# Examining the Relationship between ETFS and Their Underlying Assets in Indian Capital Market

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2 3. Data and Methodology The data for the study consists of daily closing prices of Nifty BeES for the period from March 19, 2007 to March 11, 2011 and Gold BeES for the period from March 19, 2007 to August 17, The corresponding daily closing prices of respective underlying asset, i.e., Nifty index and physical gold are also collected. The data for Nifty, Nifty BeES and Gold BeES is collected from the website of National Stock Exchange. For each of the ETFs and underlying asset first logarithmic returns have been computed as follows: Where P is the daily closing price of given ETF/underlying asset. lnr t = lnp t - lnp t-1 (1) The study applies methodology of Vector Autoregression (VAR) developed by Sims [2]. VAR model is ideal in this situation as it provides a multivariate framework where changes in particular variable are related to changes in its own lags and to changes in other variables and the lags of those variables. The model thus can help in identifying main channels of interactions and simulates the responses of a given market to innovations in other markets. The VAR model can be expresses in its standard form as: lnr t = C + p A kr t-k + t (2) Where lnr t is the m x 1 column vector of daily returns on the ETF/underlying at time t, C is the m x 1 column vector of constant terms, A k are m x m matrices of coefficients such that the (i, j)th component of A k measures the effect of change in the jth market on the ith market after k periods, t is an m x 1 column vector of unobserved disturbances assumed to satisfy the usual assumptions of the errors from an OLS regression. Eq. (2) assumes a return generating process where the return of each market (ETF and underlying) is a function of a constant term, its own lagged returns, the lagged returns of other variables in the system, plus an error term it, which is serially uncorrelated but can be contemporaneously correlated. In other words, the returns of a market incorporates not only its own past information, but also the past information of other markets. Using VAR model two important questions related to integration of two markets can be answered one, how fast are the price movements in one market transmitted to other markets; two, how much of movements in one market can be explained by innovations in other market. The first question can be answered by generating impulse response functions (IRFs) which measure the response of different markets to shock of 1 standard error in a particular market; and the second by computing forecast error variance decompositions (FEVD). Before implementing VAR methodology it is necessary to test for stationarity of return variables to avoid the problem of spurious regression (Granger and Newbold [3]; Phillips [4]). The popular Augmented Dickey-Fuller [5] test is used to test the stationarity of the variables. 4. Results and Discussion 4.1. Stationarity of Variables The results of ADF test for presence of unit root in time series of variables are presented in Table 1 below. The test results indicate that all the return series are stationary at levels or integrated of order zero i.e. I(0). Notes: Variable k 0 Table 1: Results of Stationarity Test Using ADF Test ADF Test Statistics Without trend P value With Trend P value LNIFTYR * * 00 LNIFTYBEESR * * 00 LGOLDR * * 00 LGOLDBEESR * * 00 (a) Lag selection for ADF test is automatic based on SIC (Schwartz Information Criterion) (b) MacKinnon (1996) one-sided p values use for rejection of hypothesis of unit root. 110

3 (c) Test critical values are , and for 1%, 5% and 10% respectively for test without trend and , and at 1%, 5% and 10% respectively for test with trend as deterministic term. (d) * indicated significance at 1% level. Therefore, VAR model with levels series is constructed Correlation Structure The correlation structure between the returns of ETF and underlying asset is the simplest indicator of the underlying relationship between the two variables. Table 2 below presents this correlation structure for log returns on Nifty BeES and Gold BeES with log returns on their respective underlying holdings viz., Nifty and physical gold. Table 2: Correlation Structure Between ETF and Underlying Assets Variable LNIFTYR Variable LGOLDR LNIFTYR 1 LGOLDR 1 LNIFTYBEESR LGOLDBEESR It can be seen from Table 2 above that the correlation between returns in Nifty and returns in Nifty BeES is much stronger (0.968) as compared to that between returns in physical gold and Gold BeES (0.446). Thus correlation between ETF and underlying asset in equity market is much stronger than that between ETF and underlying asset in bullion market Forecast Error Variance Decomposition (FEVD) Table 3 and Table 4 below presents the results of FEVD based on VAR analysis of variables under study. Table 3 indicates that forecast error variance in Nifty is not significantly explained by Nifty BeES. On day 1, 100% of error variance in Nifty explained by innovations in Nifty itself. On the other days also, the contribution of Nifty BeES in explaining forecast error variance in Nifty remains significantly lower at about 0.68%. On the other hand, on day 1, more than 95% of error variance in Nifty BeES is contributed by the underlying asset, i.e. Nifty Index. On the remaining days, even though the contribution of Nifty declines, it remains at significantly higher at 92%. About 8% of error variance in Nifty BeES is explained by its own innovations, i.e. developments within the ETF market. Table 3. Results of Forecast Error Variance Decomposition (FEVD) for Nifty and Nifty BeES Variance Decomposition of LNIFTYR: Day S.E. LNIFTYR LNIFTYBEESR Variance Decomposition of LNIFTYBEESR: Day S.E. LNIFTYR LNIFTYBEESR

4 Cholesky Ordering: LNIFTYR LNIFTYBEESR Table 4. Results of Forecast Error Variance Decomposition (FEVD) for Gold and Gold BeES Variance Decomposition of LGOLDR: Day S.E. LGOLDR LGOLDBEESR Variance Decomposition of LGOLDBEESR: Day S.E. LGOLDR LGOLDBEESR

5 Cholesky Ordering: LGOLDR LGOLDBEESR The similar situation, however, does not exist in case of gold based ETF. As can be seen from Table 4 above, while forecast error variance in gold market is explained largely by its own innovations (from abot 96% to 100% on various days), the innovations in Gold BeES play significant role in determining movements in gold ETF market. The innovations in market for underlying asset gold contributes to 31.62% of error variance in Gold BeES on day 1 which further increases upto 37.46% during subsequent days. On the other hand, its own innovations contribute about 62.54% to 68.38% of error variance in Gold BeES. This is in contrast with the observations made in case of ETF based on equity index above where the underlying asset is able to explain significant of variance in ETF Impulse Response Functions As stated earlier, the reactions of one market to shocks originating in other market can be traced in VAR framework using impulse response functions (IRFs). Fig.1 and Fig.2 in Appendix explain these reactions between market for ETF and market for underlying asset with respect to equity based and gold based ETFs respectively. As can be seen from Fig.1, the response of Nifty to its own shocks is 0.20 on day 1 and is reduced to zero around 6th day. Its response to shocks originating in ETF market is highly insignificant. However, the response of Nifty BeES to shocks in Nifty is instant and is marginally less than 0.20 on day 1 itself and is reduced to zero around 6th day with significant drop from day 2 onwards. Its response to its own shocks is very low at less than 0.05 on day 1. Thus shocks originating in Nifty are significant and quickly transmitted in Nifty BeES market. On the other hand, it can be seen from Fig.2 that the response of Gold BeES to shocks originating in its own market is higher (0.09) than that for shocks originating in underlying gold market (0.06), albeit marginally. 5. Conclusion From the above results and discussion it can be concluded that underlying asset does contribute to movements in prices in ETF market. However, significant difference exists between such contributions with respect to equity based ETFs and Gold based ETFs. A more closer relationship exists between Nifty and Nifty BeES as compared to that observed between physical gold prices and Gold BeES. Thus, returns on Nifty BeES may be closer to those on Nifty itself and therefore passive investment style may be advisable for investors dealing in Nifty BeES. On the other hand, investors need to monitor gold ETF market closely since developments in Gold ETF market itself rather than the underlying asset market, are found to be more significant in explaining movements in Gold BeES. Thus, here active investment style may be more useful. Future research can be directed towards identifying the factors influencing the returns on Gold ETF. These may be either the speculative behaviour of investors or macroeconomic fundamentals within the domestic or international territories. 6. References [1] Prakash N. Exchange Traded Funds in India, The Chartered Accountant. 2007: [2] C. A. Sims. Macroeconomics and Reality. Econometrica. 1980, 48: [3] C.W.J. Granger and P. Newbold. Spurious Regressions in Economterics. Journal of Econometrics. 1974, 2: [4] P. C. B. Phillips. Understanding Spurious Regressions in Econometrics. Journal of Econometrics. 1986, 33: [5] D. A Dickey and W. A. Fuller. Distribution of the Estimators for Autoregressive Time Series with Unit Root. Journal of the American Statistical Association. 1979:

6 APPENDIX Response to Cholesky One S.D. Innovations ± 2 S.E..024 Response of LNIFTYR to LNIFTYR.024 Response of LNIFTYR to LNIFTYBEESR - - Response of LNIFTYBEESR to LNIFTYR Response of LNIFTYBEESR to LNIFTYBEESR Fig.1.: Response Results of Impulse to Cholesky Response One Function S.D. Innovations for Nifty and Nifty ± 2 BeES S.E. Response of LGOLDR to LGOLDR Response of LGOLDR to LGOLDBEESR Response of LGOLDBEESR to LGOLDR Response of LGOLDBEESR to LGOLDBEESR Fig.2.: Results of Impulse Response Function for Gold and Gold BeES 114

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