Price Discovery

1. Price Discovery BY Dhanya K A

2. Introduction • Price discovery – an economic function of derivatives • Revealing information about future cash market prices through futures market • Relevance of the study

3. Objectives of the study • To assess the impact of nifty/stock futures on respective spot market prices. (Regression) • To examine the lead-lag relationship between futures and spot market prices (Granger causality test) • To check whether there exist any long-run relationship between two markets which implies the existence of price discovery (Co-integration model)

4. Research design • Based on the secondary data collected from NSE website. • Period of study is from April 2005 to March 2010. • Data base consists of monthly closing values of nifty/stock futures and their respective spot prices, from April 2005 to March 2010. Hence there is a total of 60 samples selected for the study.

5. Sample design: Top five futures contracts of March 2010 are identified and three among them are selected randomly for the purpose of the study. • Tools for analysis: Statistical and econometric tools - Regression -Granger causality - Co integration -Dickey fuller test -Jarque -Bera test -Durbin Watson test

6. Limitations of the study • The scope of the study is limited to monthly closing values of three selected indices/securities • Causality of tata futures is tested only by taking lag 1 difference while lag 2 , lag 3 differences may give a different result.

7. Hypothesis • H0 : The time series data of futures and spot prices are non stationary • H0 : Lagged futures values do not belong in the regression (Futures prices do not lead spot prices) • H0 : Both futures price series and spot price series are not co integrated

8. Analysis and Discussions

9. Stationarity of Data • H0 : The time series data of futures and spot prices are non stationary Results of Dickey fuller test

10. Transforming non stationary series into stationary • Differencing- Here first difference is taken i.e Xt – Xt-1 • Results of DF test

11. Impact of futures prices on spot prices Result of regression analysis of futures on spot price

12. Basic assumptions of regression model • Normality of errors Tested using Jarque-bera test. Skewness and Kurtosis of residuals are calculated and the following formula is applied to find JB statistic. JB = n ( (S2/6)+((K-3)2 /24) ) (source: Gujarati, pp151) • Independence of errors Tested using Durbin –Watson test for autocorrelation The d statistic is (source: kanji, pp169) d = ∑ (et - et-1) ∑ et2

13. Result of Jarque-bera test

14. Result of Durbin Watson test

15. Do futures market lead spot market? • Ho:“ Lagged futures do not belong in the regression is tested” F statistic = (RSSr - RSSur)/m RSSur/(n-k) (source ; Gujarati, pp273) Result of Granger causality test

16. Price discovery .Price discovery will happen only when there is an equillibrium relationship between two markets. . Long run relationship tells that equilibrium position will be restored . This long run relationship is established by using cointegration model Hence Cointegrated series performs price discovery

17. Long run relationship between the two markets • “H0 : Both futures price series and spot price series are not co integrated” Results of Engle – Granger co integration test

18. Findings • The futures and spot price series of nifty, bank nifty and Tata motors are non stationary in their original form • By differencing the futures and spot price series of nifty, bank nifty and Tata motors by first order, they have transformed to stationary series. • Regression model shows high predictive power for futures market • The Jarque-bera test shows that results of regression are not be reliable especially in case of nifty futures with high JB statistic of 131.8

19. Continue… • Durbin Watson test shows that the independence of errors and hence regression model follows that particular assumption • There is a lead lag relationship between nifty and bank nifty futures and their respective spot market while this is not true in case of tata futures • The long run relationship exhibited by nifty and bank nifty futures with their spot market shows that these futures contracts perform price discovery function.

20. Conclusion • Study focuses on both the short term and long term relationship between spot and futures market. • Study also examines the predictive power of futures contract • Each securities in the Indian market need to be analysed to get a clear view about the price discovery function

21. References • Gujarati, N Damodar, Sangeetha (2007) Basic econometrics, Fourth editionTata McGraw-Hill Publishing Company Limited,New Delhi. • Guptha, S.L. (2006), Financial Derivatives: Theory, Concepts and Problems, Prentice Hall of India Private Limited, New Delhi. • Kanji,K Gopal, (2006), 100 statistical tests,Third edition, Vistaar publications, New Delhi • Levine, Stephan (2005) Statistics for managers, Fourth edition, Prentice Hall of India Private Limited, New Delhi. • Berri,G.C. (2005), Business Statistics, Tata McGraw-Hill Publishing Company Limited,New Delhi. • Kapil,G & Balwinder,S (2006), “Price discovery through Indian equity futures market, “The ICFAI Journal of Applied Finance,” 12(12), 70-83. • SuchismitaBose(2007), “contribution of Indian index futures to price formation in the stock market”, Money andfinancep39 • http://www.nseindia.com/archives/fo/monthly/DU_102007.pdf

22. Thank you