Description
The documentation about Futures as a tool of price discovery.
Financial Time Series
Futures as a tool of price discovery
Table of Contents
Abstract ......................................................................................................................................................... 3 1. 2. 3. 4. Introduction .......................................................................................................................................... 3 Literature Review .................................................................................................................................. 4 Methodology......................................................................................................................................... 5 Result and Analysis ............................................................................................................................... 7 4.1 Test for Stationarity ............................................................................................................................ 7 4.2 Test for co-integration ........................................................................................................................ 9 4.3 Test for Causality................................................................................................................................. 9 4.3.1 Lag Identification........................................................................................................................ 10 4.3.2 Granger causality test ................................................................................................................ 10 5. 6. Conclusion ........................................................................................................................................... 11 References .......................................................................................................................................... 11
Futures as a tool of price discovery.
Page 2
Abstract
This paper examines whether prices in the futures market help to determine the prices in spot market and vice-versa. The paper examines the causal relationship between Nifty spot index & index futures market in India. The empirical analysis was conducted for the daily data series from November, 2004 to November, 2009 for Nifty. The objectives of the study are examined by employing stationarity, cointegration, VAR (vector autoregression) and Granger Causality tests. The results reveal that there is no long-run relationship between Nifty spot & Nifty futures prices. It can, therefore, be concluded that futures markets are not playing the leading role through price discovery process in India and said to be informationally inefficient.
1. Introduction
The relationship between spot and futures markets in price discovery has been an important area of research for regulators, academicians and practitioners for number of reasons like market efficiency, volatility and arbitrage. In perfectly efficient markets, profitable arbitrage does not exist as markets adjust instantaneously to the new information. There is no arbitrage between spot and futures market in the perfectly efficient markets as informed investors are indifferent between trading in either market as new information is reflected in both simultaneously. However, if one market reacts faster than the other due to transaction costs or market microstructure effects, a lead lag relation in returns is observed. Derivatives trading have been introduced in India to make the market more efficient and for better price discovery. The two main functions of derivatives are hedging and price discovery. Price discovery involves the process of determining the value of the asset through the interaction between buyers and sellers. Price discovery through derivatives is beneficial to both market participants and regulators. The market that provides greater liquidity, lower transaction costs, and less restriction, is likely to play a more important role in price discovery. In futures market there is more liquidity and lower transaction cost and would be forerunner of the cash market as far as information discounting is concerned. By virtue of linkages between derivatives and spot market the information is expected to flow from one market to another. The movement in future prices should contain useful information about subsequent spot prices beyond what is already embedded in the current spot price.
Futures as a tool of price discovery. Page 3
In this paper we intend to measure the price discovery between the spot and futures market. This paper is also an attempt to examine as to which market reacts faster or if there is equal feedback between the futures and the underlying markets. This paper is segmented into five sections. Section two followed by introductory section one, reviews the existing literatures. Some useful and relevant past studies on the topic are referred and summarized in this section. Methodology for the study, econometric techniques, data and time period are explained in section three. Section four deals with the results, analysis and interpretation of empirical results; while section five deals with the findings and conclusion.
2. Literature Review
There have been numerous studies undertaken to assess the price discovery efficiency of futures market, namely, commodity futures, currency futures, equity futures etc. Campbell and Diebold (2004), Zhong, Darratt and Otero (2004) and Isabel and Gilbert (2004) examined the price discovery efficiency of commodity futures market in diverse countries like United States of America, United Kingdom, Malaysia, and México. Each of these studies established the fact that a strong causal relationship exists between future and spot prices. Stoll and Whaley (1990) investigated causal relationships between spot and futures markets using intraday data for both S&P 500 and the Major Market Index (MMI). There was a feedback between spot and futures, but the futures lead was stronger than the cash Index lead. Wahab and Lashgari (1993) used daily data and co-integration analysis to examine the temporal causal linkage between Index and stock Index futures prices for both the S&P 500 and the FTSE 100 Index for the period 1988 to 1992. They found that although feedback exists between spot and futures markets for both the S&P 500 and the FTSE 100 indices, the spot to futures lead appears to be more pronounced across days relative to the futures to spot lead. Booth, So, and Tse (1999) and Upper and Werner (2002) conducted studies in Germany and established strong confirmation of information traveling from the futures market to the spot market.
Futures as a tool of price discovery.
Page 4
Susan Thomas and Kiran Karande (2001) analyzed price discovery in India’s castor seed market across multiple spot and futures market. The study concluded that the spot and futures markets in the production centre are the first to impound information about the harvest. Raju and Karande (2003) investigated the causal relationship between equity futures and cash market on National Stock Exchange by using the econometric techniques, which involved a study period of June 2000 to October 2002. They concluded that the futures market and not the spot market respond to deviations from equilibrium. They found mixed results regarding the causality relationship between two markets, one of the reasons contributing to such confusing results might be the short time period of two years considered for the study. Kailash Chandra Pradhan and Dr. K Sham Bhat investigated the relationship between the spot and futures on individual securities. The daily closing data is taken from November 9, 2001 to September 29, 2005 for the analysis. The results revealed that futures lead the spot in case of 9 individual securities, spot leads the futures in case of 7 individual securities and the feedback relation takes place between two markets in case of 9 individual securities. Sah & Kumar (2006) examined whether the futures trading in India is performing its primary role of price discovery. They employed co-integration and error correction method using data from June 12, 2000 through March 31, 2005. The result established that a long run association exists between Nifty spot and Nifty futures prices. Further the error correction model leads to the conclusion that a feedback mechanism is present between Nifty spot and Nifty futures. Madhusudan Karmakar (2009) investigated the lead-lag relationship in the first moment as well as the second moment between the S&P CNX Nifty and the Nifty future from June 2000 to March 2007. The study results show that the Nifty futures dominate the cash market in price discovery.
3. Methodology
Price Discovery This research considers Nifty Futures and Spot from Nov, 2004 to Nov, 2009 and gold futures from Jan, 2009 to Nov, 2009 to study the price discovery and effectiveness of futures as a tool
Futures as a tool of price discovery. Page 5
for risk management. Co-integration, Vector autoregression and Granger causality test were employed to examine the lead-lag relationship between the Nifty index & Nifty futures index and gold and gold futures prices of India. Augmented Dickey-Fuller (1979) test was employed to verify the stationarity of the data series. Stationarity: A data series is said to be stationary if its mean and variance are constant (nonchanging) over time and the value of covariance between two time periods depends only on the distance or lag between the two time periods and not on the actual time at which the covariance is computed. A stationary series is time independent. The stationarity of data is tested using Augmented Dickey Fuller (ADF) test. Cointegration: In general, combination of two non stationary series Xt and Yt is also non stationary. However, if there exists a combination of Xt and Yt such that it is stationary, then we can say that Xt and Yt are co-integrated. Two co-integrated series will not drift apart overtime e.g. spot and futures. Regression technique assumes data to be stationary over any time period. If mean value of time series keeps changing with time, then estimated coefficients may not provide unbiased estimates. Hence, it is necessary to test the stationarity of the time series. The interpretation of co-integration is that if two or more variables are linked to form an equilibrium relationship in the long-run, even though the series themselves in the short run may deviate from the equilibrium, they will move closer together in the long run equilibrium. Therefore, co-integration can establish whether there exists a stable long-run relationship between Nifty futures and the underlying Nifty Index and gold futures and the underlying gold commodity Index in India. Long run equilibrium relationship exists between the two markets as result of price changes in market influencing price changes in the other market. The long run equilibrium relationship is given byFt – ?0 – ?1St = et Where Ft and St are cash and future prices at time t, ?0 and ?1 are parameters and et is the error term. If Ft and St are non stationary but et is stationary, then Ft and St are co-integrated and equilibrium exists between Ft and St. Order of integration is determined by performing unit root
Futures as a tool of price discovery. Page 6
test on each of the time series. If each series is non stationary in the levels, but the first differences and deviations et, are stationary, the prices are co-integrated of order (1,1), denoted CI(1,1) with ?1 as the co-integrating coefficient. To test for cointegration, the residuals of regression of the spot price and futures price are examined. Two new variables for log of the spot series (lspot) and the log of the futures series (lfutures) are created. Regression is run using the following equation: LSPOT C LFUTURES Performing ADF test on the residual series of the above regression series would determine whether the data is cointegrated. Once the cointegration is established, lead lag relationships for the spot (rlspot) and futures (rlfutures) is examined. The number of lags of future and spot affecting the causal relationship is determined using vector autoregression test while the causal relationship is determined using Granger causality test. Optimum number of lags of spot and future returns is determined by running unrestricted VAR for different lag length and observing Akaike Information Criterion (AIC) values. The lag length corresponding to least AIC value is the optimum lag length. The lead lag relationship is determined by running Granger Causality test using the lag length derived from unrestricted VAR test. The results of this test will determine the direction of causal relationship.
4. Result and Analysis
4.1 Test for Stationarity
This study uses Augmented Dickey-Fuller unit root test to check the stationarity of the series. The results of unit root tests for Nifty futures and Nifty Index are tabulated below: Unit Root Test for 1 month Nifty Index at level 0 Null Hypothesis: LSPOT has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level
Futures as a tool of price discovery.
Prob. 0.4117
Page 7
-1.738108 -3.435352
5% level 10% level
-2.863637 -2.567936
Unit Root Test for 1 month Nifty Index at Difference 1 Null Hypothesis: D(LSPOT) has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -33.31116 -3.435356 -2.863638 -2.567937 Prob. 0.0000
Unit Root Test for 1 month Nifty futures at level 0 Null Hypothesis: LFUTURE has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -1.756719 -3.435352 -2.863637 -2.567936 Prob. 0.4024
Unit Root Test for 1 month Nifty futures at Difference 1 Null Hypothesis: D(LFUTURE) has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -34.94344 -3.435356 -2.863638 -2.567937 Prob. 0.0000
The above results indicate that Nifty futures and Nifty Index prices are not stationary at their Null Hypothesis: STRATRESIDS has a unit root levels but their returns are stationary i.e. their first differences are stationary. Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=12) t-Statistic Augmented Dickey-Fuller test statistic Futures as a tool of price discovery. 1% level Test critical values: 5% level 10% level -10.18952 -3.435356 -2.863638 -2.567937 Prob.* 0.0000
Page 8
4.2 Test for co-integration
First regression of spot price on future price was performed to calculate the values of residuals. These residuals were assigned the name as STRATRESIDS. A plot of residuals below shows that it has been stationary over a period of five years from 2005 to 2009.
8.8 8.4 .03 8.0 .02 .01 .00 -.01 -.02 2005 2006 Residual 2007 Actual 2008 2009 Fitted 7.6 7.2
However, unit root test has been performed on residuals at level 0 to confirm the observation. The results of unit root test at level 0 on residuals are tabulated below: Null Hypothesis: STRATRESIDS has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -10.18952 -3.435356 -2.863638 -2.567937 Prob. 0.0000
Since, the probability is 0.0000; we can reject the null hypothesis and conclude that residual series is stationary. This confirms that Nifty Index prices and Nifty futures prices are cointegrated.
4.3 Test for Causality
This test includes calculation of number of lags for Nifty Index (RLSPOT) and future returns (RLFUTURE) and Granger causality test on both the variables.
Futures as a tool of price discovery. Page 9
4.3.1 Lag Identification
Akaike Information Criteria (AIC) has been used to calculate the number of lags required for further tests. It has been done through performing Vector Auto Regression (VAR) test on different number of lags of RLSPOT and RLFUTURE each time and examining the AIC values. The results are tabulated below: Lag 1 2 3 4 RLFUTURE -4.91477 -4.91161 -4.90796 -4.90496 RLSPOT -5.04988 -5.04652 -5.04278 -5.03922
Since, the AIC value is minimum for lag 1; we used only one lag of RLSPOT and RLFUTURE to identify the type of relationship through Granger causality test.
4.3.2 Granger causality test
This test treats both the variables as dependent variable one at each time and examines the effect of another variable on it. The result of Granger causality test on returns from Nifty Index and Nifty futures are shown below: VAR Granger Causality/Block Exogeneity Wald Tests Dependent variable: RLSPOT Excluded RLFUTURE All Chi-sq 1.469949 1.469949 df 1 1 Prob. 0.2254 0.2254
Dependent variable: RLFUTURE Excluded RLSPOT All Chi-sq 0.274260 0.274260 df 1 1 Prob. 0.6005 0.6005
Futures as a tool of price discovery.
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Results indicate that none of the variables “Granger causes” other variable at 95% level of confidence as p-value is more than 0.05. We can conclude from this that Nifty future price does not help in price discovery of Nifty Index price or vice versa.
5. Conclusion
The study employs co-integration technique, followed by the Granger causality test, to examine the causal relationship between the NSE spot & futures markets in India. The empirical analysis was conducted for the daily data series from Nov, 2004 to Nov, 2009 for Nifty futures. The study reveals that there exists a long-run relationship between the Nifty spot & Nifty futures prices. However, the causality test does not confirm the type of relationship between two variables. The study result does not give any indication about information flow from futures to spot market or vice versa.
6. References
? Stoll H R and Whaley R E (1990), “The Dynamics of Stock Index and Stock Index Futures Returns”, Journal of Financial and Quantitative Analysis, Vol. 25, No. 4, pp. 441-468. ? Wahab, M. and Lashgari, M. (1993), “Price Dynamics and Error Correction in Stock Index and Stock Index Futures Markets: A Cointegration Approach”, The Journal of Futures Markets, Vol. 13, No. 7, pp. 711-742. ? ? Booth, C.G., So, R.W. and Tse, Y. (1999), “Price Discovery in the German Equity Index Derivatives Markets”, Journal of Futures Markets, Vol.19, No.6, pp.619- 643. Raju, M. T. and Karande, K. (2003), “Price Discovery and Volatility on NSE Futures Market”, SEBI Working Paper Series No.7, Securities and Exchange Board of India (SEBI), Mumbai. ? ? Sah, A.N. and Kumar, A. (2006), “Price Discovery in Cash and Futures Market: The Case of S&P Nifty and Nifty Futures”, The ICFAI Journal of Applied Finance, pp. 55-63. Pradhan K C, Bhatt Sham K., “Price Discovery and Causality in the NSE Futures Market”,.
Futures as a tool of price discovery.
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?
Karmakar Madhusudan (2009), “Price Discoveries and Volatility Spillovers in S&P CNX Nifty Future and its Underlying Index CNX Nifty”, Vikalpa, Vol. 34, No.2, Apr-Jun 2009.
Futures as a tool of price discovery.
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doc_643329097.docx
The documentation about Futures as a tool of price discovery.
Financial Time Series
Futures as a tool of price discovery
Table of Contents
Abstract ......................................................................................................................................................... 3 1. 2. 3. 4. Introduction .......................................................................................................................................... 3 Literature Review .................................................................................................................................. 4 Methodology......................................................................................................................................... 5 Result and Analysis ............................................................................................................................... 7 4.1 Test for Stationarity ............................................................................................................................ 7 4.2 Test for co-integration ........................................................................................................................ 9 4.3 Test for Causality................................................................................................................................. 9 4.3.1 Lag Identification........................................................................................................................ 10 4.3.2 Granger causality test ................................................................................................................ 10 5. 6. Conclusion ........................................................................................................................................... 11 References .......................................................................................................................................... 11
Futures as a tool of price discovery.
Page 2
Abstract
This paper examines whether prices in the futures market help to determine the prices in spot market and vice-versa. The paper examines the causal relationship between Nifty spot index & index futures market in India. The empirical analysis was conducted for the daily data series from November, 2004 to November, 2009 for Nifty. The objectives of the study are examined by employing stationarity, cointegration, VAR (vector autoregression) and Granger Causality tests. The results reveal that there is no long-run relationship between Nifty spot & Nifty futures prices. It can, therefore, be concluded that futures markets are not playing the leading role through price discovery process in India and said to be informationally inefficient.
1. Introduction
The relationship between spot and futures markets in price discovery has been an important area of research for regulators, academicians and practitioners for number of reasons like market efficiency, volatility and arbitrage. In perfectly efficient markets, profitable arbitrage does not exist as markets adjust instantaneously to the new information. There is no arbitrage between spot and futures market in the perfectly efficient markets as informed investors are indifferent between trading in either market as new information is reflected in both simultaneously. However, if one market reacts faster than the other due to transaction costs or market microstructure effects, a lead lag relation in returns is observed. Derivatives trading have been introduced in India to make the market more efficient and for better price discovery. The two main functions of derivatives are hedging and price discovery. Price discovery involves the process of determining the value of the asset through the interaction between buyers and sellers. Price discovery through derivatives is beneficial to both market participants and regulators. The market that provides greater liquidity, lower transaction costs, and less restriction, is likely to play a more important role in price discovery. In futures market there is more liquidity and lower transaction cost and would be forerunner of the cash market as far as information discounting is concerned. By virtue of linkages between derivatives and spot market the information is expected to flow from one market to another. The movement in future prices should contain useful information about subsequent spot prices beyond what is already embedded in the current spot price.
Futures as a tool of price discovery. Page 3
In this paper we intend to measure the price discovery between the spot and futures market. This paper is also an attempt to examine as to which market reacts faster or if there is equal feedback between the futures and the underlying markets. This paper is segmented into five sections. Section two followed by introductory section one, reviews the existing literatures. Some useful and relevant past studies on the topic are referred and summarized in this section. Methodology for the study, econometric techniques, data and time period are explained in section three. Section four deals with the results, analysis and interpretation of empirical results; while section five deals with the findings and conclusion.
2. Literature Review
There have been numerous studies undertaken to assess the price discovery efficiency of futures market, namely, commodity futures, currency futures, equity futures etc. Campbell and Diebold (2004), Zhong, Darratt and Otero (2004) and Isabel and Gilbert (2004) examined the price discovery efficiency of commodity futures market in diverse countries like United States of America, United Kingdom, Malaysia, and México. Each of these studies established the fact that a strong causal relationship exists between future and spot prices. Stoll and Whaley (1990) investigated causal relationships between spot and futures markets using intraday data for both S&P 500 and the Major Market Index (MMI). There was a feedback between spot and futures, but the futures lead was stronger than the cash Index lead. Wahab and Lashgari (1993) used daily data and co-integration analysis to examine the temporal causal linkage between Index and stock Index futures prices for both the S&P 500 and the FTSE 100 Index for the period 1988 to 1992. They found that although feedback exists between spot and futures markets for both the S&P 500 and the FTSE 100 indices, the spot to futures lead appears to be more pronounced across days relative to the futures to spot lead. Booth, So, and Tse (1999) and Upper and Werner (2002) conducted studies in Germany and established strong confirmation of information traveling from the futures market to the spot market.
Futures as a tool of price discovery.
Page 4
Susan Thomas and Kiran Karande (2001) analyzed price discovery in India’s castor seed market across multiple spot and futures market. The study concluded that the spot and futures markets in the production centre are the first to impound information about the harvest. Raju and Karande (2003) investigated the causal relationship between equity futures and cash market on National Stock Exchange by using the econometric techniques, which involved a study period of June 2000 to October 2002. They concluded that the futures market and not the spot market respond to deviations from equilibrium. They found mixed results regarding the causality relationship between two markets, one of the reasons contributing to such confusing results might be the short time period of two years considered for the study. Kailash Chandra Pradhan and Dr. K Sham Bhat investigated the relationship between the spot and futures on individual securities. The daily closing data is taken from November 9, 2001 to September 29, 2005 for the analysis. The results revealed that futures lead the spot in case of 9 individual securities, spot leads the futures in case of 7 individual securities and the feedback relation takes place between two markets in case of 9 individual securities. Sah & Kumar (2006) examined whether the futures trading in India is performing its primary role of price discovery. They employed co-integration and error correction method using data from June 12, 2000 through March 31, 2005. The result established that a long run association exists between Nifty spot and Nifty futures prices. Further the error correction model leads to the conclusion that a feedback mechanism is present between Nifty spot and Nifty futures. Madhusudan Karmakar (2009) investigated the lead-lag relationship in the first moment as well as the second moment between the S&P CNX Nifty and the Nifty future from June 2000 to March 2007. The study results show that the Nifty futures dominate the cash market in price discovery.
3. Methodology
Price Discovery This research considers Nifty Futures and Spot from Nov, 2004 to Nov, 2009 and gold futures from Jan, 2009 to Nov, 2009 to study the price discovery and effectiveness of futures as a tool
Futures as a tool of price discovery. Page 5
for risk management. Co-integration, Vector autoregression and Granger causality test were employed to examine the lead-lag relationship between the Nifty index & Nifty futures index and gold and gold futures prices of India. Augmented Dickey-Fuller (1979) test was employed to verify the stationarity of the data series. Stationarity: A data series is said to be stationary if its mean and variance are constant (nonchanging) over time and the value of covariance between two time periods depends only on the distance or lag between the two time periods and not on the actual time at which the covariance is computed. A stationary series is time independent. The stationarity of data is tested using Augmented Dickey Fuller (ADF) test. Cointegration: In general, combination of two non stationary series Xt and Yt is also non stationary. However, if there exists a combination of Xt and Yt such that it is stationary, then we can say that Xt and Yt are co-integrated. Two co-integrated series will not drift apart overtime e.g. spot and futures. Regression technique assumes data to be stationary over any time period. If mean value of time series keeps changing with time, then estimated coefficients may not provide unbiased estimates. Hence, it is necessary to test the stationarity of the time series. The interpretation of co-integration is that if two or more variables are linked to form an equilibrium relationship in the long-run, even though the series themselves in the short run may deviate from the equilibrium, they will move closer together in the long run equilibrium. Therefore, co-integration can establish whether there exists a stable long-run relationship between Nifty futures and the underlying Nifty Index and gold futures and the underlying gold commodity Index in India. Long run equilibrium relationship exists between the two markets as result of price changes in market influencing price changes in the other market. The long run equilibrium relationship is given byFt – ?0 – ?1St = et Where Ft and St are cash and future prices at time t, ?0 and ?1 are parameters and et is the error term. If Ft and St are non stationary but et is stationary, then Ft and St are co-integrated and equilibrium exists between Ft and St. Order of integration is determined by performing unit root
Futures as a tool of price discovery. Page 6
test on each of the time series. If each series is non stationary in the levels, but the first differences and deviations et, are stationary, the prices are co-integrated of order (1,1), denoted CI(1,1) with ?1 as the co-integrating coefficient. To test for cointegration, the residuals of regression of the spot price and futures price are examined. Two new variables for log of the spot series (lspot) and the log of the futures series (lfutures) are created. Regression is run using the following equation: LSPOT C LFUTURES Performing ADF test on the residual series of the above regression series would determine whether the data is cointegrated. Once the cointegration is established, lead lag relationships for the spot (rlspot) and futures (rlfutures) is examined. The number of lags of future and spot affecting the causal relationship is determined using vector autoregression test while the causal relationship is determined using Granger causality test. Optimum number of lags of spot and future returns is determined by running unrestricted VAR for different lag length and observing Akaike Information Criterion (AIC) values. The lag length corresponding to least AIC value is the optimum lag length. The lead lag relationship is determined by running Granger Causality test using the lag length derived from unrestricted VAR test. The results of this test will determine the direction of causal relationship.
4. Result and Analysis
4.1 Test for Stationarity
This study uses Augmented Dickey-Fuller unit root test to check the stationarity of the series. The results of unit root tests for Nifty futures and Nifty Index are tabulated below: Unit Root Test for 1 month Nifty Index at level 0 Null Hypothesis: LSPOT has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level
Futures as a tool of price discovery.
Prob. 0.4117
Page 7
-1.738108 -3.435352
5% level 10% level
-2.863637 -2.567936
Unit Root Test for 1 month Nifty Index at Difference 1 Null Hypothesis: D(LSPOT) has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -33.31116 -3.435356 -2.863638 -2.567937 Prob. 0.0000
Unit Root Test for 1 month Nifty futures at level 0 Null Hypothesis: LFUTURE has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -1.756719 -3.435352 -2.863637 -2.567936 Prob. 0.4024
Unit Root Test for 1 month Nifty futures at Difference 1 Null Hypothesis: D(LFUTURE) has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -34.94344 -3.435356 -2.863638 -2.567937 Prob. 0.0000
The above results indicate that Nifty futures and Nifty Index prices are not stationary at their Null Hypothesis: STRATRESIDS has a unit root levels but their returns are stationary i.e. their first differences are stationary. Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=12) t-Statistic Augmented Dickey-Fuller test statistic Futures as a tool of price discovery. 1% level Test critical values: 5% level 10% level -10.18952 -3.435356 -2.863638 -2.567937 Prob.* 0.0000
Page 8
4.2 Test for co-integration
First regression of spot price on future price was performed to calculate the values of residuals. These residuals were assigned the name as STRATRESIDS. A plot of residuals below shows that it has been stationary over a period of five years from 2005 to 2009.
8.8 8.4 .03 8.0 .02 .01 .00 -.01 -.02 2005 2006 Residual 2007 Actual 2008 2009 Fitted 7.6 7.2
However, unit root test has been performed on residuals at level 0 to confirm the observation. The results of unit root test at level 0 on residuals are tabulated below: Null Hypothesis: STRATRESIDS has a unit root t-Statistic Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -10.18952 -3.435356 -2.863638 -2.567937 Prob. 0.0000
Since, the probability is 0.0000; we can reject the null hypothesis and conclude that residual series is stationary. This confirms that Nifty Index prices and Nifty futures prices are cointegrated.
4.3 Test for Causality
This test includes calculation of number of lags for Nifty Index (RLSPOT) and future returns (RLFUTURE) and Granger causality test on both the variables.
Futures as a tool of price discovery. Page 9
4.3.1 Lag Identification
Akaike Information Criteria (AIC) has been used to calculate the number of lags required for further tests. It has been done through performing Vector Auto Regression (VAR) test on different number of lags of RLSPOT and RLFUTURE each time and examining the AIC values. The results are tabulated below: Lag 1 2 3 4 RLFUTURE -4.91477 -4.91161 -4.90796 -4.90496 RLSPOT -5.04988 -5.04652 -5.04278 -5.03922
Since, the AIC value is minimum for lag 1; we used only one lag of RLSPOT and RLFUTURE to identify the type of relationship through Granger causality test.
4.3.2 Granger causality test
This test treats both the variables as dependent variable one at each time and examines the effect of another variable on it. The result of Granger causality test on returns from Nifty Index and Nifty futures are shown below: VAR Granger Causality/Block Exogeneity Wald Tests Dependent variable: RLSPOT Excluded RLFUTURE All Chi-sq 1.469949 1.469949 df 1 1 Prob. 0.2254 0.2254
Dependent variable: RLFUTURE Excluded RLSPOT All Chi-sq 0.274260 0.274260 df 1 1 Prob. 0.6005 0.6005
Futures as a tool of price discovery.
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Results indicate that none of the variables “Granger causes” other variable at 95% level of confidence as p-value is more than 0.05. We can conclude from this that Nifty future price does not help in price discovery of Nifty Index price or vice versa.
5. Conclusion
The study employs co-integration technique, followed by the Granger causality test, to examine the causal relationship between the NSE spot & futures markets in India. The empirical analysis was conducted for the daily data series from Nov, 2004 to Nov, 2009 for Nifty futures. The study reveals that there exists a long-run relationship between the Nifty spot & Nifty futures prices. However, the causality test does not confirm the type of relationship between two variables. The study result does not give any indication about information flow from futures to spot market or vice versa.
6. References
? Stoll H R and Whaley R E (1990), “The Dynamics of Stock Index and Stock Index Futures Returns”, Journal of Financial and Quantitative Analysis, Vol. 25, No. 4, pp. 441-468. ? Wahab, M. and Lashgari, M. (1993), “Price Dynamics and Error Correction in Stock Index and Stock Index Futures Markets: A Cointegration Approach”, The Journal of Futures Markets, Vol. 13, No. 7, pp. 711-742. ? ? Booth, C.G., So, R.W. and Tse, Y. (1999), “Price Discovery in the German Equity Index Derivatives Markets”, Journal of Futures Markets, Vol.19, No.6, pp.619- 643. Raju, M. T. and Karande, K. (2003), “Price Discovery and Volatility on NSE Futures Market”, SEBI Working Paper Series No.7, Securities and Exchange Board of India (SEBI), Mumbai. ? ? Sah, A.N. and Kumar, A. (2006), “Price Discovery in Cash and Futures Market: The Case of S&P Nifty and Nifty Futures”, The ICFAI Journal of Applied Finance, pp. 55-63. Pradhan K C, Bhatt Sham K., “Price Discovery and Causality in the NSE Futures Market”,.
Futures as a tool of price discovery.
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Karmakar Madhusudan (2009), “Price Discoveries and Volatility Spillovers in S&P CNX Nifty Future and its Underlying Index CNX Nifty”, Vikalpa, Vol. 34, No.2, Apr-Jun 2009.
Futures as a tool of price discovery.
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