Description
It explains A report on Derivatives as a tool for price discovery and risk management
Derivative and Risk Management
Table of Contents
Abstract ......................................................................................................................................................... 3 1. 2. 3. Introduction .......................................................................................................................................... 3 Literature Review .................................................................................................................................. 4 Methodology......................................................................................................................................... 6 3.1 Price Discovery .................................................................................................................................... 6 3.2 Risk Management ............................................................................................................................... 7 4. Result and Analysis ............................................................................................................................... 8 4.1 Price Discovery .................................................................................................................................... 8 4.1.1 Nifty Futures ................................................................................................................................ 9 4.1.2 Gold futures ............................................................................................................................... 11 4.2 Risk Management using futures ....................................................................................................... 13 4.2.1 Nifty Futures .............................................................................................................................. 13 4.2.2 Gold Futures ............................................................................................................................... 14 5. 6. Conclusion ........................................................................................................................................... 15 References .......................................................................................................................................... 15
Derivatives as a tool of price discovery and risk management
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Abstract
This paper examines whether prices in the futures market help to determine the prices in spot market and vice-versa. This study also examines the effectiveness of futures as a tool of risk management. The paper examines the causal relationship between Nifty spot index & index futures and gold spot and gold futures market in India. The empirical analysis was conducted for the daily data series from November, 2004 to November, 2009 for nifty and Jan 2009 to Nov 2009 for gold futures. The objectives of the study are examined by employing Johansen’s cointegration test and vector error correction model (VECM).The effectiveness of futures market as risk management tool is measured by performing wilcoxon test of median on proportion of open interest as percentage of total intraday volume in futures market. The results reveal that there exists a long-run relationship between Nifty spot & Nifty futures prices and gold spot and future prices. Further, the results confirm the presence of a unidirectional relationship between the Nifty spot & Nifty futures and gold spot and future market prices in India. It can, therefore, be concluded that futures markets play the leading role through price discovery process in India and said to be informationally efficient and react more quickly to spot markets. The effectiveness of futures as risk management tool cannot be established as only less than 10% of the daily volume in nifty and gold futures is used for hedging purpose.
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.
Derivatives as a tool of price discovery and risk management Page 3
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 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. 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 is there equal feedback between the futures and the underlying markets. Also effectiveness of derivatives as risk management tool has been explored in this paper. This paper is segmented into five sections. Section two followed by introductory section one, reviews the existing literature. 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 is 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 exist 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.
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Wahab and Lashgari (1993) used daily data and cointegration 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 find 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. 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 three 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 leads 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 lead to the conclusion that a feedback mechanism is present between Nifty spot and Nifty futures.
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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
3.1 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 for risk management. Johansen (1988) cointegration and Error Correction Model (VECM) 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. Cointegration: In general combination of two non stationary series Xt and Yt is also non stationary. However, if there exist a combination of Xt and Yt such that it is stationary, then we can say that Xt and Yt are cointegrated. Two cointegrated series will not drift apart overtime example 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 cointegration 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, cointegration can establish whether there exist a stable long-run relationship between Nifty futures and the underlying Nifty and gold futures and the underlying gold commodity in India.
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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 by Ft – ?0 – ?1St = et where Ft and St are cash and future prices at time t, ?0 and ?1 are parameters et is the error term. If Ft and St are non stationary but et is stationary then Ft and St are cointegrated and equilibrium exist between Ft and St. Order of integration is determined by performing unit root 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 cointegrated of order (1,1), denoted CI(1,1) with ?1 as the cointegrating coefficient. The existence of cointegration implies that there exists causality between the spot and futures market prices which is represented by error correction model that includes last period’s equilibrium error as well as lagged values of the first differences of each variable. If spot and future prices are cointegrated then causality must exist in at least in one direction. The error correction can be written as Ft = ?0f + ?1f(Ft-1-St-1) + ?1fRf,t-1 + ?2fRf,t-2 + ?3fRs,t-1 + ?4fRs,t-2 +?ft St = ?0s + ?1s(Ft-1-St-1) + ?1sRs,t-1 + ?2sRs,t-2 + ?3sRf,t-1 + ?4sRf,t-2 +?st where Ft is Nifty futures returns and St is Nifty Index returns, ?1f and ?1s are the error correction terms and ?s represent short run effects. If “St causes Ft”, then changes in St should precede changes in Ft. ?s represent short run coefficients while ?s determines the speed of adjustment back to the longrun equilibrium. If the coefficient on the lagged Ft returns in the St equation are found to be significant, then turning points in Ft will lead turning points in St, that is, Ft causes St. Similarly, if the coefficient on the lagged St returns in the Ft equation are found to be significant, then turning points in St will lead turning points in Ft, that is, St causes Ft.
3.2 Risk Management
The number of hedgers present in the market will indicate whether futures are used as a tool for risk management or whether they are being used for speculation. In order to calculate the number of hedgers present in the market, change in open interest in nifty futures and gold futures as a
Derivatives as a tool of price discovery and risk management Page 7
percentage of total intraday volume is calculated. If the mean of this proportion is significant, then the number of hedgers present in the market can be approximated to the mean of this proportion. However, if the data is not is not normal, then Wilkoxon Signed Rank test is performed which is a test of median. If the result is significant then the median of the proportion can be approximated to the number of hedgers in the market. It can be said that certain percentage of daily volume is used for hedging purpose. The above methodology makes an assumption that all the speculators are day traders and hedgers are the ones who keep their positions open for more than one day.
4. Result and Analysis
4.1 Price Discovery
The results of unit root tests for Nifty futures and Nifty index, Mini nifty futures and mini nifty index and gold futures and gold spot price is tabulated below. Unit Root Test for 1 month nifty futures at level 0
Method ADF - Fisher Chi-square ADF - Choi Z-stat Statistic 2.37643 0.18563 Prob 0.6669 0.5736
Unit Root Test for 1 month nifty futures at Difference 1
Method ADF - Fisher Chi-square ADF - Choi Z-stat Statistic 251.917 -15.4349 Prob 0.0000 0.0000
Unit Root Test for 1 month gold futures at level 0
Method ADF - Fisher Chi-square ADF - Choi Z-stat Statistic 0.40705 1.85139 Prob 0.9819 0.9679
Unit Root Test for 1 month gold futures at Difference 1
Method ADF - Fisher Chi-square Statistic 166.294 Prob 0.0000 Page 8
Derivatives as a tool of price discovery and risk management
ADF - Choi Z-stat
-12.3923
0.0000
The above results indicate that Nifty futures and Nifty Index, mini nifty futures and nifty index, gold futures and gold spot prices are not stationary at their levels but their returns are stationary i.e. their first differences are stationary. The results of the cointegration tests for Nifty futures and Nifty index, Mini nifty futures and mini nifty index and gold futures and gold spot price are tabulated below. Before performing cointegration, akaike information test is performed which gives the best model for cointegration.
4.1.1 Nifty Futures Johansen Conintegration Test Akaike Information Criteria by Rank (rows) and Model (columns) Data Trend Rank or No. of CEs 0 1 2 None None Linear Linear Quadratic
No Intercept No Intercept No Intercept No Intercept Intercept Trend Trend Trend Trend Trend 18.7922 18.7922 18.7943 18.7943 18.7974 18.7254 18.7201* 18.7206 18.7215 18.7230 18.7314 18.7253 18.7253 18.7270 18.7270
Selected (0.05 level*) Number of Cointegrating Relations by Model. Null hypothesis states that both the markets are independent (not cointegrated).
Trend assumption: No deterministic trend Unrestricted Cointegration Rank Test (? Trace) Hypothesized No. of CE(s) None* At most 1 0.05 Critical Eigenvalue Trace Statistic Value 0.076945 103.7742 20.26184 0.002816 3.530689 9.164546
Prob.** 0.0000 0.4865
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level Unrestricted Cointegration Rank Test (? Maximum Eigenvalue) Hypothesized No. of CE(s) Max-Eigen Statistic 0.05 Critical Value
Eigenvalue
Prob.** Page 9
Derivatives as a tool of price discovery and risk management
None* At most 1
0.076945 0.002816
100.2435 3.530689
15.8921 9.164546
0.0000 0.4865
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values
According to above results null hypothesis is rejected. This means Nifty futures and Index are cointegrated of order 1. The result suggests that futures market price had positive relationship with spot market price, implying that there is a well-defined long-run relationship between the NSE futures and spot prices in India. Johansen’s ? max and ? trace statistics reveal the Nifty spot and Nifty futures prices stand in a long-run relationship between them, thus justifying the use of an ECM which establishes the causality between the two markets. The results of the price discovery regression are tabulated below.
Vector Error Correction Model Nifty Index Future return as dependent variable Coefficient Value Significance t-statistic ?1f ?1f ?2f ?3f ?4f -0.40528 0.093222 -0.01469 -0.05672 0.0374 0.18468 0.26825 0.23675 0.28149 0.24563 -2.19445 0.34751 -0.06205 -0.20148 0.15226
Variable F(t-1)-S(t-1) Rf,t-1 Rf,t-2 Rs,t-1 Rs,t-2
Variable F(t-1)-S(t-1) Rs,t-1 Rs,t-2 Rf,t-1 Rf,t-2
Nifty Index Spot return as dependent variable Coefficient Value Significance t-statistic ?1s -0.20072 0.0264 -1.15583 ?1s 0.395157 0.0156 1.56657 ?2s 0.049052 0.0389 0.22034 ?3s -0.34437 0.0375 -1.30104 ?4s -0.03222 0.0425 -0.13949
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As seen from the above table, the coefficient of error correction of Ft is not statistically significant. But the coefficient of error correction of St is significant at 5% significant level. This indicates that there exists a unidirectional causality and it runs from the futures to spot market price. This indicates information gets reflected first in the futures market and then flows to the spot market.
4.1.2 Gold futures Johansen Conintegration Test Akaike Information Criteria by Rank (rows) and Model (columns) Data Trend Rank or No. of CEs 0 1 2 None No Intercept No Trend 25.91404 25.59903 25.62918 None Intercept No Trend 25.91404 25.60464 25.64780 Linear Linear Quadratic
Intercept Intercept Intercept No Trend Trend Trend 25.91642 25.91642 25.93649 25.59553* 25.60718 25.61423 25.64780 25.65631 25.65631
Selected (0.05 level*) Number of Cointegrating Relations by Model
Null hypothesis states that both the markets are independent (not cointegrated).
Unrestricted Cointegration Rank Test (? Trace) Hypothesized No. of CE(s) None* At most 1 0.05 Critical Value 15.49471 3.841466
Eigenvalue 0.311460 1.47E-05
Trace Statistic 57.09909 0.002253
Prob.** 0.0000 0.9602
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level Unrestricted Cointegration Rank Test (? Maximum Eigenvalue) Hypothesized No. of CE(s) None* At most 1 Max-Eigen Statistic 57.09683 0.002253 0.05 Critical Value 14.26460 3.841466
Eigenvalue 0.311460 1.47E-05
Prob.** 0.0000 0.9602
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Derivatives as a tool of price discovery and risk management Page 11
According to above results null hypothesis is rejected. This means gold futures and spot are cointegrated of order 1. The result suggests that futures market price had positive relationship with spot market price, implying that there is a well-defined long-run relationship between the gold futures and spot prices in India. Johansen’s ? max and ? trace statistics reveal the Gold spot prices and gold futures prices stand in a long-run relationship between them, thus justifying the use of an ECM which establishes the causality between the two markets. The results of the price discovery regression are tabulated below.
Vector Error Correction Model Nifty Index Future return as dependent variable Coefficient Value Significance ?1f -0.99307 0.27408 ?1f 0.004354 0.21806 ?2f 0.062572 0.13850 ?3f -0.14155 0.22713 ?4f -0.19862 0.15224 Nifty Index Spot return as dependent variable Coefficient Value Significance ?1s 0.035560 0.0381 ?1s -0.05891 0.0158 ?2s 0.024455 0.0294 ?3s -0.10509 0.0463 ?4s -0.1749 0.0689
Variable F(t-1)-S(t-1) Rf,t-1 Rf,t-2 Rs,t-1 Rs,t-2
t-statistic -3.62332 0.01997 0.45180 -0.62322 -1.30468
Variable F(t-1)-S(t-1) Rs,t-1 Rs,t-2 Rf,t-1 Rf,t-2
t-statistic 0.10164 -0.21162 0.13833 -0.36245 -0.90002
As seen from the above table, the coefficient of error correction of Ft is not statistically significant. But the coefficient of error correction of St is significant at 5% significant level. This indicates that there exists a unidirectional causality and it runs from the futures to spot market price. This indicates information gets reflected first in the futures market and then flows to the spot market.
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Similar results were obtained for mini nifty which showed unidirectional causality from future to spot.
4.2 Risk Management using futures
Change in open interest as a daily volume is used to find whether futures are used as means of risk management or they are used for speculating purpose.
4.2.1 Nifty Futures Mean 95% Confidence Interval for mean Median Lower Bound Upper Bound Statistic 0.09401283 0.08737898 0.10064668 0.05419377
Test for normality
Tests of Normality Kolmogorov-Smirnova Variable Proportion Statistic 0.216190156 df 1253 Sig. 0.0000 Statistic 0.690504
Shapiro-Wilk df 1253 Sig. 0.0000
When number of observations is more than 50, Kolmogorov-Smirnova test is considered. Here null hypothesis is rejected at above 99% confidence level. This indicates data are not normal. Hence Wilcoxon test of median is performed. The null hypothesis states that median is 0.054193. Wilcoxon Signed Rank Test: Proportion
Test of median = 0.05420 versus median not = 0.05420 Variable Proportion Wilcoxon N N for Test Statistic 1253 1253 463313.00 Estimated P Median 0.0000 0.06645
The null hypothesis that median is 0.054193 is rejected. As shown in the above table, the estimated median is given as 0.06645. Hence another wilcoxon test with null hypothesis as median = 0.07 is performed. The results are tabulated below:
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Test of median = 0.07000 versus median not = 0.07000 Variable Proportion N Wilcoxon N for Test Statistic 1253 1253 374638.00 Estimated P Median 0.1560 0.06645
Here the null hypothesis of median = 0.07 is accepted. Hence it can be said that there are 7% of the total volume in the nifty futures is used for hedging purpose.
4.2.2 Gold Futures Mean 95% Confidence Interval for mean Median Lower Bound Upper Bound Statistic 0.07693 0.048972 0.104888 0.018093
Test for Normality
Tests of Normality Kolmogorov-Smirnova Variable Proportion Statistic 0.400158727 df 137 Sig. 0.0000 Statistic 0.479007
Shapiro-Wilk df 137 Sig. 0.0000
When number of observations is more than 50, Kolmogorov-Smirnova test is considered. Here null hypothesis is rejected at above 99% confidence level. This indicates data are not normal. Hence Wilcoxon test of median is performed. The null hypothesis states that median is 0.054193. Wilcoxon Signed Rank Test: Proportion
Test of median = 0.01810 versus median not = 0.01810 N for Test 137 Wilcoxon Statistic 137 5454.00 Estimated P Median 0.1180 0.02096
Variable Proportion
N
The null hypothesis that median is 0.01810 is rejected. As shown in the above table, the estimated median is given as 0.02096. Hence another wilcoxon test with null hypothesis as median = 0.025 is performed. The results are tabulated below:
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Test of median = 0.0250 versus median not = 0.0250 N for Test 137 Wilcoxon Statistic 137 3954.00 Estimated P Median 0.0970 0.02096
Variable Proportion
N
Here the null hypothesis of median = 0.025 is accepted. Hence it can be said that there are 2.5% of the total volume in the gold futures is used for hedging purpose. Similarly, wilcoxon test of median was performed on mini nifty and it can be concluded that 5.5% of the daily total volume is used for hedging purpose.
5. Conclusion
The study employs Johansen’s cointegration technique, followed by the error correction model, to examine the causal relationship between the NSE spot & futures markets and gold spot and futures market in India. The empirical analysis was conducted for the daily data series from Nov. 2004 to Nov. 2009 for nifty futures and Jan. 2009 to Nov. 2009 for gold futures. The study reveals that there exists a long-run relationship between the Nifty spot & Nifty futures prices and gold spot and gold futures. The study results also confirm the presence of unidirectional relationship between the futures and spot market prices in India with information flowing from futures to spot market. The effectiveness of futures as risk management tool cannot be established as only less than 10% of the daily volume in nifty and gold futures is used for hedging purpose.
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.
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?
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”,. 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.
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doc_870450883.docx
It explains A report on Derivatives as a tool for price discovery and risk management
Derivative and Risk Management
Table of Contents
Abstract ......................................................................................................................................................... 3 1. 2. 3. Introduction .......................................................................................................................................... 3 Literature Review .................................................................................................................................. 4 Methodology......................................................................................................................................... 6 3.1 Price Discovery .................................................................................................................................... 6 3.2 Risk Management ............................................................................................................................... 7 4. Result and Analysis ............................................................................................................................... 8 4.1 Price Discovery .................................................................................................................................... 8 4.1.1 Nifty Futures ................................................................................................................................ 9 4.1.2 Gold futures ............................................................................................................................... 11 4.2 Risk Management using futures ....................................................................................................... 13 4.2.1 Nifty Futures .............................................................................................................................. 13 4.2.2 Gold Futures ............................................................................................................................... 14 5. 6. Conclusion ........................................................................................................................................... 15 References .......................................................................................................................................... 15
Derivatives as a tool of price discovery and risk management
Page 2
Abstract
This paper examines whether prices in the futures market help to determine the prices in spot market and vice-versa. This study also examines the effectiveness of futures as a tool of risk management. The paper examines the causal relationship between Nifty spot index & index futures and gold spot and gold futures market in India. The empirical analysis was conducted for the daily data series from November, 2004 to November, 2009 for nifty and Jan 2009 to Nov 2009 for gold futures. The objectives of the study are examined by employing Johansen’s cointegration test and vector error correction model (VECM).The effectiveness of futures market as risk management tool is measured by performing wilcoxon test of median on proportion of open interest as percentage of total intraday volume in futures market. The results reveal that there exists a long-run relationship between Nifty spot & Nifty futures prices and gold spot and future prices. Further, the results confirm the presence of a unidirectional relationship between the Nifty spot & Nifty futures and gold spot and future market prices in India. It can, therefore, be concluded that futures markets play the leading role through price discovery process in India and said to be informationally efficient and react more quickly to spot markets. The effectiveness of futures as risk management tool cannot be established as only less than 10% of the daily volume in nifty and gold futures is used for hedging purpose.
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.
Derivatives as a tool of price discovery and risk management Page 3
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 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. 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 is there equal feedback between the futures and the underlying markets. Also effectiveness of derivatives as risk management tool has been explored in this paper. This paper is segmented into five sections. Section two followed by introductory section one, reviews the existing literature. 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 is 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 exist 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.
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Wahab and Lashgari (1993) used daily data and cointegration 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 find 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. 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 three 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 leads 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 lead to the conclusion that a feedback mechanism is present between Nifty spot and Nifty futures.
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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
3.1 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 for risk management. Johansen (1988) cointegration and Error Correction Model (VECM) 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. Cointegration: In general combination of two non stationary series Xt and Yt is also non stationary. However, if there exist a combination of Xt and Yt such that it is stationary, then we can say that Xt and Yt are cointegrated. Two cointegrated series will not drift apart overtime example 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 cointegration 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, cointegration can establish whether there exist a stable long-run relationship between Nifty futures and the underlying Nifty and gold futures and the underlying gold commodity in India.
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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 by Ft – ?0 – ?1St = et where Ft and St are cash and future prices at time t, ?0 and ?1 are parameters et is the error term. If Ft and St are non stationary but et is stationary then Ft and St are cointegrated and equilibrium exist between Ft and St. Order of integration is determined by performing unit root 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 cointegrated of order (1,1), denoted CI(1,1) with ?1 as the cointegrating coefficient. The existence of cointegration implies that there exists causality between the spot and futures market prices which is represented by error correction model that includes last period’s equilibrium error as well as lagged values of the first differences of each variable. If spot and future prices are cointegrated then causality must exist in at least in one direction. The error correction can be written as Ft = ?0f + ?1f(Ft-1-St-1) + ?1fRf,t-1 + ?2fRf,t-2 + ?3fRs,t-1 + ?4fRs,t-2 +?ft St = ?0s + ?1s(Ft-1-St-1) + ?1sRs,t-1 + ?2sRs,t-2 + ?3sRf,t-1 + ?4sRf,t-2 +?st where Ft is Nifty futures returns and St is Nifty Index returns, ?1f and ?1s are the error correction terms and ?s represent short run effects. If “St causes Ft”, then changes in St should precede changes in Ft. ?s represent short run coefficients while ?s determines the speed of adjustment back to the longrun equilibrium. If the coefficient on the lagged Ft returns in the St equation are found to be significant, then turning points in Ft will lead turning points in St, that is, Ft causes St. Similarly, if the coefficient on the lagged St returns in the Ft equation are found to be significant, then turning points in St will lead turning points in Ft, that is, St causes Ft.
3.2 Risk Management
The number of hedgers present in the market will indicate whether futures are used as a tool for risk management or whether they are being used for speculation. In order to calculate the number of hedgers present in the market, change in open interest in nifty futures and gold futures as a
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percentage of total intraday volume is calculated. If the mean of this proportion is significant, then the number of hedgers present in the market can be approximated to the mean of this proportion. However, if the data is not is not normal, then Wilkoxon Signed Rank test is performed which is a test of median. If the result is significant then the median of the proportion can be approximated to the number of hedgers in the market. It can be said that certain percentage of daily volume is used for hedging purpose. The above methodology makes an assumption that all the speculators are day traders and hedgers are the ones who keep their positions open for more than one day.
4. Result and Analysis
4.1 Price Discovery
The results of unit root tests for Nifty futures and Nifty index, Mini nifty futures and mini nifty index and gold futures and gold spot price is tabulated below. Unit Root Test for 1 month nifty futures at level 0
Method ADF - Fisher Chi-square ADF - Choi Z-stat Statistic 2.37643 0.18563 Prob 0.6669 0.5736
Unit Root Test for 1 month nifty futures at Difference 1
Method ADF - Fisher Chi-square ADF - Choi Z-stat Statistic 251.917 -15.4349 Prob 0.0000 0.0000
Unit Root Test for 1 month gold futures at level 0
Method ADF - Fisher Chi-square ADF - Choi Z-stat Statistic 0.40705 1.85139 Prob 0.9819 0.9679
Unit Root Test for 1 month gold futures at Difference 1
Method ADF - Fisher Chi-square Statistic 166.294 Prob 0.0000 Page 8
Derivatives as a tool of price discovery and risk management
ADF - Choi Z-stat
-12.3923
0.0000
The above results indicate that Nifty futures and Nifty Index, mini nifty futures and nifty index, gold futures and gold spot prices are not stationary at their levels but their returns are stationary i.e. their first differences are stationary. The results of the cointegration tests for Nifty futures and Nifty index, Mini nifty futures and mini nifty index and gold futures and gold spot price are tabulated below. Before performing cointegration, akaike information test is performed which gives the best model for cointegration.
4.1.1 Nifty Futures Johansen Conintegration Test Akaike Information Criteria by Rank (rows) and Model (columns) Data Trend Rank or No. of CEs 0 1 2 None None Linear Linear Quadratic
No Intercept No Intercept No Intercept No Intercept Intercept Trend Trend Trend Trend Trend 18.7922 18.7922 18.7943 18.7943 18.7974 18.7254 18.7201* 18.7206 18.7215 18.7230 18.7314 18.7253 18.7253 18.7270 18.7270
Selected (0.05 level*) Number of Cointegrating Relations by Model. Null hypothesis states that both the markets are independent (not cointegrated).
Trend assumption: No deterministic trend Unrestricted Cointegration Rank Test (? Trace) Hypothesized No. of CE(s) None* At most 1 0.05 Critical Eigenvalue Trace Statistic Value 0.076945 103.7742 20.26184 0.002816 3.530689 9.164546
Prob.** 0.0000 0.4865
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level Unrestricted Cointegration Rank Test (? Maximum Eigenvalue) Hypothesized No. of CE(s) Max-Eigen Statistic 0.05 Critical Value
Eigenvalue
Prob.** Page 9
Derivatives as a tool of price discovery and risk management
None* At most 1
0.076945 0.002816
100.2435 3.530689
15.8921 9.164546
0.0000 0.4865
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values
According to above results null hypothesis is rejected. This means Nifty futures and Index are cointegrated of order 1. The result suggests that futures market price had positive relationship with spot market price, implying that there is a well-defined long-run relationship between the NSE futures and spot prices in India. Johansen’s ? max and ? trace statistics reveal the Nifty spot and Nifty futures prices stand in a long-run relationship between them, thus justifying the use of an ECM which establishes the causality between the two markets. The results of the price discovery regression are tabulated below.
Vector Error Correction Model Nifty Index Future return as dependent variable Coefficient Value Significance t-statistic ?1f ?1f ?2f ?3f ?4f -0.40528 0.093222 -0.01469 -0.05672 0.0374 0.18468 0.26825 0.23675 0.28149 0.24563 -2.19445 0.34751 -0.06205 -0.20148 0.15226
Variable F(t-1)-S(t-1) Rf,t-1 Rf,t-2 Rs,t-1 Rs,t-2
Variable F(t-1)-S(t-1) Rs,t-1 Rs,t-2 Rf,t-1 Rf,t-2
Nifty Index Spot return as dependent variable Coefficient Value Significance t-statistic ?1s -0.20072 0.0264 -1.15583 ?1s 0.395157 0.0156 1.56657 ?2s 0.049052 0.0389 0.22034 ?3s -0.34437 0.0375 -1.30104 ?4s -0.03222 0.0425 -0.13949
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As seen from the above table, the coefficient of error correction of Ft is not statistically significant. But the coefficient of error correction of St is significant at 5% significant level. This indicates that there exists a unidirectional causality and it runs from the futures to spot market price. This indicates information gets reflected first in the futures market and then flows to the spot market.
4.1.2 Gold futures Johansen Conintegration Test Akaike Information Criteria by Rank (rows) and Model (columns) Data Trend Rank or No. of CEs 0 1 2 None No Intercept No Trend 25.91404 25.59903 25.62918 None Intercept No Trend 25.91404 25.60464 25.64780 Linear Linear Quadratic
Intercept Intercept Intercept No Trend Trend Trend 25.91642 25.91642 25.93649 25.59553* 25.60718 25.61423 25.64780 25.65631 25.65631
Selected (0.05 level*) Number of Cointegrating Relations by Model
Null hypothesis states that both the markets are independent (not cointegrated).
Unrestricted Cointegration Rank Test (? Trace) Hypothesized No. of CE(s) None* At most 1 0.05 Critical Value 15.49471 3.841466
Eigenvalue 0.311460 1.47E-05
Trace Statistic 57.09909 0.002253
Prob.** 0.0000 0.9602
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level Unrestricted Cointegration Rank Test (? Maximum Eigenvalue) Hypothesized No. of CE(s) None* At most 1 Max-Eigen Statistic 57.09683 0.002253 0.05 Critical Value 14.26460 3.841466
Eigenvalue 0.311460 1.47E-05
Prob.** 0.0000 0.9602
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Derivatives as a tool of price discovery and risk management Page 11
According to above results null hypothesis is rejected. This means gold futures and spot are cointegrated of order 1. The result suggests that futures market price had positive relationship with spot market price, implying that there is a well-defined long-run relationship between the gold futures and spot prices in India. Johansen’s ? max and ? trace statistics reveal the Gold spot prices and gold futures prices stand in a long-run relationship between them, thus justifying the use of an ECM which establishes the causality between the two markets. The results of the price discovery regression are tabulated below.
Vector Error Correction Model Nifty Index Future return as dependent variable Coefficient Value Significance ?1f -0.99307 0.27408 ?1f 0.004354 0.21806 ?2f 0.062572 0.13850 ?3f -0.14155 0.22713 ?4f -0.19862 0.15224 Nifty Index Spot return as dependent variable Coefficient Value Significance ?1s 0.035560 0.0381 ?1s -0.05891 0.0158 ?2s 0.024455 0.0294 ?3s -0.10509 0.0463 ?4s -0.1749 0.0689
Variable F(t-1)-S(t-1) Rf,t-1 Rf,t-2 Rs,t-1 Rs,t-2
t-statistic -3.62332 0.01997 0.45180 -0.62322 -1.30468
Variable F(t-1)-S(t-1) Rs,t-1 Rs,t-2 Rf,t-1 Rf,t-2
t-statistic 0.10164 -0.21162 0.13833 -0.36245 -0.90002
As seen from the above table, the coefficient of error correction of Ft is not statistically significant. But the coefficient of error correction of St is significant at 5% significant level. This indicates that there exists a unidirectional causality and it runs from the futures to spot market price. This indicates information gets reflected first in the futures market and then flows to the spot market.
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Similar results were obtained for mini nifty which showed unidirectional causality from future to spot.
4.2 Risk Management using futures
Change in open interest as a daily volume is used to find whether futures are used as means of risk management or they are used for speculating purpose.
4.2.1 Nifty Futures Mean 95% Confidence Interval for mean Median Lower Bound Upper Bound Statistic 0.09401283 0.08737898 0.10064668 0.05419377
Test for normality
Tests of Normality Kolmogorov-Smirnova Variable Proportion Statistic 0.216190156 df 1253 Sig. 0.0000 Statistic 0.690504
Shapiro-Wilk df 1253 Sig. 0.0000
When number of observations is more than 50, Kolmogorov-Smirnova test is considered. Here null hypothesis is rejected at above 99% confidence level. This indicates data are not normal. Hence Wilcoxon test of median is performed. The null hypothesis states that median is 0.054193. Wilcoxon Signed Rank Test: Proportion
Test of median = 0.05420 versus median not = 0.05420 Variable Proportion Wilcoxon N N for Test Statistic 1253 1253 463313.00 Estimated P Median 0.0000 0.06645
The null hypothesis that median is 0.054193 is rejected. As shown in the above table, the estimated median is given as 0.06645. Hence another wilcoxon test with null hypothesis as median = 0.07 is performed. The results are tabulated below:
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Test of median = 0.07000 versus median not = 0.07000 Variable Proportion N Wilcoxon N for Test Statistic 1253 1253 374638.00 Estimated P Median 0.1560 0.06645
Here the null hypothesis of median = 0.07 is accepted. Hence it can be said that there are 7% of the total volume in the nifty futures is used for hedging purpose.
4.2.2 Gold Futures Mean 95% Confidence Interval for mean Median Lower Bound Upper Bound Statistic 0.07693 0.048972 0.104888 0.018093
Test for Normality
Tests of Normality Kolmogorov-Smirnova Variable Proportion Statistic 0.400158727 df 137 Sig. 0.0000 Statistic 0.479007
Shapiro-Wilk df 137 Sig. 0.0000
When number of observations is more than 50, Kolmogorov-Smirnova test is considered. Here null hypothesis is rejected at above 99% confidence level. This indicates data are not normal. Hence Wilcoxon test of median is performed. The null hypothesis states that median is 0.054193. Wilcoxon Signed Rank Test: Proportion
Test of median = 0.01810 versus median not = 0.01810 N for Test 137 Wilcoxon Statistic 137 5454.00 Estimated P Median 0.1180 0.02096
Variable Proportion
N
The null hypothesis that median is 0.01810 is rejected. As shown in the above table, the estimated median is given as 0.02096. Hence another wilcoxon test with null hypothesis as median = 0.025 is performed. The results are tabulated below:
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Test of median = 0.0250 versus median not = 0.0250 N for Test 137 Wilcoxon Statistic 137 3954.00 Estimated P Median 0.0970 0.02096
Variable Proportion
N
Here the null hypothesis of median = 0.025 is accepted. Hence it can be said that there are 2.5% of the total volume in the gold futures is used for hedging purpose. Similarly, wilcoxon test of median was performed on mini nifty and it can be concluded that 5.5% of the daily total volume is used for hedging purpose.
5. Conclusion
The study employs Johansen’s cointegration technique, followed by the error correction model, to examine the causal relationship between the NSE spot & futures markets and gold spot and futures market in India. The empirical analysis was conducted for the daily data series from Nov. 2004 to Nov. 2009 for nifty futures and Jan. 2009 to Nov. 2009 for gold futures. The study reveals that there exists a long-run relationship between the Nifty spot & Nifty futures prices and gold spot and gold futures. The study results also confirm the presence of unidirectional relationship between the futures and spot market prices in India with information flowing from futures to spot market. The effectiveness of futures as risk management tool cannot be established as only less than 10% of the daily volume in nifty and gold futures is used for hedging purpose.
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.
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?
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”,. 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.
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