Price Discovery BY Dhanya K A

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

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)

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.

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

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.

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

Analysis and Discussions

Stationarity of Data -Calculated value is less than table value H0 : The time series data of futures and spot prices are non stationary Results of Dickey fuller test Calculated value Table value 1% sig 60df Slope Inferences Nifty spot 1.76 2.60 .081 -Calculated value is less than table value -Accept Ho -Beta Coefficient (slope) is near to Zero -Nonstationary Nifty futures 1.788 .085 Tata spot 1.274 .054 Tata futures 1.388 .064 Bank spot 1.703 .078 Bank futures 1.708 .077

Transforming non stationary series into stationary Differencing- Here first difference is taken i.e Xt – Xt-1 Results of DF test Calculated value Table value 1% sig 60df Slope Inferences Nifty spot 7.43 2.60 .990 -Calculated value is higher than table value -Reject Ho -Beta Coefficient (slope) is not near to Zero -Hence stationary Nifty futures 7.58 1.01 Tata spot 6.57 .873 Tata futures 7.34 .985 Bankspot 6.37 . 842 Bank futures

Impact of futures prices on spot prices Result of regression analysis of futures on spot price R square Betacoefficient (constant) Beta coefficient (futures) Niftyspoton futures .985 -2.323 .946 Tataspot on futures .783 -1.698 .8 Bankspoton futures .751 -11.99 .87 Regression model Niftyspot Y = -2.323+.946X Tataspot Y = -1.698+.8X Bankspot Y = -11.9+.87X

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

Result of Jarque-bera test Residuals Skewness Kurtosis JB statistic Nifty spot on futures 1.593 9.815 131.8 Tataspot on futures -.144 1.092 9.3 Bankspot on futures .22 .01 21.83 Inferences Normal distribution will have kurtosis as 3 skewness 0 and low JB statistic. Here in no cases skewness is 0 and kortosis is 3. JB statistic is not significantly low. This shows that the series is not normal and hence reliability of regression results is doubted.

Result of Durbin Watson test Residuals D statistic Table value dL, dU - 59 df Inferences Nifty spot on futures 2.958 1.55 and 1.62 As D statistic is above upper limit no autocorrelation . There is independence of errors Tataspot on futures 2.64 Bankspot on futures 308 Though regression is found to be an effective tool for prediction, it is necessary to test the reliability of the model. The results of regression will be reliable only if the basic assumptions of the model are followed.

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 Lag 1 Calculated value Table value 5% 1,57 df Inference Niftyfutures 5.1 4 As CV > TV reject Ho Tatafutures 2.5 As CV < TV acceptHo Bank futures 5.3

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

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 Residuals of original series Calculated t value Table value 1% sig 60 df Inference Nifty futures and spot 7.419 2.62 As CV>TV reject Ho. Thus series are cointegrated and hence price discovery Banknifty futures and spot 8.604

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

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.

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

References Gujarati, N Damodar, Sangeetha (2007) Basic econometrics, Fourth edition Tata 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

Thank you