4. Empirical Results
4.1 Unit-root tests
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4. Empirical Results
4.1 Unit-root tests
Before proceeding to the cointegration test, unit root tests are performed on each of the national stock indices and the exchange rate series to determine the order of cointegration of these series. We employed the Augmented Dickey-Fuller test3 and the Phillips-Perron test to conduct the unit root tests. The tests are performed for the entire sample on both the level and first difference of the stock indices and exchange rates series. Table 4-1 and Table 4-2 report the results of these tests.
Table 4-1 reveals that the null hypothesis of a unit-root in the level series cannot be rejected in the stock prices and exchange rates of all countries in the study. This indicates that both the series are non-stationary in all countries. Table 4-2 reports that the null hypothesis of a unit-root in the first difference of stock prices and exchanges series is rejected for all the countries. Therefore, all the series of USA, Japan, Germany, United Kingdom, France, Italy, Canada, Taiwan, Hong Kong, Korea, Singapore, Brazil, Russia, India and China are integrated for order one, i.e., Ι(1). This means we can apply cointegration test for these countries to examine the long-run relationship between stock prices and exchange rates.
3 The optimal lag length is selected based on Akaike’s information criterion (AIC).
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Country Lag ADF test statistic PP test statistic
USA
*and ** denote the rejection of unit-root hypothesis at 1% and 5% significance levels, respectively.
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Table 4-2: Unit-root Tests at First Differences
Country Lag ADF test statistic PP test statistic
USA
S&P 500 0 -11.2452* -11.3312*
$/€ 0 -9.4771* -9.4200*
Japan
Nikkei 0 -11.3073* -11.3983*
JPY/$ 4 -6.8491* -13.1801*
Germany
DAX 0 -12.0308* -12.0716*
€/$ 0 -10.4974* -10.4774*
United Kingdom
FTSE-100 3 -4.9468* -12.0279*
GBP/$ 0 -11.6260* -11.7465*
France
CAC 40 1 -11.4224* -11.5039*
€/$ 0 -10.3160* -10.2947*
Italy
Milan Stock 2 -6.3635* -10.9787*
€/$ 0 -10.1899* -10.1551*
Canada
Toronto 300 0 -10.1377* -10.1377*
CAD/$ 0 -13.5904* -13.5770*
Taiwan
TAIEX 5 -6.2631* -11.9775*
NTD/$ 0 -10.9775* -10.9283*
Hong Kong
Heng Seng 0 -11.6250* -11.6335*
HKD/$ 3 -5.0160* -10.2207*
Singapore
Straits Times 0 -11.3656* -11.3575*
SGD/$ 0 -12.6597* -12.6610*
Korea
KOSPI 0 -11.0334* -10.9947*
KRW/$ 0 -12.5237* -12.5178*
Brazil
BOVESPA 0 -12.9360* -12.9410*
BRL/$ 0 -12.6121* -12.6122*
Russia
RTS 6 -4.3054* -10.2225*
RUB/$ 2 -5.5335* -8.2966*
India
BES SENSEX 30 0 -12.3278* -12.3896*
INR/$ 1 -10.3000* -11.1668*
China
Shanghai SE A Share 6 -4.0874* -11.9428*
CNY/$ 4 -4.2330* -9.9670*
*and ** denote the rejection of unit-root hypothesis at 1% and 5% significance levels, respectively.
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4.2 Coefficient of Correlation
Prior to testing for cointegration, the dynamic correlation coefficients for each country will be calculated and discussed. Coefficient of correlation measures the direction, i.e., negative, zero or positive and its magnitude of the two variable’s relationship in this study. From evidences in table 4-3, we can observe several characteristics of the relationship depending on the country and the time.
First, we find substantial differences in the power of coefficients of correlation between two geographical areas. For G-7 countries, Japan, UK and Canada separately have 6 years, 8 years and 11 years of negative coefficient of correlation out of 15 years. This indicates that when pound appreciates against US dollar and when Canadian dollar appreciates against US dollar, the domestic stock markets tend to rise in these two countries. On the other hand, the stock markets tend to fall while Japanese yen appreciates against US dollar. The number of negative coefficients between US dollar and S&P 500 are 10. This means when US dollar appreciates, S&P 500 is likely to fall. For Eurozone countries, Germany, France and Italy each has 7 years, 5 years and 5 years of negative coefficient of correlation in 11 years, which means when euro appreciates against the US dollar, German stock market tends to rise but Italian and French stock markets tend to fall. We also can see the high unification of financial markets among the four European countries. The evidence is that 9 years out of the 11-year sample period from 1999 to 2009, these countries share the same trend in the relation of stock markets and exchange rates.
Contrary to the inconsistent frequency of negative correlation coefficients among G-7 countries, the emerging countries appear to be more uniform. For Taiwan, Singapore, Korea, Brazil, Russia and India, it is 13 years, 13 years, 12 years, 12 years, 12 years and 9 years out of 15-year sample period. This signifies that when the currencies in these countries appreciate against US dollar, the stock markets tend to
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rise. One of the main factors in explaining why the above countries have a uniform result is that the foreign capital plays an essential role in these countries’ stock markets. Thus, when the international capital flows into these countries for the purpose of investing in the stock markets, the exchange rates will appreciate in advance of the rise in stock markets.
Secondly, concerning the time point of view, the first business cycle from 1995 to 2001, the frequency of negative correlation coefficient between stock markets and exchange rates is steady. In 1995, 5 countries out of the 15 countries in the sample have negative correlation coefficients; for 1996, 1997, 1998 and 1999, the number is 8 countries, 7 countries, 7 countries and 7 countries, respectively. In 2000 and 2001, the number increases to 10 countries.
The second business cycle, from 2002 to 2009, however, the aggregate numbers of negative correlation coefficients vary dramatically. The number decreases greatly from 10 in 2001 to 4 in 2002. During this period comes the bottom of the economic cycle. Countries utilize depreciation policy to stimulate their export and at the same time protect its domestic market from foreign competition. The evidence is that only 4 countries had negative coefficients. Starting from 2003, another start of a bull market, the stock markets increase year by year except for year of 2005. In 2003 and 2004, 13 countries and 14 countries--the highest of all, have negative coefficients. This means appreciation in local currency along with the rise in the stock market or the depreciation of local currency along with the fall in the stock market could be observed almost worldwide. The countries with negative coefficients increase to 12 in 2006 from 3 in 2005. And starting from 2006 to 2009, the countries in the sample show a consistent performance of negative relationship between exchange rates and stock markets. Moreover, the scenario from 2001 to 2003 occurs once again
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beginning in 2007 to 2009. That is, the stock markets plunge while the currencies depreciate.
More tendencies can be observed if the entire 15-year sample period is taken into consideration. Before 2000, the global tendency in the relationship between exchange rates and stock markets is not clear. Nevertheless, since 2000, the integration of global tendency has been more observable and convincing. This is mainly thanks to financial globalization resulting from the freer worldwide trade and electronic trading system after the Millennium. Moreover, we can notice another long-term trend from table 4-4.
Results shown in table 4-4 indicate that the coefficients of correlation between developed countries and emerging countries are not conclusive. 5 countries including France, Italy, Hong Kong, Brazil and China have shown positive coefficients of correlation, while the other nine countries—USA, Japan, Germany, UK, Canada, Taiwan, Singapore, Korean, Russia and India, have shown negative.
Lastly, we draw the attention back to table 4-3 and figure 4-1. Since the beginning of a bull market in 2002, the coefficients of correlation between stock markets and exchange rates in these countries have become stronger. The frequency of negative correlation coefficients smaller than minus 5 in 2002 is 2. Afterwards, it has increased from 12 countries in 2003 to 13 in 2008 and 11 in 2009. The numbers are closely in accordance with that of negative coefficients. This implies a highly powerful relationship between the two variables. We also can discern the volatility of correlation coefficients for each country from figure 4-1. The vigorous fluctuations occur in almost every country except Brazil. In other words, the coefficients’ great volatility and the same direction of their fluctuations across countries reveal another evidence of worldwide integration in financial markets.
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1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 No. of ( ) γ < -0.5
USA 0.8145 0.0804 0.6066 (0.7302) (0.0957) (0.3580) (0.3731) 0.8082 (0.9362) (0.8031) 0.7628 (0.5921) (0.5543) (0.9445) (0.9219) 10 7 Japan 0.8106 (0.3801) (0.7165) 0.3122 (0.6495) (0.8249) (0.3368) 0.4273 (0.7443) 0.0975 0.8556 0.4814 0.8723 0.8524 0.1640 6 4
Germany 0.7277 (0.2838) 0.1835 0.8565 (0.7335) (0.7616) 0.8710 (0.6113) (0.6766) (0.8522) (0.8826) 7 6
UK 0.6943 (0.8665) (0.5623) 0.3698 0.4102 0.0254 0.3703 0.9134 (0.7070) (0.7797) 0.9323 (0.6125) (0.5198) (0.9264) (0.7978) 8 8
France 0.8110 0.3078 0.1976 0.8649 (0.7246) (0.7378) 0.8998 (0.5342) 0.0941 (0.8310) (0.8559) 5 5
Italy 0.3867 0.4225 0.1103 0.8647 (0.8263) (0.8752) 0.7525 (0.5925) 0.7664 (0.8147) (0.8350) 5 5
Canada 0.9148 (0.3474) 0.3718 (0.8472) (0.6974) (0.0069) (0.6652) 0.3022 (0.8781) (0.8906) (0.8705) 0.5594 (0.8938) (0.9498) (0.9488) 11 9
Taiwan (0.4212) (0.1570) (0.2252) (0.2400) (0.1554) (0.8999) (0.6671) (0.0092) (0.7142) (0.4242) 0.1406 0.2098 (0.4053) (0.7198) (0.4722) 13 4 HK (0.7611) (0.7738) 0.3511 0.2799 0.8702 (0.3415) (0.7175) (0.7403) 0.6553 (0.1607) 0.5626 (0.3532) (0.6104) 0.3844 0.8219 8 5
Singapore (0.0544) (0.6150) (0.9561) (0.8644) (0.2193) (0.7020) (0.5283) 0.7722 (0.2942) (0.5872) 0.6536 (0.8891) (0.4592) (0.6987) (0.9075) 13 9 Korea (0.4917) (0.9462) (0.8658) 0.2120 (0.3531) (0.6672) (0.2748) 0.7310 (0.5689) (0.4899) 0.6206 (0.6012) (0.6601) (0.8911) (0.9384) 12 8
Brazil 0.0115 0.1232 0.0676 (0.8000) (0.5508) (0.8804) (0.9189) (0.9461) (0.7493) (0.9001) (0.6553) (0.6118) (0.9832) (0.9262) (0.9746) 12 12 Russia 0.3818 0.5999 (0.7207) (0.9221) (0.4691) 0.3758 (0.8530) (0.3607) (0.8755) (0.0545) 0.2482 (0.8782) (0.9507) (0.8944) (0.9882) 11 8
India 0.3672 (0.0982) (0.4957) 0.6208 0.1314 (0.8704) 0.2587 0.4746 (0.8685) (0.8758) 0.5328 (0.6992) (0.8853) (0.9118) (0.9218) 9 7 China (0.4914) 0.8694 0.4234 (0.0089) 0.5474 0.6677 (0.7366) 0.1456 0.0366 (0.3504) (0.6993) (0.6357) (0.8455) (0.6992) 0.8366 8 5
No. of ( ) 5 8 7 7 8 10 10 4 13 14 3 12 12 13 12 138 102
γ < -0.5 1 4 5 5 3 6 7 2 12 9 3 11 10 13 11 102
Figures in parenthesis ( ) refer to negative correlation coefficient.
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Table 4-4: Correlation Coefficient (Entire Sample Period) Country Entire Sample Period Correlation Coefficient USA 1995:07~2009:08 0.2029 Japan 1995:07~2009:08 (0.3743) UK 1995:07~2009:08 (0.3119)
Canada 1995:07~2009:08 (0.6637)
Taiwan 1995:07~2009:08 (0.1744)
Hong Kong 1995:07~2009:08 0.5510
Singapore 1995:07~2009:08 (0.2118)
Korea 1995:07~2009:08 (0.5448) Brazi 1995:07~2009:08 0.0225 India 1995:07~2009:08 (0.8190) China 1995:07~2009:08 0.5247 Russia 1995:09~2009:08 (0.7142)
Germany 1999:01~2009:08 (0.0622)
France 1999:01~2009:08 0.2038
Italy 1999:01~2009:08 0.2953
Figures in parenthesis ( ) refer to negative correlation coefficient/
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3 DAX(real line); γG(dotted line) 4. FTSE-100(real line); γK(dotted line)
5. CAC 40(real line); γF(dotted line) 6. Milan Stock(real line); γI(dotted line)
Figure 4-1: Coefficients of Correlation and Average Stock Prices
‐1.2
1995 1997 1999 2001 2003 2005 2007 2009
‐1
1995 1997 1999 2001 2003 2005 2007 2009
‐1
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
‐1.5
1995 1997 1999 2001 2003 2005 2007 2009
‐1
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
‐1
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
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9. Heng Seng(real line); γH(dotted line) 10. Straits Times(real line); γS(dotted line)
11. KOSPI (real line); γKO(dotted line) 12. BOVESPA (real line); γB(dotted line)
Figure 4-1: Coefficients of Correlation and Average Stock Prices(continued)
‐1.5
1995 1997 1999 2001 2003 2005 2007 2009
‐1
1995 1997 1999 2001 2003 2005 2007 2009
‐1
1995 1997 1999 2001 2003 2005 2007 2009
‐1.2
1995 1997 1999 2001 2003 2005 2007 2009
‐1.2
1995 1997 1999 2001 2003 2005 2007 2009
‐1.2
1995 1997 1999 2001 2003 2005 2007 2009
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15. Shanghai A Share(real line); γC(dotted line)
Figure 4-1: Coefficients of Correlation and Average Stock Prices(continued)
‐1.2
1995 1997 1999 2001 2003 2005 2007 2009
‐1
1995 1997 1999 2001 2003 2005 2007 2009
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4.3 Johansen cointegration test
Since the series are of the same order, i.e., Ι (1), as we have tested in the unit-root test, we proceed to test the existence of cointegrating relations among the stock prices and exchange rates using the Johansen cointegration test. The lag length is chosen by applying the Akaike Info Criterion (AIC) on the unrestricted VAR. Between Johansen’s two likelihood ratio tests for cointegration, the trace test shows more robustness to both skewness and kurtosis (i.e., normality) in residuals than the maximum eigenvalue test4. Thus, we employ only the trace test to perform the cointegration test..
The results are reported in table 4-5. As can be seen in the table, for G-7 and some emerging countries, except Russia and China, the null hypothesis of no cointegration cannot be rejected using a 5 percent significance level. Analyzed financial markets in all developed countries do not share the same stochastic trend and consequently no stable long-term linkages between the variable exist. However, the results for emerging markets are mixed. Both Russia and China demonstrate stronger relationship between stock prices and exchange rates.
Our findings of no long-run equilibrium relationship between two financial variables are in contrast with Ajayi and Mougoué (1996), but mostly consistent with those of Bahmani-Oskooee and Sohrabian (1992) and Baharom, Habibullah and Royfaizal (2008).
4 See Cheung and Lai (1993) for details.
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* denotes the rejection of null hypothesis at 5% significance level.
Country HO H Eigenvalue Statistic
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