price series at 5-min intervals are constructed from 10:00 am to 03:30 pm, leading to a total of 15 612 observations per series. We use futures prices data for only near-month contract, and switch or rollover to the next maturing contract one week before expiration date. Hence, this rollover ensures that futures prices are quoted from the most liquid contracts and that trading behaviour linked to expiration effects is minimized. The continuously compounded returns for spot (St) and futures (Ft) are defined as the first differences of the natural logarithmic prices level:

(1)

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Table 1 presents the summary statistics of 5-min Nifty spot and futures returns.

Table 1. Summary statistics for the 5-min spot and futures (%) returns

The average percentage returns for the two markets are almost equal. As measured by SD, futures market is a little more volatile than spot. The unconditional distributions of the return series are negatively skewed and highly leptokurtic. The Jarque–Bera statistic is highly statistically significant, thus, rejecting the null hypothesis of normally distributed returns series.

Table 2 provides the Pearson correlation coefficients between spot and futures returns.

Table 2. Pearson correlation between 5-min spot and futures returns

The high positive correlation coefficient (0.84) reflects that both the markets tend to move together, reacting simultaneously to the market forces and new information.

The results of the Augmented Dickey–Fuller (ADF), Phillips–Perron (PP) and Kwiatkowski–Phillips– Schmidt–Shin (KPSS) unit root tests on the levels and first differences of the variables of interest are given in Table 3.

Table 3. Unit root tests

All the three tests suggest that the logarithm of both spot and futures price series are nonstationary in level but stationary in their logarithmic first differences. Hence, both the data series are integrated of order 1, I (1). A visual inspection of the Figs 1 and 2 suggest the same results.

Graph: Fig. 1. Time series plot of 5-min Nifty spot and futures prices: 1 March 2007 to 31 January 2008

Graph: Fig. 2. Time series plot of 5-min spot returns (RS) and futures returns (RF) series: 1 March 2007 to 31 January 2008

The Ljung-Box-Q (LB-Q) statistics are computed to test for serial correlation in the returns and squared returns series and displayed in Table 4.

Table 4. Autocorrelation of returns and squared returns

The statistically significant value of LB-Q statistics in the squared returns indicates the existence of volatility clustering in both spot and futures markets. We reject the null hypothesis of identical and independent observations and no serial dependence in both returns and squared returns series.

Engle ([8]) test of an Autoregressive Conditional Heteroscedasticity (ARCH) Lagrange Multiplier (LM) test is applied to examine time-varying volatility (Table 5).

Table 5. Evidences of time-varying conditional heteroscedasticity

The LM statistics rejects the null hypothesis of no ARCH effect in both spot and index futures returns. It indicates the presence of time-varying volatility in both markets.

The theoretical relationship between spot and futures market is based on the cost-of-carry model and efficient market hypothesis. Having established St and Ft series are I (1), Johansen–Juselius (J–J) (Johansen and Juselius, [13]) multivariate cointegration test and Vector Error Correction Model (VECM) can be used to examine the long-run and short-run deviations from equilibrium.

(2)

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(3)

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where St and Ft are contemporaneous spot and futures prices at time t; α and β are parameters; and ϵt is deviation from parity. J–J test is based on the following vector autoregressive (VAR) representation:

(4)

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where is a (2 × 1) column vector of nonstationary log-spot (St) and log-futures prices (Ft); is a (2 × 1) column vector of white noise error; A0 is a (2 × 1) column vector of constants and A is a (2 × 2) matrix of coefficients. The Equation 4 can be transformed into following:

(5)

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(6)

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where and

The existence of cointegrating relations can be examined through Π matrix. The Π matrix can be written as Π = αβ′; β represents the matrix of cointegrating parameters; and α is the matrix of the speed of adjustment parameters. To identify the number of cointegrating vectors and their estimates, J–J cointegration test uses two likelihood ratio statistics: trace and maximum eigenvalue.

(7)

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(8)

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Here T is the number of observations and is the estimated value for the ith ordered eigenvalue obtained from the Π matrix. The trace statistic tests the null hypothesis that the number of distinct cointegrating vectors is less than or equal to r against the alternative hypothesis of more than r cointegrating relationships. The maximum eigenvalue tests the null hypothesis that the number of cointegrating vectors is less than or equal to r against the alternative of r + 1 cointegrating vectors.

According to Granger representation theorem (Engle and Granger, [9]), if sets of series are cointegrated, then there exists a VECM.

(9)

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(10)

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αs and αf are the coefficients of the error correction term (ectt − 1) that can be interpreted as the speed of short-term adjustment factors. It measures how quickly each market reacts to the deviation from the long-run equilibrium.

The following bivariate autoregression is used to examine the Granger causality test between spot and futures returns.

(11)

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(12)

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The null hypothesis that futures returns does not Granger cause spot returns will be rejected if the coefficients α12(i) in Equation 11 are found to be jointly statistically significant, based on F-test. Similarly, the null hypothesis that spot Granger causes futures will be rejected if the coefficient α21(i) in Equation 12 is jointly significant; bidirectional causality is suggested if both α12(i) and α21(i) coefficients will jointly be statistically significant.

The returns series of both the markets exhibit the stylized facts of time-varying volatility, fat tails and volatility clustering. To examine the volatility spillovers between the markets, the study has used the following bivariate: Generalized Autoregressive Conditional Heteroscedastic (GARCH) (1, 1) model with Baba, Engle, Kraft and Kroner (BEKK) parameterization assuming conditional normal bivariate distribution for the vector of error distribution.

(13)

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(14)

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(15)

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The Ht matrix can be rewritten as follows:

(16)

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(17)

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is a vector of returns for spot and futures; is a vector of Gaussian error. φ0 is a vector of constants. Ht denotes conditional variance–covariance matrix; C is a lower triangular matrix of intercept coefficients. The elements of square matrix A measure the effects of shocks or 'news' on the conditional variances. The matrix G shows the degree of volatility persistence in conditional volatility. The diagonal parameter of matrix A measures the effects of own past shocks, that is, own ARCH effect, whereas the diagonal parameter of matrix G measures the own GARCH effect. The off-diagonal elements of matrices A and G measure the cross-market effects of shock and volatility.

Estimation results from J–J cointegration test are reported in Table 6.

Table 6. Johansen–Juselius cointegration analysis

The λtrace statistic rejects the null hypothesis of no cointegrating vectors (r = 0) at 5% level of significance and accepts the alternative hypothesis of more than zero cointegrating vectors. Again it accepts the null hypothesis of r ≤ 0 cointegrating vector against the alternative hypothesis of more than one cointegrating vector (r > 1). Similarly, λmax rejects the null hypothesis of no cointegrating vectors (r = 0) at 5% level of significance and accepts the alternative hypothesis of one cointegrating vector (r = 1). Again λmax test is calculated to test the null hypothesis of one cointegrating vector (r = 1) against the alternative of two cointegrating vectors. Maximum eigenvalue test statistic indicates that the null hypothesis cannot be rejected as the calculated maximal eigenvalue is less than the critical value at 5% level. Hence, both the trace and the maximum eigenvalue statistics suggest that there is only one cointegrating relationship or single common stochastic trend indicating both the markets move together in a long-run equilibrium path.

Following the Granger representation theorem, VECM is estimated and reported in Table 7.

Table 7. Vector error correction model estimates

The coefficient of the error-correction term αf is statistically significant and positive, implying that the short-run deviations of the futures prices would be adjusted in an upward direction towards the long-run equilibrium level. But the coefficient of error-correction term αs is statistically insignificant. This implies that the spot index is unresponsive to the previous period's equilibrium error; only futures prices respond to correct a shock in the system to reach the long-run equilibrium. In addition, the coefficients of lags of changes in futures prices are statistically significant, whereas the coefficients of lags of changes in spot are insignificant. It implies that futures prices lead spot prices and not vice versa. The futures market contributes largely to the price discovery, suggesting that news are first aggregated in the prices of the futures and then transferred to the stock market.

Table 8 presents the results from Granger causality test.

Table 8. Results of Granger causality test based on VAR

The null hypothesis that spot index return does not Granger cause futures index cannot be rejected as the F-statistic is statistically insignificant. However, the null hypothesis that futures does not Granger cause spot index could be rejected. Hence there is unidirectional causality from futures to spot returns.

Table 9 presents the estimates of the bivariate BEKK–GARCH (1, 1) model.

Table 9. Maximum likelihood estimates of BEKK–GARCH (1, 1)

The coefficient aff is statistically significant indicating that the past futures returns shock affects current futures returns volatility. Similarly, the statistically significant coefficient ass indicates that the past spot returns shock affects current spot returns volatility. We find evidence of bidirectional shock transmissions between spot and futures market as the pair of off-diagonal parameters afs and asf are both statistically significant. However, spot market volatility responds more to lagged shocks in the futures market. News about shocks in futures market affects the volatility of spot, and past shocks of the spot market also affects the volatility of futures market. There is bidirectional volatility linkages between spot and futures markets as both the coefficients gfs and gsf are statistically significant. However, there is pronounced spillover effect of a previous shock and volatility from the futures market to spot market. The statistically insignificant LB-Q statistics and ARCH-LM test confirm that the estimated model is well specified.

This study examines the intraday price discovery and volatility transmission between Nifty futures and spot. We find evidence that both the prices move together in a long-run equilibrium path, suggesting a violation of weak form of market efficiency. There is unidirectional causality from futures to spot market. In addition, the study finds bidirectional volatility transmission. However, there is pronounced spillover effect of a previous shock and volatility from the futures market to spot market. Hence, we conclude futures market performs the price discovery function.

The findings have significant implications for traders in implementing hedging and arbitrage trading strategies, for portfolio managers in managing risk, and also for policymakers in assessing market stability. Existence of cointegration suggests that although both markets may be in disequilibrium during the short-run, such deviations are very quickly corrected through the arbitrage process. The implementation of arbitrage trading strategies must take into account the lead–lag relationship between spot and futures markets. It gives information to traders regarding the prospective direction of price movement in the spot market, which in turn directs the trader's future actions. Mispricing of futures prices provides very short-run riskless profit-making opportunity to the arbitrageurs, and their actions will result in correcting the magnitude of basis. A better understanding of the return and volatility dynamics can improve risk management and budget-planning decisions. Because a shock tends to move futures volatility ahead of spot volatility, investors averse to volatility changes can use the volatility signal of the futures market to adjust their portfolios in the spot market for risk management.