Short and Long Run Relationship Analysis of Indian Stocks Cross Listed in U.S

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This study includes the Daily closing prices of the three dually listed Indian shares, and the Indian and the US indices.Table 1 lists the ADRs employed for this study and provides the names of the respective industries along with the listed stock exchange. The ADRs and their underlying stocks are constructed based on their mean prices as portfolio. The prices of the Indian ADRs (P_A) and their underlying shares (P_I), and the total market indices for India (NSE) (P_IM) and the US (NYSE)(P_AM) are selected samples for the financial crises period Sep 2007 to Feb 2009.The data were collected from www.adrbny.com and www.nseindia.com.E views 6.0 package is used for arranging the data and implementation of econometric analyses.

3.2. Techniques

Initially, natural logarithms of data have been taken before passing to the analysis process. Then, stationarity analysis has been performed for data pertaining to the variables used in the study. The most widely used test among parametric tests is Augmented Dickey-Fuller (ADF-1979) that considers possible structural fracture and trend in the time series. A long term relationship between time series has been searched by applying co-integration test developed by Johansen and Juselius (1990). Both granger causality and vector error correction model are carried out to establish the short run and long-run dynamics.

First step is to test whether each of the ADRs, their underlying prices are stationary. The Augmented Dickey Fuller (ADF) tests are used to test for unit roots in the time series. The basic Dickey–Fuller (DF) test ^[4] is to examine whether ρ<1 in the equation (3.1),

(3.1)

which, after subtracting from both sides, can be written as:

(3.2)

The null hypothesis is that there is a unit root in , or against the alternative or there is no unit root in . The Dickey–Fuller procedure gives a set of critical values developed to deal with the non-standard distribution issue, which are derived through simulation. A sufficient number of lagged differences are included so that the residual series is approximately white noise. If, as expected, each variable is integrated of order one, I (1), then the next step would be to test for Co integration.

Let Y_{t =}(Y_1t…,Y_kt)' denote an k x1 vector of I(1) time series. Y_tis co integrated if there exists k x1 vector such that

(3.3)

The non-stationary time series in Y_t are co integrated if there is a linear combination of them that is stationary. If some elements of are equal to zero then only the subset of the time series in Y_twith non-zero coefficients is co integrated.

There may be different vectors such that is stationary. In general, there can be linearly independent co integrating vectors. All cointegrating vectors form a co integrating matrix B ^[12].

A vector error correction (VEC) has cointegration relations built into the specification so that it restricts the long-run behavior of the endogenous variables to converge to their cointegrating relationships while allowing for short-run adjustment dynamics. The cointegration term is known as the error correction term since the deviation from long-run equilibrium is corrected gradually through a series of partial short-run adjustments.

If a bivariate I(1) vector is cointegrated with cointegrating vector then there exists an error correction model (ECM) of the form

(3.4)

(3.5)

that describes the long term relations of . If both time series are I (1) but are cointegrated (have a long term stationary relationship), there is a force that brings the error term back towards zero. If the cointegrating parameter is known, the model can be estimated by the OLS method.

The Granger causality test is employed to determine whether one return series is useful in forecasting another. Based on the definition of Granger causality, a time series X is said to Granger-cause Y if it can be shown that those X values provide statistically significant information about future values of Y.

4. Empirical Results

4.1. Descriptive Statistics

Table 2 report the descriptive statistics of two Indian ADRs viz., TCL, MTNL listed at NYSE and their underlying, US and home market indices. The sample period is from 2001 to 2012.

Table 2. Descriptive Statistics (2001-2012)

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The descriptive statistics from Table 2 of all the variables under study reveals that the variables are not normally distributed which is evident from the significant values of Jarque- Bera Test. It is observed that the mean returns are positive for all variables. The variables are skewed left and leptokurtic.

4.2. Lag Order Selection Criteria

Table 3 indicates the selected lag from LR test statistic, Final prediction error, Akaike information criterion, Schwarz information criterion and Hannan-Quinn information criterion by (*). These are the lags with the smallest value of the criterion.

Table 3 present the evidence based on the Lag Order Selection Criteria, the SC criterion & HQ suggests the use of 2 lag and 3 lag while the LR,FPE and AIC criteria suggest that 5 lags should be accommodated in the . But the subsequent analysis was estimated based on VAR with 2 lags according to Schwarz Information (SIC) criterion which is most commonly used criterion.

Table 3. lag order selection criteria – TCL (2001-2012)

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4.3. Unit Root Test

Table 4.1-4.2 reports the result of the standard unit root tests (ADF) on the integration properties of the NYSE, NIFTY, TTM, RDY and MTNL Close prices.

The choice of lag length was assigned according to the Schwarz Information criterion (SIC).

Table 4.1. Augmented Dickey Fuller (ADF) Unit Root Test

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Table 4.1 indicatesin the level form, the unit root tests are rejected for all the variables. In Table 4.2, the ADF test takes care of possible serial correlation in the error terms by adding the lagged difference terms of the regressand. The ADF test statistic is more negative than the critical value and hence the null hypothesis of unit roots in the first differences i.e. the returns of the variables is rejected at 1% level and confirms the stationarity of the returns. However, the test rejects the null of non-stationarity for all the variables when they are used in their first difference. This shows that all the series are stationary in the first difference, and integrated of order I (1) which justifies the need for cointegration test.

Table 4.2. Augmented Dickey Fuller (ADF) Unit Root Test

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4.4. Cointegration Rank Test

The Johansen Co integration Rank summary for the two ADRs under study is presented in Table 5.

Table 5. Johansen Co integration Rank Summary

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The cointegration results across the five types of model and the type of test (the ‘trace’ or ‘max’ statistics) suggest that the series are cointegrated - in other words, all specifications suggest that there are at least one cointegrating vectors. The lag number to be taken into account in application of cointegration test for each comparison was calculated according to Schwarz (SIC), information criterion as 2 (two) and was included into the model.

Table 6. Johansen Cointegration Test Results

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4.5. Johansen Cointegration Test

Results of Johansen cointegration test applied for the purpose of finding whether there is a long term relationship between the variables within the scope of the analysis, are shown in Table 6.

According to the results of Table 6, the Trace test indicates 1cointegratingeqn(s) at the 0.05 level and Max-eigenvalue test also indicates 1cointegratingeqn(s) at the 0.05 level. Thus it is proven that a long run relationship exist between the variables taken for the study.

4.6. Vector Error Correction Model

The existence of cointegration between variables suggests a long term relationship among the variables under consideration. Using VECM the speed of adjustment in the short run among the variables is analyzed. Table 7 present the short-run components of the estimated Vector Error Correction Model (VECM), with the restrictions implied by the CEs imposed.

The C₁ values (Table 7) reflect the log-run price of instancy embedded in the cointegrating vectors. C₂ coefficients reflect the long run risk premiums for the various series. The VECM model is based on 2 lags. There are 1cointegrating vectors.

According to Table 7, the coefficients in the VECM give the estimated long-run relationship among the variables shows how deviations from that long-run relationship affect the changes in the variable in the next period. The error correction coefficient for P_Ais about 0.04, with a negative sign and statistically significant. This means that the P_A deviation in period (t-1) and its long run equilibrium value is corrected by as much as 4 percent. Since the value of the Error correction coefficients is low, it can be inferred that the speed of deviation adjustment is not swift. Examination of the R², suggests that the variables P_A, P_Iaccounts for 36% and 12% of the short-run variation.

The variables that have significant influence on the Indian ADR portfolio prices are lags of its own and on the US market. The lagged returns on the Indian market and its underlying portfolio have trivial significant short-run effect on ADR portfolio prices over the sample period.

The error correction model not only validates the long run equilibrium, but also reflects the impact of short term variables fluctuations.

Table 7. Estimated Vector Error Correction Model Results

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4.7. Granger Causality Test

One of the ways to determine short run causality among variables is to employ Granger Causality Test Table 8 presents the result of pair wise causality.

Table 8. Granger Causality Test

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Conferring to Table 8 the pair wise Granger causality test reveals that Indian stocks (P_I)and Index (P_I_M) granger cause ADR(P_A).

Figure 1 represents the residuals of VECM for India-US stock and Index close during the financial crisis period (2007-2009). The abscissa axis represents the time period (Unit: Daily), ordinate axis represents the range in the values of VECM residuals expressed in percentage.

Figure 1. Residuals of VECM

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