The dynamics of Bombay stock, US stock and London gold markets.

Mishra, Banamber ; Rahman, Matiur

Abstract

The primary objective of this paper is to explore the long-run and short-run dynamics among Bombay stock market, US stock market and London gold market. Relatively simple cointegration procedures are implemented using data from January 5, 1998 through November 19, 2003. There is evidence of long-run and short-run dynamic relationships among theses markets with marginal effects on one another.

Introduction

The investors have recently renewed their interest in gold. This is a good barometer of their mood. Rise in geopolitical risk, threat of terrorism, low interest rates, apprehension of resurgence of inflation due to brisk economic recovery and oil price spike, sagging U.S. dollar and the rollercoaster stock market contribute to this shift to gold as an alternative investment and useful hedge. Gold can be a refuge in times of turmoil. When stocks are out favour, gold normally rises in prices.

Much of gold's gain has come since September 11, 2001 terrorist attacks when many mainstream investors first turned to the precious metal as an alternative to a shaky stock market. The momentum has also carried into 2003. In January 2003 alone, gold price rose 6 percent while every major stock index was down. As of February 2003 the gold price rose to $368 per ounce from $280 at the beginning of 2002. Again, during the first two months of 2004 the price of gold oscillated around $ 400 per ounce. During 1990s investors were fixated on soaring technology stocks with muted inflation and ignored gold-related investment strategies. Conjecturally, investors should periodically rebalance their portfolios to keep small percentages of 5 to 10 percent of their holdings in gold investments to offset the volatility of the broader stock market due to gold's tendency in the opposite direction. US dollar is currently weak against other major currencies. Holding international stocks is another hedge against weak US dollar and falling US stock market (Smith, 2002).

The price of gold remained fairly stable as a store of value for about 140 years since dating back to 1833. The price of gold began to change since 1971 after it was de-linked from US dollar at fixed price of $35 per ounce by the Nixon Administration to avoid a gold rush. It went up to $191 an ounce in 1975 before declining. The gold price reversed in late 1976 and reached $612 an ounce in 1980 when the former Soviet Union invaded Afghanistan. Throughout 1980s and 1990s the price of gold on average continued to fall and reached $294 in 1998. This was primarily due to attractive stock market, strong US dollar, and low inflation in the US since gold provides a classic hedge against inflation (Chu, 1995; Ullman, 1994).

Among the emerging financial markets, the Bombay stock market (the largest of 19 Indian stock markets) is very active and relatively stable ranking 32nd in the world in terms of economic environment, information exchange and social environment, considered together with 63 variables in the wealth of nations triangle index (Black, 1997). In theory, India's established stock markets, strong entrepreneurial culture, high demand for equity-capital and a large English-speaking population should be attractive to foreign investors (Karp, 1997).

To retract, India was one of the few Asian emerging markets to post gains in 1994 to the extent of 8.6 percent in terms of rupee and 7.8 percent in US dollar term. The Bombay market capitalization value soared to $127.5 billion by 30 percent and the number of listed companies jumped by 35.2 percent to 4,413 during 1994 most of which are from information technology and telecommunication sectors. The Bombay stock market rose further by more than 670 points in 1997 despite the 1997-98 Southeast Asian contagion.

The factors that contributed to the aforementioned spectacular developments in the Bombay stock market included political stability, lower corporate tax rates and simplified duty structures for imports, customs, and excise, a reduction in the minimum lending rate from 15% to 14% and its subsequent elimination, deregulations of interest rates by withdrawing most controls, 5.6% economic growth in 1994-95, convertibility on the current account, and doubling of foreign exchange reserves to $19 billion in 1994 as compared to the preceding year. The foreign exchange reserve was well above the $1 billion level during the 1991 balance of payments crisis (International Finance Corporation, 1995). To add further, India is looking forward to making rupee fully convertible and aspires to be the world's next great economy. However, tough macroeconomic criteria, such as, lower inflation and huge drop in the budget deficit are set as preconditions to make a currency convertible in the world market (IFC, 1995 and 1997). In light of the above information, Bombay stock market presents a fascinating subject of study in the global market environment. Furthermore, the Bombay stock exchange has become more integrated with the NASDAQ and NYSE, particularly after 1998 (Arshanapalli and Kulkarni, 2001).

The 2003 was a fantastic year for India. Foreign exchange reserves passed $ 100 billion mark. The reported GDP growth rate was 8.4 percent during the third quarter, and the stock market hit a record high. India opened its doors in early 1990s. More and more Indians are now reaping the benefits of globalization and liberalization. Indian companies, exposed to further competition, have been forced to innovate, take risks and cut costs. Indian success stories in pharmaceuticals and softwares are common knowledge. The auto industry is another revealing success story. Foreign companies' outsourcing to India is no longer seen as exploitation, but rather as the generator of thousands of jobs per month. Global integration is no longer resisted. It is rather seen as a tool to sharpen their competitive advantages. The level of confidence is extraordinary. What John Maynard Keynes called "animal spirits" are infusing the Indian business culture. This is a major departure for India from its past that was largely closed off to the world since 1947 to early 1990s.

This paper examines the dynamics of US stock market, Bombay stock market, and London gold market. This topic merits an in-depth investigation for several reasons which include (i) growing importance of the Bombay stock market and investors' rising interest in the Indian stocks for international portfolio diversification, (ii) increasing integration of the Indian economy with the US, and (iii) high potentials of India to emerge as another economic powerhouse in Asia. The rest of the paper is organized as follows. Section II outlines the empirical methodology. Section III documents the results, as obtained. Finally, section IV concludes.

Empirical Methodology

The empirical methodology is outlined as follows:

First, the nature of the data distribution of each variable is examined by using the standard descriptive statistics (mean, median, standard deviation, skewness and kurtosis). Second, a correlogram of the explanatory variables is computed to identify the existence of multicollinearity and its severity. Third, the time series property of each variable is investigated in terms of the ADF (Augmented Dickey" Fuller) test for unit root (nonstationarity) following [Dickey and Fuller (1981),and Fuller (1996)].

The simple ADF test, as outlined in (Dickey and Fuller, 1981), is implemented by estimating the following regression for each variable:

[DELTA][X.sub.t-1] = [alpha] + [[beta].sub.0][X.sub.t-1] + [L.summation over i=1] [[beta].sub.i][DELTA][X.sub.t-1] + [U.sub.t] (1)

where, [DELTA] = first difference operator, L = number of optimum lags, t = time subscript and U = random disturbance term.

The ADF test is performed on [[??].sub.0] (the estimated value of) to accept or reject the null hypothesis of unit root (Ho: [[beta].sub.0] = 0) against its alternative (Ha: [[beta].sub.0] < 0). It is necessary to draw some definitive inferences on stationarity/ nonstationarity property of each variable of interest to determine the appropriate estimating statistical procedure(s).

In view of the evidence of nonstationarity in each variable and the same order of integration of all the variables, the most appropriate procedure to pursue is the cointegration methodology and the subsequent estimation of the associated error-correction model. The absence of a cointegrating relationship among the variables allows the application of simple OLS (Ordinary Least Squares) to estimate the model without risking misleading results stemming from spurious correlation.

For cointegrating relationship, the following steps are pursued:

[Y.sub.t] = [alpha] + [beta][X.sub.t] + [phi][Z.sub.t] + [e.sub.t] (2)

[X.sub.t] = [alpha]' + [beta]' [Y.sub.t] + [phi]' [Z.sub.t] + [e'.sub.t] (3)

[Z.sub.t] = [alpha]" + [beta]" [X.sub.t] + [phi]" [Z.sub.t] + [e".sub.t] (4)

where, Y = natural log of the Bombay stock market index (BSE30) in US dollar term used as a proxy for Bombay stock market, X = natural log of US S&P 500 used as a proxy for US stock market, Z = natural log of London market gold prices per troy ounce in US dollar, e = random disturbance term, and t = time subscript.

Equations (2) through (4) are estimated by OLS to retrieve the estimated respective error-terms for subsequent uses in the following ADF regressions corresponding to each of the above regressions in line with (Engle and Granger, 1987):

[DELTA][[??].sub.t] = [PSI][[??].sub.t-1] + [k.summation over i=1] [[PSI].sub.i+1][DELTA][[??].sub.t-1] + [v.sub.t] (5)

[DELTA][[??]'.sub.t] = [PSI]'[[??]'.sub.t-1] + [k.summation over i=1] [[PSI]'.sub.i+1][DELTA][[??]'.sub.t-1] + [v'.sub.t] (6)

[DELTA][??]" = [PSI]" [[??]".sub.t-1] + [k.summation over i=1] [[PSI]".sub.i+1][DELTA][[??]".sub.t-1] + [v".sub.t] (7)

The null hypothesis of nocointegration (Ho: |[PSI]| = 0 or |[PSI]'| = 0 or |[PSI]"| = 0) is tested against its alternative. The rejection of the null hypothesis implies that the residual sequence is stationary. Given that all variables are I (1) and the residuals are stationary, one can conclude that the series are cointegrated of order (1, 1). On evidence of such relationship, the following error-correction models are estimated by simple OLS, as suggested in Engle and Granger (1987):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

Equations (8) through (10) are estimated by OLS. In case there is no evidence of cointegration in any of equations (5) through (7), the model is estimated with the exclusion of the relevant error-correction term ([[??].sub.t-1] or [[??]'.sub.t-1] or [[??]".sub.t-1]). The statistical significance of the estimated value of the coefficient of the error-correction term, based upon the usual t- test, confirms a long run unidirectional causal flow from the explanatory variables to the dependent variable. The statistical significance of other estimated parameters in equations (8) through (10) confirm feedback relationships among variables. The optimum lag lengths are determined by the AIC (Akaike Information Criterion), as developed in (Akaike, 1969).

Daily data are employed in this paper. The sample period runs from January 5, 1998 through November 19, 2003. This sample period is selected to focus on the period when Indian economy and financial markets started gaining discernible momentum in a freer environment created by market deregulations, increasing economic openness and enhanced global interlinkages.

Bombay Stock Index is available in local currency (Indian Rupee) that has been converted into U.S. dollar via relevant Rupee- Dollar daily exchange rates as obtained from www.onada.com. Gold prices have been obtained from www.kitco.com. Bombay Stock Index (BSE 30) and U.S. S&P 500 data have been obtained from www.yahoo.com.

Results

To examine the nature of the data distribution of each variable, the standard descriptive statistics are reported as follows:

The descriptive statistics in Table 1 reveal near- normality in the data distribution of each variable in terms of mean, median, skewness and kurtosis (below the benchmark value of 4 for normality). The numerics of mean and median are almost equal. The numerical values of standard deviation are also very low. The distributions are slightly skewed either to the left or to the right, as shown above.

To examine the time series property of each variable, the ADF test statistics are reported as follows:

As shown in Table 2, the null hypothesis of unit root (nonstationarity) cannot be rejected at 1 percent and higher levels of significance. This is a clear affirmation of nonstationarity in each time series variable. They reveal I (1) behavior being stationary on first-differencing. Next, the cointregration regressions (5) through (7) are estimated by retrieving the error terms from the OLS estimates of regressions (2) through (4). The results are reported as follows:

The coefficients of the above lagged residuals corresponding to equations (5), (6) and (7) respectively have the expected negative sign. The null hypothesis of no-cointegration is overwhelmingly rejected based upon the associated ADF statistics in comparisons with the critical values at 1 percent and higher levels of significance. The evidence thus confirms a cointegrating relationship (long-run equilibrium) among Bombay stock market, US stock market and London gold market.

Finally, the associated error-correction models (8) through (10) are estimated for long-run equilibrium causal relationships and short-run interactive relations among the above markets. The results are reported as follows:

The above table shows that there are long-run causal flows from US stock market and London gold market to Bombay stock market. This is reflected through the associated t-value of the coefficient of the error-correction term ([[??].sub.t-1]). The coefficients of the relevant lagged-values of US S&P 500, London gold prices and Bombay BSE 30 with their associated t-values and the overall F-statistic reveal short-run dynamics among these markets. The DW-statistic at 1.993 indicates white noise. However, the adjusted-[R.sup.2] ([[bar.R].sup.2]) depicts that only 4.6 percent of the changes in Bombay stock market can be explained by the changes in these markets.

Likewise, the estimates of model (9) are reported as follows:

Table 5 reveals long-run causal flows from Bombay stock market and London gold market to US stock market. Relatively weak short-run feedback relationship is evidenced among these three markets in terms of lower F-statistic. The DW-statistic at 1.9998 indicates white noise. In this case, the [[bar.R].sup.2] is even lower at 0.02 (2%).

Finally, the estimates of model (10) are reported as follows:

Similarly, there is evidence of long-run causal flows from Bombay and US stock markets to London gold market in addition to short-run interactive relationships among these three markets. The numerical value of [[bar.R].sup.2] is about the same with low F-statistic. The DW -value at 1.997 is an indication of white noise. Furthermore, the optimum lag lengths in each model are determined by the AIC criterion.

Conclusions

The data on Bombay stock market, US stock market and London gold prices in natural logarithmic form are nonstationary depicting I (1) behavior. There is evidence of long-run equilibrium relationships among them with feedbacks. The long-run causal flows are bidirectional. However, the overall effects on one another are marginal in terms of numerical values of [[bar.R].sup.2]'s and F-statistics.

REFERENCES

Akaike, H. (1969), "Fitting Autoregression for Prediction", Annals of the Institute of Statistical Mathematics, 21, pp. 243-47.

Arshanapalli, Bala and Kulkarni, Mukund S. (2001), "Interrelationship Between Indian and US Stock Markets", Journal of Management Research, 1, pp. 141-48.

Black, Herbert D. (1997), "Spreading the Risk Pushes Science Into An Art Form", The World Paper, US Edition (July/August).

Chu, Franklin. (1995), "The Golden Rule: Gold, Inflation and Monetary Policy. Bankers Magazine (March/April): 16.

Dickey, D.A. and Fuller, W.A. (1981), "Likelihood Ratio Statistics for Autoregressive Time Series With A Unit Root", Econometrica, 49, pp. 1057-72.

Fuller, W.A. (1996), Introduction to Statistical Time Series, New York: John Wiley and Sons.

Engle, R. and Granger, C.W.J. (1997), "Cointegration and Error- Correction: Representation, Estimation, and Testing", Econometrica, 35, pp. 315-329.

Granger, C.W. (1969), Investigating Causal Relations By Econometric Models and Cross-Spectral Methods, Econometrica, 37, pp. 424-438.

International Finance Corporation. (1995), Emerging Stock Markets Factbook. Washington, D.C.

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Karp, Jonathan. (1997), "India Looks Abroad For Private Investors". Wall Street Journal, (August 19).

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Smith, Graham, (2002), "Tests of the Random Walk Hypothesis for London Gold Prices", Applied Economics Letters, 9, pp. 671-674.

Ullman, Owen. (1994), "Why Greenspan Has A Touch of Gold Fever", Business Week, (March 7), p. 44.

Banamber Mishra, Professor of Finance, McNeese State University, Lake Charles, LA 70609. E-mail: bmishra@mcneese.edu

Matiur Rahman, Professor of Finance, McNeese State University, Lake Charles, LA 70609. E-mail: mrahman@mcneese.edu

Table 1: Descriptive Statistics

Descriptors Y X Z

Mean 4.40 7.05 5.69
Median 4.36 7.04 5.67
Std.Dev 0.20 0.16 0.10
Skewness 0.43 -0.24 0.84
Kurtosis 2.17 2.05 3.00

Table 2: ADF Statistics

Variables ADF Statistics Critical Values * Significance Levels

y -1.51 -3.43 1%
X -1.64 -2.86 5%
Z -0.93 -2.57 10%

 First Differences

[DELTA]y -35.07
[DELTA]x -35.61
[DELTA]z -38.61

* MacKinnon (1996) One-sided P-values.

Table 3: Estimates of Cointegration Regressions

 Associated Critical
Lagged Residuals Co-efficients ADF Statistics Values

[[??].sub.t-1] -0.03 -4.49 -3.44 *
[[??]'.sub.t-1] -0.04 -5.14 -2.86 **
[[??]'.sup.n.sub.t-1] -0.03 -4.28 -2.57 ***

(*) Significant at 1%, (* *) significant at 5%, and
(***) significant at 10%.

Table 4: Estimates of Model (8)

Variables Coefficients t-Statistic Prob.

[[??].t-1] -0.013 -3.027 0.0025
[DELTA][X.sub.t] 0.128 3.431 0.0006
[DELTA][X.sub.t-1] 0.178 4.734 0.0000
[DELTA][X.sub.t-2] 0.086 2.285 0.0225
[DELTA][X.sub.t-3] 0.076 2.018 0.0438
[DELTA][X.sub.t-4] 0.038 1.007 0.3139
[DELTA][Z.sub.t] -0.089 -1.890 0.0590
[DELTA][Z.sub.t-1] 0.024 0.518 0.6045
[DELTA][Z.sub.t-2] 0.083 1.738 0.0825
[DELTA][Z.sub.t-3] 0.110 2.319 0.0206
[DELTA][Z.sub.t-4] -0.039 -0.828 0.4079
[DELTA][Y.sub.t-1] 0.004 0.126 0.8996
[DELTA][Y.sub.t-2] -0.030 -1.097 0.2729
[DELTA][Y.sub.t-3] 0.028 1.004 0.3156
[DELTA][Y.sub.t-4] 0.041 1.497 0.1345

[R.sup.2] = 0.056, [[bar.R].sup.2] = 0.046, DW = 1.993,
n = 1298, F = 5.859

Table 5: Estimates of Model (9)

Variables Coefficients t-Statistic Prob.

[[??].sub.t-1] -0.015 -2.853 0.0044
[DELTA][y.sub.t] 0.072 3.478 0.0005
[DELTA][Y.sub.t-1] -0.024 -1.185 0.2361
[DELTA][Y.sub.t-2] 0.003 0.148 0.8824
[DELTA][Y.sub.t-3] 0.020 0.997 0.3182
[DELTA][Y.sub.t-4] -0.014 -0.666 0.5055
[DELTA][Z.sub.t] -0.098 -2.784 0.0054
[DELTA][Z.sub.t-1] 0.034 0.966 0.3342
[DELTA][Z.sub.t-2] -0.067 -1.888 0.0592
[DELTA][Z.sub.t-3] 0.023 0.661 0.5088
[DELTA][Z.sub.t-4] -0.043 -1.208 0.2274
[DELTA][X.sub.t-1] 0.015 0.533 0.5940
[DELTA][X.sub.t-2] -0.006 -0.208 0.8354
[DELTA][X.sub.t-3] -0.013 -0.453 0.6507
[DELTA][X.sub.t-4] -0.003 -0.118 0.9063

[R.sup.2] = 0.030,[[bar.R].sup.2] = 0.019, DW = 1.9998,
n = 1298, F = 3.055

Table 6: Estimates of Model (10)

Variables Coefficients t-Statistic Prob.

[[??].sup.n.sub.t-1] -0.014 -2.802 0.0051
[DELTA][Y.sub.t] -0.030 -1.805 0.0712
[DELTA][Y.sub.t-1] -0.003 -0.193 0.8469
[DELTA][Y.sub.t-2] 0.031 1.904 0.0572
[DELTA][Y.sub.t-3] -0.010 -0.615 0.5385
[DELTA][Y.sub.t-4] 0.004 0.240 0.8105
[DELTA][X.sub.t] -0.059 -0.200 0.0069
[DELTA][X.sub.t-1] -0.004 -0.200 0.8412
[DELTA][X.sub.t-2] 0.019 0.867 0.3863
[DELTA][X.sub.t-3] 0.020 0.891 0.3729
[DELTA][X.sub.t-4] -0.032 -1.453 0.1465
[DELTA][Z.sub.t-1] -0.054 -1.929 0.0540
[DELTA][Z.sub.t-2] 0.065 2.301 0.0216
[DELTA][Z.sub.t-3] 0.029 1.043 0.2970
[DELTA][Z.sub.t-4] -0.014 -0.487 0.6265

[R.sup.2] = 0.029, [[bar.R].sup.2] = 0.019, DW = 1.997,
n = 1298, F = 2.963