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An econometric study of lead-lag relationship between futures and spot markets in India.

Introduction

The issue of price discovery on futures and spot markets and the lead-lag relationship are topics of interest to traders, financial economists, and analysts. Although futures and spot markets react to the same information, the major question is which market reacts first. Profitable arbitrage should not exist in perfectly efficient markets as prices should adjust instantaneously and fully to new information. Hence, new information disseminating into the marketplace should be immediately reflected in spot prices and futures prices simultaneously. In other words, this suggests that there should be no lead-lag relationship between the cash and futures market. However, futures markets perform an important function of price discovery to help improve efficiency of the market. From this argument, futures prices and their movements provide useful information about subsequent spot prices. Due to some peculiarities in terms of capital required, cost of transactions, etc., it would precede the underlying market in the information discounting process. This paper makes and attempt to measure whether price discovery actually happens first in the futures market or not; which in effect means that whether the futures market leads the spot market or not.

From a financial point of view, there is a lead-lag relationship between the spot index and index futures contract. The lead-lag relationship investigates whether the spot market leads the futures market, whether the futures market leads the spot market, or whether the bidirectional feedback between the two markets exists. The lead-lag relationship illustrates how well the two markets are linked, and how fast one market reflects new information from the other. If feedback between spot and futures exists, it is possible that investors may use past information to predict prices (or returns) in the future. Feedback relationship exists if stock index futures price reacts to economy-wide information as found by Antoniou and Garrett (1993). Most researchers show that futures returns lead spot returns, while futures market has a stronger lead effect. Also, when a bidirectional causality exists between the two series, spot and futures have an important discovery role. Hence, an electronic market may enhance price discovery. The discovery of one price will definitely provide valuable information about the other.

It is very well known that the Indian capital market has witnessed a major transformation and structural change during the past one decade as a result of ongoing financial sector reforms. Gupta (2002) has rightly pointed out that improving market efficiency, enhancing transparency, checking unfair trade practices, and bringing the Indian capital market up to a certain international standard are some of the major objectives of these reforms. Due to such reforming process, one of the important steps taken in the secondary market is the introduction of derivative products in two major Indian stock exchanges (viz., NSE and BSE) with a view to providing tools for risk management to investors and also to improve the informational efficiency of the cash market.

The Indian capital markets have experienced the launching of derivative products on 9 June 2000 in BSE and on 12 June 2000 in NSE by the introduction of index futures. Just after one year, index options were also introduced to facilitate the investors in managing their risks. Later, stock options and stock futures on underlying stocks were also launched in July 2001 and November 2001 respectively. In India, derivatives were mainly introduced with a view to curbing the increasing volatility of the asset prices in financial markets and to introduce sophisticated risk management tools leading to higher returns by reducing risk and transaction costs as compared to individual financial assets. Though the onset of derivative trading has significantly altered the movement of stock prices in Indian spot markets, it is yet to be proved whether the derivative products have served the purpose as claimed by the Indian regulators.

According to Tse (1999), price discovery refers to the impounding of new information into the price. Several studies report that futures markets lead spot (cash) markets from a few seconds to hours (Kawaller, Koch, and Koch 1987; Stoll and Whaley 1990). According to Brooks et al. (2001) the lead-lag relationship between spot and futures markets do not last for more than half an hour. Reasons for why futures prices lead spot prices include the facts that futures markets are more informationally efficient, and they have lower transaction costs and higher liquidity. Although empirical research generally suggests that the futures market leads the cash market (i.e., futures prices contain useful information about cash prices), other researchers show that cash market may lead futures market.

Objectives of the Study

In this paper, we examine whether the price movements in futures markets lead the price movements in cash markets (i.e., whether futures discover spot prices) using data from Indian capital market. The paper offers a unique contribution in examining the lead-lag relationship between the NSE NIFTY index and the index futures covering a period since the introduction of index futures in Indian capital market.

The present study is being contemplated with the following specific objectives:

i) Investigating the lead-lag relationship between NSE Nifty stock market index and NSE Nifty futures.

ii) Analysing the possible explanations behind the variations in the above relationships over time.

The next section reviews the most relevant literature on lead-lag relationships. This is followed by the section on the data used and its sources, the detailed research methodology employed for the study, the empirical findings, and the concluding remarks.

Literature Review

The issues of price discovery on futures and spot markets and the lead-lag relationship are topics of interest to traders, financial economists, and analysts. Although futures and spot markets react to the same information, the major question is which market reacts first. Several studies examine whether the returns of index futures lead the spot index. The early study by Gardbade and Silber (1983) suggests that futures markets lead the spot. Similarly, Herbst, McCormack and West (1987) examine the lead-lag relationship between the spot and futures markets for S&P 500 and VLCI indices. They find that for S&P 500 the lead is between zero and eight minutes, while for VLCI the lead is up to sixteen minutes. More sophisticated methods of causality Value at Risk-Vector Error Correction Model (VAR-VECM) shows evidence that futures prices lead the spot prices. For example, Kawaller et al. (1987) use minute-to-minute data on the S&P 500 spot and futures contract and prove that futures lead the cash index by 20-45 minutes. Also, Stoll and Whaley (1990) find that S&P 500 and MM index futures returns lead the stock market returns by about five minutes. Similarly, Cheung and Ng (1990) analyse price changes over fifteen-minute periods for the S&P 500 index using a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. Their results show that futures returns lead spot returns by at least fifteen minutes, while Chan, Chan, and Karolyi (1991) use a bivariate GARCH model and find that S&P 500 futures returns lead spot returns by about five minutes.

Furthermore, Chan (1992) argues that this lead-lag relation is asymmetric. He suggests that under good news cash index prices lag futures prices, and more importantly, when stocks are moving together, cash and futures markets provide a support to the asymmetric lead-lag relation. In addition, Chang et al. (1995) suggest that futures market leads stock market with respect to the weekend effect. Also, Pizzi et al. (1998) suggest that both three-month and six-month S&P 500 futures contracts are the leaders of the spot market (by at least twenty minutes). Antoniou and Garrett (1993) examine the pricing relationship between the FTSE 100 index and the FTSE 100 index futures contract on the 19 and 20 October 1987 (stock market crash period). They find that, in general, the futures price leads the stock index. Further, Abhyankar (1998) examines the relationship between futures and spot returns using five-minute returns on the FTSE 100. He finds that the futures returns lead the spot returns by 15-20 minutes. Antoniou et al. (2001) use multivariate analysis (i.e., Value at Risk-Exponential Generalized Autoregressive Conditional Heteroskedasticity (VAR-EGARCH) methodology) to examine the lead-lag relationship between stock and futures markets of France, Germany, and the UK, and confirm that futures markets lead spot markets.

Brooks et al. (2001) investigate the lead-lag relationship between the spot index and futures contract for the FTSE 100 index. Their results from the Engle-Granger method show that there is a strong relationship between spot and futures prices. They also find that changes in spot index depend on the lagged changes in the spot index and futures price, while the lead-lag relationship between spot and futures markets do not last for more than half an hour. Most of the studies have suggested that the leading role of the futures market varies from five to forty minutes, while the spot market rarely leads the futures market beyond one minute. While explaining the causes behind such relation, Kawaller et al. (1987) attribute the stronger leading role of the futures market to the infrequent trading of component stocks.

Thenmozhi (2002) studied the impact of the introduction of index futures on underlying index volatility in Indian markets. Applying Variance Ratio Test and Ordinary Least Square Multiple Regression Technique she concluded that futures trading has reduced the volatility in the spot markets. Further, in a lead lag analysis, Thenmozhi found that the futures market leads the spot index returns by one day. But this study neglected inherent time-varying characteristics clustering of volatility, and possible autocorrelation. Therefore, the inferences drawn are unreliable.

This paper compares the results from the introduction of two stock index futures (NSE NIFTY and BSE SENSEX) in India. Our findings are very important since no previous work has examined the lead-lag relationship between the spot index and index futures contract traded in the BSE and NSE taking the recent times into consideration.

Data Sources

The data employed in this study comprise 1685 daily observations on the NSE NIFTY stock index and stock index futures contract and BSE SENSEX stock index and stock index futures contract. Closing prices for spot indices and closing futures prices were obtained from the official web page of the National Stock Exchange (www.nse-india.com) and Bombay Stock Exchange (www.bseindia.com ). The period of study is from July 2000 to March 2007. The study had used two most popular statistical/econometric packages for analysis, namely SPSS 11.5 version and Eviews 3.0.

The NSE NIFTY comprises fifty Indian companies, quoted on the National Stock Exchange (NSE) with the largest market capitalization (blue chips), while the BSE SENSEX comprises thirty leading Indian companies. Both the stock indices are weighted for market capitalization. Futures contracts are quoted on both NSE NIFTY and BSE SENSEX. The price of a futures contract is measured in index points multiplied by the contract multiplier, which is 50 for the NSE NIFTY contract and 200 for the BSE SENSEX contract. There are four delivery months: March, June, September, and December. Trading takes place in the three nearest delivery months, although volume in the far contract is very small. Near-month futures contract prices are used for the study. The index futures time series analysed here uses data on the near-month contract as they are most heavily traded. Though it would be better to consider using higher frequency of data rather than daily prices, the daily closing prices are taken due to non-availability of intra-day data (hourly or minute-by-minute data).

Research Methodology

In an efficient capital market where all available information is fully and instantaneously utilized to determine the market price of securities, prices in the futures and spot market should move simultaneously without any delay. However, due to market frictions such as transaction cost, capital market microstructure effects, etc., significant lead-lag relationship between the two markets has been observed.

One of the key assumptions of the ordinary regression model is that the errors have the same variance throughout the sample. This is also called the homoskedasticity model. If the error variance is not constant, the data are said to be heteroskedastic. Since ordinary least-squares regression assumes constant error variance, heteroskedasticity causes the Ordinary Least Square (OLS) estimates to be inefficient. Models that take into account the changing variance can make more efficient use of the data. This study used the econometric tools/concepts like GARCH (Generalized Auto Regressive Conditional Heteroskedasticity) and VECM (Vector Error Correction Model).

The log-spot price for time t is given by log (St) and the log-futures prices for time t is given by log (Ft), where St and Ft are spot prices and near-month futures prices respectively.

If the markets are frictionless and functioning efficiently, changes in the log-spot prices and changes in the log-futures prices are expected to occur at the same time, while the current change in the log-futures price is also expected not to be related to previous changes in the log-spot price (and vice versa). In this paper we use a bivariate cointegration model with simple GARCH errors to examine lead-lag relationship between spot and futures. The multivariate GARCH model uses information from more than one market's history. It provides more precise estimates of the parameters because it utilizes information in the entire variance-covariance matrix. The bivariate cointegration GARCH(1,1) distributions of log-spot (s) and log-futures (f) are given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where, [[DELTA].sub.St] is the change in log-spot at time t, [[DELTA].sub.Ft] is the change in log-futures at time t, [??] symbolizes error measure in GARCH model, h is the conditional variance term, [gamma] is a parameter coefficient, [[psi.sub.t-1] is the information at time t-1 and [S.sub.t-1] - [[gamma].sub.t-1] is the error term obtained from the equation [S.sub.t] = [delta] + [gamma][F.sub.t] + [[??].sub.t].

It must be noted that estimation of all multivariate GARCH models above is carried out by using conditional quasi-maximum likelihood estimation. The conditional log-likelihood function for a single observation can be written as

[L.sub.t] ([theta]) = (n/2) log (2[pi]) - (1/2) log (|[H.sub.t] ([theta])|) - (1/2) [[??].sub.t] ([theta])' [H.sup.-1.sub.t] ([theta]) [[??].sub.t] ([theta]) (2)

where [theta] represents a vector of parameters, n is the sample size, and t is the time index.

Further, Brooks et al. (2002) use a bivariate VECM (Vector Error Correction Model), which is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

However, a disadvantage of bivariate VECM is that it does not ensure the conditional variance-covariance matrix of spot and futures returns to be positive definite (Lien, Tse, and Tsui 2002).

In this paper, we employ the bivariate cointegration model, with GARCH error structure (BGARCH), which incorporates a time-varying conditional correlation coefficient between spot and futures prices. We apply several BGARCH models to our data, so we can highlight the selected model. In particular, to account for cointegration, we model the mean equations (first moment) with a bivariate error correction model (Engle and Granger 1987). We use Akaike's Information Criterion (AIC) to select the best model (representation).

Empirical Findings

First, several BGARCH (1,1) models are employed with 1, 2, 3, 4, 5, and 6 lags in the mean equation. Although most empirical applications have restricted attention to BGARCH (1,1) model, with one lag for [DELTA]s and one lag for [DELTA]f, we find that, for our data, the BGARCH (1,1) model with two lags for [DELTA]s and two lags for [DELTA]f has the lowest AIC value. Therefore, we select this model. The results are presented in Table 1 and Table 2 for NSE NIFTY, and Table 3 and Table 4 for BSE SENSEX.

From Table 1 and Table 2, we can see that for NSE NIFTY both ARCH and GARCH coefficients are significant. The ARCH coefficients (for both NSE NIFTY and BSE SENSEX) are all positive and significant thus implying volatility clustering both in the cash and in the futures returns. The ARCH coefficients are also less than unity in all cases. The sign and significance of the covariance parameters indicate significance interaction between the two prices. The combined value of ARCH and GARCH coefficients for cash and futures equation (for both NSE NIFTY and BSE SENSEX) are less than 1.0 implying that the BGARCH model is correctly specified.

Moreover, in BGARCH cash equation the coefficients, Cs (0.07238) is statistically significant and in BGARCH futures equation, the coefficient Cf (0.07892) is also significant at 1 per cent level. This implies bidirectional causality between spot prices and futures prices in NSE NIFTY. Similarly, from Table 3 and Table 4, we observe that the coefficients (C) of cash and futures equation for BSE SENSEX are significant. But the coefficients for BSE SENSEX are of smaller value than their counterparts in NSE NIFTY. This shows that bidirectional lead-lag relationship is relatively stronger in NSE NIFTY than in BSE SENSEX.

Furthermore, since the coefficient of the error correction term, [[alpha].sub.0], is always positive and significant for both NSE NIFTY (0.00894) and BSE SENSEX (0.00792), we conclude that futures market does indeed lead the spot market in both cases. Also, the coefficient of the error correction term in the futures equation, [[beta].sub.0] is positive and significant (0.00798 for NSE NIFTY and 0.00678 for BSE SENSEX), indicating that the spot market leads the futures market. We observe that lead-lag relationship is stronger for NSE NIFTY as shown by the coefficients of error term.

Concluding Remarks

The introduction of a futures market and, in particular, the impact of futures on stock market volatility is a long debate. This paper tests the empirical relationship between spot and futures traded in the National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) for the period 2001-7. In particular, we examine the lead-lag relationship between stock index and stock index futures contracts for NSE NIFTY and BSE SENSEX over the period 2001 to 2007. A lead-lag relation exists when one market reacts faster to information due to transaction costs or other capital market effects.

Using a bivariate GARCH(1,1) model, we confirm long-run relationship and lead-lag relationship between spot (cash) and futures. The study finds that the BGARCH model is correctly specified. Also we evidence a bi-directional lead-lag relationship between spot and futures prices in both the stock indices and this is relatively stronger in NSE NIFTY than in BSE SENSEX. Further, we conclude that futures market does indeed lead the spot market and this relation is more prominent in NSE NIFTY prices. For both NSE NIFTY and BSE SENSEX, we show that futures markets play a price discovery role, implying that futures prices contain useful information about spot prices. Futures markets are more informationally efficient than the underlying stock markets in India during the period 2001-7. Stock index futures reflect new information faster than spot markets because Indian traders buy or sell stocks rather than index futures, while they prefer to use futures market to exploit information about economy. Reasons for why futures prices lead spot prices include the fact that futures markets have lower transaction costs and higher liquidity. Our results are helpful to traders, speculators, and financial managers dealing with Indian stock index futures.

References

Abhyankar, A., (1998), 'Linear and nonlinear Granger causality: Evidence from the U.K. stock index futures market', Journal of Futures Markets, 18, pp. 519-40.

Antoniou, A., and I. Garrett, (1993), 'To what extent did stock index futures contribute to the October 1987 stock market crash?', Economic Journal, 10(3), pp. 1444-61.

Antoniou, A., G. Pescetto, and A. Violaris, (2001), 'Modelling international price relationships and interdependencies between EU stock index and stock index futures markets: A multivariate analysis', Working Paper, Centre for Empirical Research in Finance, Department of Economics and Finance, University of Durham.

Brooks, C., A.G. Rew, and S. Ritson, (2001), 'A trading strategy based on the lead-lag relationship between the spot index and futures contract for the FTSE 100', International Journal of Forecasting, 17, pp. 31-44.

Brooks, C., O.T. Henry, and G. Persand, (2002), 'The effect of asymmetries on optimal hedge ratios', Journal of Business, 75, pp. 333-52.

Chan, K., K.C. Chan, and G.A. Karolyi, (1991), 'Intraday volatility in the stock index and stock index futures markets', Review of Financial Studies, 4, pp. 657-84.

Chan Kalok, (1992), 'A Further Analysis of the Lead-Lag Relationship between the Cash Market and Stock Index Futures Market', Review of Financial Studies, 5(1), pp. 123-52.

Chang, E., P. Jain, and P. Locke, (1995), 'Standard & Poor's 500 index futures volatility and price changes around the New York Stock Exchange close', Journal of Business, 68, pp. 61-84.

Cheung, Y. W., and Ng, L. K. (1990), The dynamics of S&P 500 index and S&P 500 futures intraday price volatilities, Review of Futures Markets, 9, pp. 458-86.

Engle, R.F., and K.F. Kroner, (1995), 'Multivariate simultaneous generalized ARCH', Econometric Theory, 11, pp. 122-50.

Gardbade, K.D., and W.L. Silber, (1983), 'Price movements and price discovery in futures and cash markets', Review of Economics and Statistics, 65, pp. 289-97.

Gupta, O.P., (2002), Effect of Introduction of Index Futures on Stock Market Volatility: The Indian Evidence, New Delhi: Department of Financial Studies, University of Delhi, South Campus.

Herbst, A., J. McCormack, and E. West, (1987), 'Investigation of a lead-lag relationship between spot indices and their futures contracts', Journal of Futures Markets, 7, pp. 373-81.

Kawaller, I.G., P.D. Koch, and T.W. Koch, (1987), 'The temporal price relationship between S&P 500 futures and the S&P 500 index', Journal of Finance, 42, pp. 1309-29.

Lien, D., Y.K. Tse, and A.K.C. Tsui, (2002), 'Evaluating the hedging performance of the constant-correlation GARCH model', Applied Financial Economics, 12, pp. 791-8.

Pizzi, M. A., A.J. Economopoulos, and H.M. O'Neill, (1998), 'An examination of the relationship between stock index cash and futures markets: A cointegration approach', Journal of Futures Markets, 18, pp. 297-305.

Stoll, H.R., and R.E. Whaley, (1990), 'The dynamics of stock index and stock index futures returns', Journal of Financial and Quantitative Analysis, 25, pp. 441-68.

Thenmozhi, M., (2002), 'Futures Trading, Information and Spot Price Volatility of NSE-50 Index Futures Contract', NSE Newsletter, NSE Research Initiative, Paper no. 18.

Tse, Y., (1999), 'Price discovery and volatility spillovers in the DJIA index', Journal of Futures Markets, 19, pp. 911-30.

Sathya Swaroop Debasish, Department of Business Management, Fakir Mohan University, Balasore, India. Email: sathyaswaroop2000@yahoo.com

Bishnupriya Mishra, Regional College of Management, Bhubaneswar, India. Email: dr_b_mishra@yahoo.com
Table 1 : BGARCH (1,1) model of Cash Equation for NSE
Nifty

 Method: Maximum Likelihood Variables

Variables Coefficient

[C.sub.s] 0.07238
[S.sub.[dagger]-1] -0.19781
[S.sub.[dagger]-2] -0.19883
[F.sub.[dagger]-1] 0.45611
[F.sub.[dagger]-2] 0.03781
[S.sub.[dagger]-1] - [gamma][F.sub.[dagger]-1] 0.12779
[[alpha].sub.0] 0.00894
GARCH 0.91220
ARCH 0.51377
[gamma] 0.07233

 Method: Maximum Likelihood Variables

Variables t-Statistic

[C.sub.s] 2.137 **
[S.sub.[dagger]-1] -1.289
[S.sub.[dagger]-2] -1.481
[F.sub.[dagger]-1] 3.791
[F.sub.[dagger]-2] 0.557
[S.sub.[dagger]-1] - [gamma][F.sub.[dagger]-1] 2.592 *
[[alpha].sub.0] 7.892 *
GARCH 19.455 *
ARCH 9.441 *
[gamma] 56.449 *

* Significant at 1 % level; ** Significant at 5% level; s: spot

Table 2 : BGARCH(1,1) model of Futures Equation for
NSE Nifty

 Method: Maximum Likelihood Variables

Variables Coefficient

[C.sub.f] 0.07892
[S.sub.[dagger]-1] 0.15233
[S.sub.[dagger]-2] 0.02999
[F.sub.[dagger]-1] 0.05698
[F.sub.[dagger]-2] 0.12897
[S.sub.[dagger]-1] - [gamma][F.sub.[dagger]-1] 0.35970
[[beta].sub.0] 0.00798
GARCH 0.79812
ARCH 0.45998
[gamma] 0.00456

 Method: Maximum Likelihood Variables

Variables t-Statistic

[C.sub.f] 2.894 *
[S.sub.[dagger]-1] 1.456
[S.sub.[dagger]-2] -0.354
[F.sub.[dagger]-1] 0.128
[F.sub.[dagger]-2] -0.971
[S.sub.[dagger]-1] - [gamma][F.sub.[dagger]-1] 5.417 *
[[beta].sub.0] 11.233 *
GARCH 28.455 *
ARCH 15.645 *
[gamma] 7.892 *

* Significant at 1 % level; ** Significant e at 5% level; f: futures

Table 3 : BGARCH (1,1) model of Cash Equation for BSE
Sensex

 Method: Maximum Likelihood Variables

Variables Coefficient

[C.sub.s] 0.0544
[S.sub.[dagger]-1] 0.4562
[S.sub.[dagger]-2] 0.4156
[F.sub.[dagger]-1] 0.5978
[F.sub.[dagger]-2] 0.2139
[S.sub.[dagger]-1] - [gamma][F.sub.[dagger]-1] 0.1456
[[alpha].sub.0] 0.0079
GARCH 0.9788
ARCH 0.4926
[gamma] 0.0589

 Method: Maximum Likelihood Variables

Variables t-Statistic

[C.sub.s] 1.129
[S.sub.[dagger]-1] -2.779 *
[S.sub.[dagger]-2] -3.512 *
[F.sub.[dagger]-1] 5.611
[F.sub.[dagger]-2] 2.079 **
[S.sub.[dagger]-1] - [gamma][F.sub.[dagger]-1] 1.962 **
[[alpha].sub.0] -4.561
GARCH 21.378 *
ARCH 7.128 *
[gamma] 102.789 *

* Significant at 1 % level; ** Significant at 5% level; s: spot

Table 4 : BGARCH(1,1) model of Futures Equation for
BSE Sensex

 Method: Maximum Likelihood Variables

Variables Coefficient

[C.sub.f] 0.0430
[S.sub.[dagger]-1] 0.1280
[S.sub.[dagger]-2] 0.2564
[F.sub.[dagger]-1] 0.1289
[F.sub.[dagger]-2] 0.0047
[S.sub.[dagger]-1] - [gamma][F.sub.[dagger]-1] 0.3893
[[beta].sub.0] 0.0068
GARCH 0.0124
ARCH 0.9834
[gamma] 0.5538

 Method: Maximum Likelihood Variables

Variables t-Statistic

[C.sub.f] 2.164 **
[S.sub.[dagger]-1] -0.789
[S.sub.[dagger]-2] -1.562
[F.sub.[dagger]-1] 0.979
[F.sub.[dagger]-2] -0.089
[S.sub.[dagger]-1] - [gamma][F.sub.[dagger]-1] 4.372 *
[[beta].sub.0] -5.643 *
GARCH -14.567 *
ARCH 37.899 *
[gamma] 9.781 *

* Significant at 1 % level; ** Significant at 5% level; f: futures
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Author:Debasish, Sathya Swaroop; Mishra, Bishnupriya
Publication:Paradigm
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Geographic Code:9INDI
Date:Jul 1, 2008
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