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 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 -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

10. 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

11. 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 = X
Tataspot Y = X
Bankspot Y = X

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
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.

14. 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.

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
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

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
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

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 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),
SuchismitaBose(2007), “contribution of Indian index futures to price formation in the stock market”, Money andfinancep39

22. Thank you